The shifting tectonics play off the orthogonal grid of courts.
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This is orthogonal to whether WWE's style is enjoyable or not.
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Most do not have short, regular blocks, orthogonal streets, and mixed-use zoning.
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Once upon a time UX and usability were considered entirely orthogonal to security.
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We just see them as a sort of orthogonal player to what we do.
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His divisive policies are not only orthogonal to those of Penn, but to democracy.
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Orthogonal Thinker also develops relationships with other companies to develop psychedelic research and development.
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Orthogonal means you can move in one without affecting where you are in the other.
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Instead, we look to do orthogonal investing to address big unmet needs with great people.
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Orthogonal Thinker's subsidiary EI.Ventures researches and develops psychoactive compounds like psilocybin for mental health treatment.
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As a result, presence becomes absence, orthogonal becomes curvilinear, structure becomes gesture and box becomes blob.
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"Beta to Value - "Companies with greater than 0.5 beta coefficient to the Pure Orthogonal Value Factor.
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Bullshitters don't lie, he said, so much as treat the truth as irrelevant, orthogonal to their purposes.
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TED's signature format has led to countless orthogonal breakthroughs, rewiring our brains with fresh outlooks as it goes.
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Or Carolyn Bertozzi, named on 50 US patents, who invented her own field of study: bio-orthogonal chemistry.
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Every political movement, and certainly [every] intellectual movement, is obviously a bit orthogonal to the actual interest of voters.
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But really, what ends up happening is that you kind of start to move into a more orthogonal area.
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These questions involve core concerns (equity, fairness, happiness) that are often absent from, or simply orthogonal to, market transactions.
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Then there's another that he says is basically orthogonal to that, which is the dimension between individualism and communitarianism.
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The No. 2 foreign policy donor, UNICEF USA, spent just $744,000, and its activities are orthogonal to AIPAC's interests anyway.
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Researchers used a certain type of sonar signal called Orthogonal Frequency Division Multiplexing, which is stronger than typical sonar signals.
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Beneath the mask's toothy grin is an orthogonal wind tube, while thin sticks representative of raindrops dangle from two fins.
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And it will mean channeling the vehicle traffic that remains — buses and (hopefully someday electric, shared) cars — onto fewer orthogonal through routes.
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Three orthogonal sets of square coils, called Merritt coils, allowed the researchers to control the ambient magnetic fields around a participant's head.
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These waves would stretch and compress space in orthogonal directions as they went by, the same way that sound waves compress air.
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It's made by Orthogonal Games, creator of character-driven indie project The Novelist — but it's not a game about exploring other people's lives.
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But as for new applications of the technology… — well, thankfully, largely orthogonal to the crypto/ICO bubble, a few have in fact arisen.
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But there's clearly a large, and primarily working-class, segment of the population that has a view that's somewhat orthogonal to this debate.
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That might be, but it's somewhat orthogonal to the claims about the influence of the 90th percentile made in the original Gilens/Page paper.
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Two of its marquee features are multi-user, multiple-input, multiple-output technology (MU-MIMO), and something called Orthogonal Frequency Division Multiple Access (OFDMA).
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"Mithril is a unique fund: By design, its orthogonal approach is not for everybody, and it's been uniquely successful," said Jeremiah Hall, a spokesperson for Thiel.
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And that's entirely orthogonal to throwing 10x more data and compute at a big neural network so that it improves its skill by some small percentage.
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But yeah, I felt like I had a very orthogonal skillset to someone who'd grown up through marketing or through sales or through engineering or product.
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An almost suffocating elegance suffuses it, every orthogonal street a sheer face of mute, balconied 18th-century facades, each wonderfully preserved in a kind of aristocratic amber.
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Professor Christine Blasey Ford's allegations against Brett Kavanaugh raise broad and deep questions about gender and power quite orthogonal to the byzantine machinations of Washington party politics.
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Amazon is attempting to insulate itself against being disintermediated in the future by playing the roles of YouTube, Pepsi and Papa John's all at once, albeit within an orthogonal industry.
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It was also one of Amazon's most ambitious bets, and one early example of how Amazon was willing to bulldoze its way into new markets orthogonal to its core business model.
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Trump has convinced the vast majority of Republican voters to fall in line behind him, and thus behind a political persona and policy agenda that are orthogonal to the party establishment's conception of itself.
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The coupling of high-resolution image data from car and satellite, plus a 3D point cloud, results in Apple now being able to produce full orthogonal reconstructions of city streets with textures in place.
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The winning plan, by architect Bruno Milić, met the challenge with meandering modernist buildings interspersed with numerous small piazzas that follow the city's Roman orthogonal grid and narrow street which actively encourage random social encounters.
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Google's Allo struggling with memory on my personal phone Google's Allo struggling with memory on my personal phone "Today's dialog technology is mostly orthogonal," explains Dan Klein, co-founder and chief scientist of Semantic Machines.
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As the Romans knew, and city planners have since rediscovered, the hypodamic plan (or hippodamian, named after the ancient planner Miletus), with its short blocks and orthogonal streets, encourages walking, mixing, and vibrant street life.
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"The new cultural cleavage dividing Populists and Cosmopolitan Liberals," Norris and Inglehart write, is "orthogonal to the classic economic class cleavage" — in other words, the new division cuts across and splits the old economic class solidarity.
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As for public transit, way back in 2002, Barcelona's resident urban visionary Salvador Rueda began working on a redesign of the city's bus system, creating an orthogonal network of mostly perpendicular routes shaped around the coming superblocks.
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I remember there was a faculty search process that the founder, Nicholas, was running, and we called it the Professor of Other; the candidate had to be proficient in at least two orthogonal fields and be antidisciplinary.
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The question of whether robots will eat all the jobs is orthogonal to the question of whether people believe robots will eat all the jobs — and whether the tech industry will be viewed as the oppressors of the masses.
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The orthogonal alignment of their photoreceptors has led some biologists to suspect that cephalopods use polarized light to see, and don't really change color but rather modulate their light-reflecting "iridophore cells," sort of like an iridescent soap bubble.
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I can't get into Bleszinski's head to see why he might regret centering the game's diverse cast in marketing; it seems to me like the game was generally marketed in a confusing and ineffective way, but that's orthogonal to politics.
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Fixating on introversion limits your life If we may wade into useful, technical jargon, the important thing to recognize, Shiner says, is that positive and negative emotionality are "orthogonal," meaning how you stand on one is unrelated to the other.
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Compared to existing 802.11ac, Qualcomm's 802.11ax solutions support "113-streams (eight 5GHz and four 2.4GHz), 8x8 MU-MIMO, 80 MHz channels" and features such as Orthogonal Frequency Division Multiple Access (OFDMA) and traffic scheduling to increase capacity, and improve coverage and efficiency.
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They include chairs for a church in the form of a simple box, with three planes beveled into the top to form a seat, as well as the adroit stools of SESC Pompéia, each made from four orthogonal planes of economical pine.
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Paper place mats create a network of parallel diagonals, compounded by a fork and knife, disrupted by a misplaced spoon, and traversed by the butter on the pancakes, which has melted from left to right to create the image's only orthogonal line.
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If you thought that was nonsensical, just try to figure out what on earth this chunk of words about VoIP means: The proliferation of VoIP and prevalence of its use are orthogonal to the Commission's point about the relationship between mobile broadband and VoIP .
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Founded: 2016Location: HawaiiMoney raised: $5.7 million Post money valuation: $88.8 million according to Nate Sumbot, general counsel for the companyWhat they're working on: Orthogonal Thinker is an investment vehicle whose investments include Maui Raw, a vegan raw-foods producer, to Airbnb, the giant lodging platform.
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So instead of highlighting the aspects of Trump that make him so uniquely horrifying to Democrats, to reach these voters surrogates need to make an orthogonal argument, to change the subject to a topic the voters also care about and where their values are closer to Democrats' than to Trump's.
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Artists like Michael Heizer and Robert Smithson crafted on massive scale, human attempts to transfigure the landscape into an ideal image, to replicate the environment in an orthogonal direction, cutting it with marks not unlike the Nazca lines in Peru, or building upward like the pyramids of Central America and Egypt.
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A solid half of the artists in Grupo Ruptura were European immigrants, including the Austrian-born Lothar Charoux, who made whispering compositions of orthogonal and diagonal lines, and Waldemar Cordeiro, from Rome, whose intriguing paintings of interconnected circles give a tiny hint of his future as an early computer artist.
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Consider the base set of octonions, 23, e103, e210, e210, e210, e5, e6 and e7, which are unit distances in eight different orthogonal directions: They respect a group of symmetries called G2, which happens to be one of the rare "exceptional groups" that can't be mathematically classified into other existing symmetry-group families.
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Charles Long's "Untitled" (2011) stands out as a particularly masterful example of art that leverages aesthetics to amplify its message: an orthogonal steel structure intersects with silvery-white tendrils made from papier maché, plaster, and river sediment including half of an Orbit gum packet, bits of plastic bags, and scraps of netting.
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Companies, through and through, have struggled with this, even outside the realm of social networking, doing something orthogonal to what they were doing before or even to add a new capability, however cool it might be, people will use that product to do one thing because that's how they started using it 5 years ago, 10 years ago.
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If we wanted to use cryptocurrencies to help the masses suffering under profligate governments using increasingly worthless fiat currencies — which I absolutely agree is a noble goal — we wouldn't be spending our time, effort, and intellectual horsepower on the ability to use cryptocurrency A as collateral for loans denominated in cryptocurrency B. They are completely orthogonal.
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However, orthogonal hulls and tight spans differ for point sets with disconnected orthogonal hulls, or in higher-dimensional Lp spaces. describes several other results about orthogonal convexity and orthogonal visibility.
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We say that the elements and are orthogonal and write if . We say that two sets and are orthogonal and write if r and s are orthogonal for all and and we say that is orthogonal to an element if is orthogonal to . For , we define the orthogonal or annihilator of to be .
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Any orthogonal basis can be used to define a system of orthogonal coordinates . Orthogonal (not necessarily orthonormal) bases are important due to their appearance from curvilinear orthogonal coordinates in Euclidean spaces, as well as in Riemannian and pseudo-Riemannian manifolds.
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The name of "orthogonal group" originates from the following characterization of its elements. Given a Euclidean vector space of dimension , the elements of the orthogonal group are, up to a uniform scaling (homothecy), the linear maps from to that map orthogonal vectors to orthogonal vectors.
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If this inner product is 0, then the rows are orthogonal. In fact, semigroup is orthogonal to loop, small category is orthogonal to quasigroup, and groupoid is orthogonal to magma. Consequently there are 0's in R RT and it fails to be a universal relation.
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As a scalar matrix, it is represented in every basis by a matrix with -1 on the diagonal, and, together with the identity, is the center of the orthogonal group O(n). It is a product of n orthogonal reflections (reflection through the axes of any orthogonal basis); note that orthogonal reflections commute. In 2 dimensions, it is in fact rotation by 180 degrees, and in dimension 2n, it is rotation by 180 degrees in n orthogonal planes;"Orthogonal planes" meaning all elements are orthogonal and the planes intersect at 0 only, not that they intersect in a line and have dihedral angle 90°. note again that rotations in orthogonal planes commute.
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Orthogonal midplanes connect vertical cards on one side to horizontal boards on the other side. Kevin O’Connor. "Orthogonal Backplane Connector Technology Offers Design Flexibility". 2010\. Pete. "High-Speed Orthogonal Connectors Optimize Signal Integrity" . 2011.
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The product of projections is not in general a projection, even if they are orthogonal. If two projections commute then their product is a projection, but the converse is false: the product of two non-commuting projections may be a projection . If two orthogonal projections commute then their product is an orthogonal projection. If the product of two orthogonal projections is an orthogonal projection, then the two orthogonal projections commute (more generally: two self-adjoint endomorphisms commute if and only if their product is self-adjoint).
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Schönemann's PhD thesis "A solution of the orthogonal Procrustes problem with applications to orthogonal and oblique rotation," proposed a solution to the orthogonal Procrustes problem. Other Schönemann papers include "A generalized solution of the orthogonal Procrustes problem",A generalized solution of the orthogonal Procrustes problem. Psychometrika, 31, 1–10.: "The minimum average correlation between equivalent sets of uncorrelated factors",The minimum average correlation between equivalent sets of uncorrelated factors.
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The projective special orthogonal group, PSO, is defined analogously, as the induced action of the special orthogonal group on the associated projective space. Explicitly: :PSO(V) = SO(V)/ZSO(V) where SO(V) is the special orthogonal group over V and ZSO(V) is the subgroup of orthogonal scalar transformations with unit determinant. Here ZSO is the center of SO, and is trivial in odd dimension, while it equals {±1} in even dimension – this odd/even distinction occurs throughout the structure of the orthogonal groups. By analogy with GL/SL and GO/SO, the projective orthogonal group is also sometimes called the projective general orthogonal group and denoted PGO.
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There are a number of related problems to the classical orthogonal Procrustes problem. One might generalize it by seeking the closest matrix in which the columns are orthogonal, but not necessarily orthonormal. Alternately, one might constrain it by only allowing rotation matrices (i.e. orthogonal matrices with determinant 1, also known as special orthogonal matrices).
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The first is an orthogonal line passing through the corresponding Euler point to the chosen face. The second is an orthogonal line passing through the centroid of the chosen face. This orthogonal line through the twelve-point center lies midway between the Euler point orthogonal line and the centroidal orthogonal line. Furthermore, for any face, the twelve-point center lies at the midpoint of the corresponding Euler point and the orthocenter for that face.
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More specifically, they can be characterized as orthogonal matrices with determinant 1; that is, a square matrix is a rotation matrix if and only if and . The set of all orthogonal matrices of size with determinant +1 forms a group known as the special orthogonal group , one example of which is the rotation group SO(3). The set of all orthogonal matrices of size with determinant +1 or −1 forms the (general) orthogonal group .
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In mathematics, particularly linear algebra, an orthogonal basis for an inner product space is a basis for whose vectors are mutually orthogonal. If the vectors of an orthogonal basis are normalized, the resulting basis is an orthonormal basis.
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Orthogonal BVI occurs when the axes of the vortex are in orthogonal planes. In the context of helicopter application, the orthogonal interaction usually exits between the tip vortices generated by the main rotor and the blade of the tail rotor.
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There are several conditions that single out the classical orthogonal polynomials from the others. The first condition was found by Sonine (and later by Hahn), who showed that (up to linear changes of variable) the classical orthogonal polynomials are the only ones such that their derivatives are also orthogonal polynomials. Bochner characterized classical orthogonal polynomials in terms of their recurrence relations. Tricomi characterized classical orthogonal polynomials as those that have a certain analogue of the Rodrigues formula.
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Any such polygonal chain has the same length, so there are infinitely many connected orthogonal convex hulls for the point set. For point sets in the plane, the connected orthogonal convex hull can be easily obtained from the maximal orthogonal convex hull. If the maximal orthogonal convex hull of a point set K \subset \R^2 is connected, then it is equal to the connected orthogonal convex hull of K. If this is not the case, then there are infinitely many connected orthogonal convex hulls for K, and each one can be obtained by joining the connected components of the maximal orthogonal convex hull of K with orthogonally convex alternating polygonal chains with interior angle 90^\circ.
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A Latin cube of order n is equivalent to a 2-(n, 4, n) orthogonal array. Two Latin cubes of order n are orthogonal if, among the n3 pairs of elements chosen from corresponding cells of the two cubes, each distinct ordered pair of the elements occurs exactly n times. A set of k − 3 mutually orthogonal Latin cubes of order n is equivalent to a 2-(n, k, n) orthogonal array. An example of a pair of mutually orthogonal Latin cubes of order three was given as the 2-(3,5,3) orthogonal array in the Examples section above.
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The orthogonal group On(R) preserves a non-degenerate quadratic form on a module. There is a subgroup, the special orthogonal group SOn(R) and quotients, the projective orthogonal group POn(R), and the projective special orthogonal group PSOn(R). In characteristic 2 the determinant is always 1, so the special orthogonal group is often defined as the subgroup of elements of Dickson invariant 1. There is a nameless group often denoted by Ωn(R) consisting of the elements of the orthogonal group of elements of spinor norm 1, with corresponding subgroup and quotient groups SΩn(R), PΩn(R), PSΩn(R).
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In mathematics, the spin representations are particular projective representations of the orthogonal or special orthogonal groups in arbitrary dimension and signature (i.e., including indefinite orthogonal groups). More precisely, they are representations of the spin groups, which are double covers of the special orthogonal groups. They are usually studied over the real or complex numbers, but they can be defined over other fields.
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Given a Hilbert space H and a set S of mutually orthogonal vectors in H, we can take the smallest closed linear subspace V of H containing S. Then S will be an orthogonal basis of V; which may of course be smaller than H itself, being an incomplete orthogonal set, or be H, when it is a complete orthogonal set.
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Recall from the previous section that there is a homomorphism from the Clifford group onto the orthogonal group. We define the special orthogonal group to be the image of Γ0. If K does not have characteristic 2 this is just the group of elements of the orthogonal group of determinant 1. If K does have characteristic 2, then all elements of the orthogonal group have determinant 1, and the special orthogonal group is the set of elements of Dickson invariant 0.
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A circle that is orthogonal to two fixed circles is orthogonal to every circle in the pencil they determine. The circles orthogonal to two fixed circles form a pencil of circles. Two circles determine two pencils, the unique pencil that contains them and the pencil of circles orthogonal to them. The radical axis of one pencil consists of the centers of the circles of the other pencil.
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This allows the concept of rotation and reflection to be generalized to higher dimensions. In finite- dimensional spaces, the matrix representation (with respect to an orthonormal basis) of an orthogonal transformation is an orthogonal matrix. Its rows are mutually orthogonal vectors with unit norm, so that the rows constitute an orthonormal basis of V. The columns of the matrix form another orthonormal basis of V. The inverse of an orthogonal transformation is another orthogonal transformation. Its matrix representation is the transpose of the matrix representation of the original transformation.
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The figure shows a set of 16 points in the plane and the orthogonal convex hull of these points. As can be seen in the figure, the orthogonal convex hull is a polygon with some degenerate edges connecting extreme vertices in each coordinate direction. For a discrete point set such as this one, all orthogonal convex hull edges are horizontal or vertical. In this example, the orthogonal convex hull is connected.
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The concepts of Latin squares and mutually orthogonal Latin squares were generalized to Latin cubes and hypercubes, and orthogonal Latin cubes and hypercubes by . generalized these results to strength t. The present notion of orthogonal array as a generalization of these ideas, due to C. R. Rao, appears in .
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In mathematics, the Askey scheme is a way of organizing orthogonal polynomials of hypergeometric or basic hypergeometric type into a hierarchy. For the classical orthogonal polynomials discussed in , the Askey scheme was first drawn by and by , and has since been extended by and to cover basic orthogonal polynomials.
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B. Orthogonal polynomials, Random matrices. Given a weight on a contour, the corresponding orthogonal polynomials can be computed via the solution of a Riemann–Hilbert factorization problem (). Furthermore, the distribution of eigenvalues of random matrices in several classical ensembles is reduced to computations involving orthogonal polynomials (see for example ). C. Combinatorial probability.
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There is a similar description over the real numbers with U(n) replaced by the orthogonal group O(n), and Tn by the diagonal orthogonal matrices (which have diagonal entries ±1).
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Just as the orthogonal group is the structure group of vector bundles, the projective orthogonal group is the structure group of projective bundles, and the corresponding classifying space is denoted BPO.
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Orthogonal rotations constrain factors to be perpendicular to each other and hence uncorrelated. An advantage of orthogonal rotation is its simplicity and conceptual clarity, although there are several disadvantages. In the social sciences, there is often a theoretical basis for expecting constructs to be correlated, therefore orthogonal rotations may not be very realistic because they do not allow this. Also, because orthogonal rotations require factors to be uncorrelated, they are less likely to produce solutions with simple structure.
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Thus, the determinant of a rotation orthogonal matrix must be 1. The only other possibility for the determinant of an orthogonal matrix is , and this result means the transformation is a hyperplane reflection, a point reflection (for odd ), or another kind of improper rotation. Matrices of all proper rotations form the special orthogonal group.
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The rejection of a vector from a plane is its orthogonal projection on a straight line which is orthogonal to that plane. Both are vectors. The first is parallel to the plane, the second is orthogonal. For a given vector and plane, the sum of projection and rejection is equal to the original vector.
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Like the orthogonal group, the projective orthogonal group can be defined over any field and with varied quadratic forms, though, as with the ordinary orthogonal group, the main emphasis is on the real positive definite projective orthogonal group; other fields are elaborated in generalizations, below. Except when mentioned otherwise, in the sequel PO and PSO will refer to the real positive definite groups. Like the spin groups and pin groups, which are covers rather than quotients of the (special) orthogonal groups, the projective (special) orthogonal groups are of interest for (projective) geometric analogs of Euclidean geometry, as related Lie groups, and in representation theory. More intrinsically, the (real positive definite) projective orthogonal group PO can be defined as the isometries of real projective space, while PSO can be defined as the orientation-preserving isometries of real projective space (when the space is orientable; otherwise PSO = PO).
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Other orthogonal two-dimensional coordinate systems involving hyperbolas may be obtained by other conformal mappings. For example, the mapping w = z2 transforms the Cartesian coordinate system into two families of orthogonal hyperbolas.
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The line segments AB and CD are orthogonal to each other. In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms. Two elements u and v of a vector space with bilinear form B are orthogonal when . Depending on the bilinear form, the vector space may contain nonzero self-orthogonal vectors.
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Furthermore, the resulting matrix factor becomes more sparse and orthogonal.
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Since V comes equipped with a quadratic form Q, in characteristic not equal to 2 there exist bases for V that are orthogonal. An orthogonal basis is one such that for a symmetric bilinear form :\langle e_i, e_j \rangle = 0 for i eq j, and \langle e_i, e_i \rangle = Q(e_i). The fundamental Clifford identity implies that for an orthogonal basis :e_i e_j = -e_j e_i for i eq j, and e_i^2 = Q(e_i). This makes manipulation of orthogonal basis vectors quite simple.
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Similarly to orthogonal tRNAs and aminoacyl tRNA synthetases (aaRSs), orthogonal ribosomes have been engineered to work in parallel to the natural ribosomes. Orthogonal ribosomes ideally use different mRNA transcripts than their natural counterparts and ultimately should draw on a separate pool of tRNA as well. This should alleviate some of the loss of fitness which currently still arises from techniques such as Amber codon suppression. Additionally, orthogonal ribosomes can be mutated and optimized for particular tasks, like the recognition of quadruplet codons.
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We emphasize that the symplectic product here is the standard symplectic product. Leave the matrix as it is if the first row is not symplectically orthogonal to the second row or if the first row is symplectically orthogonal to all other rows. Otherwise, swap the second row with the first available row that is not symplectically orthogonal to the first row. In our example, the first row is not symplectically orthogonal to the second so we leave all rows as they are.
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If Od(R) is the orthogonal group acting on V = Rd, then the Brauer algebra has a natural action on the space of polynomials on Vn commuting with the action of the orthogonal group.
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In some contrast to the standard classical orthogonal polynomials, the polynomials under consideration differ, in so far as for arbitrary parameters only a finite number of them are orthogonal, as discussed in more detail below.
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Numerical analysis takes advantage of many of the properties of orthogonal matrices for numerical linear algebra, and they arise naturally. For example, it is often desirable to compute an orthonormal basis for a space, or an orthogonal change of bases; both take the form of orthogonal matrices. Having determinant ±1 and all eigenvalues of magnitude 1 is of great benefit for numeric stability. One implication is that the condition number is 1 (which is the minimum), so errors are not magnified when multiplying with an orthogonal matrix.
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The Mathematics Department split from the Institute in 1934. It is now known as Steklov Institute of Mathematics. Steklov's primary scientific contribution was in the area of orthogonal functional sets. He introduced a class of closed orthogonal sets, developed the asymptotic Liouville–Steklov method for orthogonal polynomials, proved theorems on generalized Fourier series, and developed an approximation technique later named Steklov function.
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Every orthogonal matrix has determinant 1 or −1. Orthogonal matrices with determinant 1 form a subgroup called special orthogonal group. Every finite group is isomorphic to a matrix group, as one can see by considering the regular representation of the symmetric group. General groups can be studied using matrix groups, which are comparatively well understood, by means of representation theory.
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Pseudospectral collocation, also known as global collocation, is a subset of orthogonal collocation in which the entire trajectory is represented by a single high-order orthogonal polynomial. As a side note: some authors use orthogonal collocation and pseudospectral collocation interchangeably. When used to solve a trajectory optimization problem whose solution is smooth, a pseudospectral method will achieve spectral (exponential) convergence.Lloyd N. Trefethen.
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Unlike the case with Latin squares, in which there are no constraints, the indexing columns of the orthogonal array representation of a Latin cube must be selected so as to form a 3-(n,3,1) orthogonal array.
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Note that \vert \Psi_k\rangle are not necessarily orthogonal to each other.
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There are two main types of factor rotation: orthogonal and oblique rotation.
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Two simple roots which are not joined by a line are orthogonal.
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In combinatorics, two Latin squares of the same size (order) are said to be orthogonal if when superimposed the ordered paired entries in the positions are all distinct. A set of Latin squares, all of the same order, all pairs of which are orthogonal is called a set of mutually orthogonal Latin squares. This concept of orthogonality is not strongly related to others that appear in algebra and analysis. A pair of orthogonal Latin squares has traditionally been called a Graeco-Latin square, although that term is now somewhat dated.
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Persistence is said to be "orthogonal" or "transparent" when it is implemented as an intrinsic property of the execution environment of a program. An orthogonal persistence environment does not require any specific actions by programs running in it to retrieve or save their state. Non- orthogonal persistence requires data to be written and read to and from storage using specific instructions in a program, resulting in the use of persist as a transitive verb: On completion, the program persists the data. The advantage of orthogonal persistence environments is simpler and less error-prone programs.
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Many of the early techniques in reducing representational overlap involved making either the input vectors or the hidden unit activation patterns orthogonal to one another. Lewandowsky and Li (1995) noted that the interference between sequentially learned patterns is minimized if the input vectors are orthogonal to each other. Input vectors are said to be orthogonal to each other if the pairwise product of their elements across the two vectors sum to zero. For example, the patterns [0,0,1,0] and [0,1,0,0] are said to be orthogonal because (0×0 + 0×1 + 1×0 + 0×0) = 0.
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This works because translations are a normal subgroup of the full group of isometries, with quotient the orthogonal group; and rotations about a fixed point are a normal subgroup of the orthogonal group, with quotient a single reflection.
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Orthogonal intersections can have a preferred orientation or may be random. In oriented orthogonal cracks, the cracks are usually complete and bond to one another forming irregular polygonal shapes and often rows of irregular polygons. In random orthogonal cracks, the cracks are incomplete and unoriented therefore they do not connect or make any general shapes. Although they do not make general shapes they are not perfectly geometric.
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In special relativity the orthogonal complement is used to determine the simultaneous hyperplane at a point of a world line. The bilinear form η used in Minkowski space determines a pseudo-Euclidean space of events. The origin and all events on the light cone are self-orthogonal. When a time event and a space event evaluate to zero under the bilinear form, then they are hyperbolic-orthogonal.
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An idempotent g is called primitive or minimal if it cannot be written as a sum of non-zero orthogonal idempotents. If e1, ..., em are pairwise orthogonal idempotents then their sum is also an idempotent and the algebra they generate consists of all linear combinations of the ei. It is an associative algebra. If e is an idempotent, then 1 − e is an orthogonal idempotent.
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One of the techniques which can create orthogonal representations at the hidden layers involves bipolar feature coding (i.e., coding using -1 and 1 rather than 0 and 1). Orthogonal patterns tend to produce less interference with each other. However, not all learning problems can be represented using these types of vectors and some studies report that the degree of interference is still problematic with orthogonal vectors.
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In mathematics, the secondary measure associated with a measure of positive density ρ when there is one, is a measure of positive density μ, turning the secondary polynomials associated with the orthogonal polynomials for ρ into an orthogonal system.
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In mathematics, orthogonal polynomials on the unit circle are families of polynomials that are orthogonal with respect to integration over the unit circle in the complex plane, for some probability measure on the unit circle. They were introduced by .
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In projective geometry and linear algebra, the projective orthogonal group PO is the induced action of the orthogonal group of a quadratic space V = (V,Q)A quadratic space is a vector space V together with a quadratic form Q; the Q is dropped from notation when it is clear. on the associated projective space P(V). Explicitly, the projective orthogonal group is the quotient group :PO(V) = O(V)/ZO(V) = O(V)/{±I} where O(V) is the orthogonal group of (V) and ZO(V)={±I} is the subgroup of all orthogonal scalar transformations of V – these consist of the identity and reflection through the origin. These scalars are quotiented out because they act trivially on the projective space and they form the kernel of the action, and the notation "Z" is because the scalar transformations are the center of the orthogonal group.
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Walsh functions and Haar wavelets are examples of orthogonal functions with discrete ranges.
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The architect Adrian de Pauger drew the orthogonal plane of the Old Square.
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The classical pure states are pairwise orthogonal, but quantum pure states are not.
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Orthogonal testing is often required as a part of a new drug application.
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An orthogonal array is linear if X is a finite field of order q, Fq (q a prime power) and the rows of the array form a subspace of the vector space (Fq)k. Every linear orthogonal array is simple.
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Let C ⊆ (Fq)n, be a linear code of dimension m with minimum distance d. Then C⊥ (the orthogonal complement of the vector subspace C) is a (linear) (d − 1)-(q, n, λ) orthogonal array where λ = qn − m − d + 1.
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In mathematics, SO(5), also denoted SO5(R) or SO(5,R), is the special orthogonal group of degree 5 over the field R of real numbers, i.e. (isomorphic to) the group of orthogonal 5×5 matrices of determinant 1.
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Plot of the Chebyshev rational functions of order n=0,1,2,3 and 4 between x=0.01 and 100. Legendre and Chebyshev polynomials provide orthogonal families for the interval while occasionally orthogonal families are required on . In this case it is convenient to apply the Cayley transform first, to bring the argument into . This procedure results in families of rational orthogonal functions called Legendre rational functions and Chebyshev rational functions.
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Any improper orthogonal 3x3 matrix B may be written as B=-A, in which A is proper orthogonal. That is, any improper orthogonal 3x3 matrix may be decomposed as a proper rotation (from which an axis of rotation can be found as described above) followed by an inversion (multiplication by -1). It follows that the rotation axis of A is also the eigenvector of B corresponding to an eigenvalue of -1.
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The Rogers–Szegő polynomials are an example of orthogonal polynomials on the unit circle.
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An orthogonal polyhedron is one all of whose faces meet at right angles, and all of whose edges are parallel to axes of a Cartesian coordinate system. (Jessen's icosahedron provides an example of a polyhedron meeting one but not both of these two conditions.) Aside from the rectangular boxes, orthogonal polyhedra are nonconvex. They are the 3D analogs of 2D orthogonal polygons, also known as rectilinear polygons. Orthogonal polyhedra are used in computational geometry, where their constrained structure has enabled advances on problems unsolved for arbitrary polyhedra, for example, unfolding the surface of a polyhedron to a polygonal net..
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Several authors have studied algorithms for constructing orthogonal convex hulls: ; ; ; . By the results of these authors, the orthogonal convex hull of points in the plane may be constructed in time , or possibly faster using integer searching data structures for points with integer coordinates.
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Emil Artin (1957) Geometric Algebra, page 119 Through the polarization identity the quadratic form is related to a symmetric bilinear form . Two vectors u and v are orthogonal when . In the case of the hyperbolic plane, such u and v are hyperbolic-orthogonal.
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Fig.2 Non-Orthogonal Grids Fig.3 Orthogonal Grids a) Structured curvilinear grid arrangements (vertices having similar neighborhood). b) Unstructured grid arrangements (vertices having variation in neighborhood). Structured Curvilinear grids 1) Grid points are identified at the intersection of co-ordinate line.
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An involutory matrix which is also symmetric is an orthogonal matrix, and thus represents an isometry (a linear transformation which preserves Euclidean distance). Conversely every orthogonal involutory matrix is symmetric.. As a special case of this, every reflection matrix is an involutory.
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The other two are the Laguerre polynomials, which are orthogonal over the half line [0,\infty), and the Hermite polynomials, orthogonal over the full line (-\infty,\infty), with weight functions that are the most natural analytic functions that ensure convergence of all integrals.
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Moreover, there exist quasi-orthogonal STBCs that achieve higher data rates at the cost of inter-symbol interference (ISI). Thus, their error-rate performance is lower bounded by the one of orthogonal rate 1 STBCs, that provide ISI free transmissions due to orthogonality.
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An alternative to fitting m data points by a simple polynomial in the subsidiary variable, z, is to use orthogonal polynomials. :Y = b_0 P^0(z) + b_1 P^1(z) \cdots + b_k P^k(z). where P0, ..., Pk is a set of mutually orthogonal polynomials of degree 0, ..., k. Full details on how to obtain expressions for the orthogonal polynomials and the relationship between the coefficients b and a are given by Guest.
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If 1 is centrally primitive, we are done. If not, it is a sum of central orthogonal idempotents, which in turn are primitive or sums of more central idempotents, and so on. The problem that may occur is that this may continue without end, producing an infinite family of central orthogonal idempotents. The condition "R does not contain infinite sets of central orthogonal idempotents" is a type of finiteness condition on the ring.
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In Euclidean space, two vectors are orthogonal if and only if their dot product is zero, i.e. they make an angle of 90° (π/2 radians), or one of the vectors is zero. Hence orthogonality of vectors is an extension of the concept of perpendicular vectors to spaces of any dimension. The orthogonal complement of a subspace is the space of all vectors that are orthogonal to every vector in the subspace.
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In mathematics, a sequence of discrete orthogonal polynomials is a sequence of polynomials that are pairwise orthogonal with respect to a discrete measure. Examples include the discrete Chebyshev polynomials, Charlier polynomials, Krawtchouk polynomials, Meixner polynomials, dual Hahn polynomials, Hahn polynomials, and Racah polynomials. If the measure has finite support, then the corresponding sequence of discrete orthogonal polynomials has only a finite number of elements. The Racah polynomials give an example of this.
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A linear function of a matrix is a linear combination of its elements (with given coefficients), where is the matrix of the coefficients; see Trace (linear algebra)#Inner product. A random orthogonal matrix is said to be distributed uniformly, if its distribution is the normalized Haar measure on the orthogonal group ; see Rotation matrix#Uniform random rotation matrices. > Theorem. Let be a random orthogonal matrix distributed uniformly, and a > fixed matrix such that , and let .
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Suppose that \mu is a probability measure on the unit circle in the complex plane, whose support is not finite. The orthogonal polynomials associated to \mu are the polynomials \Phi_n(z) with leading term z^n that are orthogonal with respect to the measure \mu.
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These polynomials are called the Bergman polynomials, and provide an orthogonal polynomial basis for Bergman space.
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The king steps one square in any direction, orthogonal or diagonal. The king does not promote.
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In mathematics, the pin group is a certain subgroup of the Clifford algebra associated to a quadratic space. It maps 2-to-1 to the orthogonal group, just as the spin group maps 2-to-1 to the special orthogonal group. In general the map from the Pin group to the orthogonal group is not onto or a universal covering space, but if the quadratic form is definite (and dimension is greater than 2), it is both. The non-trivial element of the kernel is denoted −1, which should not be confused with the orthogonal transform of reflection through the origin, generally denoted −I.
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3, pp. 569–572, 2003. and has also been modified to account for optical resonators with non-orthogonal modes.W. Suh, Z. Wang, and S. Fan, "Temporal coupled-mode theory and the presence of non- orthogonal modes in lossless multimode cavities," Quantum Electronics, IEEE Journal of, vol.
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Orthogonal frequency-division multiple access (OFDMA) is a multi-user version of the popular orthogonal frequency-division multiplexing (OFDM) digital modulation scheme. Multiple access is achieved in OFDMA by assigning subsets of subcarriers to individual users. This allows simultaneous low-data-rate transmission from several users.
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Point groups can be classified into chiral (or purely rotational) groups and achiral groups. The chiral groups are subgroups of the special orthogonal group SO(d): they contain only orientation-preserving orthogonal transformations, i.e., those of determinant +1. The achiral groups contain also transformations of determinant −1.
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Orthogonal Signal Correction (OSC) is a spectral preprocessing technique that removes variation from a data matrix X that is orthogonal to the response matrix Y. OSC was introduced by researchers at the University of Umea in 1998 and has since found applications in domains including metabolomics.
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Motorola's designers attempted to make the assembly language orthogonal while the underlying machine language was somewhat less so. Unlike PDP-11, the MC68000 (68k) used separate registers to store data and the addresses of data in memory. The ISA was orthogonal to the extent that addresses could only be used in those registers, but there was no restriction on which of the registers could be used by different instructions. Likewise, the data registers were also orthogonal across instructions.
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We say that two parameters θi and θj are orthogonal if the element of the ith row and jth column of the Fisher information matrix is zero. Orthogonal parameters are easy to deal with in the sense that their maximum likelihood estimates are independent and can be calculated separately. When dealing with research problems, it is very common for the researcher to invest some time searching for an orthogonal parametrization of the densities involved in the problem.
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An idempotent of a ring is called central if it commutes with all elements of the ring. Two idempotents e, f are called orthogonal if ef=fe=0. An idempotent is called primitive if it is nonzero and cannot be written as the sum of two orthogonal nonzero idempotents. An idempotent e is called a block or centrally primitive if it is nonzero and central and cannot be written as the sum of two orthogonal nonzero central idempotents.
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More generally, coordinate rotations in any dimension are represented by orthogonal matrices. The set of all orthogonal matrices in dimensions which describe proper rotations (determinant = +1), together with the operation of matrix multiplication, forms the special orthogonal group . Matrices are often used for doing transformations, especially when a large number of points are being transformed, as they are a direct representation of the linear operator. Rotations represented in other ways are often converted to matrices before being used.
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A popular extension of Matching Pursuit (MP) is its orthogonal version: Orthogonal Matching Pursuit (OMP). The main difference from MP is that after every step, all the coefficients extracted so far are updated, by computing the orthogonal projection of the signal onto the subspace spanned by the set of atoms selected so far. This can lead to results better than standard MP, but requires more computation. Extensions such as Multichannel MP"Piecewise linear source separation", R. Gribonval, Proc.
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They do not form a vector space under the addition of operators, e.g. both id and -id are invertible (bijective), but their sum, 0, is not. Operators preserving the Euclidean metric on such a space form the isometry group, and those that fix the origin form a subgroup known as the orthogonal group. Operators in the orthogonal group that also preserve the orientation of vector tuples form the special orthogonal group, or the group of rotations.
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While mesh being orthogonal is generated very rapidly which comes out as an advantage with this method.
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In linear algebra, an orthogonal transformation is a linear transformation T : V → V on a real inner product space V, that preserves the inner product. That is, for each pair of elements of V, we have : \langle u,v \rangle = \langle Tu,Tv \rangle \, . Since the lengths of vectors and the angles between them are defined through the inner product, orthogonal transformations preserve lengths of vectors and angles between them. In particular, orthogonal transformations map orthonormal bases to orthonormal bases.
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Let be a finite-dimensional real or complex vector space with a nondegenerate quadratic form . The (real or complex) linear maps preserving form the orthogonal group . The identity component of the group is called the special orthogonal group . (For real with an indefinite quadratic form, this terminology is not standard: the special orthogonal group is usually defined to be a subgroup with two components in this case.) Up to group isomorphism, has a unique connected double cover, the spin group .
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It is therefore sometimes said that the expansion is bi-orthogonal since the random coefficients are orthogonal in the probability space while the deterministic functions are orthogonal in the time domain. The general case of a process that is not centered can be brought back to the case of a centered process by considering which is a centered process. Moreover, if the process is Gaussian, then the random variables are Gaussian and stochastically independent. This result generalizes the Karhunen–Loève transform.
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Finally it passes through the four base points of orthogonal lines dropped from each Euler point to the face not containing the vertex that generated the Euler point. The center T of the twelve-point sphere also lies on the Euler line. Unlike its triangular counterpart, this center lies one third of the way from the Monge point M towards the circumcenter. Also, an orthogonal line through T to a chosen face is coplanar with two other orthogonal lines to the same face.
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Orthogonal collocation is technically a subset of direct collocation, but the implementation details are so different that it can reasonably be considered its own set of methods. Orthogonal collocation differs from direct collocation in that it typically uses high-order splines, and each segment of the trajectory might be represented by a spline of a different order. The name comes from the use of orthogonal polynomials in the state and control splines.Camila C. Francolin, David A. Benson, William W. Hager, Anil V. Rao.
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The aquaporin-4 tetramers accumulate to transform into orthogonal arrays of particle (OAPs) in the cell plasma membrane.
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Symmetric and orthogonal spectra are arguably the simplest ways to construct a sensible symmetric monoidal category of spectra.
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The set of all such matrices of size n forms a group, known as the special orthogonal group .
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"Costate Estimation in Optimal Control Using Integral Gaussian Quadrature Orthogonal Collocation Methods" Optimal Control Applications and Methods, 2014.
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In mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials: the Hermite polynomials, Laguerre polynomials, Jacobi polynomials (including as a special case the Gegenbauer polynomials, Chebyshev polynomials, and Legendre polynomialsSee ). They have many important applications in such areas as mathematical physics (in particular, the theory of random matrices), approximation theory, numerical analysis, and many others. Classical orthogonal polynomials appeared in the early 19th century in the works of Adrien-Marie Legendre, who introduced the Legendre polynomials. In the late 19th century, the study of continued fractions to solve the moment problem by P. L. Chebyshev and then A.A. Markov and T.J. Stieltjes led to the general notion of orthogonal polynomials.
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In synthetic organic chemistry orthogonal protection is a strategy allowing the deprotection of functional groups independently of each other. In chemistry and biochemistry, an orthogonal interaction occurs when there are two pairs of substances and each substance can interact with their respective partner, but does not interact with either substance of the other pair. For example, DNA has two orthogonal pairs: cytosine and guanine form a base-pair, and adenine and thymine form another base-pair, but other base-pair combinations are strongly disfavored. As a chemical example, tetrazine reacts with transcyclooctene and azide reacts with cyclooctyne without any cross- reaction, so these are mutually orthogonal reactions, and so, can be performed simultaneously and selectively.
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Adjustments need to be made in the calculation of line, surface and volume integrals. For simplicity, the following restricts to three dimensions and orthogonal curvilinear coordinates. However, the same arguments apply for n-dimensional spaces. When the coordinate system is not orthogonal, there are some additional terms in the expressions.
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These combinations are chosen to satisfy two conditions. First, the total amount of s and p orbital contributions must be equivalent before and after hybridisation. Second, the hybrid orbitals must be orthogonal to each other. If two hybrid orbitals were not orthogonal, by definition they would have nonzero orbital overlap.
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Orthogonal frequency-division multiplexing (OFDM) is a very promising modulation technique; perhaps its biggest problem is its high crest factor."Crest Factor Reduction of an OFDM/WiMAX Network". "Low Crest Factor Modulation Techniques for Orthogonal Frequency Division Multiplexing (OFDM)" . Many crest factor reduction techniques (CFR) have been proposed for OFDM.
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The orthogonal convex hull is also known as the rectilinear convex hull, or, in two dimensions, the - convex hull.
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A comprehensive overview of MRA and orthogonal fractional wavelets associated with the FRWT can be found in the paper.
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A uniaxial crystal (e.g. calcite, quartz) is isotropic within the plane orthogonal to the optic axis of the crystal.
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It is natural to generalize orthogonal convexity to restricted-orientation convexity, in which a set is defined to be convex if all lines having one of a finite set of slopes must intersect in connected subsets; see e.g. , , or . In addition, the tight span of a finite metric space is closely related to the orthogonal convex hull. If a finite point set in the plane has a connected orthogonal convex hull, that hull is the tight span for the Manhattan distance on the point set.
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300px 400px In geometry, the GEOS circle is derived from the intersection of four lines that are associated with a generalized triangle: the Euler line, the Soddy line, the orthic axis and the Gergonne line. Note that the Euler line is orthogonal to the orthic axis and that the Soddy line is orthogonal to the Gergonne line. These four lines provide six points of intersection of which two points occur at line intersections that are orthogonal. Consequently, the other four points form an orthocentric system.
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In mathematics, the term Pseudo Jacobi polynomials was introduced by Lesky for one of three finite sequences of orthogonal polynomials y. Since they form an orthogonal subset of Routh polynomials it seems consistent to refer to them as Romanovski-Routh polynomials, by analogy with the terms Romanovski-Bessel and Romanovski-Jacobi used by Lesky. As shown by Askey for two other sequencesth is finite sequence orthogonal polynomials of can be expressed in terms of Jacobi polynomials of imaginary argument. In following Raposo et al.
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This means that there is an orthogonal basis, made by the corresponding eigenvectors (which are necessarily orthogonal), over which the effect of the rotation matrix is just stretching it. If we write A in this basis, it is diagonal; but a diagonal orthogonal matrix is made of just +1's and -1's in the diagonal entries. Therefore, we don't have a proper rotation, but either the identity or the result of a sequence of reflections. It follows, then, that a proper rotation has some complex eigenvalue.
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Orthogonal axes in m-dimensional space, vertices of component at n on each axe, the tip at [0,...,0] for .
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The static part of the architecture builds on three orthogonal axes: Enterprise Dimensions, Levels of technical Granularity and Colloborative Views.
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In the Bott periodicity theorem, the loop spaces of the stable orthogonal group can be interpreted as reductive symmetric spaces.
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In mathematics, the Cartan–Dieudonné theorem, named after Élie Cartan and Jean Dieudonné, establishes that every orthogonal transformation in an n-dimensional symmetric bilinear space can be described as the composition of at most n reflections. The notion of a symmetric bilinear space is a generalization of Euclidean space whose structure is defined by a symmetric bilinear form (which need not be positive definite, so is not necessarily an inner product – for instance, a pseudo-Euclidean space is also a symmetric bilinear space). The orthogonal transformations in the space are those automorphisms which preserve the value of the bilinear form between every pair of vectors; in Euclidean space, this corresponds to preserving distances and angles. These orthogonal transformations form a group under composition, the orthogonal group.
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Agilent 6210 electrospray ionization orthogonal time-of-flight mass spectrometer (right) and HPLC (left) Orthogonal acceleration time of flight mass spectrometer schematic: 20 – ion source; 21 – ion transport; 22 – flight tube; 23 – isolation valve; 24 – repeller plate; 25 – grids; 26 – acceleration region; 27 – reflectron; 28 – detector. Continuous ion sources (most commonly electrospray ionization, ESI) are generally interfaced to the TOF mass analyzer by "orthogonal extraction" in which ions introduced into the TOF mass analyzer are accelerated along the axis perpendicular to their initial direction of motion. Orthogonal acceleration combined with collisional ion cooling allows separating the ion production in the ion source and mass analysis. In this technique, very high resolution can be achieved for ions produced in MALDI or ESI sources.
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The orthogonal group of all orthogonal real matrices (intuitively the set of all rotations and reflections of -dimensional space that keep the origin fixed) is isomorphic to a semidirect product of the group (consisting of all orthogonal matrices with determinant , intuitively the rotations of -dimensional space) and . If we represent as the multiplicative group of matrices }, where is a reflection of -dimensional space that keeps the origin fixed (i.e., an orthogonal matrix with determinant representing an involution), then is given by for all H in and in . In the non-trivial case ( is not the identity) this means that is conjugation of operations by the reflection (a rotation axis and the direction of rotation are replaced by their "mirror image").
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From top to bottom, the second to the fourth figures show respectively, the maximal, the connected, and the functional orthogonal convex hull of the point set. As can be seen, the orthogonal convex hull is a polygon with some degenerate "edges", namely, orthogonally convex alternating polygonal chains with interior angle 90^\circ connecting extreme vertices.
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In order to model river channel migrations over time, orthogonal functions of erosion path lines can be generated for individual point bar complexes. The orthogonal functions can be used to directly indicate the paths that channels could take in lateral migrations. The modeling of meander patterns can be useful in a variety of physical applications.
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In computer engineering, an orthogonal instruction set is an instruction set architecture where all instruction types can use all addressing modes. It is "orthogonal" in the sense that the instruction type and the addressing mode vary independently. An orthogonal instruction set does not impose a limitation that requires a certain instruction to use a specific register so there is little overlapping of instruction functionality. Orthogonality was considered a major goal for processor designers in the 1970s, and the VAX-11 is often used as the benchmark for this concept.
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A rigid transformation is formally defined as a transformation that, when acting on any vector v, produces a transformed vector T(v) of the form :T(v) = R v + t where RT = R−1 (i.e., R is an orthogonal transformation), and t is a vector giving the translation of the origin. A proper rigid transformation has, in addition, : det(R) = 1 which means that R does not produce a reflection, and hence it represents a rotation (an orientation- preserving orthogonal transformation). Indeed, when an orthogonal transformation matrix produces a reflection, its determinant is –1.
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In statistics and signal processing, the method of empirical orthogonal function (EOF) analysis is a decomposition of a signal or data set in terms of orthogonal basis functions which are determined from the data. The term is also interchangeable with the geographically weighted PCAs in geophysics. The i th basis function is chosen to be orthogonal to the basis functions from the first through i − 1, and to minimize the residual variance. That is, the basis functions are chosen to be different from each other, and to account for as much variance as possible.
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There is a homomorphism from the Pin group to the orthogonal group. The image consists of the elements of spinor norm . The kernel consists of the elements +1 and −1, and has order 2 unless K has characteristic 2. Similarly there is a homomorphism from the Spin group to the special orthogonal group of V. In the common case when V is a positive or negative definite space over the reals, the spin group maps onto the special orthogonal group, and is simply connected when V has dimension at least 3.
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Orthogonal ligand-protein pairs (also known as re-engineered ligand-receptor interfaces or re-engineered enzyme-substrate interactions) are a protein- ligand binding pair made to be independent of the original binding pair. This is done by taking a mutant protein (naturally occurring or selectively engineered), which is activated by a different ligand (carefully synthesized or selected). The intention here is that the orthogonal ligand will not interact with the original protein. The original protein will also be designed to not interact with the orthogonal ligand in certain cases.
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Regular subcarrier assignment to generate orthogonal signals There are a variety of orthogonal signal sets used in the field of MIMO radar. One of the proposed signal sets is the spectrally interleaved multi-carrier signal, which is a modified version of orthogonal frequency-division multiplexing signalSturm, Christian, et al. "Spectrally interleaved multi-carrier signals for radar network applications and multi-input multi-output radar." IET Radar, Sonar & Navigation 7.3 (2013): 261-269.. In this approach, the total amount of available subcarriers is distributed among different transmit antennas in an interleaved way.
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Odessa, FL: Psychological Assessment Resources. However, one big technical difference between Cattell's five Global Factors and popular five-factor models was Cattell's insistence on using oblique rotation in the factor analysis whereas Goldberg and Costa & McCrae used orthogonal rotation in their factor analysis. Oblique rotation allows the factors to correlate with each other, whereas orthogonal rotation restricts the factors from correlating with each other. Although personality traits are thought to be correlated, using orthogonal factor analysis makes the factors easier to understand and to work on statistically in research.
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In a three-dimensional Euclidean vector space, the orthogonal complement of a line through the origin is the plane through the origin perpendicular to it, and vice versa. Note that the geometric concept of two planes being perpendicular does not correspond to the orthogonal complement, since in three dimensions a pair of vectors, one from each of a pair of perpendicular planes, might meet at any angle. In four- dimensional Euclidean space, the orthogonal complement of a line is a hyperplane and vice versa, and that of a plane is a plane.
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Orthogonal arrays provide a uniform way to describe these diverse objects which are of interest in the statistical design of experiments.
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For a related concept see orthogonal instruction set which deals with the ability of any instruction to use any addressing mode.
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RED bases use warm colors, natural materials, and angular shapes, while BLU bases use cool colors, industrial materials, and orthogonal shapes.
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By definition, the connected orthogonal convex hull is always connected. However, it is not unique. Consider for example a pair of points in the plane not lying on an horizontal or a vertical line. The connected orthogonal convex hull of such points is an orthogonally convex alternating polygonal chain with interior angle 90^\circ connecting the points.
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Fang also has conducted research in the design of experiments. In 1972, he worked with the Tsingdao Beer factory and other factories. He and other mathematical statisticians at the Chinese Academy of Sciences promoted the industrial use of orthogonal designs. Orthogonal designs are discussed in the books and papers of Fang on "uniform designs" and also by other authors.
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Linholm, R., 1987, A Practical Approach to Sedimentology, Allen and Unwin, London, 276 p. Non-orthogonal mudcracks have a geometric pattern. In uncompleted non- orthogonal cracks they form as a single three-point star shape that is composed of three cracks. They could also form with more than three cracks but three cracks in commonly considered the minimum.
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The integers k,s,m and the real numbers \sigma_i are uniquely determined. Note that k+s+m=d. The factor I_m \oplus 0_s corresponds to the maximal invariant subspace on which P acts as an orthogonal projection (so that P itself is orthogonal if and only if k=0) and the \sigma_i-blocks correspond to the oblique components.
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Dunham Jackson (July 24, 1888 in Bridgewater, Massachusetts - November 6, 1946) was a mathematician who worked within approximation theory, notably with trigonometrical and orthogonal polynomials. He is known for Jackson's inequality. He was awarded the Chauvenet Prize in 1935.MAA presidents: Dunham Jackson His book Fourier Series and Orthogonal Polynomials (dated 1941) was reprinted in 2004.
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406x406px The Daubechies wavelets, based on the work of Ingrid Daubechies, are a family of orthogonal wavelets defining a discrete wavelet transform and characterized by a maximal number of vanishing moments for some given support. With each wavelet type of this class, there is a scaling function (called the father wavelet) which generates an orthogonal multiresolution analysis.
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For the example of the general linear group GL(n, R), this corresponds to the fact that any inner product on Rn defines a (compact) orthogonal group (its isometry group) – and that it admits an orthonormal basis: the change of basis defines the conjugating element conjugating the isometry group to the classical orthogonal group O(n, R).
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In functional analysis, an orthogonal basis is any basis obtained from an orthonormal basis (or Hilbert basis) using multiplication by nonzero scalars.
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In completed non-orthogonal cracks, they form a very geometric pattern. The pattern resembles small polygonal shaped tiles in a repetitive pattern.
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Radiomic studies have shown that image-based markers have the potential to provide information orthogonal to staging and biomarkers and improve prognostication.
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With Antonio Navarra, she is the author of the book A Guide to Empirical Orthogonal Functions for Climate Data Analysis (Springer, 2010).
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In combinatorics, two n×n Latin squares are said to be orthogonal if their superimposition yields all possible n2 combinations of entries.
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In neuroscience, a sensory map in the brain which has overlapping stimulus coding (e.g. location and quality) is called an orthogonal map.
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Orthogonal methods based ant colony search for solving continuous optimization problems. Journal of Computer Science and Technology, 23(1), pp.2-18.
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Helical fibers can oriented into either left or right- handed arrangements. Contraction of orthogonal fibers causes torsion or twisting of the hydrostat.
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Regularized theta lifts of harmonic Maass forms can be used to construct Arakelov Green functions for special divisors on orthogonal Shimura varieties.
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In communications, multiple-access schemes are orthogonal when an ideal receiver can completely reject arbitrarily strong unwanted signals from the desired signal using different basis functions. One such scheme is TDMA, where the orthogonal basis functions are nonoverlapping rectangular pulses ("time slots"). Another scheme is orthogonal frequency-division multiplexing (OFDM), which refers to the use, by a single transmitter, of a set of frequency multiplexed signals with the exact minimum frequency spacing needed to make them orthogonal so that they do not interfere with each other. Well known examples include (a, g, and n) versions of 802.11 Wi-Fi; WiMAX; ITU-T G.hn, DVB-T, the terrestrial digital TV broadcast system used in most of the world outside North America; and DMT (Discrete Multi Tone), the standard form of ADSL.
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Partial gain is calculated in the same manner as gain, but considering only a certain polarization. It is similarly additive for orthogonal polarizations.
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This terminology stems from the use of two conjugate hyperbolas in the pseudo-Euclidean plane: conjugate diameters of these hyperbolas are hyperbolic-orthogonal.
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Notable extensions are Orthogonal Matching Pursuit (OMP), Stagewise OMP (StOMP), compressive sampling matching pursuit (CoSaMP), Generalized OMP (gOMP), and Multipath Matching Pursuit (MMP).
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We remark that A is skew- symmetric (respectively, skew-Hermitian) if and only if Q is orthogonal (respectively, unitary) with no eigenvalue −1.
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G. Chebotarev); algebra and tensor analysis (N. G. Chebotarev). Analysis: orthogonal polynoms (B. M. Gagaev); special points of the differential equations systems (M.
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2, pp. 119–132.Karen Vogtmann, A Stiefel complex for the orthogonal group of a field. Commentarii Mathematici Helvetici, vol. 57 (1982), no.
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The Spieker radical circle is the circle, centered at the Spieker center, which is orthogonal to the three excircles of the medial triangle.
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In contrast with the classical convexity where there exist several equivalent definitions of the convex hull, definitions of the orthogonal convex hull made by analogy to those of the convex hull result in different geometric objects. So far, researchers have explored the following four definitions of the orthogonal convex hull of a set K \subset \R^d: #Maximal definition: The definition described in the introduction of this article. It is based on the Maxima of a point set. #Classical definition: The orthogonal convex hull of K is the intersection of all orthogonally convex supersets of K; .
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The orthogonal convex hull of a point set In geometry, a set is defined to be orthogonally convex if, for every line that is parallel to one of standard basis vectors, the intersection of with is empty, a point, or a single segment. The term "orthogonal" refers to corresponding Cartesian basis and coordinates in Euclidean space, where different basis vectors are perpendicular, as well as corresponding lines. Unlike ordinary convex sets, an orthogonally convex set is not necessarily connected. The orthogonal convex hull of a set is the intersection of all connected orthogonally convex supersets of .
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So the phase difference is attributed to the current function, e.g. whose orthogonal components are and as we have seen. When φ happens to be such that the in- phase component is zero, the current and voltage sinusoids are said to be in quadrature, which means they are orthogonal to each other. In that case, no electrical power is consumed.
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One approach is to discretize the space in terms of grids (both orthogonal, and non-orthogonal) and solving Maxwell's equations at each point in the grid. Discretization consumes computer memory, and solving the equations takes significant time. Large-scale CEM problems face memory and CPU limitations. As of 2007, CEM problems require supercomputers, high performance clusters, vector processors and/or parallelism.
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The orthogonal decomposition of a PSD matrix is used in multivariate analysis, where the sample covariance matrices are PSD. This orthogonal decomposition is called principal component analysis (PCA) in statistics. PCA studies linear relations among variables. PCA is performed on the covariance matrix or the correlation matrix (in which each variable is scaled to have its sample variance equal to one).
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In the mathematical fields of linear algebra and functional analysis, the orthogonal complement of a subspace W of a vector space V equipped with a bilinear form B is the set W⊥ of all vectors in V that are orthogonal to every vector in W. Informally, it is called the perp, short for perpendicular complement. It is a subspace of V.
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This maximizes the use of the land of the block; it does not, however, affect street frequency. Any frequency of orthogonal streets produces the same packing effect. Orthogonal geometry also minimizes disputes over lot boundaries and maximizes the number of lots that could front a given street. John Randal said Manhattan's grid plan facilitated "buying, selling and improving real estate".
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Then, we set u2=v2-proju1v2. This process is repeated to for k vectors, with the final vector being uk= vk-∑(j=1)(k-1)projukvk. This then creates a set of orthogonal standard basis vectors. The reason for using a standard orthogonal basis rather than a standard basis arises from the creation of the least squares fitting done next.
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A qutrit (or quantum trit) is a unit of quantum information that is realized by a quantum system described by a superposition of three mutually orthogonal quantum states. The qutrit is analogous to the classical base-3 trit, just as the qubit, a quantum system described by a superposition of two orthogonal states, is analogous to the classical base-2 bit.
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Every point in the complex Grassmannian manifold defines an -plane in -space. Fibering these planes over the Grassmannian one arrives at the vector bundle which generalizes the tautological bundle of a projective space. Similarly the -dimensional orthogonal complements of these planes yield an orthogonal vector bundle . The integral cohomology of the Grassmannians is generated, as a ring, by the Chern classes of .
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Chapter VII considers several methods for isolating primary traits, with numerical examples given. Chapter VIII addresses the methodological problems that can arise when the correlation matrix has negative correlations. Though most scientific investigations of primary abilities will entail oblique factors, there are situations where the factors are likely to be orthogonal. Chapter IX looks at techniques for achieving orthogonal rotations.
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In mathematics, discrete Chebyshev polynomials, or Gram polynomials, are a type of discrete orthogonal polynomials used in approximation theory, introduced by and rediscovered by .
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The frequency band allocated to each antenna beam can be identical because the uplink signals are orthogonal in polarization. This technique allows frequency reuse.
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It is apparent that HCP-ELISAs are insufficient alone for analysis of the HCP population, and therefore orthogonal methods providing complementary information are needed.
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Boc-protected amines are unreactive to most bases and nucleophiles, allowing for the use of the fluorenylmethyloxycarbonyl group (Fmoc) as an orthogonal protecting group.
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An m-dimensional Latin hypercube of order n of the rth class is an n × n × ... ×n m-dimensional matrix having nr distinct elements, each repeated nm − r times, and such that each element occurs exactly n m − r − 1 times in each of its m sets of n parallel (m − 1)-dimensional linear subspaces (or "layers"). Two such Latin hypercubes of the same order n and class r with the property that, when one is superimposed on the other, every element of the one occurs exactly nm − 2r times with every element of the other, are said to be orthogonal. A set of k − m mutually orthogonal m-dimensional Latin hypercubes of order n is equivalent to a 2-(n, k, nm − 2) orthogonal array, where the indexing columns form an m-(n, m, 1) orthogonal array.
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Larger Lie groups, as higher-dimensional manifolds, may be imagined as smooth surfaces composed of many circles (and hyperbolas) twisting around one another. At each point in a N-dimensional Lie group there can be N different orthogonal circles, tangent to N different orthogonal directions in the Lie group, spanning the N-dimensional Lie algebra of the Lie group. For a Lie group of rank R, one can choose at most R orthogonal circles that do not twist around each other, and so form a maximal torus within the Lie group, corresponding to a collection of R mutually-commuting Lie algebra generators, spanning a Cartan subalgebra. Each elementary particle state can be thought of as a different orthogonal direction, having an integral number of twists around each of the R directions of a chosen maximal torus.
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However, the set of linear functions is not complete, and the orthogonal variables are not fast or random if nonlinearity in A comes into play.
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There is no standard terminology for these matrices. They are sometimes called "orthonormal matrices", sometimes "orthogonal matrices", and sometimes simply "matrices with orthonormal rows/columns".
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Angled surfaces do not nullify the analogy as the resultant force can be split into orthogonal components and each dealt with in the same way.
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It represents the exterior envelope of a vertex-centered orthogonal projection of the 600-cell, one of six convex regular 4-polytopes, into 3 dimensions.
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Angled surfaces do not nullify the analogy as the resultant force can be split into orthogonal components and each dealt with in the same way.
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Note the apparent planarity, which masks the actual orthogonal orientation of the two rings. A fully carbo-cyclic spiro compound. Spiro[5.5]undecane, again shown in line-angle representation and in apparent planarity, masking the actual most populated chair conformation of each ring, and their actual orthogonal orientation to one another. Spiro compounds have at least two molecular rings with only one common atom.
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In relativity and in Riemannian geometry, the most useful kind of moving frames are the orthogonal and orthonormal frames, that is, frames consisting of orthogonal (unit) vectors at each point. At a given point p a general frame may be made orthonormal by orthonormalization; in fact this can be done smoothly, so that the existence of a moving frame implies the existence of a moving orthonormal frame.
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An experimental run is a row of the orthogonal array, that is, apply the corresponding factors at the levels which appear in the row. When using one of these designs, the treatment units and trial order should be randomized as much as the design allows. For example, one recommendation is that an appropriately sized orthogonal array be randomly selected from those available, then randomize the run order.
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Though these wavelets are orthogonal, they do not have compact supports. There is a certain class of wavelets, unique in some sense, constructed using B-splines and having compact supports. Even though these wavelets are not orthogonal they have some special properties that have made them quite popular. The terminology spline wavelet is sometimes used to refer to the wavelets in this class of spline wavelets.
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Figure 1: An external view of the EEPROM module shows the coordinate axis used while performing orthogonal magnetic current imaging. These axes are used to define the scanning planes in the body of the paper.Figure 2: Radiography, showing three orthogonal views of the part, reveals internal construction of the module.Figure 3: A magnetic current image overlay on an x-ray image of the EEPROM module.
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Linear contrasts are very useful and can be used to test complex hypotheses when used in conjunction with ANOVA or multiple regression. In essence, each contrast defines and tests for a particular pattern of differences among the means. Contrasts should be constructed "to answer specific research questions", and do not necessarily have to be orthogonal. A simple (not necessarily orthogonal) contrast is the difference between two means.
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If we wish to use curvilinear coordinates for vector calculus calculations, adjustments need to be made in the calculation of line, surface and volume integrals. For simplicity, we again restrict the discussion to three dimensions and orthogonal curvilinear coordinates. However, the same arguments apply for n-dimensional problems though there are some additional terms in the expressions when the coordinate system is not orthogonal.
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A Wollaston prism A Wollaston prism is an optical device, invented by William Hyde Wollaston, that manipulates polarized light. It separates light into two separate linearly polarized outgoing beams with orthogonal polarization. The two beams will be polarized according to the optical axis of the two right angle prisms. The Wollaston prism consists of two orthogonal prisms of birefringent material—typically a uniaxial material such as calcite.
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In linear algebra, a branch of mathematics, a k-frame is an ordered set of k linearly independent vectors in a space; thus k ≤ n, where n is the dimension of the vector space, and if k = n an n-frame is precisely an ordered basis. If the vectors are orthogonal, or orthonormal, the frame is called an orthogonal frame, or orthonormal frame, respectively.
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Since vector fields can be visualized as stream-lines of a stationary flow or as Faraday’s lines of force, a non-vanishing vector field in space generates a space-filling system of lines through each point, known to mathematicians as a congruence (i.e., a local foliation). Ricci’s vision filled Riemann’s n-dimensional manifold with n congruences orthogonal to each other, i.e., a local orthogonal grid.
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These definitions are made by analogy with the classical theory of convexity, in which is convex if, for every line , the intersection of with is empty, a point, or a single segment. Orthogonal convexity restricts the lines for which this property is required to hold, so every convex set is orthogonally convex but not vice versa. For the same reason, the orthogonal convex hull itself is a subset of the convex hull of the same point set. A point belongs to the orthogonal convex hull of if and only if each of the closed axis-aligned orthants having as apex has a nonempty intersection with .
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Several sets of orthogonal functions have become standard bases for approximating functions. For example, the sine functions and are orthogonal on the interval x \in (-\pi, \pi) when m eq n and n and m are positive integers. For then :2 \sin (mx) \sin (nx) = \cos \left((m - n)x\right) - \cos\left((m+n) x\right), and the integral of the product of the two sine functions vanishes.Antoni Zygmund (1935) Trigonometrical Series, page 6, Mathematical Seminar, University of Warsaw Together with cosine functions, these orthogonal functions may be assembled into a trigonometric polynomial to approximate a given function on the interval with its Fourier series.
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In linear algebra, orthogonalization is the process of finding a set of orthogonal vectors that span a particular subspace. Formally, starting with a linearly independent set of vectors {v1, ... , vk} in an inner product space (most commonly the Euclidean space Rn), orthogonalization results in a set of orthogonal vectors {u1, ... , uk} that generate the same subspace as the vectors v1, ... , vk. Every vector in the new set is orthogonal to every other vector in the new set; and the new set and the old set have the same linear span. In addition, if we want the resulting vectors to all be unit vectors, then the procedure is called orthonormalization.
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In mathematics, singular integral operators on closed curves arise in problems in analysis, in particular complex analysis and harmonic analysis. The two main singular integral operators, the Hilbert transform and the Cauchy transform, can be defined for any smooth Jordan curve in the complex plane and are related by a simple algebraic formula. In the special case of Fourier series for the unit circle, the operators become the classical Cauchy transform, the orthogonal projection onto Hardy space, and the Hilbert transform a real orthogonal linear complex structure. In general the Cauchy transform is a non-self-adjoint idempotent and the Hilbert transform a non- orthogonal complex structure.
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In mathematics, the Romanovski polynomials are one of three finite subsets of real orthogonal polynomials discovered by Vsevolod Romanovsky (Romanovski in French transcription) within the context of probability distribution functions in statistics. They form an orthogonal subset of a more general family of little-known Routh polynomials introduced by Edward John Routh in 1884. The term Romanovski polynomials was put forward by Raposo, with reference to the so-called 'pseudo-Jacobi polynomials in Lesky's classification scheme. It seems more consistent to refer to them as Romanovski–Routh polynomials, by analogy with the terms Romanovski–Bessel and Romanovski–Jacobi used by Lesky for two other sets of orthogonal polynomials.
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The forward link of a 3G code-division multiple-access (CDMA) system may become a limiting factor when the number of users increases maximal capacity. The conventional channelization code, Walsh code does not have enough available bits to cope with maximal use. Therefore, the quasi-orthogonal function (QOF), which can process optimal cross-correlation with Walsh code has been used as a method to get around the limitations of the Walsh Codes. To enhance the overall capacity in such scenarios, alternative sets of orthogonal functions called the quasi-orthogonal functions (QOF), which possess optimal minimax cross correlation with Walsh code sets of variable length, have been incorporated in IS-2000.
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The LLL algorithm for computing a nearly-orthogonal basis was used to show that integer programming in any fixed dimension can be done in polynomial time.
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Spherical harmonics can be separated into two set of functions. One is hemispherical functions (HSH), orthogonal and complete on hemisphere. Another is complementary hemispherical harmonics (CHSH).
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In taxonomy, an orthogonal classification is one in which no item is a member of more than one group, that is, the classifications are mutually exclusive.
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In mathematics, the q-Hahn polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties.
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In mathematics, the q-Charlier polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties.
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In mathematics, the continuous q-Legendre polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties.
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The six-state protocol (SSP) is the quantum cryptography protocol that is the version of BB84 that uses a six-state polarization scheme on three orthogonal bases.
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The structure of CRY1 is almost entirely made up of alpha helices, with several loops and few beta sheets. The molecule is arranged as an orthogonal bundle.
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In mathematical analysis, the Rademacher–Menchov theorem, introduced by and , gives a sufficient condition for a series of orthogonal functions on an interval to converge almost everywhere.
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Solutions of linear differential equations with boundary conditions can often be written as a weighted sum of orthogonal solution functions (a.k.a. eigenfunctions), leading to generalized Fourier series.
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The outer veto covers the top of the detector tank. It consists of strips with a 5 cm x 1 cm cross section laid in orthogonal directions.
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In mathematics, the continuous q-Hahn polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties.
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Choosing a set of orthogonal basis vectors is often done by considering what set of basis vectors will make the mathematics most convenient. Choosing a basis vector that is in the same direction as one of the forces is desirable, since that force would then have only one non-zero component. Orthogonal force vectors can be three-dimensional with the third component being at right-angles to the other two.
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Direct oblimin rotation is the standard method when one wishes a non-orthogonal (oblique) solution – that is, one in which the factors are allowed to be correlated. This will result in higher eigenvalues but diminished interpretability of the factors. See below. Promax rotation is an alternative non-orthogonal (oblique) rotation method which is computationally faster than the direct oblimin method and therefore is sometimes used for very large datasets.
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In crystallography, the orthorhombic crystal system is one of the 7 crystal systems. Orthorhombic lattices result from stretching a cubic lattice along two of its orthogonal pairs by two different factors, resulting in a rectangular prism with a rectangular base (a by b) and height (c), such that a, b, and c are distinct. All three bases intersect at 90° angles, so the three lattice vectors remain mutually orthogonal.
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In proof theory, a coherent space (also coherence space) is a concept introduced in the semantic study of linear logic. Let a set C be given. Two subsets S,T ⊆ C are said to be orthogonal, written S ⊥ T, if S ∩ T is ∅ or a singleton. The dual of a family F ⊆ ℘(C) is the family F ⊥ of all subsets S ⊆ C orthogonal to every member of F, i.e.
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Orthogonal transformations in two- or three-dimensional Euclidean space are stiff rotations, reflections, or combinations of a rotation and a reflection (also known as improper rotations). Reflections are transformations that reverse the direction front to back, orthogonal to the mirror plane, like (real-world) mirrors do. The matrices corresponding to proper rotations (without reflection) have a determinant of +1. Transformations with reflection are represented by matrices with a determinant of −1.
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A 4D clifford torus, stereographically projected into 3D, looks like a torus. A double rotation can be seen as a helical path. In 4D, a double rotation symmetry can be generated as the composite of two orthogonal rotations.Charles Howard Hinton (1906) The Fourth Dimension (Google eBook) S. Sonnenschein & Company p.223 It is similar to 3D screw axis which is the composite of a rotation and an orthogonal translation.
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The approaches seen in,G. Yang, F. Liu, L. Li, H. Wang, C. Zhao, and Z. Wang, “2D orthogonal polynomials for concurrent dual-band digital predistortion,” in 2013 IEEE MTT-S Int. Microwave Symp. Dig., June 2013, pp. 1350–1410Quindroit, N. Naraharisetti, P. Roblin, S. Gheitanchi, V. Mauer, and M. Fitton, “Concurrent dual-band digital predistortion for power amplifier based on orthogonal polynomials,” in 2013 IEEE MTT-S Int.
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The generalized Coulson–Fischer theory for the hydrogen molecule, discussed in Modern valence bond theory, is used to describe every electron pair in a molecule. The orbitals for each electron pair are expanded in terms of the full basis set and are non-orthogonal. Orbitals from different pairs are forced to be orthogonal - the strong orthogonality condition. This condition simplifies the calculation but can lead to some difficulties.
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They generalize many other families of orthogonal polynomials, such as Jack polynomials and Hall–Littlewood polynomials and Askey–Wilson polynomials, which in turn include most of the named 1-variable orthogonal polynomials as special cases. Koornwinder polynomials are Macdonald polynomials of certain non-reduced root systems. They have deep relationships with affine Hecke algebras and Hilbert schemes, which were used to prove several conjectures made by Macdonald about them.
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Using system images is the simplest persistence strategy. Notebook hibernation is an example of orthogonal persistence using a system image because it does not require any actions by the programs running on the machine. An example of non-orthogonal persistence using a system image is a simple text editing program executing specific instructions to save an entire document to a file. Shortcomings: Requires enough RAM to hold the entire system state.
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In relativistic cosmology, Weyl's postulate stipulates that in a fluid cosmological model, the world lines of the fluid particles, which act as the source of the gravitational field and which are often taken to model galaxies, should be hypersurface orthogonal. That is, the world lines should be everywhere orthogonal to a family of spatial hyperslices. Sometimes, the additional hypothesis is added that the world lines form timelike geodesics.
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An orthogonal set of idempotents with sum 1 is said to be a complete set or a partition of 1. If each idempotent in the set is minimal it is called a Jordan frame. Since the number of elements in any orthogonal set of idempotents is bounded by dim E, Jordan frames exist. The maximal number of elements in a Jordan frame is called the rank r of E.
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In four dimensions the Hodge dual of a bivector is a bivector, and the space Λ2ℝ4 is dual to itself. Normal vectors are not unique, instead every plane is orthogonal to all the vectors in its Hodge dual space. This can be used to partition the bivectors into two 'halves', in the following way. We have three pairs of orthogonal bivectors: (e12, e34), (e13, e24) and (e14, e23).
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So even if we can narrow down the state of a quantum system to just two possibilities, we still cannot clone it in general (unless the states happen to be orthogonal). Another way of stating the no-cloning theorem is that amplification of a quantum signal can only happen with respect to some orthogonal basis. This is related to the emergence of the rules of classical probability via quantum decoherence.
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In another version, if both disjoint convex sets are open, then there is a hyperplane in between them, but not necessarily any gap. An axis which is orthogonal to a separating hyperplane is a separating axis, because the orthogonal projections of the convex bodies onto the axis are disjoint. The hyperplane separation theorem is due to Hermann Minkowski. The Hahn–Banach separation theorem generalizes the result to topological vector spaces.
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A Biorthogonal wavelet is a wavelet where the associated wavelet transform is invertible but not necessarily orthogonal. Designing biorthogonal wavelets allows more degrees of freedom than orthogonal wavelets. One additional degree of freedom is the possibility to construct symmetric wavelet functions. In the biorthogonal case, there are two scaling functions \phi,\tilde\phi, which may generate different multiresolution analyses, and accordingly two different wavelet functions \psi,\tilde\psi.
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Jean-Louis Cazaux described the movement of the pieces as follows: ;Boat :Analogous to the rook in Western chess, the boat slides any number of spaces in the orthogonal directions (i.e. left, right, up, down). ;King :As in Western chess, the king steps one space in any direction. ;Horse :As with the knight in Western chess, the horse leaps one orthogonal and then one diagonal in any direction.
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In mathematics, a biorthogonal polynomial is a polynomial that is orthogonal to several different measures. Biorthogonal polynomials are a generalization of orthogonal polynomials and share many of their properties. There are two different concepts of biorthogonal polynomials in the literature: introduced the concept of polynomials biorthogonal with respect to a sequence of measures, while Szegő introduced the concept of two sequences of polynomials that are biorthogonal with respect to each other.
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In many CISCs, an instruction could access either registers or memory, usually in several different ways. This made the CISCs easier to program, because a programmer could remember only thirty to a hundred instructions, and a set of three to ten addressing modes rather than thousands of distinct instructions. This was called an orthogonal instruction set. The PDP-11 and Motorola 68000 architecture are examples of nearly orthogonal instruction sets.
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The material to be used for the building construction was concrete and the general plan was an orthogonal frame. Officially, the reconstruction was completed in the mid-1960s.
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In mathematics, the continuous dual q-Hahn polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties.
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In mathematics, the q-Racah polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by . give a detailed list of their properties.
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The ancient Romans also employed regular orthogonal structures on which they molded their colonies.Morris 1972, pp. 39-41, 51-60; Kolb 1984, pp. 169-238; Benevolo, Leonardo (1993).
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M.J. Baker, 2012. Projection of a vector onto a plane. Published on www.euclideanspace.com. The projection of a vector on a plane is its orthogonal projection on that plane.
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The classical orthogonal convex hull can be equivalently defined as the smallest orthogonally convex superset of a set K \subset \R^2, by analogy to the following definition of the convex hull: the convex hull of K is the smallest convex superset of K. The classical orthogonal convex hull might be disconnected. If a point set has no pair of points on a line parallel to one of the standard basis vectors, the classical orthogonal convex hull of such point set is equal to the point set itself. A well known property of convex hulls is derived from the Carathéodory's theorem: A point x \in \R^d is in the interior of the convex hull of a point set K \subset \R^d if, and only if, it is already in the convex hull of d+1 or fewer points of K. This property is also valid for classical orthogonal convex hulls.
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The diagonal matrix elements \langle a_i,b_i\rangle are the singular values of the latter matrix. By the uniqueness of the singular value decomposition, the vectors \hat y_i are then unique up to a real, orthogonal or unitary transformation among them, and the vectors \hat w_i and \hat w'_i (and hence \hat v_i) are unique up to equal real, orthogonal or unitary transformations applied simultaneously to the sets of the vectors \hat w_i associated with a common value of \theta_i and to the corresponding sets of vectors \hat w'_i (and hence to the corresponding sets of \hat v_i). A singular value 1 can be interpreted as \cos\,0 corresponding to the angles 0 introduced above and associated with F\cap G and a singular value 0 can be interpreted as \cos \pi/2 corresponding to right angles between the orthogonal spaces F\cap G^\bot and F^\bot\cap G, where superscript \bot denotes the orthogonal complement.
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To show property 2 of the tight span, consider some point x in X; we must find y in X such that f(x)+f(y)=d(x,y). But if x is in one of the four quadrants having z as apex, y can be taken as any point in the opposite quadrant, so property 2 is satisfied as well. Conversely it can be shown that every point of the tight span corresponds in this way to a point in the orthogonal convex hull of these points. However, for point sets with the Manhattan metric in higher dimensions, and for planar point sets with disconnected orthogonal hulls, the tight span differs from the orthogonal convex hull.
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Some numerical applications, such as Monte Carlo methods and exploration of high-dimensional data spaces, require generation of uniformly distributed random orthogonal matrices. In this context, "uniform" is defined in terms of Haar measure, which essentially requires that the distribution not change if multiplied by any freely chosen orthogonal matrix. Orthogonalizing matrices with independent uniformly distributed random entries does not result in uniformly distributed orthogonal matrices, but the decomposition of independent normally distributed random entries does, as long as the diagonal of contains only positive entries . replaced this with a more efficient idea that later generalized as the "subgroup algorithm" (in which form it works just as well for permutations and rotations).
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The orthogonal ribosomes described above all focus on optimizing the 16S rRNA. Thus far, this optimized 16S rRNA was combined with natural large-subunits to form orthogonal ribosomes. If the 23S rRNA, the main RNA- component of the large ribosomal subunit, is to be optimized as well, it had to be assured, that there was no crosstalk in the assembly of orthogonal and natural ribosomes (see figureX B). To ensure that optimized 23S rRNA would only form into ribosomes with the optimized 16S rRNA, the two rRNAs were combined into one transcript. By inserting the sequence for the 23S rRNA into a loop-region of the 16S rRNA sequence, both subunits still adopt functioning folds.
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When performing statistical analysis, independent variables that affect a particular dependent variable are said to be orthogonal if they are uncorrelated, since the covariance forms an inner product. In this case the same results are obtained for the effect of any of the independent variables upon the dependent variable, regardless of whether one models the effects of the variables individually with simple regression or simultaneously with multiple regression. If correlation is present, the factors are not orthogonal and different results are obtained by the two methods. This usage arises from the fact that if centered by subtracting the expected value (the mean), uncorrelated variables are orthogonal in the geometric sense discussed above, both as observed data (i.e.
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Any t-(v, t, λ) orthogonal array would be considered trivial since they are easily constructed by simply listing all the t-tuples of the v-set λ times.
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Half-lines from in the axis-plane are not displaced; half-lines from orthogonal to are displaced through ; all other half-lines are displaced through an angle less than .
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If we restrict ourselves to matrices with determinant 1, then we get another group, the special linear group, SL(n). Geometrically, this consists of all the elements of GL(n) that preserve both orientation and volume of the various geometric solids in Euclidean space. If instead we restrict ourselves to orthogonal matrices, then we get the orthogonal group O(n). Geometrically, this consists of all combinations of rotations and reflections that fix the origin.
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Specifically, if we choose an orthonormal basis of \R^3, every rotation is described by an orthogonal 3×3 matrix (i.e. a 3×3 matrix with real entries which, when multiplied by its transpose, results in the identity matrix) with determinant 1. The group SO(3) can therefore be identified with the group of these matrices under matrix multiplication. These matrices are known as "special orthogonal matrices", explaining the notation SO(3).
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But both Khla si ko and Tiger and buffaloes have only orthogonal movement of pieces, and only move one space at a time. Tigers in both games capture by the short leap as in draughts and Alquerque, and only in orthogonal directions. Diagonal movements or captures are not allowed in both games. A game called Dragons and Swans is played exactly the same way with the same board and number of pieces.
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A variant of symmetric spectra are orthogonal spectra, where one substitutes the symmetric group by the orthogonal group (see Mandell et al., 2001). They have the advantage that the naively defined homotopy groups coincide with those in the stable homotopy category, which is not the case for symmetric spectra. (I.e., the sphere spectrum is now cofibrant.) On the other hand, symmetric spectra have the advantage that they can also be defined for simplicial sets.
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Unfortunately, there may not be a Hadamard matrix of size s. In this case, we choose one of size slightly larger than s. Now the submatrix of H which defines our choices need no longer have exactly orthogonal rows, but if the size of H is only slightly larger than s the rows will be approximately orthogonal. The number of units per stratum need not be exactly 2, and typically will not be.
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Closely related to pericyclic processes are reactions that are pseudopericyclic. Although a pseudopericyclic reaction proceeds through a cyclic transition state, two of the orbitals involved are constrained to be orthogonal and cannot interact. Perhaps the most famous example is the hydroboration of an olefin. Although this appears to be a 4-electron Hückel topology forbidden group transfer process, the empty p orbital and sp2 hybridized B–H bond are orthogonal and do not interact.
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Orthogonal collocation is a method for the numerical solution of partial differential equations. It uses collocation at the zeros of some orthogonal polynomials to transform the partial differential equation (PDE) to a set of ordinary differential equations (ODEs). The ODEs can then be solved by any method. It has been shown that it is usually advantageous to choose the collocation points as the zeros of the corresponding Jacobi polynomial (independent of the PDE system).
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Quantum operations can be used to describe the process of quantum measurement. The presentation below describes measurement in terms of self-adjoint projections on a separable complex Hilbert space H, that is, in terms of a PVM (Projection-valued measure). In the general case, measurements can be made using non-orthogonal operators, via the notions of POVM. The non-orthogonal case is interesting, as it can improve the overall efficiency of the quantum instrument.
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Eutactic stars are useful largely because of their relationship with the geometry of polytopes and groups of orthogonal transformations. Schläfli showed early on that the vectors from the center of any regular polytope to its vertices form a eutactic star. Brauer and Coxeter proved the following generalization:. : > A star is eutactic if it is transformed to itself by some irreducible group > of orthogonal transformations that acts transitively on pairs of opposite > vectors.
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In a spherical coordinate system, the radius describes the distance of a point from a fixed origin. Its position if further defined by the polar angle measured between the radial direction and a fixed zenith direction, and the azimuth angle, the angle between the orthogonal projection of the radial direction on a reference plane that passes through the origin and is orthogonal to the zenith, and a fixed reference direction in that plane.
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Consider a secretary's performance, which might be measured by number of breaks per hour and the time required to complete reports. The two measures are orthogonal because they do not overlap. However, it is possible that repeated evaluations could show a reliable association between a higher number of breaks per hour and less time required to complete reports. The history of General Electric provides a clear example of developing orthogonal performance measures.
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For distinction, the latter is then called a Hamel basis. Not only does the theorem exhibit suitable basis functions as sufficient for approximation purposes, but also together with the Gram–Schmidt process, it enables one to construct a basis of orthogonal vectors. Such orthogonal bases are the Hilbert space generalization of the coordinate axes in finite-dimensional Euclidean space. The solutions to various differential equations can be interpreted in terms of Hilbert spaces.
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In mathematics, Favard's theorem, also called the Shohat–Favard theorem, states that a sequence of polynomials satisfying a suitable 3-term recurrence relation is a sequence of orthogonal polynomials. The theorem was introduced in the theory of orthogonal polynomials by and , though essentially the same theorem was used by Stieltjes in the theory of continued fractions many years before Favard's paper, and was rediscovered several times by other authors before Favard's work.
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STBCs as originally introduced, and as usually studied, are orthogonal. This means that the STBC is designed such that the vectors representing any pair of columns taken from the coding matrix is orthogonal. The result of this is simple, linear, optimal decoding at the receiver. Its most serious disadvantage is that all but one of the codes that satisfy this criterion must sacrifice some proportion of their data rate (see Alamouti's code).
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An example would be the subgroup O(2), the orthogonal group, inside the general linear group GL(2, R). A related example is the circle group SO(2) inside SL(2, R). Evidently SO(2) inside GL(2, R) is compact and not maximal. The non-uniqueness of these examples can be seen as any inner product has an associated orthogonal group, and the essential uniqueness corresponds to the essential uniqueness of the inner product.
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The tertiary veins run perpendicular to the secondary veins with an even spacing, while the quaternary veins are orthogonal to the tertiaries forming reticulated pattern of pentagonal and quadrangular spaces.
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In 1967 McKnight, McAfee and Sipler published an IMS-TOF combination. Their instrument included an orthogonal TOF. In 1969 Cohen et al. filed a patent on an IMS-QMS system.
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The structure of these proteins consists of a complex bundle of five alpha-helices, which is composed of an up-down 3-helix bundle plus an orthogonal 2-helix bundle.
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The LPM uses Lagrange polynomials for the approximations, and Legendre-Gauss-Lobatto (LGL) points for the orthogonal collocation. A costate estimation procedure for the Legendre pseudospectral method was also developed.
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Arthur Erdélyi FRS, FRSE (2 October 1908 – 12 December 1977) was a Hungarian- born British mathematician. Erdélyi was a leading expert on special functions, particularly orthogonal polynomials and hypergeometric functions.
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As a result, the modulation index m is 0.5. This is the smallest FSK modulation index that can be chosen such that the waveforms for 0 and 1 are orthogonal.
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In the singlet state, the spin-paired electrons occupy the sp2 hybrid orbital, orthogonal to an empty p-orbital. Conversion of singlet to triplet fluorenylidene is achieved through intersystem crossing (ISC).
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An enhanced CDMA version known as interleave-division multiple access (IDMA) uses the orthogonal interleaving as the only means of user separation in place of signature sequence used in CDMA system.
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Partial directivity is calculated in the same manner as the partial directive gain, but without consideration of antenna efficiency (i.e. assuming a lossless antenna). It is similarly additive for orthogonal polarizations.
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In mathematics, the J-homomorphism is a mapping from the homotopy groups of the special orthogonal groups to the homotopy groups of spheres. It was defined by , extending a construction of .
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These proceed in a suprafacial- antarafacial sense, such as the dimerisation of ketene, in which the orthogonal set of p orbitals allows the reaction to proceed via a crossed transition state.
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The resulting metric tensor allowed for accurate predictions of the neuronal connections between the three intrinsically orthogonal vestibular canals and the six extraocular muscles that control the movement of the eye.
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Vogtmann's early work concerned homological properties of orthogonal groups associated to quadratic forms over various fields.Karen Vogtmann, Spherical posets and homology stability for O_{n,n}. Topology, vol. 20 (1981), no.
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In mathematics, particularly linear algebra, an orthonormal basis for an inner product space V with finite dimension is a basis for V whose vectors are orthonormal, that is, they are all unit vectors and orthogonal to each other. For example, the standard basis for a Euclidean space Rn is an orthonormal basis, where the relevant inner product is the dot product of vectors. The image of the standard basis under a rotation or reflection (or any orthogonal transformation) is also orthonormal, and every orthonormal basis for Rn arises in this fashion. For a general inner product space V, an orthonormal basis can be used to define normalized orthogonal coordinates on V. Under these coordinates, the inner product becomes a dot product of vectors.
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Orthographic projection (sometimes referred to as orthogonal projection, used to be called analemma) is a means of representing three-dimensional objects in two dimensions. It is a form of parallel projection, in which all the projection lines are orthogonal to the projection plane, resulting in every plane of the scene appearing in affine transformation on the viewing surface. The obverse of an orthographic projection is an oblique projection, which is a parallel projection in which the projection lines are not orthogonal to the projection plane. The term orthographic is sometimes reserved specifically for depictions of objects where the principal axes or planes of the object are also parallel with the projection plane, but these are better known as multiview projections.
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A coordinate system where the x axis has been bent toward the z axis. The simplest 3D case of a skew coordinate system is a Cartesian one where one of the axes (say the x axis) has been bent by some angle \phi, staying orthogonal to one of the remaining two axes. For this example, the x axis of a Cartesian coordinate has been bent toward the z axis by \phi, remaining orthogonal to the y axis.
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More generally, given a map between normed vector spaces T\colon V \to W, one can analogously ask for this map to be an isometry on the orthogonal complement of the kernel: that (\ker T)^\perp \to W be an isometry (compare Partial isometry); in particular it must be onto. The case of an orthogonal projection is when W is a subspace of V. In Riemannian geometry, this is used in the definition of a Riemannian submersion.
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In addition to being considered in computational geometry, range searching, and orthogonal range searching in particular, has applications for range queries in databases. Colored range searching is also used for and motivated by searching through categorical data. For example, determining the rows in a database of bank accounts which represent people whose age is between 25 and 40 and who have between $10000 and $20000 might be an orthogonal range reporting problem where age and money are two dimensions.
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Schematic depiction of a Rietveld joint. The three battens are shown in the primary colours red, blue and yellow, where the yellow batten is oriented orthogonal to the screen. The locations of the dowels are shown in gray; the dowel connecting the yellow batten to the blue batten is the third and final one. A Rietveld joint, also called a Cartesian node in furniture-making, is an overlapping joint of three battens in the three orthogonal directions.
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As mentioned in the previous section a Latin square of order n can be thought of as a 2-(n, 3, 1) orthogonal array. Actually, the orthogonal array can lead to six Latin squares since any ordered pair of distinct columns can be used as the indexing columns. However, these are all isotopic and are considered equivalent. For concreteness we shall always assume that the first two columns in their natural order are used as the indexing columns.
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Orthogonal array testing is a black box testing technique which is a systematic, statistical way of software testing. It is used when the number of inputs to the system is relatively small, but too large to allow for exhaustive testing of every possible input to the systems. It is particularly effective in finding errors associated with faulty logic within computer software systems. Orthogonal arrays can be applied in user interface testing, system testing, regression testing and performance testing.
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Two elements v and w of V are called orthogonal if . The kernel of a bilinear form B consists of the elements that are orthogonal to every element of V. Q is non-singular if the kernel of its associated bilinear form is {0}. If there exists a non-zero v in V such that , the quadratic form Q is isotropic, otherwise it is anisotropic. This terminology also applies to vectors and subspaces of a quadratic space.
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Many algorithms use orthogonal matrices like Householder reflections and Givens rotations for this reason. It is also helpful that, not only is an orthogonal matrix invertible, but its inverse is available essentially free, by exchanging indices. Permutations are essential to the success of many algorithms, including the workhorse Gaussian elimination with partial pivoting (where permutations do the pivoting). However, they rarely appear explicitly as matrices; their special form allows more efficient representation, such as a list of indices.
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In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials) are a class of classical orthogonal polynomials. They are orthogonal with respect to the weight on the interval . The Gegenbauer polynomials, and thus also the Legendre, Zernike and Chebyshev polynomials, are special cases of the Jacobi polynomials. The definition is in IV.1; the differential equation - in IV.2; Rodrigues' formula is in IV.3; the generating function is in IV.4; the recurrent relation is in IV.5.
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When G is a classical group, such as a symplectic group or orthogonal group, this is particularly transparent. If (V, ω) is a symplectic vector space then a partial flag in V is isotropic if the symplectic form vanishes on proper subspaces of V in the flag. The stabilizer of an isotropic flag is a parabolic subgroup of the symplectic group Sp(V,ω). For orthogonal groups there is a similar picture, with a couple of complications.
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In most cases of least squares fitting, the model coefficients for previously added terms change depending on what was successively added. For example, the X1 coefficient might change depending on whether or not an X2 term was included in the model. This is not the case when the design is orthogonal, as is a 23 full factorial design. For orthogonal designs, the estimates for the previously included terms do not change as additional terms are added.
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The Topic-based Vector Space Model (TVSM) (literature: ) extends the vector space model of information retrieval by removing the constraint that the term- vectors be orthogonal. The assumption of orthogonal terms is incorrect regarding natural languages which causes problems with synonyms and strong related terms. This facilitates the use of stopword lists, stemming and thesaurus in TVSM. In contrast to the generalized vector space model the TVSM does not depend on concurrence-based similarities between terms.
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He also mentions the combination of these quadrupoles with an orthogonal TOFMS. In 1998 Clemmer developed an IMS-TOF combination, using a co-axial IMS-TOF setup. In 1999 Clemmer developed an IMS- TOF with an orthogonal TOF system. This work led to the development of an ion mobility-quadrupole-CID-TOFMS instrument by Micromass in the UK and ultimately led Micromass / Waters corporation to develop of the world's first commercial ion mobility-mass spectrometer instrument in 2006.
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This is inconsistent with discrete frames covering the entire visual scene. Kline, Holcombe, and Eagleman (2006) also showed that reversed rotation of a radial grating in one part of the visual field was independent of superimposed orthogonal motion in the same part of the visual field. The orthogonal motion was of a circular grating contracting so as to have the same temporal frequency as the radial grating. This is inconsistent with discrete frames covering local parts of visual scene.
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Orthogonal frequency- division multiplexing (OFDM) is a digital multi-carrier modulation scheme. OFDM conveys data on several parallel data channels by incorporating closely spaced orthogonal sub-carrier signals. OFDM is a favorable communication scheme in underwater acoustic communications thanks to its resilience against frequency selective channels with long delay spreads.E. Demirors, G. Sklivanitis, T. Melodia, S. N. Batalama, and D. A. Pados, "Software-defined Underwater Acoustic Networks: Toward a High-rate Real-time Reconfigurable Modem," IEEE Communications Magazine, vol.
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Let , , and be three mutually orthogonal straight lines in space and , , be the three corresponding vanishing points respectively. If we know the coordinates of one of these points, say , and the direction of a straight line on the image plane, which passes through a second point, say , we can compute the coordinates of both along with their sex. and 3\. Let , , and be three mutually orthogonal straight lines in space and , , be the three corresponding vanishing points respectively.
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In this method the field free ionization region allows for high precision in the electron energy and also high electron energy resolution. Measuring the electric fields down the ion flight tube determines autodetachment and metastable decomposition as well as field detachment of weakly bound negative ions. The first description of an electron ionization orthogonal-acceleration TOF MS (EI oa-TOFMS) was in 1989. By using "orthogonal-acceleration" with the EI ion source the resolving power and sensitivity was increased.
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The pheromone deposit mechanism of COAC is to enable ants to search for solutions collaboratively and effectively. By using an orthogonal design method, ants in the feasible domain can explore their chosen regions rapidly and efficiently, with enhanced global search capability and accuracy. The orthogonal design method and the adaptive radius adjustment method can also be extended to other optimization algorithms for delivering wider advantages in solving practical problems.X Hu, J Zhang, and Y Li (2008).
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The orthogonal complements of the roots form a set of hyperplanes which all go through the positive cone. Then the ample cone is a connected component of the complement of these hyperplanes in the positive cone. Any two such components are isomorphic via the orthogonal group of the lattice Pic(X), since that contains the reflection across each root hyperplane. In this sense, the Picard lattice determines the ample cone up to isomorphism.Huybrechts (2016), Corollary 8.2.11.
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An orthogonal wavelet is entirely defined by the scaling filter – a low-pass finite impulse response (FIR) filter of length 2N and sum 1. In biorthogonal wavelets, separate decomposition and reconstruction filters are defined. For analysis with orthogonal wavelets the high pass filter is calculated as the quadrature mirror filter of the low pass, and reconstruction filters are the time reverse of the decomposition filters. Daubechies and Symlet wavelets can be defined by the scaling filter.
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In geometry, a point group in three dimensions is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere. It is a subgroup of the orthogonal group O(3), the group of all isometries that leave the origin fixed, or correspondingly, the group of orthogonal matrices. O(3) itself is a subgroup of the Euclidean group E(3) of all isometries. Symmetry groups of objects are isometry groups.
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One common orthogonal midplane connects many vertical telephone line cards on one side, each one connected to copper telephone wires, to a horizontal communications card on the other side."AirMax VS Orthogonal" . A "virtual midplane" is an imaginary plane between vertical cards on one side that directly connect to horizontal boards on the other side; the card-slot aligners of the card cage and self-aligning connectors on the cards hold the cards in position. Michael Fowler.
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It is claimed that because the technique is effectively fingerprinting the GPU, the entropy is "orthogonal" to the entropy of previous browser fingerprint techniques such as screen resolution and browser JavaScript capabilities.
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In the garden terrace of Caramuru Building, an orthogonal prismatic volume houses an apartment for the directors of the company, while an attached cylindrical volume houses the engine room of the elevators.
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The monograph Orthogonal polynomials, published in 1939, contains much of his research and has had a profound influence in many areas of applied mathematics, including theoretical physics, stochastic processes and numerical analysis.
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This property makes them suitable for use in detonation trains which require precise timing and homogeneous delivery of force across a complex surface (but see also shaped charge for an orthogonal technique).
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Orthogonal unit differences describes properties of game elements that cannot be compared by inherent numbers. Ideally, every game element has at least one unique trait. This also helps creating intransitivity and counters.
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For any other (k − 1)-dimensional subspace G, some f in the linear span of the first k eigenvectors must be orthogonal to G. Hence λ(G) ≤ (Df,f)/(f,f) ≤ λk.
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An idempotent linear operator P is a projection operator on the range space along its null space . P is an orthogonal projection operator if and only if it is idempotent and symmetric.
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Different DoE strategies are available, including random generator sequences, Factorial, Orthogonal and Iterative Techniques, as well as D-Optimal or Cross Validation. Monte Carlo and Latin hypercube are available for robustness analysis.
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Christoffel generalized the Gaussian quadrature method for integration and, in connection to this, he also introduced the Christoffel–Darboux formula for Legendre polynomials (he later also published the formula for general orthogonal polynomials).
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In a rectilinear subdivision, all edges are parallel to one of the d orthogonal axis. In this case, point location can be answered in O(logd-1 n) time with O(n) space.
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An investigation of the amber initiator tRNA showed that it was orthogonal to the regular AUG start codon showing no detectable off-target translation initiation events in a genomically recoded E. coli strain.
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In differential geometry, a branch of mathematics, a Riemannian submersion is a submersion from one Riemannian manifold to another that respects the metrics, meaning that it is an orthogonal projection on tangent spaces.
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The visual feature array is a model of the primary visual cortex (V1). It matches the cortex in functionality, while the structure is orthogonal, thus making it easy to implement on a computer.
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The NYT Bestseller list is divided into section, including fiction, non-fiction, and children's literature. With the advent of e-book technology, the NYT added an orthogonal e-book section to the list.
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Like all special orthogonal groups of n > 2, SO(8) is not simply connected, having a fundamental group isomorphic to Z2. The universal cover of SO(8) is the spin group Spin(8).
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On the other hand, using dual antennas with orthogonal polarities along with a 2x2 MIMO chipset effectively enable two independent carrier signals to be sent and received along the same long distance path.
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The Fast Wavelet Transform is a mathematical algorithm designed to turn a waveform or signal in the time domain into a sequence of coefficients based on an orthogonal basis of small finite waves, or wavelets. The transform can be easily extended to multidimensional signals, such as images, where the time domain is replaced with the space domain. This algorithm was introduced in 1989 by Stéphane Mallat. It has as theoretical foundation the device of a finitely generated, orthogonal multiresolution analysis (MRA).
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In kinematics, the acceleration of a particle moving along a curve in space is the time derivative of its velocity. In most applications, the acceleration vector is expressed as the sum of its normal and tangential components, which are orthogonal to each other. Siacci's theorem, formulated by the Italian mathematician Francesco Siacci (1839–1907), is the kinematical decomposition of the acceleration vector into its radial and tangential components. In general, the radial and tangential components are not orthogonal to each other.
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The equation calculates the inner product of two column vectors. The inner product of two vectors is zero if the vectors are orthogonal. In P2, the line between the points x1 and x2 may be represented as a column vector ℓ that satisfies the equations and , or in other words a column vector ℓ that is orthogonal to x1 and x2. The cross product will find such a vector: the line joining two points has homogeneous coordinates given by the equation .
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Yajisan-Kazusan is played on a rectangular grid, the structure of which directly resembles that of Yajilin: Some cells contain numbers with an arrow indicating an orthogonal direction. Ostensibly, the number indicates the number of shaded cells which appear in the line of the orthogonal direction indicated by the arrow. Shaded cells may not touch orthogonally, and all unshaded cells must form a single, continuous group. However, unlike many of Nikoli's other puzzles, not all of the clue numbers are correct.
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When a Graeco-Latin square is viewed as a pair of orthogonal Latin squares, each of the Latin squares is said to have an orthogonal mate. In an arbitrary Latin square, a selection of positions, one in each row and one in each column whose entries are all distinct is called a transversal of that square.This has gone under several names in the literature, formule directrix (Euler), directrix, 1-permutation, and diagonal amongst others. Consider one symbol in a Graeco- Latin square.
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ODI Sensor The One Degree Imager (ODI) is the flagship of WIYN's new instrument initiatives. ODI utilizes both WIYN's one degree field of view and excellent image quality. The original design for ODI was to cover the one square degree field using a total of 64 Orthogonal Transfer Arrays (OTAs) with a total of 1 GigaPixel and a pixelscale of 0.11 arcseconds per pixel. Orthogonal transfer arrays allow to actively improve image sharpness by correcting images for tip/tilt motion during the integration.
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Let ρ be a measure of positive density on an interval I and admitting moments of any order. We can build a family {Pn} of orthogonal polynomials for the inner product induced by ρ. Let us call {Qn} the sequence of the secondary polynomials associated with the family P. Under certain conditions there is a measure for which the family Q is orthogonal. This measure, which we can clarify from ρ is called a secondary measure associated initial measure ρ.
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Sturm–Liouville theory is a theory of a special type of second order linear ordinary differential equation. Their solutions are based on eigenvalues and corresponding eigenfunctions of linear operators defined via second-order homogeneous linear equations. The problems are identified as Sturm-Liouville Problems (SLP) and are named after J.C.F. Sturm and J. Liouville, who studied them in the mid-1800s. SLPs have an infinite number of eigenvalues, and the corresponding eigenfunctions form a complete, orthogonal set, which makes orthogonal expansions possible.
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A classification of polarities over arbitrary fields follows from the classification of sesquilinear forms given by Birkhoff and von Neumann. Orthogonal polarities, corresponding to symmetric bilinear forms, are also called ordinary polarities and the locus of absolute points forms a non-degenerate conic (set of points whose coordinates satisfy an irreducible homogeneous quadratic equation) if the field does not have characteristic two. In characteristic two the orthogonal polarities are called pseudopolarities and in a plane the absolute points form a line.
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Symmetry with respect to all rotations about all points implies translational symmetry with respect to all translations, so space is homogeneous, and the symmetry group is the whole E(m). With the modified notion of symmetry for vector fields the symmetry group can also be E+(m). For symmetry with respect to rotations about a point we can take that point as origin. These rotations form the special orthogonal group SO(m), the group of m×m orthogonal matrices with determinant 1.
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Map of Pella, showing the grid plan of the city Traditionally, the Greek philosopher Hippodamus (5th century BC) is regarded as the first town planner and ‘inventor’ of the orthogonal urban layout. Aristotle called him "the father of city planning",Aristotle, Politica II and until well into the 20th century, he was indeed regarded as such. This is, however, only partly justified. The Hippodamian plan that was called after him, is an orthogonal urban layout with more or less square street blocks.
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Orthogonality as a property of term rewriting systems describes where the reduction rules of the system are all left-linear, that is each variable occurs only once on the left hand side of each reduction rule, and there is no overlap between them. Orthogonal term rewriting systems have the consequent property that all reducible expressions (redexes) within a term are completely disjoint -- that is, the redexes share no common function symbol. For example, the term rewriting system with reduction rules : \rho_1\ :\ f(x, y) \rightarrow g(y) : \rho_2\ :\ h(y) \rightarrow f(g(y), y) is orthogonal -- it is easy to observe that each reduction rule is left-linear, and the left hand side of each reduction rule shares no function symbol in common, so there is no overlap. Orthogonal term rewriting systems are confluent.
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As with the orthogonal group, the projective orthogonal group can be generalized in two main ways: changing the field or changing the quadratic form. Other than the real numbers, primary interest is in complex numbers or finite fields, while (over the reals) quadratic forms can also be indefinite forms, and are denoted PO(p,q) by their signature. The complex projective orthogonal group, PO(n,C) should not be confused with the projective unitary group, PU(n): PO preserves a symmetric form, while PU preserves a hermitian form – PU is the symmetries of complex projective space (preserving the Fubini–Study metric). In fields of characteristic 2 there are added complications: quadratic forms and symmetric bilinear forms are no longer equivalent, I = -I, and the determinant needs to be replaced by the Dickson invariant.
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Steel AutoDrafter workflow extracts planar drawings and material take-off from a structural steel model prepared in STAAD.Pro. It produces excellent quality plans at any level and sections in any of the orthogonal directions.
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His results are from the fields of mathematical analysis and topological groups, in particular he researched orthogonal systems of functions, singular integrals, analytic functions, differential equations, set theory, function approximation and calculus of variations.
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Let be an n-dimensional, non-degenerate symmetric bilinear space over a field with characteristic not equal to 2. Then, every element of the orthogonal group is a composition of at most n reflections.
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For orthogonal and symplectic groups the Weingarten functions were evaluated by . Their theory is similar to the case of the unitary group. They are parameterized by partitions such that all parts have even size.
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The visual impression of a game should not contradict with its balancing. On the contrary: Especially real models, e.g. historic facts, can serve as inspiration for mechanics, counters, orthogonal unit differences or intransitive relations.
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However, Staph. A. Sortase A does not recognize LPXTA substrates and thus are orthogonal to the LPXTA sequence. In addition, Sortase A has also been used to piecewise create proteins, protein domains, and peptides.
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The idea of a planned out urban area evolved as different civilizations adopted it. Beginning in the 8th century BCE, Greek city states were primarily centered on orthogonal (or grid- like) plans.Kolb, Frank (1984).
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Multiple inheritance allows programmers to use more than one totally orthogonal hierarchy simultaneously, such as allowing Cat to inherit from Cartoon character and Pet and Mammal and access features from within all of those classes.
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The most famous, and indeed motivational, example of paradoxical sets is the Banach–Tarski paradox, which divides the sphere into paradoxical sets for the special orthogonal group. This result depends on the axiom of choice.
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Rather it is temporarily stored by the device and given back, once every seconds. Note that the term in quadrature only implies that two sinusoids are orthogonal, not that they are components of another sinusoid.
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Other mass analyzers coupled to ICP systems include double focusing magnetic-electrostatic sector systems with both single and multiple collector, as well as time of flight systems (both axial and orthogonal accelerators have been used).
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Images of a gravity-bound or man-made environment are particularly anisotropic in the orientation domain, with more image structure located at orientations parallel with or orthogonal to the direction of gravity (vertical and horizontal).
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While spherical polar coordinates are one orthogonal coordinate system for expressing vectors and tensors using polar and azimuthal angles and radial distance, the spherical basis are constructed from the standard basis and use complex numbers.
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In mathematics, Al-Salam–Carlitz polynomials U(x;q) and V(x;q) are two families of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by . give a detailed list of their properties.
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Polarization-division multiplexing uses the polarization of electromagnetic radiation to separate orthogonal channels. It is in practical use in both radio and optical communications, particularly in 100 Gbit/s per channel fiber optic transmission systems.
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If U\sim B_p(a,b) and H is a constant p\times p orthogonal matrix, then HUH^T\sim B(a,b). Also, if H is a random orthogonal p\times p matrix which is independent of U, then HUH^T\sim B_p(a,b), distributed independently of H. If A is any constant q\times p, q\leq p matrix of rank q, then AUA^T has a generalized matrix variate beta distribution, specifically AUA^T\sim GB_q\left(a,b;AA^T,0\right).
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Green indicates one intersection, blue indicates two intersections, and red indicates three or more. The top two polygons are monotone with respect to L while the bottom two are not. In geometry, a polygon P in the plane is called monotone with respect to a straight line L, if every line orthogonal to L intersects P at most twice. Similarly, a polygonal chain C is called monotone with respect to a straight line L, if every line orthogonal to L intersects C at most once.
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MIMO Wireless Networks Channels, Techniques and Standards for Multi-Antenna, Multi-User and Multi-Cell Systems. By Bruno Clerckx and Claude Oestges (Auth.) (2013) section 1.8 Spatial multiplexing techniques make the receivers very complex, and therefore they are typically combined with Orthogonal frequency-division multiplexing (OFDM) or with Orthogonal Frequency Division Multiple Access (OFDMA) modulation, where the problems created by a multi-path channel are handled efficiently. The IEEE 802.16e standard incorporates MIMO-OFDMA. The IEEE 802.11n standard, released in October 2009, recommends MIMO-OFDM.
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As each taper is pairwise orthogonal to all other tapers, the windowed signals provide statistically independent estimates of the underlying spectrum. The final spectrum is obtained by averaging over all the tapered spectra. Thomson chose the Slepian or discrete prolate spheroidal sequences as tapers since these vectors are mutually orthogonal and possess desirable spectral concentration properties (see the section on Slepian sequences). In practice, a weighted average is often used to compensate for increased energy loss at higher order tapersPercival, D. B., and A. T. Walden.
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The value of λj and direction of pj must be determined so that the resulting orbital can be normalized and so that it is orthogonal to the first hybrid orbital. The hybrid can certainly be normalized, as it is the sum of two normalized wavefunctions. Orthogonality must be established so that the two hybrid orbitals can be involved in separate covalent bonds. The inner product of orthogonal orbitals must be zero and computing the inner product of the constructed hybrids gives the following calculation.
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Mixing and matching the ligand-binding domains and DNA- binding domains of different hormone receptors can be used as an inducible expression mechanism to study the action of any gene with a hormone response element in its promoter. Selectively altering the ligand-binding domain to make it orthogonal to the natural ligand-receptor interface, as well as the making the DNA-binding domain and hormone response element orthogonal, would give a researcher precise control of a gene's transcription in order to study a gene's action.
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Varimax rotation is an orthogonal rotation of the factor axes to maximize the variance of the squared loadings of a factor (column) on all the variables (rows) in a factor matrix, which has the effect of differentiating the original variables by extracted factor. Each factor will tend to have either large or small loadings of any particular variable. A varimax solution yields results which make it as easy as possible to identify each variable with a single factor. This is the most common orthogonal rotation option.
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These studies revealed an unexpected and highly nontrivial fact: unlike similar theories in other structures, the standard method in p-adic analysis leads to nothing except the Haar basis. Moreover, any p-adic orthogonal wavelet basis generated by test functions is some modification of the Haar basis. In his last work on this topic, an orthogonal p-adic wavelet basis generated by functions with non-compact support was constructed, while all previously known bases, as well as frames, were generated by the test functions.
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OVSF code tree Orthogonal variable spreading factor (OVSF) is an implementation of code division multiple access (CDMA) where before each signal is transmitted, the signal is spread over a wide spectrum range through the use of a user's code. Users' codes are carefully chosen to be mutually orthogonal to each other. These codes are derived from an OVSF code tree, and each user is given a different code. An OVSF code tree is a complete binary tree that reflects the construction of Hadamard matrices.
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A one-piece sheet metal vivaldi antenna undergoing testing in an anechoic chamber Vivaldi antennas can be made for linear polarized waves or – using two devices arranged in orthogonal direction – for transmitting / receiving both polarization orientations. If fed with 90-degree phase-shifted signals, orthogonal devices can transmit/receive circular-oriented electromagnetic waves. Vivaldi antennas are useful for any frequency, as all antennas are scalable in size for use at any frequency. Printed circuit technology makes this type antenna cost effective at microwave frequencies exceeding 1 GHz.
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An additional orthogonal classification of hyper-heuristics considers the source providing feedback during the learning process, which can be either one instance (on-line learning) or many instances of the underlying problem studied (off-line learning).
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However, some applications require the full wave to be used and three-component or 3-C geophones are used. In analog devices, three moving coil elements are mounted in an orthogonal arrangement within a single case.
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They are named after the English mathematician William Kingdon Clifford. The most familiar Clifford algebras, the orthogonal Clifford algebras, are also referred to as (pseudo-)Riemannian Clifford algebras, as distinct from symplectic Clifford algebras.see for ex.
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As structural information about protein-ligand interfaces have become available, bump-and-hole pairs have been used to elucidate the substrates of specific proteins from various protein classes, as well as develop orthogonal neoenzyme-neosubstrate therapeutics.
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Représentations distinguées pour le groupe orthogonal. Comptes Rendus de l'Académie des Sciences, Série I, 312(13):957–961, 1991.H. Jacquet and K. F. Lai. A relative trace formula, Compositio Mathematica, 54(2), 243–310 (1985).
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The J-homomorphism is a homomorphism from the homotopy groups of orthogonal groups to stable homotopy groups of spheres, which causes the period 8 Bott periodicity to be visible in the stable homotopy groups of spheres.
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Lie groups occur in abundance throughout mathematics and physics. Matrix groups or algebraic groups are (roughly) groups of matrices (for example, orthogonal and symplectic groups), and these give most of the more common examples of Lie groups.
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In mathematics, the generalized dihedral groups are a family of groups with algebraic structures similar to that of the dihedral groups. They include the finite dihedral groups, the infinite dihedral group, and the orthogonal group O(2).
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Scherk's first surface is asymptotic to two infinite families of parallel planes, orthogonal to each other, that meet near z = 0 in a checkerboard pattern of bridging arches. It contains an infinite number of straight vertical lines.
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The TI-990 used a fairly orthogonal instruction set. The basic instruction formats allowed for one, two and three word instructions. The model 990/12 CPU allowed for a four word instruction with the extended mode operations.
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Poincaré disk with 3 ultraparallel (hyperbolic) straight lines Hyperbolic straight lines consist of all arcs of Euclidean circles contained within the disk that are orthogonal to the boundary of the disk, plus all diameters of the disk.
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Microwave Symp. DigX. Yang, P. Roblin, D. Chaillot, S. Mutha, J. Strahler, J. Kim, M. Ismail, J. Wood, and J. Volakis, “Fully orthogonal multi-carrier predistortion linearization for RF power amplifiers,” in IEEE Int. Microwave Symp. Dig.
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The Clifford algebra on Rp,q is denoted Clp,q(R). A standard orthonormal basis {ei} for Rp,q consists of mutually orthogonal vectors, p of which have norm +1 and q of which have norm −1.
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Frequency-hopping is used by Bluetooth to reduce the cross-talk and collision probability between nodes in different VPANs. Other techniques include orthogonal frequency-division multiple access (OFDMA) and multi-carrier code division multiple access (MC-CDMA).
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With such modified SIMCA methods, classification of an object requires both that its orthogonal distance from the model and its projection within the model (i.e. score value within the region defined by the ellipsoid) are not significant.
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An element is orthogonal to another element with respect to the sesquilinear form (written ) if . This relation need not be symmetric, i.e. does not imply . A sesquilinear form is reflexive (or orthosymmetric) if implies for all in .
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The PRIME specificationNarrowband orthogonal frequency division multiplexing power line communication transceivers for PRIME networks. International Telecommunication Union. 2012. is structured into Physical Layer, MAC Layer and Convergence Layer. For operations and control, a "Management Plane is specified".
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Simon Sidon or Simon Szidon (1892 in Versec, Kingdom of Hungary – 27 April 1941, Budapest, Hungary) was a reclusive Hungarian mathematician who worked on trigonometric series and orthogonal systems and who introduced Sidon sequences and Sidon sets.
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Rather, Jab, which is termed the exchange constant, is a function of Eqs. (4), (5), and (6), namely, However, with orthogonal orbitals (in which S = 0), for example with different orbitals in the same atom, Jab = Jex.
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Expressions for the convolution coefficients are easily obtained because the normal equations matrix, JTJ, is a diagonal matrix as the product of any two orthogonal polynomials is zero by virtue of their mutual orthogonality. Therefore, each non-zero element of its inverse is simply the reciprocal the corresponding element in the normal equation matrix. The calculation is further simplified by using recursion to build orthogonal Gram polynomials. The whole calculation can be coded in a few lines of PASCAL, a computer language well-adapted for calculations involving recursion.
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A tensor representation of a matrix group is any representation that is contained in a tensor representation of the general linear group. For example, the orthogonal group O(n) admits a tensor representation on the space of all trace-free symmetric tensors of order two. For orthogonal groups, the tensor representations are contrasted with the spin representations. The classical groups, like the symplectic group, have the property that all finite- dimensional representations are tensor representations (by Weyl's construction), while other representations (like the metaplectic representation) exist in infinite dimensions.
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Summing these component forces using vector addition yields the original force. Resolving force vectors into components of a set of basis vectors is often a more mathematically clean way to describe forces than using magnitudes and directions. This is because, for orthogonal components, the components of the vector sum are uniquely determined by the scalar addition of the components of the individual vectors. Orthogonal components are independent of each other because forces acting at ninety degrees to each other have no effect on the magnitude or direction of the other.
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The Bauhinia blakeana flower on the Hong Kong flag has C5 symmetry; the star on each petal has D5 symmetry. In geometry, a two-dimensional point group or rosette group is a group of geometric symmetries (isometries) that keep at least one point fixed in a plane. Every such group is a subgroup of the orthogonal group O(2), including O(2) itself. Its elements are rotations and reflections, and every such group containing only rotations is a subgroup of the special orthogonal group SO(2), including SO(2) itself.
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A projection on a vector space V is a linear operator P : V \mapsto V such that P^2 = P. When V has an inner product and is complete (i.e. when V is a Hilbert space) the concept of orthogonality can be used. A projection P on a Hilbert space V is called an orthogonal projection if it satisfies \langle Px, y \rangle = \langle x, Py \rangle for all x,y \in V. A projection on a Hilbert space that is not orthogonal is called an oblique projection.
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Orthogonal protection of L-Tyrosine (Protecting groups are marked in blue, the amino acid is shown in black). (1) Fmoc-protected amino group, (2) benzyl ester protected carboxyl group and (3) tert-butyl ether protected phenolic hydroxyl group of Tyrosine. Orthogonal protection is a strategy allowing the specific deprotection of one protective group in a multiply-protected structure without affecting the others. For example, the amino acid tyrosine could be protected as a benzyl ester on the carboxyl group, a fluorenylmethylenoxy carbamate on the amine group, and a tert-butyl ether on the phenol group.
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Otherwise, the separation of the resulting mixture of reaction products is virtually impossible.Weng C. Chan, Peter D. White: Fmoc Solid Phase Peptide Synthesis, S. 10–12. The technique was introduced in the field of peptide synthesis by Robert Bruce Merrifield in 1977. As a proof of concept orthogonal deprotection is demonstrated in a photochemical transesterification by trimethylsilyldiazomethane utilizing the kinetic isotope effect: :Orthogonal protection Application in Photochemistry Due to this effect the quantum yield for deprotection of the right-side ester group is reduced and it stays intact.
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For example, in the two dimensional Euclidean plane, every orthogonal transformation is either a reflection across a line through the origin or a rotation about the origin (which can be written as the composition of two reflections). Any arbitrary composition of such rotations and reflections can be rewritten as a composition of no more than 2 reflections. Similarly, in three-dimensional Euclidean space, every orthogonal transformation can be described as a single reflection, a rotation (2 reflections), or an improper rotation (3 reflections). In four-dimensions, double rotations are added that represent 4 reflections.
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Asynchronous CDMA offers a key advantage in the flexible allocation of resources i.e. allocation of spreading sequences to active users. In the case of CDM (synchronous CDMA), TDMA, and FDMA the number of simultaneous orthogonal codes, time slots, and frequency slots respectively are fixed, hence the capacity in terms of the number of simultaneous users is limited. There are a fixed number of orthogonal codes, time slots or frequency bands that can be allocated for CDM, TDMA, and FDMA systems, which remain underutilized due to the bursty nature of telephony and packetized data transmissions.
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The rotation group generalizes quite naturally to n-dimensional Euclidean space, \R^n with its standard Euclidean structure. The group of all proper and improper rotations in n dimensions is called the orthogonal group O(n), and the subgroup of proper rotations is called the special orthogonal group SO(n), which is a Lie group of dimension . In special relativity, one works in a 4-dimensional vector space, known as Minkowski space rather than 3-dimensional Euclidean space. Unlike Euclidean space, Minkowski space has an inner product with an indefinite signature.
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Using a birefringent cavity fiber laser, an induced vector soliton may be formed due to the cross-coupling between the two orthogonal polarization components. If a strong soliton is formed along one principal polarization axis, then a weak soliton will be induced along the orthogonal polarization axis. The intensity of the weak component in an induced vector soliton may be so weak that by itself it could not form a soliton in the SPM. The characteristics of this type of soliton have been modeled numerically and confirmed by experiment.
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Symmetry with respect to all rotations about all points implies translational symmetry with respect to all translations (because translations are compositions of rotations about distinct points), and the symmetry group is the whole E+(). This does not apply for objects because it makes space homogeneous, but it may apply for physical laws. For symmetry with respect to rotations about a point, one can take that point as origin. These rotations form the special orthogonal group SO(), which can be represented by the group of orthogonal matrices with determinant 1\.
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Then we must normalize each of the orthogonal eigenvectors to turn them into unit vectors. Once this is done, each of the mutually orthogonal, unit eigenvectors can be interpreted as an axis of the ellipsoid fitted to the data. This choice of basis will transform our covariance matrix into a diagonalised form with the diagonal elements representing the variance of each axis. The proportion of the variance that each eigenvector represents can be calculated by dividing the eigenvalue corresponding to that eigenvector by the sum of all eigenvalues.
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The detection of charged particles within the chamber is possible by the ionizing of particles of gas due to the motion of the charged particle. The Fermilab detector CDF II contains a drift chamber called the Central Outer Tracker. The chamber contains argon and ethane gas, and wires separated by 3.56 millimetres gaps.Fermilab - glossary-photo- J. L. Lee Retrieved 2012-02-12 If two drift chambers are used with the wires of one orthogonal to the wires of the other, both orthogonal to the beam direction, a more precise detection of the position is obtained.
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The positions containing this symbol must all be in different rows and columns, and furthermore the other symbol in these positions must all be distinct. Hence, when viewed as a pair of Latin squares, the positions containing one symbol in the first square correspond to a transversal in the second square (and vice versa). A given Latin square of order n possesses an orthogonal mate if and only if it has n disjoint transversals. The Cayley table (without borders) of any group of odd order forms a Latin square which possesses an orthogonal mate.
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Carrier Interferometry (CI) is a spread spectrum scheme designed to be used in an Orthogonal Frequency-Division Multiplexing (OFDM) communication system for multiplexing and multiple access, enabling the system to support multiple users at the same time over the same frequency band. Like MC-CDMA, CI-OFDM spreads each data symbol in the frequency domain. That is, each data symbol is carried over multiple OFDM subcarriers. But unlike MC-CDMA, which uses binary- phase Hadamard codes (code values of 0 or 180 degrees) or binary pseudonoise, CI codes are complex-valued orthogonal codes.
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Orthogonal polarization spectral imaging (OPS imaging) is a method for imaging small blood vessels in tissue like the nail bed or lip. It uses a light source of linearly polarized light with a wavelength of 550 nanometers, an isosbestic point for hemoglobin, thus imaging the erythrocytes as they are flowing through the small blood vessels. The reflected light orthogonal (at a 90° angle) to the emitted light is recorded, thus eliminating direct reflections. The depolarized light forms an image of the microcirculation on a CCD, which can be captured through single frames or on videotape.
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First, for successful translation of a novel amino acid, the codon to which the novel amino acid is assigned cannot already code for one of the 20 natural amino acids. Usually a nonsense codon (stop codon) or a four-base codon are used. Second, a novel pair of tRNA and aminoacyl tRNA synthetase are required, these are called the orthogonal set. The orthogonal set must not crosstalk with the endogenous tRNA and synthetase sets, while still being functionally compatible with the ribosome and other components of the translation apparatus.
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Since in a group every element must be invertible, the most general matrix groups are the groups of all invertible matrices of a given size, called the general linear groups. Any property of matrices that is preserved under matrix products and inverses can be used to define further matrix groups. For example, matrices with a given size and with a determinant of 1 form a subgroup of (that is, a smaller group contained in) their general linear group, called a special linear group. Orthogonal matrices, determined by the condition :M'M = I, form the orthogonal group.
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By Wedderburn's theorem every finite skewfield is a field and an automorphism of order two (other than the identity) can only exist in a finite field whose order is a square. These facts help to simplify the general situation for finite Desarguesian planes. We have: If is a polarity of the finite Desarguesian projective plane where for some prime , then the number of absolute points of is if is orthogonal or if is unitary. In the orthogonal case, the absolute points lie on a conic if is odd or form a line if .
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Non-orthogonal frequency-division multiplexing (N-OFDM) is a method of encoding digital data on multiple carrier frequencies with non-orthogonal intervals between frequency of sub-carriersRU2054684 (C1) G01R 23/16. Amplitude-frequency response measurement technique// Slyusar V. – Appl. Number SU 19925055759, Priority Data: 19920722. – Official Publication Data: 1996-02-20 Slyusar, V. I. Smolyar, V. G. Multifrequency operation of communication channels based on super-Rayleigh resolution of signals// Radio electronics and communications systems c/c of Izvestiia- vysshie uchebnye zavedeniia radioelektronika.. – 2003, volume 46; part 7, pages 22–27.
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They are usually installed with orthogonal axes to the slope surface and therefore, at first, approximately orthogonal to the surface of the creep. Sometimes anchorage problems occur, as in the case of silty-clayey ground. Where there is water or the anchors are embedded in a clayey sub- layer, the adherence of the anchor to the ground must be confirmed. The surface contained within the grid of the beam frame should also be protected, using geofabrics, in order to prevent erosion from removing the ground underlying the beam frame.
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However, whereas every irreducible tensor representation of SO(2) and SO(3) is of this kind, the special orthogonal groups in higher dimensions have additional irreducible representations that do not arise in this manner. The special orthogonal groups have additional spin representations that are not tensor representations, and are typically not spherical harmonics. An exception are the spin representation of SO(3): strictly speaking these are representations of the double cover SU(2) of SO(3). In turn, SU(2) is identified with the group of unit quaternions, and so coincides with the 3-sphere.
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The Geek Code was invented by Robert A. Hayden in 1993 and was defined at geekcode.com.[ It was inspired by a similar code for the bear subculture - which in turn was inspired by the Yerkes spectral classification system for describing stars.Unlike the Geek Code, the Yerkes system uses classes, subclasses and peculiarities for categorization. These systems differ in their orthogonality: the Geek Code is very orthogonal in the computer science sense (where variables may be projected onto basis vectors), where the Yerkes system is very orthogonal in the taxonomic sense (representing mutually exclusive classes).
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In Fourier analysis, such as the Fourier transform or the discrete Fourier transform, the sinusoids being fitted to the data are all mutually orthogonal, so there is no distinction between the simple out-of-context dot-product-based projection onto basis functions versus an in-context simultaneous least-squares fit; that is, no matrix inversion is required to least-squares partition the variance between orthogonal sinusoids of different frequencies. This method is usually preferred for its efficient fast Fourier transform implementation, when complete data records with equally spaced samples are available.
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Bioorthogonal chemistry refers to chemical reactions occurring inside living systems without reacting with naturally present cellular components. In supramolecular chemistry the notion of orthogonality refers to the possibility of two or more supramolecular, often non-covalent, interactions being compatible; reversibly forming without interference from the other. In analytical chemistry, analyses are "orthogonal" if they make a measurement or identification in completely different ways, thus increasing the reliability of the measurement. Orthogonal testing thus can be viewed as "cross-checking" of results, and the "cross" notion corresponds to the etymologic origin of orthogonality.
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Creating a least-squares fit begins by assuming some function, in the case of the reconstruction an nth degree polynomial, and fitting the curve to the data using constants. The accuracy of the fit can be increased by increasing the degree of the polynomial being used to fit the data. If a set of non-orthogonal standard basis functions was used, it becomes necessary to recalculate the constant coefficients of the function describing the fit. However, by using the orthogonal set of basis functions, it is not necessary to recalculate the constant coefficients.
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Pseudospectral methods, also known as orthogonal collocation methods, in optimal control arose from spectral methods which were traditionally used to solve fluid dynamics problems.Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A., Spectral Methods in Fluid Dynamics, Springer-Verlag, New York, 1988. Fornberg, B., A Practical Guide to Pseudospectral Methods, Cambridge University Press, 1998. Seminal work in orthogonal collocation methods for optimal control problems date back to 1979 with the work of ReddienReddien, G.W., "Collocation at Gauss Points as a Discretization in Optimal Control,"SIAM Journal on Control and Optimization, Vol.
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Let be a compact oriented Riemannian manifold. The Hodge decomposition states that any -form on uniquely splits into the sum of three components: :\omega = \alpha + \beta + \gamma , where is exact, is co-exact, and is harmonic. One says that a form is co-closed if and co-exact if for some form , and that is harmonic if . This follows by noting that exact and co- exact forms are orthogonal; the orthogonal complement then consists of forms that are both closed and co-closed: that is, of harmonic forms.
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In geometry, an orthocentric tetrahedron is a tetrahedron where all three pairs of opposite edges are perpendicular. It is also known as an orthogonal tetrahedron since orthogonal means perpendicular. It was first studied by Simon Lhuilier in 1782, and got the name orthocentric tetrahedron by G. de Longchamps in 1890.. In an orthocentric tetrahedron the four altitudes are concurrent. This common point is called the orthocenter, and it has the property that it is the symmetric point of the center of the circumscribed sphere with respect to the centroid.
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The corner point grid consists of cubes that are usually much coarser in the horizontal direction and each corner of the cube is arbitrarily defined to follow the major features in the grid. Converting directly from orthogonal to corner point can cause problems such as creating discontinuity in fluid flow. An intermediate stratigraphic grid ensures that important structures are not misrepresented in the transfer. The stratigraphic grid has the same number of cells as the orthogonal seismic grid, but the boundaries are defined by stratigraphic surfaces and the cells follow the stratigraphic organization.
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The combination of these qualities makes BODIPY fluorophores promising for imaging applications. The position of the absorption and emission bands remain almost unchanged in solvents of different polarity as the dipole moment and transition dipole are mutually orthogonal.
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The lines will be perpendicular if and only if . This method is simplified from the dot product (or, more generally, the inner product) of vectors. In particular, two vectors are considered orthogonal if their inner product is zero.
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In public media, integrated media and media meshing also refer to the use of multiple orthogonal and perhaps interactive forms, such as news releases, websites, polls, wikis, blogs or forum sources, rather than just a single broadcast mode.
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These do not span the space, but leave a line which does not rotate – like the axis of rotation in three dimensions, except rotations do not take place about this line but in multiple planes orthogonal to it.
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D4, Dynkin diagram of SO(8) In mathematics, SO(8) is the special orthogonal group acting on eight-dimensional Euclidean space. It could be either a real or complex simple Lie group of rank 4 and dimension 28.
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Artin describes GL(n, k) group structure. More details are given about vector spaces over finite fields. Chapter five is "The Structure of Sympletic and Orthogonal Groups". It includes sections on elliptic spaces, Clifford algebra, and spinorial norm.
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Hertwig noticed that elongated egg divides not randomly, but orthogonal to its long axis. The new daughter cells were formed along the longest axis of the cell. That observation got name of 'Hertwig's rule' or 'long axis rule'.
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For instance, the structure of faux bow tie spiropentadiene, shown above, makes clear that the planes that are defined by the atoms of each ring—i.e., the best-fit plane of each cyclopropene—are orthogonal (perpendicular) to one another.
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An orthogonal probe beam detects the precession using optical rotation of linearly polarized light. In a typical SERF magnetometer, the spins merely tip by a very small angle because the precession frequency is slow compared to the relaxation rates.
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The Smale conjecture, named after Stephen Smale, is the statement that the diffeomorphism group of the 3-sphere has the homotopy-type of its isometry group, the orthogonal group O(4). It was proved in 1983 by Allen Hatcher.
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The latitude of transition between equatorial-orthogonal and polar-convergent longitude lines has been selected to allow the folding of the projection into a perfect cube -- "cubing the sphere"; indeed in this way the Arctic Circle becomes a square.
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In mathematics, the Al-Salam–Chihara polynomials Qn(x;a,b;q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by . give a detailed list of the properties of Al-Salam–Chihara polynomials.
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A polytope is called monostatic if, when filled homogeneously, it is stable on only one facet. Alternatively, a polytope is monostatic if its centroid (the center of mass) has an orthogonal projection in the interior of only one facet.
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To convert a given handedness of polarized light to the other handedness one can use a half-waveplate. A half-waveplate shifts a given linear component of light one half of a wavelength relative to its orthogonal linear component.
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Benzyl trichloroethanimidate Carboximidates can act as protecting group for alcohols. For example, the base catalyzed reaction of benzyl alcohol upon trichloroacetonitrile yields a trichloroacetimidate. This species has orthogonal stability to acetate and TBS protections and may be cleaved by acid hydrolysis.
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However, the precise definitions of SIM and MIM have been a source of inconsistency. There are attempts to provide orthogonal definitions for canonical motifs in biological networks and algorithms to enumerate them, especially SIM, MIM and Bi-Fan (2x2 MIM).
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The sphere becomes the midsphere of the realization: each edge of the polyhedron is tangent to it, at the point where two tangent primal circles and two dual circles orthogonal to the primal circles and tangent to each other all meet.
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There are 121 orbits of vectors v of norm –2, corresponding to the 121 isomorphism classes of 25-dimensional even lattices L of determinant 2. In this correspondence, the lattice L is isomorphic to the orthogonal complement of the vector v.
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Post-war conservation efforts that began in 1994 restored many surviving buildings in the Foch-Allenby district within a pedestrian setting. Extended to the sea, Foch and Allenby Streets are the origin of the orthogonal grid of Beirut’s new waterfront district.
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On the equator of the eye (region circumferencing the largest diameter orthogonal to the visual axis). Its causes are scleritis & degeneration of sclera in pathological myopia. It occurs more commonly in the regions of sclera which are perforated by vortex veins.
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In orthogonal curvilinear coordinates, separation of variables can still be used, but in some details different from that in Cartesian coordinates. For instance, regularity or periodic condition may determine the eigenvalues in place of boundary conditions. See spherical harmonics for example.
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His breakthrough in pairwise balanced designs, and orthogonal Latin squares built upon the groundwork set before him, by R. C. Bose, E. T. Parker, S. S. Shrikhande, and Haim Hanani is widely referenced in Combinatorial Design Theory and Coding Theory.
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A cross product, that is a vector-valued, bilinear, anticommutative and orthogonal product of two vectors, is defined in seven dimensions. Along with the more usual cross product in three dimensions it is the only such product, except for trivial products.
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Due to biorthogonality, is orthogonal to where is any polynomial of degree in . Hence, only the highest-order terms of and matter in the dot products and . The leading coefficients of and are and , respectively. It follows that :, and thus :.
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According to this category most of the time applications can be found in time of flight (TOF) or orthogonal TOF mass spectrometry (OA-TOF MS), Fourier transform ion cyclotron resonance (FT-ICR MS) and quadrupole or ion trap mass spectrometry.
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By selecting only the first PGD modes, a reduced order model of the solution is obtained. Because of this, PGD is considered a dimensionality reduction algorithm. In addition, it is considered as a generalized form of the Proper Orthogonal Decomposition.
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In contrast, perfect transmission is possible if one wishes to convert classical information to quantum information then back to classical information. For classical bits, this can be done by encoding them in orthogonal quantum states, which can always be distinguished.
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Because its modes are not orthogonal, DMD-based representations can be less parsimonious than those generated by PCA. However, they can also be more physically meaningful because each mode is associated with a damped (or driven) sinusoidal behavior in time.
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In mathematics, the dual q-Hahn polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. give a detailed list of their properties. The polynomials are given in terms of basic hypergeometric functions and the Pochhammer symbol.
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Both the EPQ and Big Five approaches extensively use self-report questionnaires. The factors are intended to be orthogonal (uncorrelated),Hans Eysenck, (1990). Biological dimensions of personality. In L. A. Pervin (Ed.), Handbook of personality: Theory and research (pp. 244–276).
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In networking, multipacket reception refers to the capability of networking nodes for decoding/demodulating signals from a number of source nodes concurrently. In wireless communications, Multipacket reception is achieved using physical layer technologies like orthogonal CDMA, MIMO and space–time codes.
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In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after Frits Zernike, the Dutch optical physicist, and the inventor of phase contrast microscopy, they play an important role in beam optics.
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The ancient Romans, inspired by the Greeks, also used orthogonal plans for their cities. City planning in the Roman world was developed for military defense and public convenience. The spread of the Roman Empire subsequently spread the ideas of urban planning.
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The design of STBCs is based on the so-called diversity criterion derived by Tarokh et al. in their earlier paper on space–time trellis codes. Orthogonal STBCs can be shown to achieve the maximum diversity allowed by this criterion.
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The diamond did not exhibit any trigons on the octahedral faces (111) or noticeable striae on the dodecahedral faces (110) and the crystallographic orientation was derived from the presence of two orthogonal inversions on one of the hexahedral faces (100).
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Circulation 1987;76(1):237–43.Abboud S., Smith JM., Shargorodsky B., Laniado S., Sadeh D., Cohen RJ. High frequency electrocardiography of three orthogonal leads in dogs during a coronary artery occlusion. Pacing Clin Electrophysiol 1989;12(4 Pt 1):574–81.
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Moreover, one can use as basis functions any pair of orthogonal polarization states, not just linear polarizations. For instance, choosing right and left circular polarizations as basis functions simplifies the solution of problems involving circular birefringence (optical activity) or circular dichroism.
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These are then separately modulated onto two orthogonal basis functions. In this implementation, two sinusoids are used. Afterwards, the two signals are superimposed, and the resulting signal is the QPSK signal. Note the use of polar non-return-to-zero encoding.
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For many practical purposes this definition may be extended to allow cases when some edges of P are orthogonal to L, and a simple polygon may be called monotone if a line segment that connects two points in P and is orthogonal to L completely belongs to P. Following the terminology for monotone functions, the former definition describes polygons strictly monotone with respect to L. The "with respect to" part is necessary for drawing the strict/nonstrict distinction: a polygon nonstrictly monotone with respect to L is strictly monotone with respect to a line L1 rotated from L by a sufficiently small angle.
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The unrotated output maximizes variance accounted for by the first and subsequent factors, and forces the factors to be orthogonal. This data-compression comes at the cost of having most items load on the early factors, and usually, of having many items load substantially on more than one factor. Rotation serves to make the output more understandable, by seeking so- called "Simple Structure": A pattern of loadings where each item loads strongly on only one of the factors, and much more weakly on the other factors. Rotations can be orthogonal or oblique (allowing the factors to correlate).
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The Macdonald polynomials P_\lambda are a two-parameter family of orthogonal polynomials indexed by a positive weight λ of a root system, introduced by Ian G. Macdonald (1987). They generalize several other families of orthogonal polynomials, such as Jack polynomials and Hall–Littlewood polynomials. They are known to have deep relationships with affine Hecke algebras and Hilbert schemes, which were used to prove several conjectures made by Macdonald about them. introduced a new basis for the space of symmetric functions, which specializes to many of the well-known bases for the symmetric functions, by suitable substitutions for the parameters q and t.
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A common problem in computer graphics is to generate a non-zero vector in R3 that is orthogonal to a given non-zero one. There is no single continuous function that can do this for all non-zero vector inputs. This is a corollary of the hairy ball theorem. To see this, consider the given vector as the radius of a sphere and note that finding a non-zero vector orthogonal to the given one is equivalent to finding a non-zero vector that is tangent to the surface of that sphere where it touches the radius.
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Map of the Archeological site Located at the intersection of six roads, the city was walled but not fortified. Originally designed for a population of around 15,000, the city quickly outgrew its original specifications and spilled beyond the orthogonal grid in a more loosely organized fashion. At the time of its founding, the area surrounding the city was a fertile agricultural area, about 1000 meters above sea level. The original Roman grid plan is magnificently visible in the orthogonal design, highlighted by the decumanus maximus (east–west-oriented street) and the cardo (north–south-oriented street) lined by a partially restored Corinthian colonnade.
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The most efficient way to reflect radar waves back to the emitting radar is with orthogonal metal plates, forming a corner reflector consisting of either a dihedral (two plates) or a trihedral (three orthogonal plates). This configuration occurs in the tail of a conventional aircraft, where the vertical and horizontal components of the tail are set at right angles. Stealth aircraft such as the F-117 use a different arrangement, tilting the tail surfaces to reduce corner reflections formed between them. A more radical method is to omit the tail, as in the B-2 Spirit.
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For the second phase, each player chooses a "ka" from among the tokens next to the passage, or tokens one column away from the passage whichever method both players agree upon. The "ka" then enters the passage and captures any odd number of tokens of the same color that it forms a line with from any orthogonal direction. From there on (third phase), each player's "ka" moves any number of vacant spaces in an orthogonal direction provided it can capture an odd number of tokens of the same color. However, the "ka" at this phase of the game captures tokens differently.
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Clifford algebras exhibit a 2-fold periodicity over the complex numbers and an 8-fold periodicity over the real numbers, which is related to the same periodicities for homotopy groups of the stable unitary group and stable orthogonal group, and is called Bott periodicity. The connection is explained by the geometric model of loop spaces approach to Bott periodicity: their 2-fold/8-fold periodic embeddings of the classical groups in each other (corresponding to isomorphism groups of Clifford algebras), and their successive quotients are symmetric spaces which are homotopy equivalent to the loop spaces of the unitary/orthogonal group.
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Within the city walls the urban area was divided into an orthogonal plan, with space allotted for civic, sacred, and private architecture. The plan represents a subtle adaptation of an orthogonal plan to the complicated topography of the hill. The forum was found on a saddle between two heights, with the sacred area, with the Capitolium, linked to it by a broad street. Recent excavations have suggested that the original layout provided for about 248 houses, of which 20 were intended for the decurions, and were double the size of the houses of the ordinary citizens.
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PCA of the multivariate Gaussian distribution centered at (1, 3) with a standard deviation of 3 in roughly the (0.878, 0.478) direction and of 1 in the orthogonal direction. The vectors shown are unit eigenvectors of the (symmetric, positive-semidefinite) covariance matrix scaled by the square root of the corresponding eigenvalue. (Just as in the one-dimensional case, the square root is taken because the standard deviation is more readily visualized than the variance. The eigendecomposition of a symmetric positive semidefinite (PSD) matrix yields an orthogonal basis of eigenvectors, each of which has a nonnegative eigenvalue.
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In a similar way, the sample rate is equivalent to the pixel pitch on a display screen, whereas the optical resolution of a display screen is equivalent to temporal uncertainty. Note that both this form of image space and time resolutions are orthogonal to measurement resolution, even though space and time are also orthogonal to each other. Both an image or an oscilloscope capture can have a signal to noise ratio, since both also have measurement resolution. An oscilloscope is the temporal equivalent of a microscope, and it is limited by temporal uncertainty the same way a microscope is limited by optical resolution.
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For double-pulse LIBS one distinguishes between orthogonal and perpendicular configuration. In perpendicular configuration the laser fires twice on the same spot on the specimen with a pulse separation in the order of one to a couple of tens of microseconds. Depending on pulse separation, the second pulse is more or less absorbed by the plasma plume caused by the previous pulse, resulting in a reheating of the laser plasma leading to signal enhancement. In orthogonal configuration a laser pulse is fired parallel to the sample surface either before or after the perpendicular pulse hits the specimen.
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The Interpersonal Circumplex is a taxonomy of interpersonal personality traits and behaviours. The circumplex consists of orthogonal dimensions and concentric circles indicating the level of intensity The interpersonal circle or interpersonal circumplex is a model for conceptualizing, organizing, and assessing interpersonal behavior, traits, and motives. The interpersonal circumplex is defined by two orthogonal axes: a vertical axis (of status, dominance, power, ambitiousness, assertiveness, or control) and a horizontal axis (of agreeableness, compassion, nurturant, solidarity, friendliness, warmth, affiliation or love). In recent years, it has become conventional to identify the vertical and horizontal axes with the broad constructs of agency and communion.
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Inertial navigation is a self-contained navigation technique in which measurements provided by accelerometers and gyroscopes are used to track the position and orientation of an object relative to a known starting point, orientation and velocity. Inertial measurement units (IMUs) typically contain three orthogonal rate-gyroscopes and three orthogonal accelerometers, measuring angular velocity and linear acceleration respectively. By processing signals from these devices it is possible to track the position and orientation of a device. Inertial navigation is used in a wide range of applications including the navigation of aircraft, tactical and strategic missiles, spacecraft, submarines and ships.
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If the six connectors that join any pair of orthocentric points are extended to six lines that intersect each other, they generate seven intersection points. Four of these points are the original orthocentric points and the additional three points are the orthogonal intersections at the feet of the altitudes. The joining of these three orthogonal points into a triangle generates an orthic triangle that is common to all the four possible triangles formed from the four orthocentric points taken three at a time. The incenter of this common orthic triangle must be one of the original four orthocentric points.
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Orthogonal diameters of a circle with a square of tangents, midpoints of parallel chords and an affine image, which is an ellipse with conjugate diameters, a parallelogram of tangents and midpoints of chords. A circle has the following property: : The midpoints of parallel chords lie on a diameter. An affine transformation preserves parallelism and midpoints of line segments, so this property is true for any ellipse. (Note that the parallel chords and the diameter are no longer orthogonal.) ; Definition: Two diameters d_1,\, d_2 of an ellipse are conjugate if the midpoints of chords parallel to d_1 lie on d_2\ .
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In telecommunications, orthogonal frequency-division multiplexing (OFDM) is a type of digital transmission and a method of encoding digital data on multiple carrier frequencies. OFDM has developed into a popular scheme for wideband digital communication, used in applications such as digital television and audio broadcasting, DSL internet access, wireless networks, power line networks, and 4G/5G mobile communications. OFDM is a frequency-division multiplexing (FDM) scheme that was introduced by Robert W. Chang of Bell Labs in 1966. In OFDM, multiple closely spaced orthogonal subcarrier signals with overlapping spectra are transmitted to carry data in parallel.webe.
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The two polynomials, and with , are orthogonal, if and only if, In other words, for arbitrary parameters, only a finite number of Romanovski polynomials are orthogonal. This property is referred to as finite orthogonality. However, for some special cases in which the parameters depend in a particular way on the polynomial degree infinite orthogonality can be achieved. This is the case of a version of equation () that has been independently encountered anew within the context of the exact solubility of the quantum mechanical problem of the trigonometric Rosen–Morse potential and reported in Compean & Kirchbach (2006).
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Orbital angular momentum (OAM) multiplexing is a physical layer method for multiplexing signals carried on electromagnetic waves using the orbital angular momentum of the electromagnetic waves to distinguish between the different orthogonal signals. Orbital angular momentum is one of two forms of angular momentum of light. OAM is distinct from, and should not be confused with, light spin angular momentum. The spin angular momentum of light offers only two orthogonal quantum states corresponding to the two states of circular polarization, and can be demonstrated to be equivalent to a combination of polarization multiplexing and phase shifting.
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Reflection through the origin is an orthogonal transformation corresponding to scalar multiplication by -1, and can also be written as -I, where I is the identity matrix. In three dimensions, this sends (x, y, z) \mapsto (-x, -y, -z), and so forth.
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To generate an orthogonal matrix, take an one and a uniformly distributed unit vector of dimension . Construct a Householder reflection from the vector, then apply it to the smaller matrix (embedded in the larger size with a 1 at the bottom right corner).
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Theory, IT-32:4 (1986), pp. 464–470. # Maximum Entropy and the Moment Problem, H. J. Landau, Bull. Amer. Math. Soc., 16:1 (1987), pp. 47-77\. # Polynomials Orthogonal on the Semicircle, II, Walter Gautschi, H. J. Landau and Gradimir Milovanović, Constr. Approx.
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3D braided fabrics are fabrics in which yarn runs through the braid in all three directions, formed by inter-plaiting three orthogonal sets of yarn.M, Subramanian Senthil Kannan, and Kumaravel S (2008). "A Comprehensive Look at 3-D Fabrics." The Indian Textile Journal.
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She has published many papers on wireless and optical communications, focusing specifically on Orthogonal frequency-division multiplexing. Her work has led to a number of commercialized patents. Between 1974 and 1977, she worked as a design engineer at Hewlett-Packard Ltd., Scotland.
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In mathematics, a Brauer algebra is an algebra introduced by used in the representation theory of the orthogonal group. It plays the same role that the symmetric group does for the representation theory of the general linear group in Schur–Weyl duality.
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The other path is used to conduct an additional step-size control. This step-size control aims to make consecutive movements of the distribution mean orthogonal in expectation. The step-size control effectively prevents premature convergence yet allowing fast convergence to an optimum.
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Metro stations can be found at both the eastern and western extremities of the District Centre. Current buildings in the District Centre include the Raddison Blue Hotel, a mall, residential villas and government organizations. Future construction will follow an orthogonal grid plan.
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The most common method is the Gram–Schmidt process. Which creates a set of orthogonal basis vectors, which can then easily be normalized. This method begins by first selecting any standard basis β={v1, v2,...,vn}. Next, set the first vector v1=u1.
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It is a rectified tetrahedron. It is a square bipyramid in any of three orthogonal orientations. It is also a triangular antiprism in any of four orientations. An octahedron is the three-dimensional case of the more general concept of a cross polytope.
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The building with orthogonal masonry has six rooms. The windows are supported by vaults. There is a big cistern under the front yard of the building. There are two sarcophagi, the ruins of an olive press and a mill around the building.
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Noting that signature matrices are both symmetric and involutory, they are thus orthogonal. Consequently, any linear transformation corresponding to a signature matrix constitutes an isometry. Geometrically, signature matrices represent a reflection in each of the axes corresponding to the negated rows or columns.
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Wannier functions of triple- and single-bonded nitrogen dimers in palladium nitride. The Wannier functions are a complete set of orthogonal functions used in solid-state physics. They were introduced by Gregory Wannier. Wannier functions are the localized molecular orbitals of crystalline systems.
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For cooling to occur along all directions, the atom must see this friction force along all three Cartesian axes; this is most easily achieved by illuminating the atom with three orthogonal laser beams, which are then reflected back along the same direction.
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Fleischer, M. (1970) New mineral names. American Mineralogist, 55, 533. Marthozite is orthorhombic, meaning that it has three axes of unequal lengths all orthogonal to each other. Since it is orthorhombic, marthozite is biaxial, meaning that it has three different indices of refraction.
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The Orthokaryotes (Cavalier-Smith 2017) are a proposed Eukaryote clade consisting of the Jakobea and the Neokaryotes. Together with its sister Discicristata it forms a basal Eukaryote clade. They are characterized by stacked Golgi, orthogonal centrioles, and two opposite posterior ciliary roots.
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The elements in a subarray are spaced 3.75 meters apart. The antenna elements of the two orthogonal polarizations are connected in separate identical phased arrays. The crossed dipoles are grouped into square 5×5 subarrays.Falkovich, I.S., Konovalenko, A.A., Gridin, A.A., et al.
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Its subgroups are referred to as matrix groups or linear groups. The dihedral group example mentioned above can be viewed as a (very small) matrix group. Another important matrix group is the special orthogonal group SO(n). It describes all possible rotations in n dimensions.
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After a devastating fire in 1624, the town of Oslo was moved to a new location and rebuilt as a fortified city with an orthogonal layout surrounded by ramparts, and renamed Christiania. King Christian also founded the trading city of Kristiansand, naming it after himself.
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Metascape is a free gene annotation and analysis resource that helps biologists make sense of one or multiple gene lists. Metascape provides automated meta-analysis tools to understand either common or unique pathways and protein networks within a group of orthogonal target-discovery studies.
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Furthermore, the use of a consistent dual orthogonal grid (e.g. Cartesian grid) in conjunction with an explicit time integration scheme (e.g. leap-frog-scheme) leads to compute and memory-efficient algorithms, which are especially adapted for transient field analysis in radio frequency (RF) applications.
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Furthermore, the use of a consistent dual orthogonal grid (e.g. Cartesian grid) in conjunction with an explicit time integration scheme (e.g. leap-frog-scheme) leads to compute and memory-efficient algorithms, which are especially adapted for transient field analysis in radio frequency (RF) applications.
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Note that the frequency domain method is not limited to the design of nonsubsampled filter banks (read Feilner, Manuela, Dimitri Van De Ville, and Michael Unser. "An orthogonal family of quincunx wavelets with continuously adjustable order." Image Processing, IEEE Transactions on 14.4 (2005): 499-510.).
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Such equations are usually solved by an iteration procedure, called in this case self-consistent field method. In quantum chemistry, one often represents the Hartree–Fock equation in a non-orthogonal basis set. This particular representation is a generalized eigenvalue problem called Roothaan equations.
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4, pages 555–570 (1961). doi:10.1016/0041-5553(63)90168-X The basic idea is to perform a QR decomposition, writing the matrix as a product of an orthogonal matrix and an upper triangular matrix, multiply the factors in the reverse order, and iterate.
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For a symmetric matrix A, upon convergence, AQ = QΛ, where Λ is the diagonal matrix of eigenvalues to which A converged, and where Q is a composite of all the orthogonal similarity transforms required to get there. Thus the columns of Q are the eigenvectors.
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Orthogonal persistence is widely adopted in operating systems for hibernation and in platform virtualization systems such as VMware and VirtualBox for state saving. Research prototype languages such as PS-algol, Napier88, Fibonacci and pJama, successfully demonstrated the concepts along with the advantages to programmers.
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Temperature gradient of tool, workpiece and chip during orthogonal cutting. As can easily be seen, heat is removed from the workpiece and the tool to the chip. Crater wear occurs around the 720 degree area of the tool. At high temperature zones crater wear occurs.
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The moment problem for the Stieltjes–Wigert polynomials is indeterminate; in other words, there are many other measures giving the same family of orthogonal polynomials (see Krein's condition). Koekoek et al. (2010) give in Section 14.27 a detailed list of the properties of these polynomials.
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It is further subdivided into three groups: isometric, dimetric and trimetric projection, depending on the exact angle at which the view deviates from the orthogonal. A typical characteristic of axonometric projection (and other pictorials) is that one axis of space is usually displayed as vertical.
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When working in the schematic domain, we usually only work with front end of line (FEOL) process corners as these corners will affect the performance of devices. But there is an orthogonal set of process parameters that affect back end of line (BEOL) parasitics.
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It also becomes possible to use other groups to make this construction. To do this, fix an inner product on . Over , one replaces by the orthogonal group , and by restricting to orthonormal frames, one gets the identity :. In particular, the dimension of the Grassmannian is .
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Marilyn Janet Breen (born 1944)Birth year from Library of Congress catalog entry, retrieved 2018-12-01. is a professor of mathematics at the University of Oklahoma.Univ. of Oklahoma faculty listing, retrieved 2014-12-21. Her research involves geometry, including visibility and orthogonal polygons.
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New York: Guilford. though there are often small positive correlations between factors. The five factor model in particular has been criticized for losing the orthogonal structure between factors. Hans Eysenck has argued that fewer factors are superior to a larger number of partly related ones.
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Such a device may be part of a VSAT antenna feed or a terrestrial microwave radio feed; for example, OMTs are often used with a feed horn to isolate orthogonal polarizations of a signal and to transfer transmit and receive signals to different ports.
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Because the Rindler observers are vorticity-free, they are also hypersurface orthogonal. The orthogonal spatial hyperslices are \scriptstyle t \;=\; t_0; these appear as horizontal half-planes in the Rindler chart and as half-planes through \scriptstyle T \;=\; X \;=\; 0 in the Cartesian chart (see the figure above). Setting \scriptstyle dt \;=\; 0 in the line element, we see that these have the ordinary Euclidean geometry, \scriptstyle d\sigma^2 \;=\; dx^2 \,+\, dy^2 \,+\, dz^2,\; \forall x\,>\,0,\; \forall y,\, z. Thus, the spatial coordinates in the Rindler chart have a very simple interpretation consistent with the claim that the Rindler observers are mutually stationary.
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A new pattern of spectral sidebands was first experimentally observed on the polarization-resolved soliton spectra of the polarization-locked vector solitons of fiber lasers. The new spectral sidebands are characterized by the fact that their positions on the soliton's spectrum vary with the strength of the linear cavity birefringence, and while one polarization component's sideband has a spectral peak, the orthogonal polarization component has a spectral dip, indicating the energy exchange between the two orthogonal polarization components of the vector solitons. Numeric simulations also confirmed that the formation of the new type of spectral sidebands was caused by the FWM between the two polarization components.H. Zhang et al.
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The result is less water loss by the plant. The natural response by the plant using abscisic acid to bind PYR1 in drought conditions is not strong enough and is activated too late to significantly hinder crop yield loss. Abscisic acid is also currently too expensive to synthesize to be used as a spray to control drought response artificially on a mass scale. The ability to control this externally by spraying the PYR1MANDI (orthogonal receptor) with mandipropamid (orthogonal ligand and fungicide) has the potential to reduce crop yield loss during droughts in plants with these engineered receptors, and has been confirmed to work in canola.
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Subgroups of the projective orthogonal group correspond to subgroups of the orthogonal group that contain -I (that have central symmetry). As always with a quotient map (by the lattice theorem), there is a Galois connection between subgroups of O and PO, where the adjunction on O (given by taking the image in PO and then the preimage in O) simply adds -I if absent. Of particular interest are discrete subgroups, which can be realized as symmetries of projective polytopes – these correspond to the (discrete) point groups that include central symmetry. Compare with discrete subgroups of the Spin group, particularly the 3-dimensional case of binary polyhedral groups.
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An additive view of this group arises from consideration of hyperbolic sectors and their hyperbolic angles. From the point of view of the classical groups, the group of squeeze mappings is , the identity component of the indefinite orthogonal group of 2 × 2 real matrices preserving the quadratic form . This is equivalent to preserving the form via the change of basis :x=u+v,\quad y=u-v\,, and corresponds geometrically to preserving hyperbolae. The perspective of the group of squeeze mappings as hyperbolic rotation is analogous to interpreting the group (the connected component of the definite orthogonal group) preserving quadratic form as being circular rotations.
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Michael Korenberg of Queen's University in Kingston, Ontario, developed a method for choosing a sparse set of components from an over-complete set, such as sinusoidal components for spectral analysis, called fast orthogonal search (FOS). Mathematically, FOS uses a slightly modified Cholesky decomposition in a mean-square error reduction (MSER) process, implemented as a sparse matrix inversion. As with the other LSSA methods, FOS avoids the major shortcoming of discrete Fourier analysis, and can achieve highly accurate identifications of embedded periodicities and excels with unequally spaced data; the fast orthogonal search method has also been applied to other problems such as nonlinear system identification.
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The sockets are offset from the angled arms of the valve body, which branch at roughly 45 degrees from the neck thread axis in the same plane. The connection socket axes are orthogonal to the plane of the arms, and the valve spindles are orthogonal to their outlets and the axis of each arm, with the knobs to the outsides. The most commonly used cylinder valve type is the single outlet plain valve, sometimes known as a "K" valve, which allows connection of a single regulator, and has no reserve function. It simply opens to allow gas flow, or closes to shut it off.
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A Neel wall is a narrow transition region between magnetic domains, named after the French physicist Louis Neel. In the Neel wall, the magnetization smoothly rotates from the direction of magnetization within the first domain to the direction of magnetization within the second. In contrast to Bloch walls, the magnetization rotates about a line that is orthogonal to the normal of the domain wall (in other words, it rotates such that it points out of the domain wall plane in a 3D system). It consists of a core with fast varying rotation (where the magnetization points nearly orthogonal to the two domains) and two tails where the rotation logarithmically decays.
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If is a polarity of a finite projective plane (which need not be desarguesian), , of order then the number of its absolute points (or absolute lines), is given by: : , where is a non- negative integer. Since is an integer, if is not a square, and in this case, is called an orthogonal polarity. R. Baer has shown that if is odd, the absolute points of an orthogonal polarity form an oval (that is, points, no three collinear), while if is even, the absolute points lie on a non-absolute line. In summary, von Staudt conics are not ovals in finite projective planes (desarguesian or not) of even order.
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If the two circles α and β cross each other, then their two circles of antisimilitude each pass through both crossing points, and bisect the angles formed by the arcs of α and β as they cross. If a circle γ crosses circles α and β at equal angles, then γ is crossed orthogonally by one of the circles of antisimilitude of α and β; if γ crosses α and β in supplementary angles, it is crossed orthogonally by the other circle of antisimilitude, and if γ is orthogonal to both α and β then it is also orthogonal to both circles of antisimilitude.
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There are 665 orbits of vectors v of norm –4, corresponding to the 665 isomorphism classes of 25-dimensional unimodular lattices L. In this correspondence, the index 2 sublattice of the even vectors of the lattice L is isomorphic to the orthogonal complement of the vector v.
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This is shown in Figure 3. Figure 2 shows non-orthogonal grids. The figure shows the grid lines do not intersect at 90 degree angle. In both these cases the domain boundaries coincide with the co ordinate lines therefore all the geometrical details can be incorporated.
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White moves first. During their turn, players move one of their pieces either one or two spaces in any direction. Diagonal distances are equivalent to orthogonal distances, i.e. it is legal to move to a square whose relative position is two squares away both vertically and horizontally.
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Invagination can be referenced as one of the steps of the establishment of the body plan. The term, originally used in embryology, has been adopted in other disciplines as well. There is more than one type of movement for invagination. Two common types are axial and orthogonal.
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A smooth parallel coordinate plot is achieved with splines. In the smooth plot, every observation is mapped into a parametric line (or curve), which is smooth, continuous on the axes, and orthogonal to each parallel axis. This design emphasizes the quantization level for each data attribute.
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These earthquakes have a complex rupture process. The rupture of these earthquakes occurred on multiple, almost orthogonal faults. This is rare in a single earthquake. This earthquake had an overall relatively slow rupture speed, although the speed was above the S-wave velocity in some fault segments.
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Gábor Szegő () (January 20, 1895 - August 7, 1985) was a Hungarian-American mathematician. He was one of the foremost mathematical analysts of his generation and made fundamental contributions to the theory of orthogonal polynomials and Toeplitz matrices building on the work of his contemporary Otto Toeplitz.
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Benjamin Olinde Rodrigues (6 October 1795 – 17 December 1851), more commonly known as Olinde Rodrigues, was a French banker, mathematician, and social reformer. In mathematics Rodrigues is remembered for Rodrigues' rotation formula for vectors, the Rodrigues formula about series of orthogonal polynomials and the Euler–Rodrigues parameters.
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17K Family is a 4-bit single-chip microcontroller, especially dedicated for DTS (Digital Tuning Systems) and remote controls. It has 2 plane of 128× 4-bit register files, and sophisticated fully orthogonal instruction set. This instruction set is completely different from that of 78K Family.
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Note that any pair of studentized residual ti and tj (where i eq j), are NOT i.i.d. They have the same distribution, but are not independent due to constraints on the residuals having to sum to 0 and to have them be orthogonal to the design matrix.
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In this manner, Sylvester constructed Hadamard matrices of order 2k for every non-negative integer k.J.J. Sylvester. Thoughts on inverse orthogonal matrices, simultaneous sign successions, and tessellated pavements in two or more colours, with applications to Newton's rule, ornamental tile-work, and the theory of numbers.
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Orthogonal projection onto a line, , is a linear operator on the plane. This is an example of an endomorphism that is not an automorphism. In mathematics, an endomorphism is a morphism from a mathematical object to itself. An endomorphism that is also an isomorphism is an automorphism.
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However, orthographic and orthogonal more correctly refer to the right angle formed between the projection rays and the projection plane, versus the angle formed between the subject of the drawing and the projection plane. Thus, orthographic projections include axonometric or auxiliary views in addition to multiviews.
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Where the obliquity of the SWIR increases so does its length. This lengthening results in a decrease in mantle upwelling and a ridge geometry characteristic of ultra-slow spreading ridges (<12 mm/yr). The orthogonal supersegment is similar to larger ridge segments of the Mid- Atlantic Ridge.
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In the case of function spaces, families of orthogonal functions are used to form a basis. By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in other fields including art and chemistry.
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Orthogonality and rotation of coordinate systems compared between left: Euclidean space through circular angle ϕ, right: in Minkowski spacetime through hyperbolic angle ϕ (red lines labelled c denote the worldlines of a light signal, a vector is orthogonal to itself if it lies on this line).
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The cross product in relation to the exterior product. In red are the orthogonal unit vector, and the "parallel" unit bivector. The cross product can be defined in terms of the exterior product. It can be generalized to an external product in other than three dimensions.
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There are a variety of Hare game boards. The more common one is a two-ended spearhead-like board with orthogonal and diagonal lines running through it. Three pieces representing the hounds are of one color, and one piece representing the hare is of another color.
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Conversely, there is an affine geometry based on any given skew field k. Axioms 4a and 4b are equivalent to Desargues' theorem. When Pappus's hexagon theorem holds in the affine geometry, k is commutative and hence a field. Chapter three is titled "Symplectic and Orthogonal Geometry".
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Dimensions and Principles of Declassification. In Proc. of the IEEE Computer Security Foundations Workshop, 2005. Information declassification constructs can be classified in four orthogonal dimensions: What information is released, Who is authorized to access the information, Where the information is released, and When is the information released.
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In mathematics, Gegenbauer polynomials or ultraspherical polynomials C(x) are orthogonal polynomials on the interval [−1,1] with respect to the weight function (1 − x2)α–1/2. They generalize Legendre polynomials and Chebyshev polynomials, and are special cases of Jacobi polynomials. They are named after Leopold Gegenbauer.
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The conductivity parallel to an electric field E is called Pedersen conductivity. The conductivity orthogonal to E and the geomagnetic field Bo is the Hall conductivity. Ohmic losses and thus Joule heating occur when Pedersen currents flow. The component parallel to Bo still increases with altitude.
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In Deming regression, a type of linear curve fitting, if the dependent and independent variables have equal variance this results in orthogonal regression in which the degree of imperfection of the fit is measured for each data point as the perpendicular distance of the point from the regression line.
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In another approach the preserved one-dimensional trait is the orthogonal direction. This gives rise for the notion of polyhedral terrain in three dimensions: a polyhedral surface with the property that each vertical (i.e., parallel to Z axis) line intersects the surface at most by one point or segment.
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The quotient group R/Z is isomorphic to the circle group, the group of complex numbers of absolute value 1 under multiplication, or correspondingly, the group of rotations in 2D about the origin, that is, the special orthogonal group SO(2). An isomorphism is given by (see Euler's identity).
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These are precisely the transformations which preserve lengths and angles. Finally, if we impose both restrictions, then we get the special orthogonal group SO(n), which consists of rotations only. These groups are our first examples of infinite non-abelian groups. They are also happen to be Lie groups.
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10110 It is quite common for spheroidal weathering, a form of chemical weathering, to occur as groundwater circulates through orthogonal joint sets in the near-surface.D. T. Nicholson, "Speroidal weathering." In S.A. Goudie, ed., Encyclopedia of Geomorphology, volume 2 J–Z (Routledge New York, New York, 2004, ), p.
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My Darling is a town in Capricorn District Municipality in the Limpopo province of South Africa. It is located northwest of the Makgabeng Plateau, known for Hananwa rock art. It is also located south of the Kingdom of Mapungubwe. My Darling is planned on an orthogonal street system.
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This is only unambiguous on purely orthogonal or diagonal atoms. In a later article on bent riders Betza introduced a way to glue moves corresponding to different board steps into a single trajectory: t[FR] would mean start as F, then continue as rook (in the outward directions).
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Since independence, Colonia del Sacramento has expanded to the north and east, but the original Bairro Histórico (historic quarter in Portuguese or Barrio Histórico, current Spanish spelling) retains its irregular, terrain-fitting street plan built by the Portuguese, contrasting with the wider, orthogonal calles in the newer Spanish area.
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The three orthogonal components, (green), (red), and (blue), each increasing at a constant rate. The point is at the intersection between the three colored surfaces. In concrete situations, and in many mathematical illustrations, a positive angular coordinate is measured counterclockwise as seen from any point with positive height.
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909x909px An example of orthogonal ligand-receptor interfaces are RASSL and DREADD. They are G protein-coupled receptors that are activated by synthesized ligands that wouldn't normally exist in the cell, such as the anti-psychotic Clozapine, allowing researchers to control the interaction externally and independent of internal activation.
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The notion of compressor/decompressor states is orthogonal to the operational modes. Whatever the mode is, both the compressor and the decompressor work in one of their three states. They are basically finite state machines. Every incoming packet may cause the compressor/decompressor to change its internal state.
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A simple rotation about a rotation centre leaves an entire plane through (axis-plane) fixed. Every plane that is completely orthogonal to intersects in a certain point . Each such point is the centre of the 2D rotation induced by in . All these 2D rotations have the same rotation angle .
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Stainless steel bifilar sundial in Italy Invented by the German mathematician Hugo Michnik in 1922, the bifilar sundial has two non-intersecting threads parallel to the dial. Usually the second thread is orthogonal to the first. The intersection of the two threads' shadows gives the local solar time.
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M. H. Mohamed and Z.-H. Zhang, "Method of Forming Variable Cross-Sectional Shaped Three- Dimensional Fabrics". US Patent 5085252, 4 February 1992. The architecture of the 3D orthogonal woven fabric consists of three different sets of yarns; warp yarns (y-yarn), weft yarns (x-yarn), and (z-yarn).
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The number theoretic Hilbert transform is an extension () of the discrete Hilbert transform to integers modulo an appropriate prime number. In this it follows the generalization of discrete Fourier transform to number theoretic transforms. The number theoretic Hilbert transform can be used to generate sets of orthogonal discrete sequences().
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If it is −1, the basis has the opposite orientation. More generally, if the determinant of A is positive, A represents an orientation-preserving linear transformation (if A is an orthogonal or matrix, this is a rotation), while if it is negative, A switches the orientation of the basis.
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An element e in E is called an idempotent if e2 = e. Two idempotents are said to be orthogonal if ef = 0. This is equivalent to orthogonality with respect to the inner product, since (ef,ef) = (e,f). In this case g = e + f is also an idempotent.
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Many simplified approximations are available for analysing and designing optical systems. Most of these use a single scalar quantity to represent the electric field of the light wave, rather than using a vector model with orthogonal electric and magnetic vectors.M. Born and E. Wolf (1999). Principle of Optics.
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The converses are not true, and the above switches between "left" and "right" are not typos. Whether the ACCP holds on the right or left side of R, it implies that R has no infinite set of nonzero orthogonal idempotents, and that R is a Dedekind finite ring.
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The Hawking energy or Hawking mass is one of the possible definitions of mass in general relativity. It is a measure of the bending of ingoing and outgoing rays of light that are orthogonal to a 2-sphere surrounding the region of space whose mass is to be defined.
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Database Programming & Design. San Francisco, CA: Miller-Freeman. #a new design principle (with C. J. Date) now known as the Principle of Orthogonal Design (POOD) His work on logic applied to relational databases and on design without nulls (1993) has been republished several times.McGoveran, D., (Dec.1993-Mar.
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Put another way, the uncertainty in information carried by this wavelet is minimized. However they have the downside of being non-orthogonal, so efficient decomposition into the basis is difficult. Since their inception, various applications have appeared, from image processing to analyzing neurons in the human visual system.
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Mashuga 1998Crowl 2003 The same information can be depicted in a normal orthogonal diagram, showing only two substances, implicitly using the feature that the sum of all three components is 100 percent. The diagrams below only concerns one fuel; the diagrams can be generalized to mixtures of fuels.
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Of course, orthogonality is a property that must be verified. Efficient (linear) algorithms have been developed to verify that origami matrices (or tensors/n-dimensional arrays) are orthogonal. The significance of orthogonality is one of view consistency. Aggregating (contracting) along a particular dimension offers a 'view' of a program.
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Due to the nature of hyperbolic curves, a particular combination of a primary and two secondary stations can possibly result in a "grid" where the grid lines intersect at shallow angles. For ideal positional accuracy, it is desirable to operate on a navigational grid where the grid lines are closer to right angles (orthogonal) to each other. As the receiver travels through a chain, a certain selection of secondaries whose TD lines initially formed a near-orthogonal grid can become a grid that is significantly skewed. As a result, the selection of one or both secondaries should be changed so that the TD lines of the new combination are closer to right angles.
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Before entering the orthogonal acceleration region or the pulser, the ions produced in continuous (ESI) or pulsed (MALDI) sources are focused (cooled) into a beam of 1–2 mm diameter by collisions with a residual gas in RF multipole guides. A system of electrostatic lenses mounted in high-vacuum region before the pulser makes the beam parallel to minimize its divergence in the direction of acceleration. The combination of ion collisional cooling and orthogonal acceleration TOF Dodonov, A. F., Chernushevich, I. V., Dodonova, T. F., Raznikov, V. V., Tal’rose, V. L. Inventor’s Certificate No. 1681340A1, USSR, February 25, 1987.A.F. Dodonov, I.V. Chernushevich and V.V. Laiko, Time-of-Flight Mass Spectrometry (1994) ACS Symposium Series 549, Chap. VII.
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When mobile-to-base links cannot be precisely coordinated, particularly due to the mobility of the handsets, a different approach is required. Since it is not mathematically possible to create signature sequences that are both orthogonal for arbitrarily random starting points and which make full use of the code space, unique "pseudo-random" or "pseudo-noise" sequences called spreading sequences are used in asynchronous CDMA systems. A spreading sequence is a binary sequence that appears random but can be reproduced in a deterministic manner by intended receivers. These spreading sequences are used to encode and decode a user's signal in asynchronous CDMA in the same manner as the orthogonal codes in synchronous CDMA (shown in the example above).
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Proponents of the Big Five and the HEXACO model of personality structure respectively have argued that the dimensions of these models are orthogonal and irreducible and that Digman's two higher-order factors are not valid. They argued that intercorrelations between personality factors of the Big Five and the HEXACO model can be explained due to lower order traits that represent blends of otherwise orthogonal factors, and that postulating higher-order factors is unnecessary. For example, interpersonal warmth blends both extraversion and agreeableness. Costa and McCrae pointed out that in an analysis of three different personality scales designed to assess five factor model traits, Digman's two-factor solution could not be replicated across these instruments.
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Studying signal transduction pathways and attempting to identify the action of proteins involved in these pathways is difficult due to the abundance and complexity of interactions, families of proteins with the same or similar action, and the relative a lack of selectivity for substrates (a good example of which are protein kinases). A method has been developed to use a radioactively labeled ATP orthogonal analog with an orthogonal kinase that uses the ATP analog to phosphorylate its substrates, allowing for identification of its targets within the pathway by the radioactive label that it will add the target. Variations on this approach can be used to identify the function of signal transduction proteins whose function remains undetermined.
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1–3 attempt to break the problem into two orthogonal problems and deal with each separately in order to reduce the feedback sampling bandwidth over that of 1D DPD (hopefully to that of MDDPD). They break the application of the pre-distortion and model extraction into in- band and interband systems. It is stated that correction of interband inter- modulation distortion (IMD) generates inband IMD and that if the fully orthogonal polynomials are applied properly this will no longer be the case. It appears that this approach in essence is trying to make (()) and (()) into (()) and (()) as the orthogonality of the inband and interband coefficients is guaranteed if the polynomials are properly derived and applied as in (()) and (()).
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A densely defined operator T is symmetric, if the subspace (defined in a previous section) is orthogonal to its image under J (where J(x,y):=(y,-x)).Follows from and the definition via adjoint operators. Equivalently, an operator T is self-adjoint if it is densely defined, closed, symmetric, and satisfies the fourth condition: both operators , are surjective, that is, map the domain of T onto the whole space H. In other words: for every x in H there exist y and z in the domain of T such that and . An operator T is self-adjoint, if the two subspaces , are orthogonal and their sum is the whole space H \oplus H .
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Multipole moments in mathematics and mathematical physics form an orthogonal basis for the decomposition of a function, based on the response of a field to point sources that are brought infinitely close to each other. These can be thought of as arranged in various geometrical shapes, or, in the sense of distribution theory, as directional derivatives. Multipole expansions are related to the underlying rotational symmetry of the physical laws and their associated differential equations. Even though the source terms (such as the masses, charges, or currents) may not be symmetrical, one can expand them in terms of irreducible representations of the rotational symmetry group, which leads to spherical harmonics and related sets of orthogonal functions.
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In the case that the eigenspace for eigenvalue 1 is the orthogonal complement of that for eigenvalue −1, i.e., every eigenvector with eigenvalue 1 is orthogonal to every eigenvector with eigenvalue −1, such an affine involution is an isometry. The two extreme cases for which this always applies are the identity function and inversion in a point. The other involutive isometries are inversion in a line (in 2D, 3D, and up; this is in 2D a reflection, and in 3D a rotation about the line by 180°), inversion in a plane (in 3D and up; in 3D this is a reflection in a plane), inversion in a 3D space (in 3D: the identity), etc.
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Many variations of the basic problem can be considered. Alan Hartman solves a problem of this type with the requirement that no trio walks in a row of four more than once using Steiner quadruple systems. More recently a similar problem known as the Social Golfer Problem has gained interest that deals with 32 golfers who want to get to play with different people each day in groups of 4, over the course of 10 days. As this is a regrouping strategy where all groups are orthogonal, this process within the problem of organising a large group into smaller groups where no two people share the same group twice can be referred to as orthogonal regrouping.
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In a series of four papers between 2010 and 2012, Jean-Loup Waldspurger proved the local Gan–Gross–Prasad conjecture for tempered representations of special orthogonal groups over p-adic fields. In 2012, Colette Moeglin and Waldspurger then proved the local Gan–Gross–Prasad conjecture for generic non-tempered representations of special orthogonal groups over p-adic fields. In his 2013 thesis, Raphaël Beuzart-Plessis proved the local Gan–Gross–Prasad conjecture for the tempered representations of unitary groups in the p-adic Hermitian case under the same hypotheses needed to establish the local Langlands conjecture. Hongyu He proved the Gan-Gross- Prasad conjectures for discrete series representations of the real unitary group U(p,q).
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A tensor whose components in an orthonormal basis are given by the Levi-Civita symbol (a tensor of covariant rank ) is sometimes called a permutation tensor. Under the ordinary transformation rules for tensors the Levi-Civita symbol is unchanged under pure rotations, consistent with that it is (by definition) the same in all coordinate systems related by orthogonal transformations. However, the Levi-Civita symbol is a pseudotensor because under an orthogonal transformation of Jacobian determinant −1, for example, a reflection in an odd number of dimensions, it should acquire a minus sign if it were a tensor. As it does not change at all, the Levi-Civita symbol is, by definition, a pseudotensor.
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The close connections between Fourier analysis, the periodogram, and least-squares fitting of sinusoids have long been known. Most developments, however, are restricted to complete data sets of equally spaced samples. In 1963, Freek J. M. Barning of Mathematisch Centrum, Amsterdam, handled unequally spaced data by similar techniques, including both a periodogram analysis equivalent to what is now referred to the Lomb method, and least-squares fitting of selected frequencies of sinusoids determined from such periodograms, connected by a procedure that is now known as matching pursuit with post-backfitting or orthogonal matching pursuit.Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad, "Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition," in Proc.
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The seamount splits an old peridotite block, the remains of which project on either side of the ridge, and fills the rift valley in between, resulting in a double-peaked volcano sitting on the SWIR. East of the seamount (11°30'-10°24'E) there is a 180 km-long and 4,200 m-deep amagmatic segment. Reaching a maximum depth of 4,700 m, its deepest part has a rough floor void of signs of recent volcanism but filled with irregular horst blocks partially made of serpentinised peridotite. The "orthogonal supersegment" (16 to 25°E), in contrast, is almost perfectly orthogonal relative to the spreading direction and is composed of magmatic accretionary segments linked by short non-transform offsets.
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In a M-ary signaling system like MFSK, an "alphabet" of M tones is established and the transmitter selects one tone at a time from the alphabet for transmission. M is usually a power of 2, so each tone transmission from the alphabet represents log2 M data bits. MFSK is classed as an M-ary orthogonal signaling scheme because each of the M tone detection filters at the receiver responds only to its tone and not at all to the others; this independence provides the orthogonality. Like other M-ary orthogonal schemes, the required Eb/N0 ratio for a given probability of error decreases as M increases without the need for multisymbol coherent detection.
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The property of completeness is crucial in advanced treatments and applications of quantum mechanics. For instance, the existence of projection operators or orthogonal projections relies on the completeness of the space. These projection operators, in turn, are essential for the statement and proof of many useful theorems, e.g. the spectral theorem.
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In mathematics, the Mostow–Palais theorem is an equivariant version of the Whitney embedding theorem. It states that if a manifold is acted on by a compact Lie group with finitely many orbit types, then it can be embedded into some finite-dimensional orthogonal representation. It was introduced by and .
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Steinberg, p.58 Broadway, an existing road, was not included in the 1811 plan, and was added to the grid later. The plan also called for 155 orthogonal cross streets. The location of the cross streets was fixed at the boundaries of parcels into which the land had previously been divided.
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In this case, if the vector has the norm 1, then is just the probability that the quantum system resides in the state . It defines a discrete probability distribution on . if and only if is the same quantum state as . if and only if and are orthogonal (see inner product space).
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Variation becomes even more central in Taguchi's thinking. Taguchi proposed extending each experiment with an "outer array" (possibly an orthogonal array); the "outer array" should simulate the random environment in which the product would function. This is an example of judgmental sampling. Many quality specialists have been using "outer arrays".
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A laser accelerometer comprises a frame having three orthogonal input axes and multiple proof masses, each proof mass having a predetermined blanking surface. A flexible beam supports each proof mass. The flexible beam permits movement of the proof mass on the input axis. A laser light source provides a light ray.
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William Shieh is an electrical engineer at the University of Melbourne in Glen Waverley, Victoria, Australia. He was named a Fellow of the Institute of Electrical and Electronics Engineers in 2013 for his contributions to coherent optical orthogonal frequency-division multiplexing. He was also made a Fellow of the Optical Society.
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Any element of the group O(3,2) of orthogonal transformations of R3,2 maps any one-dimensional subspace of null vectors in R3,2 to another such subspace. Hence the group O(3,2) acts on the Lie quadric. These transformations of cycles are called "Lie transformations". They preserve the incidence relation between cycles.
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The thermal Hall effect is the thermal analog of the Hall effect. Here, a thermal gradient is produced across a solid instead of an electric field. When a magnetic field is applied, an orthogonal temperature gradient develops. For conductors, a significant portion of the thermal current is carried by the electrons.
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By definition, the standard basis is a sequence of orthogonal unit vectors. In other words, it is an ordered and orthonormal basis. However, an ordered orthonormal basis is not necessarily a standard basis. For instance the two vectors representing a 30° rotation of the 2D standard basis described above, i.e.
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BMC encoding on BPSK modulation allows synchronizing the listening of the carrier on a specific Responder or Controller signal, rejecting all other signals as noise. The listener device can also have two listening channels with synchronized sampling at 90° (phase quadrature) and help to distinguish even signals with orthogonal interference.
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An oblique coordinate system is one in which the axes are not necessarily orthogonal to each other; that is, they meet at angles other than right angles. When using coordinate transformations as described above, the new coordinate system will often appear to have oblique axes compared to the old system.
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Improved N(α)-acetylated peptide enrichment following dimethyl labeling and SCX J. Proteom. Res. 12, 3277–3287 (2013). Additional orthogonal chromatography treatments change the biochemical character of the peptides for further enrichment before final LC-MS/MS analysis. Groups have continued to adapt and improve this technology for protease-substrate discovery.
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This work was the subject of Henri Lebesgue's lectures in 1938. Later Bricard discovered notable 6-bar linkages.K. Wohlhart, The two types of the orthogonal Bricard linkage, Mechanism and machine theory, vol. 28 (1993), 809-817.. Bricard also gave one of the first geometric proofs of Morley's trisector theorem in 1922.
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They can be complex numbers, as in a complex exponential plane wave. When the values of F are vectors, the wave is said to be a longitudinal wave if the vectors are always collinear with the vector \vec n, and a transverse wave if they are always orthogonal (perpendicular) to it.
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Nobel lecture of R. A. Zsigmondy: Properties of colloids (including a short explanation of the ultramicroscope) The first application of this illumination scheme for fluorescence microscopy was published in 1993 by Voie et al. under the name orthogonal-plane fluorescence optical sectioning (OPFOS). for imaging of the internal structure of the cochlea.
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A horizon sensor is an optical instrument that detects light from the 'limb' of Earth's atmosphere, i.e., at the horizon. Thermal infrared sensing is often used, which senses the comparative warmth of the atmosphere, compared to the much colder cosmic background. This sensor provides orientation with respect to Earth about two orthogonal axes.
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Beam-splitting polarizers split the incident beam into two beams of differing linear polarization. For an ideal polarizing beamsplitter these would be fully polarized, with orthogonal polarizations. For many common beam-splitting polarizers, however, only one of the two output beams is fully polarized. The other contains a mixture of polarization states.
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The strict orthogonal geometry forces roads and lots over creeks, marshes, and woodlots, thus disturbing the local ecology. It is said of the 1811 NY grid plan that it flattened all obstacles in its way. By contrast, the unconstrained geometry of the Radburn-type networks provides sufficient flexibility to accommodate natural features.
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The N-terminal catalytic domain and the C-terminal zinc finger straddle the DNA with the long axis of the protein oriented roughly orthogonal to the helical axis of the DNA. Residues that contact DNA are located in the catalytic domain and in a beta-hairpin loop formed by the zinc finger.
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Orthogonal arrays played a central role in the development of Taguchi methods by Genichi Taguchi, which took place during his visit to Indian Statistical Institute in the early 1950s. His methods were successfully applied and adopted by Japanese and Indian industries and subsequently were also embraced by US industry albeit with some reservations.
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For , Spin(n) is simply connected and thus the universal covering group for . By far the most famous example of a spin group is , which is nothing but , or the group of unit quaternions. The Pin and Spin groups are found within Clifford algebras, which themselves can be built from orthogonal matrices.
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This scenario is called a brane cosmology. The force of gravity is not due to open strings; the gravitons which carry gravitational forces are vibrational states of closed strings. Because closed strings do not have to be attached to D-branes, gravitational effects could depend upon the extra dimensions orthogonal to the brane.
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In 2002 a new method was published called orthogonal projections to latent structures (OPLS). In OPLS, continuous variable data is separated into predictive and uncorrelated information. This leads to improved diagnostics, as well as more easily interpreted visualization. However, these changes only improve the interpretability, not the predictivity, of the PLS models.
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However, once you know the first n − 1 components, the constraint tells you the value of the nth component. Therefore, this vector has n − 1 degrees of freedom. Mathematically, the first vector is the orthogonal, or least-squares, projection of the data vector onto the subspace spanned by the vector of 1's.
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The N-terminal has a multi-helical structure that forms an orthogonal bundle. The C-terminal domain contains an ATP-binding site and is therefore probably the site of ATP hydrolysis. In eukaryotes, helicase function is provided by the MCM (Minichromosome maintenance) complex. The DnaB helicase is the product of the dnaB gene.
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In a more general form, Sylvester's law of inertia says that, when working over an ordered field, the numbers of diagonal elements in the diagonalized form of a matrix that are positive, negative and zero respectively are independent of the chosen orthogonal basis. These three numbers form the signature of the bilinear form.
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Taking a step orthogonal to this hyperplane will allow the search process to cover all the dimensions of the search space. Population size is a fundamental parameter in the performance of population-based heuristics. Larger populations promote exploration, but they also allow fewer generations, and this can reduce the chance of convergence.
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A spherical triangle The area of a spherical triangle on the unit sphere is . The isometry group of the unit sphere in is the orthogonal group , with the rotation group as the subgroup of isometries preserving orientation. It is the direct product of with the antipodal map, sending to ., Chapter II, Spherical geometry.
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17, No. 2, March 1979. and some of the first work using orthogonal collocation methods in engineering can be found in the chemical engineering literature.Cuthrell, J.E. and Biegler, L.T., “Simultaneous Optimization and Solution Methods for Batch Reactor Control Profiles,” Computers and Chemical Engineering, Vol. 13, Nos. 1/2, 1989, pp.49–62.
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An early investor was Austin Ventures. It initially backed the multi-band orthogonal frequency division multiplexing approach taken by the MultiBand OFDM Alliance. A number of competing technologies were discussed by the IEEE 802.15 standards committee in 2004. In October 2005, $20 million in financing included investors Centennial Ventures and Pharos Capital.
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An algebraic proof, based on the variational interpretation of eigenvalues, has been published in Magnus' Matrix Differential Calculus with Applications in Statistics and Econometrics. From the geometric point of view, B'AB can be considered as the orthogonal projection of A onto the linear subspace spanned by B, so the above results follow immediately.
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Wolfgang Hahn (April 30, 1911 – January 10, 1998) was a German mathematician who worked on special functions, in particular orthogonal polynomials. He introduced Hahn polynomials, Hahn difference, Hahn q-addition (or Jackson- Hahn-Cigler q-addition), and the Hahn–Exton q-Bessel function. He was an honorary member of the Austrian Mathematical Society.
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The ALSP protocol is based on a set of orthogonal issues that comprise ALSP's problem space: simulation-to-simulation communication, object management, and time management. These issues are addressed by a layered protocol that has at the top a simulation protocol with underlying simulation/ACM, object management, time management, and event distribution protocols.
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The agricultural development of northern Abitibi and the northern part of Témiscamingue by a relatively homogeneous population of French Canadian Catholic settlers has introduced a mainly rural land development. There, small towns, gravitating around a low density node generally composed of a wooden Roman Catholic church, an elementary school and few houses spread over the territory, according to an orthogonal division on the land, with rectangular parcels. Those small towns are gravitating themselves around a larger city, as La Sarre, Amos, Macamic and Ville-Marie, where major institutional equipments are established. If small towns might seem more or less vernacular, major cities are often more planned and influenced by Anglo-Saxon urban planning, with sometime an orthogonal grid with lane network.
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ONETEP (Order-N Electronic Total Energy Package) is a linear-scaling density functional theory software package able to run on parallel computers. It uses a basis of non-orthogonal generalized Wannier functions (NGWFs) expressed in terms of periodic cardinal sine (psinc) functions, which are in turn equivalent to a basis of plane-waves. ONETEP therefore combines the advantages of the plane-wave approach (controllable accuracy and variational convergence of the total energy with respect to the size of the basis) with computational effort that scales linearly with the size of the system. The ONETEP approach involves simultaneous optimization of the density kernel (a generalization of occupation numbers to non-orthogonal basis, which represents the density matrix in the basis of NGWFs) and the NGWFs themselves.
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In other words, asynchronous CDMA is ideally suited to a mobile network where large numbers of transmitters each generate a relatively small amount of traffic at irregular intervals. CDM (synchronous CDMA), TDMA, and FDMA systems cannot recover the underutilized resources inherent to bursty traffic due to the fixed number of orthogonal codes, time slots or frequency channels that can be assigned to individual transmitters. For instance, if there are N time slots in a TDMA system and 2N users that talk half of the time, then half of the time there will be more than N users needing to use more than N time slots. Furthermore, it would require significant overhead to continually allocate and deallocate the orthogonal-code, time-slot or frequency-channel resources.
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PCA of a multivariate Gaussian distribution centered at (1,3) with a standard deviation of 3 in roughly the (0.866, 0.5) direction and of 1 in the orthogonal direction. The vectors shown are the eigenvectors of the covariance matrix scaled by the square root of the corresponding eigenvalue, and shifted so their tails are at the mean. The principal components of a collection of points in a real p-space are a sequence of p direction vectors, where the i^{th} vector is the direction of a line that best fits the data while being orthogonal to the first i-1 vectors. Here, a best-fitting line is defined as one that minimizes the average squared distance from the points to the line.
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Depending on the field of application, it is also named the discrete Karhunen–Loève transform (KLT) in signal processing, the Hotelling transform in multivariate quality control, proper orthogonal decomposition (POD) in mechanical engineering, singular value decomposition (SVD) of X (Golub and Van Loan, 1983), eigenvalue decomposition (EVD) of XTX in linear algebra, factor analysis (for a discussion of the differences between PCA and factor analysis see Ch. 7 of Jolliffe's Principal Component Analysis),Jolliffe I.T. Principal Component Analysis, Series: Springer Series in Statistics, 2nd ed., Springer, NY, 2002, XXIX, 487 p. 28 illus. Eckart–Young theorem (Harman, 1960), or empirical orthogonal functions (EOF) in meteorological science, empirical eigenfunction decomposition (Sirovich, 1987), empirical component analysis (Lorenz, 1956), quasiharmonic modes (Brooks et al.
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Non-clonability can be seen as a property of arbitrary sets of quantum states. If we know that a system's state is one of the states in some set S, but we do not know which one, can we prepare another system in the same state? If the elements of S are pairwise orthogonal, the answer is always yes: for any such set there exists a measurement which will ascertain the exact state of the system without disturbing it, and once we know the state we can prepare another system in the same state. On the other hand, if S contains a pair of elements that are not pairwise orthogonal, then an argument like that given above shows that the answer is no.
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This section is composed of orthogonal magmatic accretionary segments linked by oblique amagmatic accretionary segments. The oblique portion of this area (9 to 16°E), the "oblique supersegment" is highly variable in axial orientation, ranging from orthogonal to 56°, and its series of magmatic and amagmatic segments results in abruptly fluctuating magmatism and ultra-slow spreading. West of a discontinuity at 16°E axial depth drops 500 m and there is an abrupt change in morphology and magnetism. In the western end of this area (9°30'–11°45') a short magmatic ridge segment intersects the Shaka FZ. The rough topography here obscures the SWIR which runs into the western flank of the Joseph Mayes Seamount, one of few volcanic centres along the oblique supersegment.
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To present a stereoscopic motion picture, two images are projected superimposed onto the same screen through orthogonal polarizing filters (Usually at 45 and 135 degrees).Make Your own Stereo Pictures Julius B. Kaiser The Macmillan Company 1955 page 271 The viewer wears linearly polarized eyeglasses which also contain a pair of orthogonal polarizing filters oriented the same as the projector. As each filter only passes light which is similarly polarised and blocks the orthogonally polarized light, each eye only sees one of the projected images, and the 3D effect is achieved. Linearly polarised glasses require the viewer to keep his or her head level, as tilting of the viewing filters will cause the images of the left and right channels to bleed over to the opposite channel.
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For example, Ronald A. Fisher, Henry B. Mann, and Rosemary A. Bailey applied Abelian groups to the design of experiments. Experimental designs were also studied with affine geometry over finite fields and then with the introduction of association schemes by R. C. Bose. Orthogonal arrays were introduced by C. R. Rao also for experimental designs.
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Any two polar circles of two triangles in an orthocentric system are orthogonal. The polar circles of the triangles of a complete quadrilateral form a coaxal system. A triangle's circumcircle, its nine-point circle, its polar circle, and the circumcircle of its tangential triangle are coaxal.Altshiller-Court, Nathan, College Geometry, Dover Publications, 2007 (orig. 1952).
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Madan Lal Mehta is known for his work on random matrices. His book "Random Matrices" is considered classic in the field. Eugene Wigner cited Mehta during his SIAM review on Random Matrices. Together with Michel Gaudin, Mehta developed the orthogonal polynomial method, a basic tool to study the eigenvalue distribution of invariant matrix ensembles.
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Ahmed I. Zayed is an Egyptian American mathematician. His research interestes include Sampling Theory, Wavelets, Medical Imaging, Fractional Fourier transform，Sinc Approximations, Boundary Value Problems, Special Functions and Orthogonal polynomials, Integral transforms. Zayed is a Professor and Chair of Department of Mathematical Sciences at DePaul University.Full Time Faculty , Department of Mathematical Sciences at DePaul University.
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An example of generalized convexity is orthogonal convexity.Rawlins G.J.E. and Wood D, "Ortho-convexity and its generalizations", in: Computational Morphology, 137-152. Elsevier, 1988. A set in the Euclidean space is called orthogonally convex or ortho-convex, if any segment parallel to any of the coordinate axes connecting two points of lies totally within .
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In the case of three non-collinear points in the plane, the triangle with these points as its vertices has a unique Steiner inellipse that is tangent to the triangle's sides at their midpoints. The major axis of this ellipse falls on the orthogonal regression line for the three vertices.Minda and Phelps (2008), Corollary 2.4.
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The idea of a projection-valued measure is generalized by the positive operator-valued measure (POVM), where the need for the orthogonality implied by projection operators is replaced by the idea of a set of operators that are a non-orthogonal partition of unity. This generalization is motivated by applications to quantum information theory.
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SO(4) is commonly identified with the group of orientation-preserving isometric linear mappings of a 4D vector space with inner product over the real numbers onto itself. With respect to an orthonormal basis in such a space SO(4) is represented as the group of real 4th-order orthogonal matrices with determinant +1.
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The formation of multiple native disulfides remains challenging of native peptide synthesis by solid-phase methods. Random chain combination typically results in several products with nonnative disulfide bonds. Stepwise formation of disulfide bonds is typically the preferred method, and performed with thiol protecting groups. Different thiol protecting groups provide multiple dimensions of orthogonal protection.
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Smolna Street in Warsaw Smolna () is one of the streets of Warsaw's city centre. It is entirely contained in the Śródmieście district, and runs for approximately 400m, orthogonal to the Vistula river. It is a one-way street, running eastwards from Charles de Gaulle roundabout to Jerusalem Avenue, approximately 1km west of the river.
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Sua Ghin Gnua is a two-player abstract strategy board game from Thailand, formerly known as Siam. Another name for the game is Tigers and Oxen. It is a hunt game played on a 5x5 square grid with only orthogonal lines. One player plays the three tigers, and the other player plays the twelve oxen.
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A 5x5 square grid is used consisting of twenty-five intersection points (here-in-forth referred to as "points"). The square grid consists only of orthogonal lines, that is, there are no diagonal lines. It is not an Alquerque board. There are three tiger pieces that are black, and twelve oxen pieces that are white.
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Jessen's icosahedron In Jessen's icosahedron, sometimes called Jessen's orthogonal icosahedron, the 12 isosceles faces are arranged differently so that the figure is non-convex and has right dihedral angles. It is scissors congruent to a cube, meaning that it can be sliced into smaller polyhedral pieces that can be rearranged to form a solid cube.
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Basis function centers can be randomly sampled among the input instances or obtained by Orthogonal Least Square Learning Algorithm or found by clustering the samples and choosing the cluster means as the centers. The RBF widths are usually all fixed to same value which is proportional to the maximum distance between the chosen centers.
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A left hand can be held, as shown in the illustration, so as to represent three mutually orthogonal axes on the thumb, fore finger and middle finger. Each finger is then assigned to a quantity (mechanical force, magnetic field and electric current). The right and left hand are used for generators and motors respectively.
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AK Peters, 2003, , p. 9 In 1846 Arthur Cayley acknowledgedArthur Cayley (1846) "Sur Quelques Proprietes des Determinants Gauches", Crelle's Journal 32: 119–23, and Collected Mathematical Papers of Arthur Cayley, volume 1, page 335 Euler's and Rodrigues' priority describing orthogonal transformations. Rodrigues is credited as originating the idea of the artist as an avant-garde.
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Like principal components analysis, correspondence analysis creates orthogonal components and, for each item in a table, a set of scores (sometimes called factor scores, see Factor analysis). Correspondence analysis is performed on a contingency table, C, of size m×n where m is the number of rows and n is the number of columns.
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Mutation testing was originally proposed by Richard Lipton as a student in 1971,Mutation 2000: Uniting the Orthogonal by A. Jefferson Offutt and Roland H. Untch. and first developed and published by DeMillo, Lipton and Sayward.Richard A. DeMillo, Richard J. Lipton, and Fred G. Sayward. Hints on test data selection: Help for the practicing programmer.
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In an isentropic wave, the speed changes from v to (v + dv), with deflection d \theta. We have oriented the coordinate system orthogonal to the wave. We write the basic (continuity, momentum and 1st, 2nd law of thermodynamics) equations for this infinitesimal control volume. Expansion waves over curved surface Control Volume Analysis Assumptions: # Steady flow.
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The town was built on an old Leipzig road that lined the eastern edge of the small town. The town of Jiřetín belongs to a group of upper towns, founded along the Saxony border. The base of Jiřetín is the exact square of the square from which the regular orthogonal network of streets unfolded.
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The patterns were drawn on nautical charts as a set of hyperbolic lines in the appropriate colour. Receivers identified which hyperbola they were on and a position could be plotted at the intersection of the hyperbola from different patterns, usually by using the pair with the angle of cut closest to orthogonal as possible.
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In particular, some universal bounds are derived for codes and designs in polynomial-type association schemes. In classical coding theory, dealing with codes in a Hamming scheme, the MacWilliams transform involves a family of orthogonal polynomials known as the Krawtchouk polynomials. These polynomials give the eigenvalues of the distance relation matrices of the Hamming scheme.
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Black moves first. # Each piece may move any unobstructed distance along a rank or file (like the rook in chess). # A man is captured if the enemy places a piece adjacent to it on each side in an orthogonal line. Multiple men in a line can be captured together (Kowalski later abandoned this feature).
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In OFDM, the subcarrier frequencies are chosen so that the subcarriers are orthogonal to each other, meaning that crosstalk between the subchannels is eliminated and intercarrier guard bands are not required. This greatly simplifies the design of both the transmitter and the receiver. In conventional FDM, a separate filter for each subchannel is required.
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Fontaine was born in Claveyson. He first got a taste for maths by reading the Géométrie de l'infini of Fontenelle and gave solutions to the problems of the tautochrone curve, the brachistochrone curve and orthogonal trajectories. He was elected a member of the Académie des sciences in 1733. He died, aged 67, in Cuiseaux.
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The new Nazca Plate was then directed into an orthogonal subduction with South America causing ever-since uplift in the Andes, but causing most impact in the Miocene. While the various segments of the Andes have their own uplift histories, as a whole the Andes have risen significantly in last 30 million years (Oligocene–present).
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The third description of the flow field's state is swirl. Swirl is the tangential flow component of the velocity vector. The velocity profile should be referred to as the axial velocity profile. As the velocity vector can be resolved into three mutually orthogonal components, the velocity profile only represents the axial component of velocity. fig.
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It begins with metric structures on vector spaces before defining symplectic and orthogonal geometry and describing their common and special features. There are sections on geometry over finite fields and over ordered fields. Chapter four is on general linear groups. First there is Jean Dieudonne's theory of determinants over "non-commutative fields" (division rings).
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The arrays built in the early 1960s were either cross (orthogonal linear) or L-shaped. The aperture of these arrays ranges from 10 to 25 km. Modern seismic arrays such as NORES and ARCES are located on concentric rings spaced at log-periodic intervals. Each ring consists of an odd number of seismometer sites.
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In both cases the conics are contained in two mutually orthogonal planes. In extreme cases (if the ellipse is a circle) the hyperbola degenerates to a line and the cyclide is a torus of revolution. A further special property of a cyclide is: : (CL): Any curvature line of a Dupin cyclide is a circle.
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The distance measure is computed between the object in the photograph and the 3D CAD model projection at a given pose. Perspective projection or orthogonal projection is possible depending on the pose representation used. This approach is appropriate for applications where a 3D CAD model of a known object (or object category) is available.
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Indiana Jones and His Desktop Adventures gameplay. Note the top-down view along with the directional arrows and round health meter in the lower right. The playing area is displayed from an overhead perspective. The player- controlled Indiana Jones is limited to orthogonal movement, which is controlled with the arrow keys or with the mouse.
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6 are arccos(-1/sqrt(5)) = 116.565°, and at the remaining four vertices with 5.6.6, they are 121.717° each. It is the Goldberg polyhedron GV(2,0), containing pentagonal and hexagonal faces. It also represents the exterior envelope of a cell-centered orthogonal projection of the 120-cell, one of six (convex regular 4-polytopes).
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Although the three languages are tailored for different things, they can not be separated entirely. The user interface invokes a certain application logic and this application logic manipulates the data of the application. This is an example of non-orthogonal concerns. The languages overlap because the concerns that they represent cannot be separated entirely.
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With Waldspurger, Moeglin completed the proof of the local Gan–Gross–Prasad conjecture for generic L-packets of representations of orthogonal groups in 2012. She did much work on the programme of James Arthur to classify automorphic representations of classical groups, and she was invited to present Arthur's ultimate solution to his conjectures at the Bourbaki seminar.
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Starting in 1994, LSFM was developed as orthogonal plane fluorescence optical sectioning microscopy or tomography (OPFOS) mainly for large samples and later as the selective/single plane illumination microscopy (SPIM) also with sub-cellular resolution. This introduced an illumination scheme into fluorescence microscopy, which has already been used successfully for dark field microscopy under the name ultramicroscopy.
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The functional orthogonal convex hull is not defined using properties of sets, but properties of functions about sets. Namely, it restricts the notion of convex function as follows. A function f: \R^d \rightarrow \R is called orthogonally convex if its restriction to each line parallel to a non-zero of the standard basis vectors is a convex function.
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In the mathematical subject of knot theory, the average crossing number of a knot is the result of averaging over all directions the number of crossings in a knot diagram of the knot obtained by projection onto the plane orthogonal to the direction. The average crossing number is often seen in the context of physical knot theory.
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We thus have two new kinds of isometry subgroups: all translations, and rotations sharing a fixed point. Both are subgroups of the even subgroup, within which translations are normal. Because translations are a normal subgroup, we can factor them out leaving the subgroup of isometries with a fixed point, the orthogonal group. Translation addition with mirrors :Proof.
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Ewen A. Whitaker, Mapping and Naming the Moon (Cambridge University Press, 1999), p. 33. Lunar Orbiter 4 image of Mare Frigoris and vicinity. This regional view is nearly orthogonal at top but highly oblique at bottom, and north is up and slightly to the right. Mare Frigoris is the dark band extending from upper left to lower right.
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In contrast, the NS320xx series were originally designed as single-chip implementations of the VAX-11 ISA. Although this had to change due to legal issues, the resulting system retained much of the VAX-11's overall design philosophy and remained completely orthogonal. This included the elimination of the separate data and address registers found in the 68k.
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The following characteristics of the platform are described:F-104G Starfighter Maintenance Manual. # Three accelerometers in orthogonal directions provide the basic sensing elements. They measure acceleration along the two grid coordinate axes and the vertical (Z) axis. The Z accelerometer is not used by the LN3-2A itself but provides vertical acceleration data for the automatic flight control system.
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Hence, transcendence for Maslow is not so much an extension of his original pyramid as an orthogonal dimension. Theory X, Y and Z all play a role in how a company should manage successfully. Maslow believed the ideal organization would harness the human drive for self-transcendence, as well as the motivations of his original pyramid.
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A space with quadratic form is split (or metabolic) if there is a subspace which is equal to its own orthogonal complement; equivalently, the index of isotropy is equal to half the dimension. The hyperbolic plane is an example, and over a field of characteristic not equal to 2, every split space is a direct sum of hyperbolic planes.
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This principle states that when torque or stretch is applied to free pipe, the magnetization will change. Stuck pipe will have no change in magnetization. There is a magnet on the bottom of the tool that creates a small magnetic field. There are four co-planar orthogonal multi-axis high sensitivity magnetometers located above the magnet.
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Lenses may be cut or ground after manufacturing to give them a different shape or size. The lens axis may then not pass through the physical centre of the lens. Toric or sphero-cylindrical lenses have surfaces with two different radii of curvature in two orthogonal planes. They have a different focal power in different meridians.
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Nevertheless, such a choice has a severe shortcoming: the corresponding states are solutions of two different Hamiltonians, each neglecting the presence of the other well. Thus these states are not orthogonal, creating complications. Typically, the coupling is estimated by the transfer Hamiltonian within this approach. For these reasons, it is more convenient to use the set of Wannier functions.
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First, if F is not algebraically closed, then isotropic subspaces may not exist: for a general theory, one needs to use the split orthogonal groups. Second, for vector spaces of even dimension 2m, isotropic subspaces of dimension m come in two flavours ("self-dual" and "anti-self- dual") and one needs to distinguish these to obtain a homogeneous space.
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The main shrine is dedicated to Arkadeep as is the smaller second shrine. A small third shrine, between the two, is dedicated to a reclining Vishnu and may have had water channelled into the temple, entering the Vishnu shrine. The two Shiva shrines are orthogonal in configuration. The entrance is through a transverse barrel vault gopuram.
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Nevertheless, a transparently relativistic kinematics appears when a point of the counter-sphere is used to represent an inertial frame of reference. Indeed, if , then there is a such that , and a such that . Then if , , and , the set is a pan-orthogonal basis stemming from t, and the orthogonalities persist through applications of the ordinary or hyperbolic rotations.
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14 Each class is represented by the core form of a Witt decomposition.Lorenz (2008) p. 30 The Witt group of k is the abelian group W(k) of equivalence classes of non- degenerate symmetric bilinear forms, with the group operation corresponding to the orthogonal direct sum of forms. It is additively generated by the classes of one-dimensional forms.
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Szegő's most important work was in analysis. He was one of the foremost analysts of his generation and made fundamental contributions to the theory of Toeplitz matrices and orthogonal polynomials. He wrote over 130 papers in several languages. Each of his four books, several written in collaboration with others, has become a classic in its field.
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Gilbert's research discoveries have included the existence of multifractal behavior in TCP-based internet traffic,. the development of streaming algorithms based on random projections for aggregating information from large data streams using very small amounts of working memory,. and a foundational analysis of the ability of orthogonal matching pursuit to recover sparse signals with her student Joel Tropp.
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False diffusion is defined as an error having a diffusion-like appearance, obtained when the upwind scheme is used in multidimensional cases to solve for the distribution of transported properties flowing non-orthogonally to one or more of the system's major axes. The error is absent when the flow is orthogonal or parallel to each major axis.
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311 It is an orthogonal building, whose southern, eastern, and western sides are decorated with monumental pointed arches. Its dimensions are 27 × 18 m. The entrance was through a low gate on the northern side, leading to a small room, probably used as a treasury. This room was topped by six lead-covered domes, supported by two massive pillars.
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Artibus et Historiae, Vol. 15, No. 29 (1994), pp. 9–53 geometric orthogonal perspective,Elkins, John, "On the Arnolfini Portrait and the Lucca Madonna: Did Jan van Eyck Have a Perspectival System?". The Art Bulletin, Vol. 73, No. 1 (March 1991), pp. 53–62 and expansion of the picture space with the use of a mirror.
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Radiography was performed on the module in three orthogonal views: side, end, and top-down; as shown in Figure 2. For purposes of this paper the top-down x-ray view shows the x-y plane of the module. The side view shows the x-z plane, and the end view shows the y-z plane.
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There are windows and doorways leading to park-like outdoor settings. All of the figures are dressed in identical attire and have featureless bulb-shaped heads. Identical characters such as these can be found in many other Escher works. In the world of Relativity, there are three sources of gravity, each being orthogonal to the two others.
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The active site of the synthetase is modified to accept only the novel amino acid. Most often, a library of mutant synthetases is screened for one which charges the tRNA with the desired amino acid. The synthetase is also modified to recognize only the orthogonal tRNA. The tRNA synthetase pair is often engineered in other bacteria or eukaryotic cells.
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Digital X-ray equipment mounted in the radiation treatment device is often used to picture the patient’s internal anatomy at time before or during treatment, which then can be compared to the original planning CT series. Usage of an orthogonal set-up of two radiographic axes is common, to provide means for highly accurate patient position verification.
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The first pulse creates transverse spin magnetization. The spins precess during the evolution time t1, which is incremented during the course of the 2D experiment. The second pulse produces longitudinal magnetization equal to the transverse magnetization component orthogonal to the pulse direction. Thus, the idea is to produce an initial condition for the mixing period τm.
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If gaps face gaps, the term bretessé is used. There is at least one emblazonment suggesting that the orle is only embattled on its outer edge. Italian armory has a variant, Ghibelline battlement, with notched merlons. In a line raguly the extensions are oblique rather than orthogonal, like the stumps of limbs protruding from a tree-trunk.
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The action is transitive and so all cycles are Lie equivalent. In particular, points are not preserved by general Lie transformations. The subgroup of Lie transformations preserving the point cycles is essentially the subgroup of orthogonal transformations which preserve the chosen timelike direction. This subgroup is isomorphic to the group O(3,1) of Möbius transformations of the sphere.
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Built on the ancient orthogonal structure that had the current "Via Medaglie d'oro" and "Via Enrico d'Aste" respectively as the Roman camp main road axes (cardo and decumanus), the town has its planimetric hub in the historical San Michele Square. Around it some palaces were built, which were historically the seats of political and religious authorities.
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Orthogonal projection of a cantor cube showing a hexaflake. A hexaflake is a fractal constructed by iteratively exchanging hexagons by a flake of seven hexagons;. it is a special case of the n-flake. The hexaflake has 7n−1 hexagons in its nth iteration, each smaller by 1/3 than the hexagons in the previous iteration.
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3a did consolidate 23 physical layer specifications into two proposals: multi-band orthogonal frequency division multiplexing (MB- OFDM), supported by the WiMedia Alliance, and direct sequence - UWB (DS-UWB), supported by the UWB Forum. Major members Motorola and Freescale Semiconductor left the group in April 2006 and the UWB Forum disbanded. Its website remained into mid-2007.
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Serial relay transmission is used for long distance communication and range-extension in shadowy regions. It provides power gain. In this topology signals propagate from one relay to another relay and the channels of neighboring hop are orthogonal to avoid any interference. Parallel relay transmission may be used where serial relay transmission suffers from multi-path fading.
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The extracted building outlines are then simplified using an orthogonal algorithm to obtain better cartographic quality. Watershed analysis can be conducted to extract the ridgelines of building roofs. The ridgelines as well as slope information are used to classify the buildings per type. The buildings are then reconstructed using three parametric building models (flat, gabled, hipped).
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Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression, including variants for ordinary (unweighted), weighted, and generalized (correlated) residuals. Numerical methods for linear least squares include inverting the matrix of the normal equations and orthogonal decomposition methods.
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Free-flow electrophoresis (FFE) is a carrier-free electrophoresis technique that allows preparative protein separation in a laminar buffer stream by using an orthogonal electric field. By making use of a pH-gradient, that can for example be induced by ampholytes, this technique allows to separate protein isoforms up to a resolution of < 0.02 delta-pI.
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One method to validate a power- law relation tests many orthogonal predictions of a particular generative mechanism against data. Simply fitting a power-law relation to a particular kind of data is not considered a rational approach. As such, the validation of power-law claims remains a very active field of research in many areas of modern science.
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Locus of point C A triangle ABC has a fixed side [AB] with length c. Determine the locus of the third vertex C such that the medians from A and C are orthogonal. Choose an orthonormal coordinate system such that A(−c/2, 0), B(c/2, 0). C(x, y) is the variable third vertex.
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Edmond Nicolas Laguerre (9 April 1834, Bar-le-Duc – 14 August 1886, Bar-le- Duc) was a French mathematician and a member of the Académie française (1885). His main works were in the areas of geometry and complex analysis. He also investigated orthogonal polynomials (see Laguerre polynomials). Laguerre's method is a root-finding algorithm tailored to polynomials.
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QR decompositions can also be computed with a series of Givens rotations. Each rotation zeroes an element in the subdiagonal of the matrix, forming the R matrix. The concatenation of all the Givens rotations forms the orthogonal Q matrix. In practice, Givens rotations are not actually performed by building a whole matrix and doing a matrix multiplication.
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Gangopadhyay A., Cornillon P., Watts R.D. (1992). "A test of the Parsons-Veronis hypothesis on the separation of the Gulf Stream". Journal of Physical Oceanography, 22, 1286-1301 By applying empirical orthogonal function analysis to temperatures at 200 metres, Joyce et al. in 2001 constructed a similar index to the GSNW index extending back to the 1950s.
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Jessen's icosahedron Jessen's icosahedron, sometimes called Jessen's orthogonal icosahedron, is a non-convex polyhedron with the same number of vertices, edges and faces as the regular icosahedron. Its faces meet only in right angles, even though they cannot all be made parallel to the coordinate planes. It is named for Børge Jessen who investigated it in 1967.
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The designers attempted to make the assembly language orthogonal. That is, instructions are divided into operations and address modes, and almost all address modes are available for almost all instructions. There are 56 instructions and a minimum instruction size of 16 bits. Many instructions and addressing modes are longer to include more address or mode bits.
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Although six different sides can be drawn, usually three views of a drawing give enough information to make a three-dimensional object. These views are known as front view, top view and end view. Other names for these views include plan, elevation and section. The terms orthographic projection and orthogonal projection are sometimes reserved specifically for multiview.
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NCEP T62 Gaussian grid points A Gaussian grid is used in the earth sciences as a gridded horizontal coordinate system for scientific modeling on a sphere (i.e., the approximate shape of the Earth). The grid is rectangular, with a set number of orthogonal coordinates (usually latitude and longitude). The gridpoints along each latitude (or parallel), i.e.
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Only about 20% of the Roman city has been excavated. The city has the typical orthogonal layout of Roman military camps, with two principal roads meeting at the forum. The Roman city is considerably larger than the Greek one. During the Republican period a temple was built dedicated to the Capitoline Triad: Jupiter, Juno, and Minerva.
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In mathematics, the Iwasawa decomposition (aka KAN from its expression) of a semisimple Lie group generalises the way a square real matrix can be written as a product of an orthogonal matrix and an upper triangular matrix (a consequence of Gram–Schmidt orthogonalization). It is named after Kenkichi Iwasawa, the Japanese mathematician who developed this method.
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Diagram of the centrosome cycle. Centrosomes are the major microtubule organizing centers (MTOC) in mammalian cells. Failure of centrosome regulation can cause mistakes in chromosome segregation and is associated with aneuploidy. A centrosome is composed of two orthogonal cylindrical proteins, called centrioles, which are surrounded by an electron and protein dense amorphous cloud of pericentriolar material (PCM).
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Digital video comprises a series of digital images displayed in rapid succession. In the context of video these images are called frames. The rate at which frames are displayed is known as the frame rate and is measured in frames per second (FPS). Every frame is an orthogonal bitmap digital image and so comprises a raster of pixels.
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Hadwiger proved a theorem characterizing eutactic stars, systems of points in Euclidean space formed by orthogonal projection of higher-dimensional cross polytopes. He found a higher-dimensional generalization of the space-filling Hill tetrahedra.. And his 1957 book Vorlesungen über Inhalt, Oberfläche und Isoperimetrie was foundational for the theory of Minkowski functionals, used in mathematical morphology.
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In board games such as chess which feature a grid of squares, 'orthogonal' is used to mean "in the same row/'rank' or column/'file'". This is the counterpart to squares which are "diagonally adjacent". In the ancient Chinese board game Go a player can capture the stones of an opponent by occupying all orthogonally-adjacent points.
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The topographic wetness index (TWI), also known as the compound topographic index (CTI), is a steady state wetness index. It is commonly used to quantify topographic control on hydrological processes. The index is a function of both the slope and the upstream contributing area per unit width orthogonal to the flow direction. The index was designed for hillslope catenas.
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VAX has been perceived as the quintessential CISC ISA, with its very large number of assembly-language-programmer-friendly addressing modes and machine instructions, highly orthogonal architecture, and instructions for complex operations such as queue insertion or deletion, number formatting, and polynomial evaluation. It is historically one of the most studied and commented-on ISA's in computer history.
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This type of boundary incorporates two sets of screw dislocations. If the Burgers vectors of the dislocations are orthogonal, then the dislocations do not strongly interact and form a square network. In other cases, the dislocations may interact to form a more complex hexagonal structure. These concepts of tilt and twist boundaries represent somewhat idealized cases.
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The rotation matrices for each form a group, the special orthogonal group, . This algebraic structure is coupled with a topological structure inherited from in such a way that the operations of multiplication and taking the inverse are analytic functions of the matrix entries. Thus is for each a Lie group. It is compact and connected, but not simply connected.
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The continuous Hahn polynomials pn(x;a,b,c,d) are orthogonal with respect to the weight function :w(x)=\Gamma(a+ix)\,\Gamma(b+ix)\,\Gamma(c-ix)\,\Gamma(d-ix). In particular, they satisfy the orthogonality relationKoekoek, Lesky, & Swarttouw (2010), p. 200.Askey, R. (1985), "Continuous Hahn polynomials", J. Phys. A: Math. Gen. 18: pp. L1017-L1019.
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The PRIME physical layer is based on OFDM (Orthogonal Frequency Division Multiplexing) and Differential Phase Shift Keying (BPSK, DQPSK and D8PSK) as carrier modulation. To address averse power line channel properties, robustness mechanism convolutional encoding (optional), scrambling and interleaving are used. PRIME Specification v1.4 also introduces repetition codingDraft Specification for PoweRline Intelligent Metering Evolution. PRIME Alliance TWG.
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In the familiar three-dimensional space of daily life, there are three coordinate axes—usually labeled x, y, and z—with each axis orthogonal (i.e. perpendicular) to the other two. The six cardinal directions in this space can be called up, down, east, west, north, and south. Positions along these axes can be called altitude, longitude, and latitude.
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It is accessed by six sets of stairs, each decorated with pinnacles. The main entrance is on the northern side of the building. The outer walls of the Great Mosque are not precisely orthogonal to one another so that the plan of the building has a noticeable trapezoidal outline.; Figure 7.2 is a plan of the mosque.
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A dingbat apartment building In architecture, shoebox style is a functionalist style of modern architecture characterised by predominantly rectilinear, orthogonal shapes, with regular horizontal rows of windows or glass walls.The Encyclopedia Americana (1989) , p. 238. Dingbat apartments are an undistinguished shoebox style. The puritan and repetitive shoebox style is seen as a way to low-cost construction.
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A fundamental generalization of metamodels is origami. The essential idea is that a program's design need not be represented by a single expression; multiple expressions can be used. This involves the use of multiple orthogonal GenVoca models. :: Example: Let T be a tool model, which has features P (parse), H (harvest),D (doclet), and J (translate to Java).
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This example covers only the case for real, separate eigenvalues. Real, repeated eigenvalues require solving the coefficient matrix with an unknown vector and the first eigenvector to generate the second solution of a two-by-two system. However, if the matrix is symmetric, it is possible to use the orthogonal eigenvector to generate the second solution.
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The offices and classrooms have flat sheeted ceilings with timber cover battens laid out in a variety of orthogonal patterns. Timber framed vertical sliding black boards remain in some of the rooms. Exposed air conditioning ducts have been installed in some classrooms and offices. The courtyard at the rear of the building contains a lush tropical garden.
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A 5x6 square grid is used with a triangular board attached on two opposite sides of the square grid specifically on the two shorter sides of the square grid. The square grid only consist of orthogonal lines; there are no diagonal lines. Each player has 16 pieces of which one set is black, and the other is white.
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A t-(v,k,λ) orthogonal array (t ≤ k) is a λvt × k array whose entries are chosen from a set X with v points such that in every subset of t columns of the array, every t-tuple of points of X appears in exactly λ rows. In this formal definition, provision is made for repetition of the t-tuples (λ is the number of repeats) and the number of rows is determined by the other parameters. In many applications these parameters are given the following names: : v is the number of levels, : k is the number of factors, : λvt is the number of experimental runs, : t is the strength, and : λ is the index. An orthogonal array is simple if it does not contain any repeated rows.
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The singular value decomposition was originally developed by differential geometers, who wished to determine whether a real bilinear form could be made equal to another by independent orthogonal transformations of the two spaces it acts on. Eugenio Beltrami and Camille Jordan discovered independently, in 1873 and 1874 respectively, that the singular values of the bilinear forms, represented as a matrix, form a complete set of invariants for bilinear forms under orthogonal substitutions. James Joseph Sylvester also arrived at the singular value decomposition for real square matrices in 1889, apparently independently of both Beltrami and Jordan. Sylvester called the singular values the canonical multipliers of the matrix A. The fourth mathematician to discover the singular value decomposition independently is Autonne in 1915, who arrived at it via the polar decomposition.
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In vector analysis, a vector with polar coordinates and Cartesian coordinates can be represented as the sum of orthogonal components: Similarly in trigonometry, the angle sum identity expresses: : And in functional analysis, when is a linear function of some variable, such as time, these components are sinusoids, and they are orthogonal functions. A phase-shift of changes the identity to: :, in which case is the in-phase component. In both conventions is the in-phase amplitude modulation, which explains why some authors refer to it as the actual in-phase component. IQ phasor diagram IQ modulation and demodulation block diagram Phase shifter using IQ modulator When a sinusoidal voltage is applied to either a simple capacitor or inductor, the resultant current that flows is "in quadrature" with the voltage.
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Listing's law states that the eye does not achieve all possible 3D orientations and that, instead, all achieved eye orientations can be reached by starting from one specific "primary" reference orientation and then rotating about an axis that lies within the plane orthogonal to the primary orientation's gaze direction (line of sight / visual axis). This plane is called Listing's plane. It can be shown that Listing's law implies that, if we start from any chosen eye orientation, all achieved eye orientations can be reached by starting from this orientation and then rotating about an axis that lies within a specific plane that is associated with this chosen orientation. (Only for the primary reference orientation is the gaze direction orthogonal to its associated plane.) Listing's law can be deduced without starting with the orthogonality assumption.
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Instead, paths in these directions, and any other path that does not bisect one of the six cell edges, will "zig-zag"; since no two directions are orthogonal, it is impossible to move forward in one direction without moving backwards slightly in the other. Games that traditionally use the four cardinal directions, or otherwise suit a square grid, may adapt to a hex grid in different ways. For example, hexagonal chess replaces the four directions of orthogonal movement (along ranks and files) with the six directions to adjacent cells, through cell edges. The four directions of diagonal movement are likewise replaced with the six directions that lie through vertices of the cell; these "diagonal" movements travel along the edge between a pair of adjacent cells before arriving at another cell.
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A midplane is defined as a plane that is orthogonal to an edge joining any two vertices that also contains the centroid of an opposite edge formed by joining the other two vertices. If the tetrahedron's altitudes do intersect, then the Monge point and the orthocenter coincide to give the class of orthocentric tetrahedron. An orthogonal line dropped from the Monge point to any face meets that face at the midpoint of the line segment between that face's orthocenter and the foot of the altitude dropped from the opposite vertex. A line segment joining a vertex of a tetrahedron with the centroid of the opposite face is called a median and a line segment joining the midpoints of two opposite edges is called a bimedian of the tetrahedron.
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Another well-defined problem for the nine dots starting point is to connect the dots with a single straight line. The solution involves looking outside the two- dimensional sheet of paper on which the nine dots are drawn and coning the paper three-dimensionally aligning the dots along a spiral, thus a single line can be drawn connecting all nine dots - which would appear as three lines in parallel on the paper, when flattened out.W. Neville Holmes, Fashioning a Foundation for the Computing Profession, July 2000 If solving the four line solution is called lateral thinking, then solving the one line solution could well be called orthogonal thinking,Curtis Ogden, Orthogonal Thinking & Doing, 25 September 2015 as it requires two distinct phases: drawing the line and assembling the line.
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There are two common methods used to manufacture accelerometers. One is based upon the principles of piezoresistance and the other is based on the principles of piezoelectricity. Both methods ensure that unwanted orthogonal acceleration vectors are excluded from detection. Manufacturing an accelerometer that uses piezoresistance first starts with a semiconductor layer that is attached to a handle wafer by a thick oxide layer.
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Lindhe graduated from the Royal School of Dentistry in Malmö, Sweden. He completed specialty training in oral surgery and periodontology at the University of Lund. He began his career as a professor of roentgenology (now referred to as oral and maxillofacial radiology) in 1957 at Lund. The title of his 1964 doctoral thesis at Lund was Orthogonal cutting of dentine: a methodological study.
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Ion scattering makes using triple- and further stage reflectrons impractical. The effect of ion scattering on mass resolution in single- and dual-stage reflectrons can be diminished by utilizing polarized grid geometry.D.S. Selby, V. Mlynski, M. Guilhaus, Demonstrating the effect of the ‘polarised grid geometry’ for orthogonal acceleration time-of-flight mass spectrometers, Rapid Communications in Mass Spectrometry, 14(7), 616 (2000).
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Thus an estimate of the spacecraft attitude is given by the proper orthogonal matrix as Note that computational efficiency has been achieved in this procedure by replacing the matrix inverse with a transpose. This is possible because the matrices involved in computing attitude are each composed of a triad of orthonormal basis vectors. "TRIAD" derives its name from this observation.
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130 The elements are commonly arranged in a linear array.Lipsky, p. 130 A Butler matrix can also feed a circular array giving 360° coverage. A further application with a circular antenna array is to produce n omnidirectional beams with orthogonal phase-modes so that multiple mobile stations can all simultaneously use the same frequency, each using a different phase- mode.
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The Unified Modeling Language has a notation for describing state machines. UML state machines overcome the limitations of traditional finite-state machines while retaining their main benefits. UML state machines introduce the new concepts of hierarchically nested states and orthogonal regions, while extending the notion of actions. UML state machines have the characteristics of both Mealy machines and Moore machines.
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These are all grids in that a regularly spaced armature leaves recurring openings and that they could, conceivably, expand outward. The emergence of the pure, rectilinear, orthogonal grid, or Hippodamian grid, is explained by the natural tendency of people to walk in a straight line, particularly in the absence of obstacles and on level land.Spiro Kostof. 1991. The City Shaped.
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Doxiadis emphasized the importance of mobility and designed a large orthogonal grid (2 km by 2 km) of arterials to expedite circulation, as seen in Islamabad. He also recognized the need to separate "man from machine"Doxiadis, C. A (1975) Anthropopolis: City for Human Development (W. W. Norton & Co ) and introduced traffic-impermeable neighbourhoods also generally resembling the Radburn plan.
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Quartimax rotation is an orthogonal alternative which minimizes the number of factors needed to explain each variable. This type of rotation often generates a general factor on which most variables are loaded to a high or medium degree. Such a factor structure is usually not helpful to the research purpose. Equimax rotation is a compromise between varimax and quartimax criteria.
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Lentoid. Lentoid is a geometric shape of a three-dimensional body, best described as a circle viewed from one direction and a convex lens viewed from every orthogonal direction. It has no strict mathematical definition, but may be described as the volume enclosed within overlapping paraboloids. The term is most often used in describing jewelry and cellular phenomena in microbiology.
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The transformation P is the orthogonal projection onto the line m. In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that P^2=P. That is, whenever P is applied twice to any value, it gives the same result as if it were applied once (idempotent). It leaves its image unchanged.
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Magnetometer The magnetometer (MAG) used two sets of three sensors. The three sensors allowed the three orthogonal components of the magnetic field section to be measured. One set was located at the end of the magnetometer boom and, in that position, was about from the spin axis of the spacecraft. The second set, designed to detect stronger fields, was from the spin axis.
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Stimulus-response associations may be both encoded and decoded in one non-iterative transformation. The mathematical basis requires no optimization of parameters or error backpropagation, unlike connectionist neural networks. The principal requirement is for stimulus patterns to be made symmetric or orthogonal in the complex domain. HAM typically employs sigmoid pre-processing where raw inputs are orthogonalized and converted to Gaussian distributions.
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In geometry of 4 dimensions or higher, a duopyramid or fusil is a polytope constructed by 2 orthogonal polytopes with edges connecting all pairs of vertices between the two. The term fusil is used by Norman Johnson as a rhombic-shape.Norman W. Johnson, Geometries and Transformations (2018), p.167 The term duopyramid was used by George Olshevsky, as the dual of a duoprism.
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This method and its more efficient version (fast orthogonal algorithm) were invented by Korenberg. In this method the orthogonalization is performed empirically over the actual input. It has been shown to perform more precisely than the crosscorrelation method. Another advantage is that arbitrary inputs can be used for the orthogonalization and that fewer data points suffice to reach a desired level of accuracy.
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The main difficulty lies in showing that a distance- preserving map, which is a priori only continuous, is actually differentiable. The second theorem, which is much more difficult to prove, states that the isometry group of a Riemannian manifold is a Lie group. For instance, the group of isometries of the two-dimensional unit sphere is the orthogonal group O(3).
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Movement on these detachments led to deposition of thick sequences of continental clastic sediments in their hanging walls and was in part responsible for the exhumation of late Caledonian ultra high-pressure metamorphic rocks, including eclogites, in their footwalls. The displacements on these structures range from nearly orthogonal to the Caledonian chain in the south to being strongly oblique in mid-Norway.
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The autoencoder weights are not equal to the principal components, and are generally not orthogonal, yet the principal components may be recovered from them using the singular value decomposition. However, the potential of Autoencoders resides in their non- linearity, allowing the model to learn more powerful generalizations compared to PCA, and to reconstruct back the input with a significantly lower loss of information.
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For example, the knight itself moves two squares in one orthogonal direction and one in the other—it moves hippogonally. It is a (1,2) hippogonal mover, sometimes referred to as a (1,2) leaper. Other hippogonally moving pieces include the camel, a fairy chess piece, which moves three squares in one direction and one in the other, and thus is a (1,3) hippogonal mover.
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The formed surface was left as the final finish without any added fascia. The distance between the core and the facade is on all sides. To support its thin orthogonal frame, 432 Park Avenue features larger columns at its base than on the upper floors. The columns are about deep at the bottom of the tower, narrowing to at the top.
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George-ericksenite features a structural arrangement that is composed of slabs of polyhedra orthogonal to [100]. These slabs feature the same composition as the mineral itself and are a half of a unit thick in the [100] direction. These are connected to adjacent slabs solely by hydrogen bonding. The edges of each slab are bounded by near- planar layers of anions.
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The propellers are hard anodized, epoxy coated on the exterior, and protected by zinc anodes. They have been made from polycarbonate plastic (LEXAN) and, more recently, from Noryl. Propeller sensors make use of Cartesian coordinate system and provide orthogonal velocity components in the horizontal plane. The measured coordinates need only be rotated in the conventional directions east-west and north-south.
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Park et al. created an orthogonal receptor-ligand interface between PYR1 and mandipropamid. PYR1 normally binds to abscisic acid which together then bind and inactivate to PP2C as a drought stress response, which stops PP2C from deactivating SnRK2. This causes a cascade that leads to the activation of the slow anion channel 1 and closing of the leaf guard cells and stomata.
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Orthogonal spaceships in Conway's Game of Life of varying speeds. Note some spaceships “overtake” others due to speed differences. In a cellular automaton, a finite pattern is called a spaceship if it reappears after a certain number of generations in the same orientation but in a different position. The smallest such number of generations is called the period of the spaceship.
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Case 2 BWS studies can use Orthogonal Main Effects Plans (OMEPs) or efficient designs, although the former has predominated to date. Case 3 BWS studies may use any of the types of design typically used for a DCE, with the proviso that the number of profiles (alternatives) in a choice set must be three or more for the BWS task to make sense.
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With the introduction of matrices, the Euler theorems were rewritten. The rotations were described by orthogonal matrices referred to as rotation matrices or direction cosine matrices. When used to represent an orientation, a rotation matrix is commonly called orientation matrix, or attitude matrix. The above- mentioned Euler vector is the eigenvector of a rotation matrix (a rotation matrix has a unique real eigenvalue).
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Newton's opinion had raised a huge controversy among French scientists. Pierre Louis Maupertuis, Alexis Claude Clairaut, and Pierre Charles Le Monnier traveled to Lapland, where they were to measure the length of several degrees of latitude orthogonal to the arctic circle, while Louis Godin, Pierre Bouguer, and La Condamine were sent to South America to perform similar measurements around the equator.
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The spin 4-vector is orthogonal to the velocity 4-vector. Fermi-Walker transport preserves this relation. If there is no acceleration, Fermi-Walker transport is just parallel transport along a geodesic and gives the spin precession due to the geodetic effect. For the acceleration due to uniform circular motion in flat Minkowski spacetime, Fermi Walker transport gives the Thomas precession.
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Principal component analysis creates variables that are linear combinations of the original variables. The new variables have the property that the variables are all orthogonal. The PCA transformation can be helpful as a pre-processing step before clustering. PCA is a variance-focused approach seeking to reproduce the total variable variance, in which components reflect both common and unique variance of the variable.
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With the introduction of matrices the Euler theorems were rewritten. The rotations were described by orthogonal matrices referred to as rotation matrices or direction cosine matrices. When used to represent an orientation, a rotation matrix is commonly called orientation matrix, or attitude matrix. The above-mentioned Euler vector is the eigenvector of a rotation matrix (a rotation matrix has a unique real eigenvalue).
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In methane, CH4, the calculated p/s ratio is approximately 3 consistent with "ideal" sp3 hybridisation, whereas for silane, SiH4, the p/s ratio is closer to 2. A similar trend is seen for the other 2p elements. Substitution of fluorine for hydrogen further decreases the p/s ratio. The 2p elements exhibit near ideal hybridisation with orthogonal hybrid orbitals.
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Quartimax rotation is an orthogonal rotation that maximizes the squared loadings for each variable rather than each factor. This minimizes the number of factors needed to explain each variable. This type of rotation often generates a general factor on which most variables are loaded to a high or medium degree. Equimax rotation is a compromise between varimax and quartimax criteria.
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Common factor analysis software is capable of producing an unrotated solution. This refers to the result of a principal axis factoring with no further rotation. The so-called unrotated solution is in fact an orthogonal rotation that maximizes the variance of the first factors. The unrotated solution tends to give a general factor with loadings for most of the variables.
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Assuming the hidden variable to be polarisation direction (parallel on the two sides in real applications, not orthogonal), equation () becomes where \phi = b - a. The predicted quantum correlation can be derived from this and is shown in the figure. The realist prediction (solid curve) for quantum correlation in an optical Bell test. The quantum-mechanical prediction is the dotted curve.
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A Time/Utility Function (TUF), née Time/Value Function, specifies the application-specific utility that an action (e.g., task, mechanical movement) yields depending on its completion time. TUFs and their utility interpretations (semantics), scales, and values are derived from application domain-specific subject matter knowledge. One frequent interpretation of utility is an action's relative importance, which is orthogonal to its timeliness.
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The pods are covered with a skin of 26,000 triangular shingles, many of which open to let in air and light. Like her other structures, the bridge-pavilion is composed entirely of diagonal slopes and curves, with no right-angles of orthogonal forms. By its curving shape and low profile, the bridge-pavilion fits smoothly into the grassy landscape along the river.
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According to the Davenport theorem, a unique decomposition is possible if and only if the second axis is perpendicular to the other two axes. Therefore, axes 1 and 3 must be in the plane orthogonal to axis 2.M. Shuster and L. Markley, Generalization of Euler angles, Journal of the Astronautical Sciences, Vol. 51, No. 2, April–June 2003, pp.
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The business logic supported full cross-dimensional calculations, automatic ordering of rules using static data-flow analysis, and the identification and solution of simultaneous equations. The rules treated all dimensions in an orthogonal fashion. The aggregation process did not distinguish between simple summation or average calculations, and more complex non-commutative calculations. Both could be applied to any dimension member.
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In terms of the affine subspace , an isotropic line through the origin is :x_2 = \pm i x_1 . In projective geometry, the isotropic lines are the ones passing through the circular points at infinity. In the real orthogonal geometry of Emil Artin, isotropic lines occur in pairs: :A non-singular plane which contains an isotropic vector shall be called a hyperbolic plane.
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The rigidity of quinuclidine and the orthogonal orientation of the nitrogen bridge in relations to the amide carbonyl group is presumed important for the optimal binding. The stability of some of the more potent quinuclidine amide derivatives in rat in vitro models have been low however by adding a methyl group to position 2 on the quinuclidine ring the stability has increased greatly.
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She is also a 1992 MacArthur Fellow. The name Daubechies is widely associated with the orthogonal Daubechies wavelet and the biorthogonal CDF wavelet. A wavelet from this family of wavelets is now used in the JPEG 2000 standard. Her research involves the use of automatic methods from both mathematics, technology and biology to extract information from samples like bones and teeth.
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Turk and Pentland combined the conceptual approach of the Karhunen–Loève theorem and factor analysis, to develop a linear model. Eigenfaces are determined based on global and orthogonal features in human faces. These features are established in an unsupervised machine learning process with the help of the Gaussian blur. A human face is calculated as a weighted combination of a number of Eigenfaces.
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It is these scalar-like properties which give rise to its name. In this setting, a pseudoscalar changes sign under a parity inversion, since if :(e1, e2) -> (u1, u2) is a change of basis representing an orthogonal transformation, then :e1e2 -> u1u2 = ±e1e2, where the sign depends on the determinant of the transformation. Pseudoscalars in geometric algebra thus correspond to the pseudoscalars in physics.
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The turbopumps use solid propellant cartridge for start up, while the gas generator and combustion chamber use pyrotechnic igniter. It can restart for two burn profile missions. All subsystems are attached to the combustion chamber and gimbal is achieved by rotating the whole engine on two orthogonal planes with two independent actuators. These actuators use high pressure hydrogen as hydraulic fluid.
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In 2014 it was shown that by altering the peptidyl transferase center of the 23S rRNA, ribosomes could be created which draw on orthogonal pools of tRNA. The 3’ end of tRNAs is universally conserved to be CCA. The two cytidines base pair with two guanines the 23S rRNA to bind the tRNA to the ribosome. This interaction is required for translational fidelity.
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In 2015, it was also demonstrated by Christian Kern et al. that an anisotropic perforation of a single material can lead to a yet more unusual effect namely the parallel Hall effect. This means that the induced electric field inside a conducting media is no longer orthogonal to the current and the magnetic field but is actually parallel to the latest.
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Negative luminescence has also been observed in semiconductors in orthogonal electric and magnetic fields. In this case, the junction of a diode is not necessary and the effect can be observed in bulk material. A term that has been applied to this type of negative luminescence is galvanomagnetic luminescence. Negative luminescence might appear to be a violation of Kirchhoff's law of thermal radiation.
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The Lie transformations preserve the contact elements, and act transitively on Z3. For a given choice of point cycles (the points orthogonal to a chosen timelike vector v), every contact element contains a unique point. This defines a map from Z3 to the 2-sphere S2 whose fibres are circles. This map is not Lie invariant, as points are not Lie invariant.
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Barbarossa and collaborators derived the optimal precoding matrices for wireless communication systems,. The proposed strategies are particularly suitable for MIMO communication systems, with channel state information at the transmit side. He contributed to the introduction of game theory to wireless communications. Together with Fasano, Barbarossa introduced an optimal space- time coding technique, named Trace-Orthogonal Design, for MIMO systems with no channel information.
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Orientation selectivity is expressed by cells within the visual cortex, when such cells increase impulse or signal activity for specific oriented degree of shape presented within the visual field. Orientation selectivity can also be expressed by simple cells if the orientation of a stimulus is orthogonal to the preferred degree of orientation, which results in the inhibition of impulse activity.
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There are only sixteen dwarfs in Koom Valley Thud. Fifteen are placed so as to fill two diagonal sides of the board and the orthogonal side between them. The sixteenth is placed next to the Thudstone, called the Rock in this variant, on the dwarfs' side. The eight trolls are arranged in a symmetrical pattern in three groups on the other side.
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Ribbon Terrain is characterized by ribbons and folds that are typically orthogonal to one another. Ribbons are long and narrow extensional troughs that are separated by narrow ridges. Ribbon terrain can be found both in large crustal plateaus and within tessera inliers. S-C Terrain is named such due to its geometric similarity to S-C tectonic fabrics on Earth.
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MD 187 was relocated to an orthogonal intersection with MD 355 at its northern end in 1967. This replaced an acute intersection with MD 355 north of Montrose Road now named Hoya Street. The old alignment remained in the state highway system until 1987 when the part north of Montrose Road became a ramp from southbound MD 355 to Montrose Road.
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A software blueprint is the final product of a software blueprinting process. Its name derives from an analogy with the term blueprint as used within the traditional construction industry. Therefore, a true software blueprint should share a number of key properties with its building-blueprint counterpart. Software blueprinting relies on achieving a clean separation between logically orthogonal aspects of the software.
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Most common geometric transformations that keep the origin fixed are linear, including rotation, scaling, shearing, reflection, and orthogonal projection; if an affine transformation is not a pure translation it keeps some point fixed, and that point can be chosen as origin to make the transformation linear. In two dimensions, linear transformations can be represented using a 2×2 transformation matrix.
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There exist a certain class of problems that although they are solvable in principle they require so much time or space that it is not practical to attempt to solve them. These problems are called intractable. There is another form of complexity called hierarchical complexity. It is orthogonal to the forms of complexity discussed so far, which are called horizontal complexity.
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Principal Component analysis and common factor analysis are two ways of extracting data. Principal axis factoring, ML factor analysis, alpha factor analysis and image factor analysis is most useful ways of EFA. It employees various factor rotation methods which can be classified into orthogonal (resulting in uncorrelated factors) and oblique (resulting correlated factors). The ‘psych’ package in R is useful for EFA.
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Dynamic balance is provided through the three semicircular canals. These three canals are orthogonal (at right angles) to each other. At the end of each canal is a slight enlargement, known as the ampulla, which contains numerous cells with filaments in a central area called the cupula. The fluid in these canals rotates according to the momentum of the head.
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The Novelist is a 2013 independent video game by Kent Hudson through his company Orthogonal Games. The game was first released on Dec 10, 2013 through Steam. The Novelist can be played in two formats: in stealth or storytelling mode. The game's story line is told through the viewpoint of a spectral figure that oversees the Kaplan family's daily life while on vacation.
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In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization is a decomposition of a matrix A into a product A = QR of an orthogonal matrix Q and an upper triangular matrix R. QR decomposition is often used to solve the linear least squares problem and is the basis for a particular eigenvalue algorithm, the QR algorithm.
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This means that Spin(2,1) is not the universal cover: it is not simply connected. In detail, there are projective representations of the special orthogonal group SO(2,1) which do not arise from linear representations of SO(2,1), or of its double cover, the spin group Spin(2,1). Anyons are evenly complementary representations of spin polarization by a charged particle.
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Edouard Van Beneden made the first observation of centrosomes (which are composed of two orthogonal centrioles) in 1883. In 1895, Theodor Boveri named the organelle a "centrosome".Boveri, T. Ueber das Verhalten der Centrosomen bei der Befruchtung des Seeigel-Eies nebst allgemeinen Bemerkungen über Centrosomen und Verwandtes. Verh. d. Phys.-Med. Ges. zu Würzburg, N. F., Bd. XXIX, 1895. link.
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In the theory of random matrices, the circular ensembles are measures on spaces of unitary matrices introduced by Freeman Dyson as modifications of the Gaussian matrix ensembles. The three main examples are the circular orthogonal ensemble (COE) on symmetric unitary matrices, the circular unitary ensemble (CUE) on unitary matrices, and the circular symplectic ensemble (CSE) on self dual unitary quaternionic matrices.
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Intuitively, if the light rays are converging, this means that the light is moving backwards inside of the ball. If all the rays around the entire surface are converging, we say that there is a trapped null surface. More formally, if every null congruence orthogonal to a spacelike two-surface has negative expansion, then such surface is said to be trapped.
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Haskell features lazy evaluation, lambda expressions, pattern matching, list comprehension, type classes and type polymorphism. It is a purely functional language, which means that functions generally have no side effects. A distinct construct exists to represent side effects, orthogonal to the type of functions. A pure function can return a side effect that is subsequently executed, modeling the impure functions of other languages.
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Each second, about 65 billion () solar neutrinos pass through every square centimeter on the part of the Earth orthogonal to the direction of the Sun. Since neutrinos are insignificantly absorbed by the mass of the Earth, the surface area on the side of the Earth opposite the Sun receives about the same number of neutrinos as the side facing the Sun.
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These numbers occur also in other, related areas. In matrix theory, the Radon–Hurwitz number counts the maximum size of a linear subspace of the real n×n matrices, for which each non-zero matrix is a similarity transformation, i.e. a product of an orthogonal matrix and a scalar matrix. In quadratic forms, the Hurwitz problem asks for multiplicative identities between quadratic forms.
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A linear retarder has a slow axis and a fast axis, and the two axes are orthogonal to each other. Polarized light travels at higher speed when its electric field vector is aligned with the fast axis of a retarder. In contrast, polarized light travels at lower speed when its electric field vector is aligned with the slow axis of a retarder.
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Breaking a polygon into monotone polygons A simple polygon is monotone with respect to a line , if any line orthogonal to intersects the polygon at most twice. A monotone polygon can be split into two monotone chains. A polygon that is monotone with respect to the y-axis is called y-monotone. A monotone polygon with vertices can be triangulated in time.
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Among other things, the orthogonal structure of the monastery, the town fortifications and the Chorgasse and Predigergasse lane are evident, and especially the latter is important for this quarter; it leads from Neumarkt in a straight line to the southern portal, which was the main entrance to the church. The northern part of the convent was predominantly used for agricultural purpose.
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The element of this subspace that has the smallest length (that is, is closest to the origin) is the answer we are looking for. It can be found by taking an arbitrary member of and projecting it orthogonally onto the orthogonal complement of the kernel of . This description is closely related to the Minimum norm solution to a linear system.
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Cobalt(II) fluoride is a chemical compound with the formula (CoF2). It is a pink crystalline solid compound which is antiferromagnetic at low temperatures (TN=37.7 K)Ashcroft/Mermin: Solid State Physics (Tab. 33.2) The formula is given for both the red tetragonal crystal, (CoF2), and the tetrahydrate red orthogonal crystal, (CoF2·4H2O). CoF2 is used in oxygen-sensitive fields, namely metal production.
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From the companies Barkingside R&D; department, Brown found a experimental weld-testing machine. Both these machines were cannibalised for parts. To measure the position of the transducer, Brown selected an 'X-Y' orthogonal measuring frame system. This was measured in place by a sine/cosine potentiometer that was used to calculate the position of the transducer from the angle of its rotations.
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These were probably cisterns, connected with the city's water supply, perhaps settling basins on arrival of the aqueduct. The two main rooms are connected with other ancient structures along the axis represented today by Guido Paglia square, Duomo square and Marino Boffa square (where the city forum was supposed to exist), all oriented according to the probable orthogonal arrangement of the urban area.
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Jean-Loup Waldspurger (born 1953) is a French mathematician working on the Langlands program and related areas. He proved Waldspurger's theorem, the Waldspurger formula, and the local Gan–Gross–Prasad conjecture for orthogonal groups. He played a role in the proof of the fundamental lemma, reducing the conjecture to a version for Lie algebras. This formulation was ultimately proven by Ngô Bảo Châu.
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She remained there for 64 years of her life. In 1955, she got a first doctorate degree on the application of analytic continuation to numeric methods. In 1972 she obtained a secondary doctorate on the use of orthogonal transformations to solve algebraic problems. In October 1985, she was awarded an honorary doctorate at Umeå University, Sweden, with which she has collaborated.
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Their appearance may be due to a combination of erosion by underground rainwater and then by subsequent weathering after they were exposed. Most of the pillars emerge without a break from the underlying granite. Their structural base may be of orthogonal or vertically-aligned sheet jointing. They obtained their name because a traveller in a coach saw the formation in the distance.
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Work by Sewell Wright on path coefficients and Truman L. Kelley on multiple factors differs from factor analysis, which Thurstone sees as an extension of professor Spearman's work. Mathematical Introduction. A brief presentation of matrices, determinants, matrix multiplication, diagonal matrices, the inverse, the characteristic equation, summation notation, linear dependence, geometric interpretations, orthogonal transformations, and oblique transformations. Chapter I. The Factor Problem.
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In mathematics, Bender–Dunne polynomials are a two-parameter family of sequences of orthogonal polynomials studied by . They may be defined by the recursion: : P_0(x) = 1, : P_{1}(x) = x , and for n > 1: : P_n(x) = x P_{n-1}(x) + 16 (n-1) (n-J-1) (n + 2 s -2) P_{n-2}(x) where J and s are arbitrary parameters.
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384px Parabolic coordinates are a two-dimensional orthogonal coordinate system in which the coordinate lines are confocal parabolas. A three-dimensional version of parabolic coordinates is obtained by rotating the two-dimensional system about the symmetry axis of the parabolas. Parabolic coordinates have found many applications, e.g., the treatment of the Stark effect and the potential theory of the edges.
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However, there is a great variation in compressibility across the orthogonal x-y plane. It is reported that controlling the centrifugal speed of production may aid in regulating the thickness of a material. For example, centrifuging at 18000 rpm during synthesis produced phosphorene with an average diameter of 210 nm and a thickness of 2.8 ± 1.5 nm (2–7 layers).
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In a wider sense, an improper rotation may be defined as any indirect isometry; i.e., an element of E(3)\E+(3): thus it can also be a pure reflection in a plane, or have a glide plane. An indirect isometry is an affine transformation with an orthogonal matrix that has a determinant of −1. A proper rotation is an ordinary rotation.
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The Sha-Amun-en-su mummy also underwent a three-dimensional laser scan coordinated by Jorge Lopes, from the Tri-dimensional Experimentation Nucleus of the Pontifical Catholic University of Rio de Janeiro. That procedure allowed the generation of three-dimensional data files (called "orthogonal coordinates") that served as the basis for making a small-scale replica of the singer's skeleton.
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Accordingly, E+ above corresponds to the spatially symmetric/spin-singlet solution and E− to the spatially antisymmetric/spin-triplet solution. J. H. Van Vleck presented the following analysis:Van Vleck, J. H.: Electric and Magnetic Susceptibilities, Oxford, Clarendon Press, p. 318 (1932). :The potential energy of the interaction between the two electrons in orthogonal orbitals can be represented by a matrix, say Eex.
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The remaining building is a theater. The shops are densely clustered in orthogonal patterns, and are mostly found on the south side of the railway tracks. The government buildings, including the Village Hall (Hinsdale Memorial Building) and U.S. Post Office are on the north side. An article entitled "Hinsdale the Beautiful" in Campbell's Illustrated Journal prompted city officials to further beautify the city.
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The GEOS circle is that circle centered at a point equidistant from X650 (the intersection of the orthic axis with the Gergonne line) and X20 (the intersection of the Euler line with the Soddy line and is known as the de Longchamps point) and passes through these points as well as the two points of orthogonal intersection. The orthogonal intersection points are X468 (the intersection of the orthic axis with the Euler line) and X1323 (the Fletcher point, the intersection of the Gergonne line with the Soddy line). The orthocentric system comprises X650, X20, X1375 (the intersection of the Euler line with the Gergonne line and is known as the Evans point) and X3012 (the intersection of the Soddy line and the orthic axis). The X(i) point notation is the Clark Kimberling ETC classification of triangle centers.
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The projective orthogonal group over a finite field is used in the construction of a family of finite simple groups of Lie type, namely the Chevalley groups of type Dn. The orthogonal group over a finite field, O(n,q) is not simple, since it has SO as a subgroup and a non- trivial center ({±I}) (hence PO as quotient). These are both fixed by passing to PSO, but PSO itself is not in general simple, and instead one must use a subgroup (which may be of index 1 or 2), defined by the spinor norm (in odd characteristic) or the quasideterminant (in even characteristic).ATLAS, p. xi The quasideterminant can be defined as (-1)^D where D is the Dickson invariant (it is the determinant defined by the Dickson invariant), or in terms of the dimension of the fixed space.
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It was replaced by orthogonal frequency-division multiple access and other frequency-division multiple access schemes. This is combined with MIMO antenna arrays, dynamic channel allocation, and channel-dependent scheduling. The first publicly available LTE services were branded "4G" and opened in Sweden's capital city Stockholm (Ericsson system) and Norway's capital city Oslo (a Huawei system) on 14 December 2009. The user terminals were manufactured by Samsung.
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Depiction is reference conveyed through pictures. Basically a picture refers to its object through a non-linguistic two-dimensional scheme. A picture is not writing or notation. A depictive two-dimensional scheme is called a picture plane and may be constructed according to descriptive geometry where they are usually divided between projections (orthogonal and various oblique angles) and perspectives (according to number of vanishing points).
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D'Aguilon extensively studied stereographic projection, which he wanted to use a means to aid architects, cosmographers, navigators and artists. For centuries, artists and architects had sought formal laws of projection to place objects on a screen. Aguilon's Opticorum libri sex successfully treated projections and the errors in perception. D'Aguillon adopted Alhazen's theory that only light rays orthogonal to the cornea and lens surface are clearly registered.
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The explosion at Santorini (between the Late Minoan IA and the Late Minoan IB) buried and preserved an example of a habitat: Akrotiri. Excavations since 1967 have uncovered a built-up area covering one hectare, not counting the defensive wall.Les Civilisations égéennes, p. 331. The layout ran in a straight line, with a more or less orthogonal network of paved streets fitted with drains.
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Cognitive style is a characteristic of the user, and can be measured by cognitive styles analysis. The interface and functional features of an application can be harmonized or non-harmonized in accordance with a user's cognitive style. Cognitive styles fall on two orthogonal dimensions: Wholist–Analytic and Verbal–Imagery. So an application success might vary, depending on how it caters to individual cognitive style.
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When the number of oscillators (particles) is increased to three, the orthogonal matrix can no longer be described by a single angle; instead, three are required (Euler angles). Furthermore, in the quantum case, the matrices may be complex. This requires the introduction of complex phases in addition to the rotation angles, which are associated with CP violation but do not influence the observable effects of neutrino oscillation.
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This variant is played on a board obtained by drawing two sets of circles with orthogonal axes of rotation on the sphere. Both players pieces are initially arranged on opposite hemispheres. Each player has a standard set of king, queen, bishop, knight and rook arranged in a square pattern surrounding a central empty square. These pieces are surrounded by 16 pawns in another square layer.
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Their algorithm takes time where is the smaller of the two dimensions of the input shape and is the larger of the two dimensions. The same method was later extended to orthogonally convex shapes that might be connected only diagonally instead of requiring orthogonal connectivity.; . A part of a solver for full nonogram puzzles, used 2-satisfiability to combine information obtained from several other heuristics.
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MathSciNet lists 73 publications for Heinrich, dated from 1976 to 2012. Several of Heinrich's research publications concern orthogonal Latin squares, analogous concepts in graph theory, and applications of these concepts in parallel computing. As well, she has published works on finding spanning subgraphs with constraints on the degree of each vertex, and on Alspach's conjecture on disjoint cycle covers of complete graphs, among other topics.
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When analyzing shock waves in a flow field, which are still attached to the body, the shock wave which is deviating at some arbitrary angle from the flow direction is termed oblique shock. These shocks require a component vector analysis of the flow; doing so allows for the treatment of the flow in an orthogonal direction to the oblique shock as a normal shock.
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However, the orthogonality (i.e., independence) of factors is often an unrealistic assumption. Oblique rotations are inclusive of orthogonal rotation, and for that reason, oblique rotations are a preferred method. Allowing for factors that are correlated with one another is especially applicable in psychometric research, since attitudes, opinions, and intellectual abilities tend to be correlated, and since it would be unrealistic in many situations to assume otherwise.
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A surface generated by revolving a plane curve about a fixed line in its plane as an axis is called a surface of revolution. The plane curve is called the generatrix of the surface. A section of the surface, made by intersecting the surface with a plane that is perpendicular (orthogonal) to the axis, is a circle. Simple examples occur when the generatrix is a line.
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GGH involves a private key and a public key. The private key is a basis B of a lattice L with good properties (such as short nearly orthogonal vectors) and a unimodular matrix U. The public key is another basis of the lattice L of the form B'=UB. For some chosen M, the message space consists of the vector (m_1,..., m_n) in the range -M .
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The fundamental part of the HHT is the empirical mode decomposition (EMD) method. Breaking down signals into various components, EMD can be compared with other analysis methods such as Fourier transform and Wavelet transform. Using the EMD method, any complicated data set can be decomposed into a finite and often small number of components. These components form a complete and nearly orthogonal basis for the original signal.
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The bilinear quadrilateral element, also known as the Q4 element, is a type of element used in finite element analysis which is used to approximate in a 2D domain the exact solution to a given differential equation. The element consists of a combination of two sets of Lagrange polynomials, each one used to define the variation of a field in each orthogonal direction of the local referential.
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Professor Salehi's current research interests include fiber-optic communications and optical multiaccess networks, in particular, optical orthogonal codes (OOC); fiber-optic CDMA; femtosecond or ultra-short light pulse CDMA; spread time CDMA; holographic CDMA; wireless indoor optical CDMA; all-optical synchronization; and applications of erbium-doped fiber amplifiers (EDFAs) in optical systems. he is father of OOC code generation and he is also given OCDMA concept.
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Severini proved Egorov's theorem one year earlier than Dmitri EgorovEgorov's proof is given in the paper . in the paper , whose main theme is however sequences of orthogonal functions and their properties.Also, according to , Severini, while acknowledging his own priority in the publication of the result, was unwilling to disclose it publicly: it was Leonida Tonelli who, in the note , credited him the priority for the first time.
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One of the interesting property of this notion lies in the fact that two isotypical representations are either quasi-equivalent or disjoint (in analogy with the fact that irreducible representations are either unitarily equivalent or disjoint). This can be understood through the correspondence between factor representations and minimal central projection (in a von Neumann algebra),.Dixmier Two minimal central projections are then either equal or orthogonal.
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The scheduling of receivers with different spatial signatures allows good separability. Diversity coding techniques are used when there is no channel knowledge at the transmitter. In diversity methods, a single stream (unlike multiple streams in spatial multiplexing) is transmitted, but the signal is coded using techniques called space-time coding. The signal is emitted from each of the transmit antennas with full or near orthogonal coding.
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It is an extension of the Rademacher system of orthogonal functions.. Walsh functions, the Walsh system, the Walsh series,. and the fast Walsh–Hadamard transform are all named after the American mathematician Joseph L. Walsh. They find various applications in physics and engineering when analyzing digital signals. Historically, various numerations of Walsh functions have been used; none of them is particularly superior to another.
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A hippogonal (pronounced ) chess move is one similar to a knight's move. That is, a leap m squares in one of the orthogonal directions, and n squares in the other, for integer values of m and n. It need not be a 2:1 ratio for m and n. A specific type of hippogonal move can be written (m,n), usually with the smaller number first.
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A plane partition. Partition theory studies various enumeration and asymptotic problems related to integer partitions, and is closely related to q-series, special functions and orthogonal polynomials. Originally a part of number theory and analysis, it is now considered a part of combinatorics or an independent field. It incorporates the bijective approach and various tools in analysis and analytic number theory and has connections with statistical mechanics.
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During the propagation of both temporal solitons and spatial solitons, despite being in a medium with birefringence, the orthogonal polarizations can copropagate as one unit without splitting due to the strong cross-phase modulation and coherent energy exchange between the two polarizations of the vector soliton which may induce intensity differences between these two polarizations. Thus vector solitons are no longer linearly polarized but rather elliptically polarized.
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Shown here is a bioorthogonal ligation between biomolecule X and reactive partner Y. To be considered bioorthogonal, these reactive partners cannot perturb other chemical functionality naturally found within the cell. Although effective bioorthogonal reactions such as copper-free click chemistry have been developed, development of new reactions continues to generate orthogonal methods for labeling to allow multiple methods of labeling to be used in the same biosystems.
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However, in general, expansion is not applied for Gabor wavelets, since this requires computation of bi-orthogonal wavelets, which may be very time-consuming. Therefore, usually, a filter bank consisting of Gabor filters with various scales and rotations is created. The filters are convolved with the signal, resulting in a so-called Gabor space. This process is closely related to processes in the primary visual cortex.
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A vector measuring current meter (VMCM) is an instrument used for obtaining measurements of horizontal velocity in the upper ocean, which exploits two orthogonal cosine response propeller sensors that directly measure the components of horizontal velocity.Weller, R. A., and R. E. Davis, 1980: A vector measuring current meter. Deep-Sea Research Part A, 27, 565-582. VMCM was developed in the late 1970s by Drs.
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Though Metawave managed to sell switched beam antennas to at least one major carrier, the company went out of business in 2004. In 1997, AT&T; Wireless Group announced plans to offer fixed wireless service at speeds up to 512 kbit/s. Project Angel promised non-line of sight (NLOS) coverage using beamforming and orthogonal frequency division multiplexing (OFDM). Service was launched in ten cities in 2000.
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The chapel was accessible from the northern palace and from the northern tower on the third floor level. Main entrance to the chapel was placed in the south wall at the second floor level. At the level of the first floor, there is a small orthogonal sacristy adjacent to the southern wall of the chapel. In the past, this room was vaulted with a barrel vault.
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However, as \beta \rightarrow 1 the radiation grows like \gamma^6 as the particle tries to lose its energy in the form of EM waves. Also, when the acceleration and velocity are orthogonal the power is reduced by a factor of 1-\beta^2=1/\gamma^2, i.e. the factor \gamma^6 becomes \gamma^4. The faster the motion becomes the greater this reduction gets.
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In mathematics, the group of rotations about a fixed point in four-dimensional Euclidean space is denoted SO(4). The name comes from the fact that it is the special orthogonal group of order 4. In this article rotation means rotational displacement. For the sake of uniqueness rotation angles are assumed to be in the segment except where mentioned or clearly implied by the context otherwise.
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Static procedures are appropriate when higher mode effects are not significant. This is generally true for short, regular buildings. Therefore, for tall buildings, buildings with torsional irregularities, or non-orthogonal systems, a dynamic procedure is required. In the linear dynamic procedure, the building is modelled as a multi-degree-of-freedom (MDOF) system with a linear elastic stiffness matrix and an equivalent viscous damping matrix.
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The combined orbits of the three stars together give a parallax significantly more precise than the HIPPARCOS parallax. The inclinations of the two orbits are known accurately enough to calculate their relative inclination. The two orbital planes are within 30° of being orthogonal, with the inner orbit being prograde and the outer retrograde. Although slightly surprising, this situation is not necessarily rare in triple systems.
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White moves first. In general, the pieces move as in orthodox chess, with the center (cell 4) being considered orthogonal and diagonal to every adjacent cell. Pawn movement Pawns move one step orthogonally forward and capture to one step diagonally forward, as in orthodox chess. A movement "forward" can be defined as one that places the pawn closer to the starting cell of its enemy king.
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Note that Gaussian quadrature can also be adapted for various weight functions, but the technique is somewhat different. In Clenshaw–Curtis quadrature, the integrand is always evaluated at the same set of points regardless of w(x), corresponding to the extrema or roots of a Chebyshev polynomial. In Gaussian quadrature, different weight functions lead to different orthogonal polynomials, and thus different roots where the integrand is evaluated.
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These were based on an orthogonal frequency-division multiplexing technology known as FLASH-OFDM developed by Flarion (since 2006 owned by Qualcomm). However, other service providers soon adopted 802.16e (the mobile version of WiMAX). In September 2008, the Association of Radio Industries and Businesses in Japan adopted the 802.20-2008 standard as ARIB STD-T97. Kyocera markets products supporting the standard under the iBurst name.
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A binomial QMF – properly an orthonormal binomial quadrature mirror filter – is an orthogonal wavelet developed in 1990. The binomial QMF bank with perfect reconstruction (PR) was designed by Ali Akansu, and published in 1990, using the family of binomial polynomials for subband decomposition of discrete-time signals.A.N. Akansu, An Efficient QMF-Wavelet Structure (Binomial-QMF Daubechies Wavelets), Proc. 1st NJIT Symposium on Wavelets, April 1990.
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Mutually orthogonal Latin squares have a great variety of applications. They are used as a starting point for constructions in the statistical design of experiments, tournament scheduling, and error correcting and detecting codes. Euler's interest in Graeco-Latin squares arose from his desire to construct magic squares. The French writer Georges Perec structured his 1978 novel Life: A User's Manual around a 10×10 Graeco-Latin square.
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Players decide who will play the black and white pieces, and who will start first. A 3 in-a-row is defined as exactly three pieces of the same color adjacent to one another in an orthogonal direction. The player who forms the 3 in-a-row is allowed to capture one of their opponent's piece from anywhere on the board. This is known as a "ta'na".
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A bifilar dial showing the two wires Stainless steel bifilar sundial in Italy Particular of the steel threads A bifilar dial is a type of sundial invented by the German mathematician Hugo Michnik in 1922. It has two non-touching threads parallel to the dial. Usually the second thread is orthogonal-(perpendicular) to the first. The intersection of the two threads' shadows gives the local apparent time.
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300x300px Gastruloids are three dimensional aggregates of embryonic stem cells (ESCs) that, under appropriate culture conditions develop an embryo-like organization with three orthogonal axes and a precise distribution of the primordia for multiple derivatives of the three germ layers in the absence of extraembryonic tissues. Significantly, they lack fore- mid- and hindbrain. They are a model system for the study of mammalian development and disease.
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A highly efficient gold and palladium combined methodology for the Sonogashira coupling of a wide array of electronically and structurally diverse aryl and heteroaryl halides have been reported. The orthogonal reactivity of the two metals shows high selectivity and extreme functional group tolerance in Sonogashira coupling. A brief mechanistic study reveals that the gold-acetylide intermediate enters into palladium catalytic cycle at the transmetalation step.
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Cyclooctene undergoes ring-opening metathesis polymerization to give polyoctenamers, which are marketed under the name Vestenamer. cis-Cyclooctene (COE) is a substrate known for quite selectively forming the epoxide, as compared to other cycloalkenes, e.g. cyclohexene. Low amounts of radical by- products are found only. This behaviour is attributed to the difficulty of functionalizing allylic CH centers, which almost orthogonal allylic C-H bonds.
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Compounds with disphenoidal geometry (See-Saw Geometry) have two types of ligands: axial and equatorial. The axial pair lie along a common bond axis so that are related by a bond angle of 180°. The equatorial pair of ligands is situated in a plane orthogonal to the axis of the axial pair. Typically the bond distance to the axial ligands is longer than to the equatorial ligands.
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Effects coding is used when one does not have a particular comparison or control group and does not have any planned orthogonal contrasts. The intercept is the grand mean (the mean of all the conditions). The regression coefficient is the difference between the mean of one group and the mean of all the group means (e.g. the mean of group A minus the mean of all groups).
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In mathematics, Rodrigues' formula (formerly called the Ivory–Jacobi formula) is a formula for the Legendre polynomials independently introduced by , and . The name "Rodrigues formula" was introduced by Heine in 1878, after Hermite pointed out in 1865 that Rodrigues was the first to discover it. The term is also used to describe similar formulas for other orthogonal polynomials. describes the history of the Rodrigues formula in detail.
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Vilmos Totik (Mosonmagyaróvár, March 8, 1954) is a Hungarian mathematician, working in classical analysis, harmonic analysis, orthogonal polynomials, approximation theory, potential theory. He is a professor of the University of Szeged. Since 1989 he is also a part-time professor at the University of South Florida (Tampa). He received the Lester R. Ford Award in 2000 for his expository article A tale of two integrals.
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Brown managed to scrounge an older Mark IV flaw detector in Glasgow along with a 6-inch electrostatically-deflected Cathode-ray tube taken from the company stores in Glasgow. From the companies Barkingside R&D; department, Brown found an experimental weld-testing machine. Both these machines were cannibalised for parts. To measure the position of the transducer, Brown selected an 'X-Y' orthogonal measuring frame system.
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DFTs may be applied to composite OFDM signals, avoiding the need for the banks of oscillators and demodulators associated with individual subcarriers. Fast Fourier transforms are numerical algorithms used by computers to perform DFT calculations. FFTs also enable OFDM to make efficient use of bandwidth. The subchannels must be spaced apart in frequency just enough to ensure that their time-domain waveforms are orthogonal to each other.
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All data should be on the same scale for CA to be applicable, keeping in mind that the method treats rows and columns equivalently. It is traditionally applied to contingency tables — CA decomposes the chi-squared statistic associated with this table into orthogonal factors. Because CA is a descriptive technique, it can be applied to tables whether or not the \chi^2 statistic is appropriate.
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The intersection of the extended base and the altitude is called the foot of the altitude. The length of the altitude, often simply called "the altitude", is the distance between the extended base and the vertex. The process of drawing the altitude from the vertex to the foot is known as dropping the altitude at that vertex. It is a special case of orthogonal projection.
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The kernel of this homomorphism is the translation group, showing that it is a normal subgroup of the Euclidean group. The isometries that fix a given point form the stabilizer subgroup of the Euclidean group with respect to . The restriction to this stabilizer of above group homomorphism is an isomorphism. So the isometries that fix a given point form a group isomorphic to the orthogonal group.
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Costs for streets depend largely on four variables: street width, street length, block width and pavement width. Two inherent characteristics of the grid plan, frequent intersections and orthogonal geometry, facilitate pedestrian movement. The geometry helps with orientation and wayfinding and its frequent intersections with the choice and directness of route to desired destinations. In ancient Rome, the grid plan method of land measurement was called centuriation.
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In mathematics, the Cayley transform, named after Arthur Cayley, is any of a cluster of related things. As originally described by , the Cayley transform is a mapping between skew-symmetric matrices and special orthogonal matrices. The transform is a homography used in real analysis, complex analysis, and quaternionic analysis. In the theory of Hilbert spaces, the Cayley transform is a mapping between linear operators .
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This seminal work led to a patent application. The memory device and method of propagation were described in a paper presented at the 13th Annual Conference on Magnetism and Magnetic Materials, Boston, Massachusetts, 15 September 1967. The device used anisotropic thin magnetic films that required different magnetic pulse combinations for orthogonal propagation directions. The propagation velocity was also dependent on the hard and easy magnetic axes.
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One may define a partial order on the idempotents of a ring as follows: if a and b are idempotents, we write if and only if . With respect to this order, 0 is the smallest and 1 the largest idempotent. For orthogonal idempotents a and b, is also idempotent, and we have and . The atoms of this partial order are precisely the primitive idempotents.
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Aberration is more accurately calculated using Earth's instantaneous velocity relative to the barycenter of the Solar System. Note that the displacement due to aberration is orthogonal to any displacement due to parallax. If parallax were detectable, the maximum displacement to the south would occur in December, and the maximum displacement to the north in June. It is this apparently anomalous motion that so mystified early astronomers.
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An initial approach to this question was the definition and detailed study of the so-called classical groups over finite and other fields by . These groups were studied by L. E. Dickson and Jean Dieudonné. Emil Artin investigated the orders of such groups, with a view to classifying cases of coincidence. A classical group is, roughly speaking, a special linear, orthogonal, symplectic, or unitary group.
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A complex number lies in a complex plane having one real and one imaginary dimension, which may be represented as an Argand diagram. So a single complex dimension comprises two spatial dimensions, but of different kinds - one real and the other imaginary. The unitary plane comprises two such complex planes, which are orthogonal to each other. Thus it has two real dimensions and two imaginary dimensions.
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A three-dimensional orthotope is also called a right rectangular prism, rectangular cuboid, or rectangular parallelepiped. A special case of an n-orthotope, where all edges are equal length, is the n-cube. By analogy, the term "hyperrectangle" or "box" refers to Cartesian products of orthogonal intervals of other kinds, such as ranges of keys in database theory or ranges of integers, rather than real numbers.See e.g. .
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This is defined as the plane, orthogonal to the tangential plane, which contains the object point being considered and intersects the optical axis at the entrance pupil of the optical system. This plane contains the chief ray, but does not contain the optic axis. It is therefore a skew plane, in other words not a meridional plane. Rays propagating in this plane are called sagittal rays.
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There is a standard technique (see for example ) for computing the change of variables to normal coordinates , at a point as a formal Taylor series expansion. If the coordinates , at (0,0) are locally orthogonal, write : : where , are quadratic and , cubic homogeneous polynomials in and . If and are fixed, and can be considered as formal power series solutions of the Euler equations: this uniquely determines , , , , and .
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Textile-reinforced mortars (TRM) (also known as fibre-reinforced cementitious mortars (FRCM)) are composite materials used in structural strengthening of existing buildings, most notably in seismic retrofitting. The material consists of bidirectional orthogonal textiles made from knitted or woven rovings of high-strength fibres (e.g. carbon, glass or basalt), embedded in a inorganic mortars.. The textiles can also be made from natural fibres, e.g. hemp or flax.
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More generally, this beam may be described as a superposition of transverse modes. Accurate description of such a beam involves expansion over some complete, orthogonal set of functions (over two-dimensions) such as Hermite polynomials or the Ince polynomials. Unstable laser resonators on the other hand, have been shown to produce fractal shaped beams. Some intracavity elements are usually placed at a beam waist between folded sections.
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Labeling can take place in all three orthogonal cut planes and results can be visualized as a three-dimensional rendering. This makes it easier to ensure that the segmentation maintains reasonable shape in 3D. ; Automatic segmentation: ITK-SNAP provides automatic functionality segmentation using the level-set method. This makes it possible to segment structures that appear somewhat homogeneous in medical images using very little human interaction.
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A special case of modal dispersion is polarization mode dispersion (PMD), a fiber dispersion phenomenon usually associated with single-mode fibers. PMD results when two modes that normally travel at the same speed due to fiber core geometric and stress symmetry (for example, two orthogonal polarizations in a waveguide of circular or square cross-section), travel at different speeds due to random imperfections that break the symmetry.
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In Möbius geometry, tangency between a line and a circle becomes a special case of tangency between two circles. This equivalence is extended further in Lie sphere geometry. Radius and tangent line are perpendicular at a point of a circle, and hyperbolic-orthogonal at a point of the unit hyperbola. The parametric representation of the unit hyperbola via radius vector is p(a) \ =\ (\cosh a, \sinh a) .
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Also, notice that any element r \in R that isn't in I will have a non-zero action on the module R/I, implying the set R-I can be thought of as the set of orthogonal elements to the ideal I. For noncommutative rings R, there is a similar notion of the annihilator for left and right modules, called the left-annihilator and the right-annihilator.
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I mirrored myself in this character and found myself found at home found Horizontal vision in front. E.4. This image recalls some of Le Corbusier's paintings from the 1930s. It is orthogonal, architectural and labyrinthine. Will appear I sense it the splendor of brut concrete and the grandeur which it will have had to think the marriage of lines to weight the forms To weight...
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A.N. Akansu and M.J.T. Smith,Subband and Wavelet Transforms: Design and Applications, Kluwer Academic Publishers, 1995. A.N. Akansu and M.J. Medley, Wavelet, Subband and Block Transforms in Communications and Multimedia, Kluwer Academic Publishers, 1999.A.N. Akansu, P. Duhamel, X. Lin and M. de Courville Orthogonal Transmultiplexers in Communication: A Review, IEEE Trans. On Signal Processing, Special Issue on Theory and Applications of Filter Banks and Wavelets. Vol.
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It is a particular case of the first family described in #2. # The Apollonian circles are two families of mutually orthogonal circles. The first family consists of the circles with all possible distance ratios to two fixed foci (the same circles as in #1), whereas the second family consists of all possible circles that pass through both foci. These circles form the basis of bipolar coordinates.
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Poly(3-alkylthiophenes) are the archetypical materials for solar cells and transistors. Conducting polymers have backbones of contiguous sp2 hybridized carbon centers. One valence electron on each center resides in a pz orbital, which is orthogonal to the other three sigma-bonds. The electrons in these delocalized orbitals have high mobility when the material is doped by oxidation, which removes some of these delocalized electrons.
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In mathematics, the Rogers polynomials, also called Rogers–Askey–Ismail polynomials and continuous q-ultraspherical polynomials, are a family of orthogonal polynomials introduced by in the course of his work on the Rogers–Ramanujan identities. They are q-analogs of ultraspherical polynomials, and are the Macdonald polynomials for the special case of the A1 affine root system . and discuss the properties of Rogers polynomials in detail.
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Coordinate surfaces of the three-dimensional parabolic coordinates. The red paraboloid corresponds to τ=2, the blue paraboloid corresponds to σ=1, and the yellow half-plane corresponds to φ=-60°. The three surfaces intersect at the point P (shown as a black sphere) with Cartesian coordinates roughly (1.0, -1.732, 1.5). The two-dimensional parabolic coordinates form the basis for two sets of three- dimensional orthogonal coordinates.
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In mathematics, the Mehler–Heine formula introduced by and describes the asymptotic behavior of the Legendre polynomials as the index tends to infinity, near the edges of the support of the weight. There are generalizations to other classical orthogonal polynomials, which are also called the Mehler–Heine formula. The formula complements the Darboux formulae which describe the asymptotics in the interior and outside the support.
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Figure 4 Reinforced concrete shear wall with both horizontal and vertical reinforcement. Concrete shear walls are reinforced with both horizontal and vertical reinforcement (Figure 4). A reinforcement ratio is defined as the ratio of the gross concrete area for a section taken orthogonal to the reinforcement. Construction codes of practice define maximum and minimum amounts of reinforcement as well as the detailing of steel bars.
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The first 21 Zernike polynomials, ordered vertically by radial degree and horizontally by azimuthal degree In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike, winner of the 1953 Nobel Prize in Physics and the inventor of phase-contrast microscopy, they play important roles in various optics branches such as beam optics and imaging.
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Hippodamus is also reported to have played an important role in the (re-)planning of the city of Piraeus, and he is also associated to Thurii and Rhodes. It seems that the importance of Hippodamus’ ideas was not so much in the orthogonal plan, but rather in the distribution of functions and social classes across the city. (Kolb 1984, pp. 115-120; Cahill, Nicholas (2002).
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It is also uncertain how many enemy pieces a player can capture if in one move a player forms two or more 3 in-a-rows. In Dara, only one enemy piece is allowed to be captured per turn. Lastly, it is also uncertain whether diagonal 3 in-a-rows count. In Dara they do not count, only orthogonal 3 in-a- rows count.
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Rendezvous Strategy of the Japanese Logistics Support Vehicle to the International Space Station, Success! Space station snags SpaceX Dragon capsule ; Z-bar approach An approach of the active, or "chaser", spacecraft horizontally from the side and orthogonal to the orbital plane of the passive spacecraft—that is, from the side and out-of-plane of the orbit of the passive spacecraft—is called a Z-bar approach.
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The V-bar, or velocity vector, extends along a line directly ahead of the station. Shuttles approach the ISS along the V-bar when docking at the PMA-2 docking port. ; R-bar approach The R-bar approach consists of the chaser moving below or above the target spacecraft, along its radial vector. The motion is orthogonal to the orbital velocity of the passive spacecraft.
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Typically, an HDR reservoir forms in the shape of an ellipsoid, with its longest axis orthogonal to the least principal Earth stress. This pressure-stimulated region is then accessed by two production wells, drilled to intersect the HDR reservoir near the elongated ends of the stimulated region. In most cases, the initial borehole becomes the injection well for the three-well, pressurized water-circulating system.
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The player's piece leaps over it (as in draughts), and lands on a vacant point immediately beyond. The leap must be in a straight line, and follow the pattern on the board. If possible, the piece can continue to capture in any (orthogonal) direction. It is uncertain whether captures are compulsory, but in games like Kotu Ellima, Sixteen Soldiers, and Peralikatuma, captures are compulsory.
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The first two steps of the Gram–Schmidt process In mathematics, particularly linear algebra and numerical analysis, the Gram–Schmidt process is a method for orthonormalizing a set of vectors in an inner product space, most commonly the Euclidean space Rn equipped with the standard inner product. The Gram–Schmidt process takes a finite, linearly independent set S = {v1, ..., vk} for and generates an orthogonal set that spans the same k-dimensional subspace of Rn as S. The method is named after Jørgen Pedersen Gram and Erhard Schmidt, but Pierre-Simon Laplace had been familiar with it before Gram and Schmidt. In the theory of Lie group decompositions it is generalized by the Iwasawa decomposition. The application of the Gram–Schmidt process to the column vectors of a full column rank matrix yields the QR decomposition (it is decomposed into an orthogonal and a triangular matrix).
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However, by co-mutating the binding nucleotides in such a way, that they can still base pair, the translational fidelity can be conserved. The 3’-end of the tRNA is mutated from CCA to CGA, while two cytidine nucleotides in the ribosomes A- and P-sites are mutated to guanidine. This leads to ribosomes which do not accept naturally occurring tRNAs as substrates and to tRNAs, which cannot be used as substrate by natural ribosomes. To use such tRNAs effectively, they would have to be aminoacylated by specific, orthogonal aaRSs. Most naturally occurring aaRSs recognize the 3’-end of their corresponding tRNA. aaRSs for these 3’-mutated tRNAs are not available yet. Thus far, this system has only been shown to work in an in- vitro translation setting where the aminoacylation of the orthogonal tRNA was achieved using so called “flexizymes”. Flexizymes are ribozymes with tRNA- amino-aclylation activity.
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Multiple-input, multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) is the dominant air interface for 4G and 5G broadband wireless communications. It combines multiple-input, multiple-output (MIMO) technology, which multiplies capacity by transmitting different signals over multiple antennas, and orthogonal frequency-division multiplexing (OFDM), which divides a radio channel into a large number of closely spaced subchannels to provide more reliable communications at high speeds. Research conducted during the mid-1990s showed that while MIMO can be used with other popular air interfaces such as time-division multiple access (TDMA) and code-division multiple access (CDMA), the combination of MIMO and OFDM is most practical at higher data rates. MIMO-OFDM is the foundation for most advanced wireless local area network (wireless LAN) and mobile broadband network standards because it achieves the greatest spectral efficiency and, therefore, delivers the highest capacity and data throughput.
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In the best possible case, one has data streams of measurements of all the system variables, equally spaced in time, say :s1(t), s2(t), ... , sk(t) for : t = t1, t2,..., tn, beginning at several different initial conditions. Then the task of finding a vector field, and thus a differential equation model consists of fitting functions, for instance, a cubic spline, to the data to obtain a set of continuous time functions :x1(t), x2(t), ... , xk(t), computing time derivatives dx1/dt, dx2/dt,...,dxk/dt of the functions, then making a least squares fit using some sort of orthogonal basis functions (orthogonal polynomials, radial basis functions, etc.) to each component of the tangent vectors to find a global vector field. A differential equation then can be read off the global vector field. There are various methods of creating the basis functions for the least squares fit.
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Given positive (or more generally irreducible non-negative matrix) A, the Perron–Frobenius eigenvector is the only (up to multiplication by constant) non-negative eigenvector for A. Other eigenvectors must contain negative or complex components since eigenvectors for different eigenvalues are orthogonal in some sense, but two positive eigenvectors cannot be orthogonal, so they must correspond to the same eigenvalue, but the eigenspace for the Perron–Frobenius is one-dimensional. Assuming there exists an eigenpair (λ, y) for A, such that vector y is positive, and given (r, x), where x – is the left Perron–Frobenius eigenvector for A (i.e. eigenvector for AT), then rxTy = (xT A) y = xT (Ay) = λxTy, also xT y > 0, so one has: r = λ. Since the eigenspace for the Perron–Frobenius eigenvalue r is one-dimensional, non-negative eigenvector y is a multiple of the Perron–Frobenius one.
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Mizan Rahman (September 16, 1932 – January 5, 2015) was a Bangladeshi Canadian mathematician and writer. He specialized in fields of mathematics such as hypergeometric series and orthogonal polynomials. He also had interests encompassing literature, philosophy, scientific skepticism, freethinking and rationalism. He co-authored Basic Hypergeometric SeriesGeorge Gasper and Mizan Rahman, Basic Hypergeometric Series, first edition, 1990; second extended edition, 2004, Encyclopedia of Mathematics and Its Applications, 96, Cambridge University Press. .
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The Euler line E is sensitive to the symmetries of P in the following ways: 1\. If P has a line of reflection symmetry L, then E is either L or a point on L. 2\. If P has a center of rotational symmetry C, then E=C. 3\. If all but one of the sides of P have equal length, then E is orthogonal to the last side.
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In an ideal optical fiber, the core has a perfectly circular cross-section. In this case, the fundamental mode has two orthogonal polarizations (orientations of the electric field) that travel at the same speed. The signal that is transmitted over the fiber is randomly polarized, i.e. a random superposition of these two polarizations, but that would not matter in an ideal fiber because the two polarizations would propagate identically (are degenerate).
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In January 1829, Stamatis Voulgaris, a Greek engineer of the French army, presented the plan of the new city to the Governor Kapodistrias, who approved it. Voulgaris applied the orthogonal rule in the urban complex of Patras. However his initial plan was modified in 1830. Two special genres can be considered the Cycladic architecture, featuring whitewashedhouses, in the Cyclades and the Epirotic architecture in the region of Epirus, featuring stone houses.
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Conducting polymers have backbones of contiguous sp2 hybridized carbon centers. One valence electron on each center resides in a pz orbital, which is orthogonal to the other three sigma-bonds. All the pz orbitals combine with each other to a molecule wide delocalized set of orbitals. The electrons in these delocalized orbitals have high mobility when the material is "doped" by oxidation, which removes some of these delocalized electrons.
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However, the complexity was often beyond what could be achieved using current technology. For this reason, most machines from the 1960s offered only partial orthogonality, as much as the designers could afford. It was in the 1970s that the introduction of large scale integration significantly reduced the complexity of computer designs and fully orthogonal designs began to emerge. By the 1980s, such designs could be implemented on a single-chip CPU.
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There is no single straightforward generalization of polygon monotonicity to higher dimensions. In one approach the preserved monotonicity trait is the line L. A three-dimensional polyhedron is called weakly monotonic in direction L if all cross-sections orthogonal to L are simple polygons. If the cross-sections are convex, then the polyhedron is called weakly monotonic in convex sense. Both types may be recognized in polynomial time.
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A Malaysian variant called Apit-sodok is closely related. The game is documented in R.J. Wilkinson's work Papers on Malay Subjects (1910), and Raja Samusah's article The Malay Game of Apit (1932), and both refer to the game as Apit. Samusah also refers to the game as Sodok Apit. Both authors describe custodian and intervention capture, but only Samusah describes orthogonal movement of pieces as in the rook in chess.
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These orthogonal (opposite) factors were presented in a quadrant configuration labeled LBI, LBE, RBI, and RBE. There are many variants and overlapping grey zones that allow for more specific descriptions of horses. Again these are based on how humans view horses and therefore tend to approach them. The goal is to provide a positive language for perceiving horses and use this terminology to link to recommended natural training approaches.
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The number turns up frequently in geometry, particularly in figures with pentagonal symmetry. The length of a regular pentagon's diagonal is times its side. The vertices of a regular icosahedron are those of three mutually orthogonal golden rectangles. There is no known general algorithm to arrange a given number of nodes evenly on a sphere, for any of several definitions of even distribution (see, for example, Thomson problem).
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The search coil magnetometer or induction magnetometer, based on an inductive sensor (also known as inductive loop and inductive coil), is a magnetometer which measures the varying magnetic flux due to Lenz's law. An inductive sensor connected to a conditioning electronic circuit constitutes a search coil magnetometer. It is a vector magnetometer which can measure one or more components of the magnetic field. A classical configuration uses three orthogonal inductive sensors.
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The Cartesian coordinate system in the plane. The prototypical example of a coordinate system is the Cartesian coordinate system. In the plane, two perpendicular lines are chosen and the coordinates of a point are taken to be the signed distances to the lines. 250px In three dimensions, three mutually orthogonal planes are chosen and the three coordinates of a point are the signed distances to each of the planes.
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The problem of colored range counting considers the case where points have categorical attributes. If the categories are considered as colors of points in geometric space, then a query is for how many colors appear in a particular range. Prosenjit Gupta and others described a data structure in 1995 which solved 2D orthogonal colored range counting in O(n^2\log ^2 n) space and O(\log ^2 n) query time.
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Vector magnetometers measure one or more components of the magnetic field electronically. Using three orthogonal magnetometers, both azimuth and dip (inclination) can be measured. By taking the square root of the sum of the squares of the components the total magnetic field strength (also called total magnetic intensity, TMI) can be calculated by the Pythagorean theorem. Vector magnetometers are subject to temperature drift and the dimensional instability of the ferrite cores.
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Room in the hotel. The hotel is raised above street level on pilotis, five massive sculptural piers, which hoist the building thirty feet over the park below. On the east side of the structure "[a] single, sloped concrete pier, along which a tantalizing set of fire stairs runs, supports the building by the hotel entrance." The elevation of this structure is one clear distinction from the orthogonal street grid of Manhattan.
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50in Philadelphia's case, William Penn specified the city's orthogonal pattern when he founded it in 1682, although its blocks turned out to be too large, encouraging the creation of intermediate streets, while James Oglethorpe's Savannah, with its significantly smaller blocks, was not conducive to large-scale development, restricting the city's economic influence.Higgins pp.67–68 New Amsterdam, however, had not been laid out in a grid pattern by the Dutch.
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CDMA is analogous to the last example where people speaking the same language can understand each other, but other languages are perceived as noise and rejected. Similarly, in radio CDMA, each group of users is given a shared code. Many codes occupy the same channel, but only users associated with a particular code can communicate. In general, CDMA belongs to two basic categories: synchronous (orthogonal codes) and asynchronous (pseudorandom codes).
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Geodesics on a sphere are arcs of great circles (yellow curve). On a 2D-manifold (such as the sphere shown), the direction of the accelerating geodesic is uniquely fixed if the separation vector is orthogonal to the "fiducial geodesic" (green curve). As the separation vector changes to after a distance , the geodesics are not parallel (geodesic deviation).Misner, Thorne, Wheeler, Gravitation The above equations are valid in flat spacetime.
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A subtle technical problem afflicts some uses of orthogonal matrices. Not only are the group components with determinant +1 and −1 not connected to each other, even the +1 component, , is not simply connected (except for SO(1), which is trivial). Thus it is sometimes advantageous, or even necessary, to work with a covering group of SO(n), the spin group, . Likewise, has covering groups, the pin groups, Pin(n).
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The bumped cyclosporin A was found to interact efficiently with the hole-modified cyclophilin mutant, but not endogenous cyclophilin. The orthogonal CID pair was used to inhibit calcineurin-mediated dephosphorylation of nuclear factor of activated T cells in a cell- and tissue-specific manner. More recently, this first bump-and-hole pair was used to induce the assembly of ten-eleven translocation 2 dioxygenase in cells for temporally controlled DNA demethylation.
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The capture must be done in an orthogonal direction following the slanted or diagonal design of the board. Only one enemy piece can be captured per turn. A captured piece is removed from the board. 6\. If a player's piece has been captured, then the player at the beginning of his or her next turn must take one piece from their reserve, and drop it on any vacant space.
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In Rome, at the crossing between viale Regina Margherita and via Nomentana, tram and trolleybus lines cross: tram on viale Regina Margherita and trolleybus on via Nomentana. The crossing is orthogonal, therefore the typical arrangement was not available. In Milan, most tram lines cross its circular trolleybus line once or twice. Trolleybus and tram wires run parallel in streets such as viale Stelvio, viale Umbria and viale Tibaldi.
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These are small (< 20 μm in diameter) flagellated protists. The life cycle of consists of two main stages: flagellated trophozoites and cysts, which are the reproductive stage in the life cycle. Morphologically the trophozoites of Colpodella are similar to Perkinsus zoospores, although the two taxa are not specifically related. The motile stages of both genera have a pair of anterior orthogonal flagella, vesicular mitochondrial cristae, inner alveolar membranes and micropores.
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CEM models extensively make use of symmetry, and solve for reduced dimensionality from 3 spatial dimensions to 2D and even 1D. An eigenvalue problem formulation of CEM allows us to calculate steady state normal modes in a structure. Transient response and impulse field effects are more accurately modeled by CEM in time domain, by FDTD. Curved geometrical objects are treated more accurately as finite elements FEM, or non-orthogonal grids.
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The rotation group in four dimensions, SO(4), has six degrees of freedom. This can be seen by considering the 4 × 4 matrix that represents a rotation: as it is an orthogonal matrix the matrix is determined, up to a change in sign, by e.g. the six elements above the main diagonal. But this group is not linear, and it has a more complex structure than other applications seen so far.
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In music, normal modes of vibrating instruments (strings, air pipes, drums, etc.) are called "harmonics" or "overtones". The most general motion of a system is a superposition of its normal modes. The modes are normal in the sense that they can move independently, that is to say that an excitation of one mode will never cause motion of a different mode. In mathematical terms, normal modes are orthogonal to each other.
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Oblique rotations permit correlations among factors. An advantage of oblique rotation is that it produces solutions with better simple structure when factors are expected to correlate, and it produces estimates of correlations among factors.. These rotations may produce solutions similar to orthogonal rotation if the factors do not correlate with each other. Several oblique rotation procedures are commonly used. Direct oblimin rotation is the standard oblique rotation method.
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The high complexity of the d-dimensional data structures led to the study of special types of subdivision. One important example is the case of arrangements of hyperplanes. An arrangement of n hyperplanes defines O(nd) cells, but point location can be performed in O(log n) time with O(nd) space by using Chazelle's hierarchical cuttings. Another special type of subdivision is called rectilinear (or orthogonal) subdivision.
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The easternmost part of the system, the Eger Graben shows two distinct phases of extension at the end of the Eocene and during the early Miocene. The first phase was oblique to the rift axis and led to the formation of en-echelon W-E trending fault sets. The second was orthogonal to the rift axis, leading to overprinting of the early W-E faults by later SW-NE trending faults.
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In healthcare, the flow of a patient between healthcare professionals is considered as a workflow - with activities that include all kinds of diagnostic or therapeutic treatments. The workflow is considered as a case, and workflow management in healthcare is to handle these cases. Case handling is orthogonal to content-oriented workflows. Some content-oriented workflow approaches are not related to case handling, but, for example, to automated manufacturing.
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He makes this distinction because value is only added during the processing steps in the process not by the transportation, inspection and delay steps. He states that whereas many see Process and Operations in parallel he sees them at right angles (orthogonal) (see Value Stream Mapping). This starkly throws most of the operations into the waste category. Many of the TPS/Lean techniques work in a similar way.
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A special sub-family of polygon partition problems arises when the large polygon is a rectilinear polygon (also called: orthogonal polygon). In this case, the most important component shape to consider is the rectangle. Rectangular partitions have many applications. In VLSI design, it is necessary to decompose masks into the simpler shapes available in lithographic pattern generators, and similar mask decomposition problems also arise in DNA microarray design.
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A pseudoscalar in a geometric algebra is a highest-grade element of the algebra. For example, in two dimensions there are two orthogonal basis vectors, e_1, e_2 and the associated highest- grade basis element is :e_1 e_2 = e_{12}. So a pseudoscalar is a multiple of e12. The element e12 squares to −1 and commutes with all even elements – behaving therefore like the imaginary scalar i in the complex numbers.
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At this point, the Z axis is now orthogonal to the plane in which any ABC vector without a common- mode component can be found. Any balanced ABC vector waveform (a vector without a common mode) will travel about this plane. This plane will be called the zero plane and is shown below by the hexagonal outline. Plane of the vectors without common mode indicated by the hexagonal outline.
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The Z axis is orthogonal to this plane, and the X axis is parallel to the projection of the A axis onto the zero plane. The X and Y basis vectors are on the zero plane. Notice that the X axis is parallel to the projection of the A axis onto the zero plane. The X axis is slightly larger than the projection of the A axis onto the zero plane.
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Although he was a child prodigy, Charlie now laments the fact that his best years in his research will never come ahead of schedule again. Eppes is a multiple Ph.D. ("Decoy Effect"), a recipient of the Milton Prize and a nominee for the Fields Medal. Following his five-year research on random matrices, Charlie worked on sequences with orthogonal symmetry. He has also provided insights for possibly solving the P vs.
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The image of the text as rendered by the user's browser is then recovered by the ToDataURL Canvas API method. The hashed text- encoded data becomes the user's fingerprint. Canvas fingerprinting methods have been shown to produce 5.7 bits of entropy. Because the technique obtains information about the user's GPU, the information entropy gained is "orthogonal" to the entropy of previous browser fingerprint techniques such as screen resolution and JavaScript capabilities.
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Earth's rotation is not a simple rotation around an axis that would always remain parallel to itself. Earth's rotational axis itself rotates about a second axis, orthogonal to Earth's orbit, taking about 25,800 years to perform a complete rotation. This phenomenon is called the precession of the equinoxes. Because of this precession, the stars appear to move around Earth in a manner more complicated than a simple constant rotation.
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Rarita–Schwinger operators, also known as Stein–Weiss operators, arise in representation theory for the Spin and Pin groups. The operator Rk is a conformally covariant first order differential operator. Here k = 0, 1, 2, .... When k = 0, the Rarita–Schwinger operator is just the Dirac operator. In representation theory for the orthogonal group, O(n) it is common to consider functions taking values in spaces of homogeneous harmonic polynomials.
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The planar Lie quadric Q consists of the points [x] in projective space represented by vectors x with x · x = 0. To relate this to planar geometry it is necessary to fix an oriented timelike line. The chosen coordinates suggest using the point [1,0,0,0,0] ∈ RP4. Any point in the Lie quadric Q can then be represented by a vector x = λ(1,0,0,0,0) + v, where v is orthogonal to (1,0,0,0,0).
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'Araqhama and the plaza of Manyaraki The main settlement at Ollantaytambo has an orthogonal layout with four longitudinal streets crossed by seven parallel streets.Protzen, Inca Architecture, p. 50. At the center of this grid, the Incas built a large plaza that may have been up to four blocks large; it was open to the east and surrounded by halls and other town blocks on its other three sides.Protzen, Inca Architecture, stones.
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Lattice reduction in two dimensions: the black vectors are the given basis for the lattice (represented by blue dots), the red vectors are the reduced basis In mathematics, the goal of lattice basis reduction is given an integer lattice basis as input, to find a basis with short, nearly orthogonal vectors. This is realized using different algorithms, whose running time is usually at least exponential in the dimension of the lattice.
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It can be simply kept on steel structure for only rest type supports. To simultaneously restrict in another direction separate plate or Lift up Lug can be used. A pipe anchor is a rigid support that restricts movement in all three orthogonal directions and all three rotational directions, i.e. restricting al the 6 degrees of freedom This usually is a welded stanchion that is welded or bolted to steel or concrete.
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The RQ decomposition transforms a matrix A into the product of an upper triangular matrix R (also known as right-triangular) and an orthogonal matrix Q. The only difference from QR decomposition is the order of these matrices. QR decomposition is Gram–Schmidt orthogonalization of columns of A, started from the first column. RQ decomposition is Gram–Schmidt orthogonalization of rows of A, started from the last row.
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Given a starting width, both algorithms create perfect mazes of unlimited height. Most maze generation algorithms require maintaining relationships between cells within it, to ensure the end result will be solvable. Valid simply connected mazes can however be generated by focusing on each cell independently. A binary tree maze is a standard orthogonal maze where each cell always has a passage leading up or leading left, but never both.
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As with the street width, any pattern can have wide or narrow pavements. Of all three factors that affect cost, street width, street length and pavement width, only street length is pattern dependent. An objective cost comparison would, therefore, rely on this variable with the full understanding that the other variables, though optional, can play a role. Traditional orthogonal grid patterns generally have greater street frequencies than discontinuous patterns.
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In 2016 Gasera completed a three-year collaboration with the European Union in the DOGGIES (Detection of Olfactory traces by orthoGonal Gas identification technologIES) project, developing technology that imitates sniffer dogs for border patrol and the police. The technology can be used for detecting different drugs, such as amphetamine, cocaine, heroin and cannabis. DOGGIES was funded by the European Commission under the 7th Framework Programme for Research and Technological Development.
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Latency is also down 75%. To improve spectrum efficient utilization, the new version introduces better power-control methods to avoid interference with neighboring networks, orthogonal frequency-division multiple access (OFDMA), higher order 1024-QAM, and up-link direction added with the down-link of MIMO and MU-MIMO to further increase throughput, as well as dependability improvements of power consumption and security protocols such as Target Wake Time and WPA3.
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Porter and Duff gave a geometric interpretation of the alpha compositing formula by studying orthogonal coverages. Another derivation of the formula, based on a physical reflectance/transmittance model, can be found in a 1981 paper by Bruce A. Wallace. A third approach is found by starting out with two very simple assumptions. For simplicity, we shall here use the shorthand notation a \odot b for representing the over operator.
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Partial derivatives are key to target-aware image resizing algorithms. Widely known as seam carving, these algorithms require each pixel in an image to be assigned a numerical 'energy' to describe their dissimilarity against orthogonal adjacent pixels. The algorithm then progressively removes rows or columns with the lowest energy. The formula established to determine a pixel's energy (magnitude of gradient at a pixel) depends heavily on the constructs of partial derivatives.
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Inertial navigation system (INS) is a dead reckoning type of navigation system that computes its position based on motion sensors. Before actually navigating, the initial latitude and longitude and the INS's physical orientation relative to the earth (e.g., north and level) are established. After alignment, an INS receives impulses from motion detectors that measure (a) the acceleration along three axes (accelerometers), and (b) rate of rotation about three orthogonal axes (gyroscopes).
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Egorov studied potential surfaces and triply orthogonal systems, and made significant contributions to the broader areas of differential geometry and integral equations. His work influenced that of Jean Gaston Darboux on differential geometry and mathematical analysis. A theorem in real analysis and integration theory, Egorov's Theorem, is named after him.He published a proof of this theorem in the short paper , and the result become widely acknowledged under his name.
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2008 Sep;48(9):1733-46. To investigate the AD of a training set of chemicals one can directly analyse properties of the multivariate descriptor space of the training compounds or more indirectly via distance (or similarity) metrics. When using distance metrics care should be taken to use an orthogonal and significant vector space. This can be achieved by different means of feature selection and successive principal components analysis.
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The Bousbir, a Yoshiwara-inspired colonial brothel district. In the 1920s, the colonial administration created a (prostitution quarter) south of the Hubous that came to be known as Bousbir. It was inspired by the Yoshiwara in Tokyo and operated by a private company called . Albert Laprade first set up a rectangular area with an orthogonal street layout, while and Edmond Brion manipulated traditional Moroccan forms employed in the Hubous.
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A prominent model proposed by Jamil Zaki and Craig Williams (2013) conceptualizes different classes of interpersonal emotion regulation along two orthogonal dimensions. The first, intrinsic vs extrinsic, refers to the target of regulatory efforts. Intrinsic regulation involves an attempt to change one's own emotions through social contact, while extrinsic regulation involves trying to change the emotions of another person or group of people. The second dimension, response-dependent vs.
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