Giden Sundback patented the "separable fastener" in 1917, as well.
|
|
Yet the tasks of peer review and publication are separable.
|
|
You know, I think there's three things that are very separable.
|
|
But I tend to think that liberalism and democracy are not really separable.
|
|
But Bossert's syntax was dubious, seemingly suggesting climate change impacts and causes are easily separable.
|
|
I wanted to show that in the ebb and flow of life, nothing is totally separable.
|
|
In "The People v Democracy", Yascha Mounk of Harvard University stresses that liberalism and democracy are separable.
|
|
They are equally convincing that scientific space endeavors aren't separable from military ones, and they never were.
|
|
As this might suggest, Trump fans' economic and cultural worries are not as separable as the Democrats hope.
|
|
And if consciousness is separable from the body, then it's possible to have survival beyond the physical body.
|
|
The justices said the "pictorial, graphic, or sculptural features" must be "separable" from the design of a utilitarian object.
|
|
On the other hand I would say that no brain function is completely separable from bodily and environmental context.
|
|
"These spaces are not separable from me even if I no longer live in these places," Suh tells Creators.
|
|
In 1917, the U.S. gave a Swedish immigrant a patent for a "separable fastener," now known as a zipper.
|
|
These losses, and the auguries of them haunting the play, could not have been separable from the reception it received.
|
|
In 1917, the United States gave a Swedish immigrant a patent for his "separable fastener" also known as a zipper.
|
|
In 1917, the United States gave a Swedish immigrant a patent for his "separable fastener," also known as a zipper.
|
|
Instead, it offers limited protection for "useful items," such as apparel and accessories, Zerbo explains, which means only "separable creative elements" are covered.
|
|
Then again, the Trump brand's value may have been enhanced by his electoral victory in ways that are separable from his possible corruption.
|
|
Physical activity is a non-separable part of this experience, and it's couched within a traditional role playing game (RPG) game design style.
|
|
The production of that album is extremely elaborate, and the Stellia represent every layer with forensic precision, so it's separable and distinguishable from the next.
|
|
I do think these are separable things and I worry that there's such a rise of cynicism relative to anything a tech company does now.
|
|
This "Great White Hunter" is hardly separable from the white Western imperialist bent on the conquest of the other, who is likened to a savage beast.
|
|
Nowotny and his team have found that separable odors aren't perceived at the same time; rather, the coffee and croissant odors are processed very rapidly in alternation.
|
|
This crackdown is by no means separable from the suffocating atmosphere of fear and abuse experienced by all Egyptians on a daily basis, regardless of their sexual orientations.
|
|
In the U.S., when that expression is part of a useful object, it only protects to the extent that the creative part is "separable" from the functional part.
|
|
To make headway on this question, it is crucial to clearly distinguish two conceptually and empirically separable aspects of "big government" — the regulatory state and the redistributive state.
|
|
Stein, which said that statuettes of Balinese dancers, used as lamp bases, could hold a copyright because the statuettes were physically separable from the lamps' functional electrical elements.
|
|
On the one hand, the stripe patterns would seem easily separable from the underlying garment: the colors and shapes could be removed, leaving essentially a white tennis dress.
|
|
Our society, which is less separable than we'd like from the cruder societies that came before it, has created a perfect storm of reasons to dismiss rape victims.
|
|
Law professor Nicholas Bagley said that Congress could pass a law, signed by the president, stating that it believes the individual mandate is separable from the ACA – making its intent clear.
|
|
"'Pure pleasure' (as from a drug) and 'meaningful happiness' really are conceptually separable," Brian Earp, a research associate with the Oxford University Center for Neuroethics in the United Kingdom, tells VICE.
|
|
Producer Mike WiLL Made It contributes hypnotically mechanical synth megahooks, stringing those ubiquitous high wispy keyboards across lower piano chords, constructing a giant lumbering metal animal-machine with discrete, mentally separable cogs.
|
|
It also prompts us to wonder whether the spirit of bar-going—the lack of structure and glut of spontaneity that draws us to bars—is separable from the loosening properties of alcohol.
|
|
Right now, it often doesn't, because the things being made—clothes, costumes, prosthetic hands—are useful articles whose designs are generally not separable from the underlying functionality and thus not subject to copyright.
|
|
That's because they decompose the issues into tests, frame the dispute as separable from broader foreign policy and remind stakeholders that to comply today increases the odds of getting them to comply tomorrow.
|
|
European philosophers like Thomas Hobbes and René Descartes, seeking to build a foundation of truth that was separable from the vicissitudes of emotion, articulated sharp divisions between war and peace, mind and body.
|
|
Rather I think ideals of diversity and meritocracy are two different ways of shaping an elite, which can advance together but which are just as often separable, or even in tension with each other.
|
|
To put it another way, the legacy of King Henry VIII, and his determination to assert English independence in both politics and religion (which were hardly separable in his time) seems perversely durable and stubborn.
|
|
Useful articles like clothing and accessories cannot have a copyright overall, but courts allow art embedded in those useful articles to have a copyright so long as the art is "separable" from the utilitarian parts.
|
|
Questions like these have bewildered courts across the country: No fewer than ten different tests have been articulated to determine whether the design of a useful article is separable from the useful elements and thus amenable to copyright.
|
|
But this is also a video that works well on TikTok specifically: the premise of the video is that the brother only got the audio, bolstering the idea that audio is often discrete and separable from videos on TikTok.
|
|
Her views on U.S. responsibility for Venezuela's democratic and food crises, for example, have been criticized by some as apologia for strong-arm leader Nicolás Maduro, whose record on human rights is abysmal and separable from arguments about U.S. interventions there.
|
|
Part of that might be explained by our existential condition: most of us feel that we have a core self, separate and separable from our body, and most of us find it hard to accept that we will someday cease to exist.
|
|
Impossible's solution for squeezing more battery life — and, therefore, more flight time — out of a similarly sized package is relatively simple: instead of relying on a separable battery pack that gets snapped on or slotted into the drone, all the individual battery cells are tucked throughout its structure.
|
|
Indeed, the considerable physical, financial, and emotional lengths to which many, many people will go to reproduce via IVF and other assisted reproductive means (a billion dollar industry) is evidence of a drive to reproduce that is separate, or at least separable, from any of the other reasons we have sex (e.g.
|
|
The great mistake of the modernist school of urban planning — best represented by Le Corbusier, who came within a hair of completely reshaping Barcelona in the 1930s, though his plan was ultimately thwarted by civil war — was to imagine the citizens and functions of a city as discrete, separable gears in a machine.
|
|
And while the two are not entirely separable, (because God gifts individuals with the ability to create great art and God created a world of great beauty and called it very good), there is a distinction between the building's function as a sacred space of worship and the building's beauty as a work of art.
|
|
Even with the H0LiCOW data in the mix now, the new Hubble constant measurement and the one determined from the cosmic microwave background aren't statistically separable to the very high degree of significance astrophysics demands, Anže Slosar, group leader of the Cosmology and Astrophysics Group at the Brookhaven National Laboratory in New York, who was not involved with the study, explained to Gizmodo.
|
|
Though Mill used the new word only in passing, it was not separable from the main point of his speech, which was intended to show the perils of any kind of abstract solution to Ireland's problems: So far from being a set of maxims and rules to be applied without regard to times, places, and circumstances, the function of political economy is to enable us to find the rules which ought to govern any state of circumstances with which we have to deal—circumstances which are never the same in any two cases.
|
|
A separable extension is an extension that may be generated by separable elements, that is elements whose minimal polynomials are separable.
|
|
An algebraic closure Kalg of K contains a unique separable extension Ksep of K containing all (algebraic) separable extensions of K within Kalg. This subextension is called a separable closure of K. Since a separable extension of a separable extension is again separable, there are no finite separable extensions of Ksep, of degree > 1. Saying this another way, K is contained in a separably- closed algebraic extension field. It is unique (up to isomorphism).
|
|
Thus, in some cases, the non-separable wavelets can be implemented in a separable fashion. Unlike separable wavelet, the non-separable wavelets are capable of detecting structures that are not only horizontal, vertical or diagonal (show less anisotropy).
|
|
Let E\supseteq F be a field extension. An element \alpha\in E is separable over if it is algebraic over , and its minimal polynomial is separable (the minimal polynomial of an element is necessarily irreducible). If \alpha,\beta\in E are separable over , then \alpha+\beta, \alpha\beta and 1/\alpha are separable over F. Thus the set of all elements in separable over forms a subfield of , called the separable closure of in .Isaacs, Lemma 19.15, p.
|
|
300 The separable closure of in an algebraic closure of is simply called the separable closure of . Like the algebraic closure, it is unique up to an isomorphism, and in general, this isomorphism is not unique. A field extension E\supseteq F is separable, if is the separable closure of in . This is the case if and only if is generated over by separable elements.
|
|
In mathematics, S-space is a regular topological space that is hereditarily separable but is not a Lindelöf space. L-space is a regular topological space that is hereditarily Lindelöf but not separable. A space is separable if it has a countable dense set and hereditarily separable if every subspace is separable. It had been believed for a long time that S-space problem and L-space problem are dual, i.e.
|
|
If E\supseteq L\supseteq F are field extensions, then is separable over if and only if is separable over and is separable over .Isaacs, Corollary 18.12, p. 281 If E\supseteq F is a finite extension (that is is a -vector space of finite dimension), then the following are equivalent. # is separable over .
|
|
Separable polynomials are used to define separable extensions: A field extension is a separable extension if and only if for every , which is algebraic over , the minimal polynomial of over is a separable polynomial. Inseparable extensions (that is extensions which are not separable) may occur only in characteristic . The criterion above leads to the quick conclusion that if P is irreducible and not separable, then D P(X) = 0. Thus we must have :P(X) = Q(Xp) for some polynomial Q over K, where the prime number p is the characteristic.
|
|
Such systems are referred to as separable systems. However, the region of support for the filter banks might not be separable. In that case designing of filter bank gets complex. In most cases we deal with non-separable systems.
|
|
By definition, a Hilbert space is separable provided it contains a dense countable subset. Along with Zorn's lemma, this means a Hilbert space is separable if and only if it admits a countable orthonormal basis. All infinite-dimensional separable Hilbert spaces are therefore isometrically isomorphic to . In the past, Hilbert spaces were often required to be separable as part of the definition.
|
|
In commutative algebra, an étale or separable algebra is a special type of algebra, one that is isomorphic to a finite product of separable extensions.
|
|
In German, among other languages, some verbs can exist as separable and inseparable forms with different meanings. For example, umfahren one can even construct an exactly opposite meaning (although the separable form is colloquial for überfahren): The infinitive form umfahren is only identical in its written form. When spoken, the non-separable form is stressed as umfahren, whereas the separable is stressed as umfahren.
|
|
In mathematics, a separable algebra is a kind of semisimple algebra. It is a generalization to associative algebras of the notion of a separable field extension.
|
|
Every second-countable manifold is separable and paracompact. Moreover, if a manifold is separable and paracompact then it is also second- countable. Every compact manifold is second-countable and paracompact.
|
|
There are several equivalent definitions of separable algebras. A K-algebra A is separable if and only if it is projective when considered as a left module of A^e in the usual way. Moreover, an algebra A is separable if and only if it is flat when considered as a right module of A^e in the usual way. Separable extensions can also be characterized by means of split extensions: A is separable over K if all short exact sequences of A-A-bimodules that are split as A-K-bimodules also split as A-A-bimodules.
|
|
If the dual of a normed space is separable, then so is the space itself. The converse is not true: for example, the space is separable, but its dual is not.
|
|
Any separable extension A / K of commutative rings is formally unramified. The converse holds if A is a finitely generated K-algebra. A separable flat (commutative) K-algebra A is formally étale.
|
|
Springer, 1999. are ideal for sampling rough stochastic processes. Since optimal lattices, in general, are non-separable, designing interpolation and reconstruction filters requires non-tensor-product (i.e., non-separable) filter design mechanisms.
|
|
Degenerate motion also signals that the Hamilton–Jacobi equations are completely separable in more than one coordinate system; for example, the Kepler problem is completely separable in both spherical coordinates and parabolic coordinates.
|
|
The Coulomb interaction between two protons is a special problem, in that its expansion in separable potentials does not converge, but this is handled by matching the Faddeev solutions to long range Coulomb solutions, instead of to plane waves. Separable potentials are interactions that do not preserve a particle's location. Ordinary local potentials can be expressed as sums of separable potentials. The physical nucleon-nucleon interaction, which involves exchange of mesons, is not expected to be either local or separable.
|
|
In quantum mechanics, separable quantum states are states without quantum entanglement.
|
|
Only the Gaussian function is both separable and isotropic. The separable forms of all other window functions have corners that depend on the choice of the coordinate axes. The isotropy/anisotropy of a two-dimensional window function is shared by its two- dimensional Fourier transform. The difference between the separable and radial forms is akin to the result of diffraction from rectangular vs.
|
|
A reflexive Banach space is separable if and only if its continuous dual is separable. This follows from the fact that for every normed space Y, separability of the continuous dual implies separability .Theorem 1.12.11 and Corollary 1.12.
|
|
In an older definition, P(X) was considered separable if each of its irreducible factors in K[X] is separable in the modern definition.N. Jacobson, Basic Algebra I, p. 233 In this definition, separability depended on the field K, for example, any polynomial over a perfect field would have been considered separable. This definition, although it can be convenient for Galois theory, is no longer in use.
|
|
The main difference, when compared to the one-dimensional wavelets, is that multi-dimensional sampling requires the use of lattices (e.g., the quincunx lattice). The wavelet filters themselves can be separable or non-separable regardless of the sampling lattice.
|
|
As confirmed by experimental results, simultaneous solutions have less error than separable quaternion solutions.
|
|
All compact, separable ordered spaces are order-isomorphic to a subset of the split interval.
|
|
A separable verb is a verb that is composed of a lexical core and a separable particle. In some sentence positions, the core verb and the particle appear in one word, whilst in others the core verb and the particle are separated. The particle cannot be accurately referred to as a prefix because it can be separated from the core verb. German, Dutch, Afrikaans and Hungarian are notable for having many separable verbs.
|
|
In the case of systems composed of m > 2 subsystems, the classification of quantum-entangled states is richer than in the bipartite case. Indeed, in multipartite entanglement apart from fully separable states and fully entangled states, there also exists the notion of partially separable states.
|
|
The textual form, therefore, is not separable from the manuduction of the soul toward beatific vision.
|
|
If K is a perfect field --- for example a field of characteristic zero, or a finite field, or an algebraically closed field --- then every extension of K is separable so that separable K-algebras are finite products of matrix algebras over finite-dimensional division algebras over field K. In other words, if K is a perfect field, there is no difference between a separable algebra over K and a finite-dimensional semisimple algebra over K. It can be shown by a generalized theorem of Maschke that an associative K-algebra A is separable if for every field extension \scriptstyle L/K the algebra \scriptstyle A\otimes_K L is semisimple.
|
|
Testing for separability in the general case is an NP-hard problem. Leinaas et. al. formulated an iterative, probabilistic algorithm for testing if a given state is separable. When the algorithm is successful, it gives an explicit, random, representation of the given state as a separable state.
|
|
The relationship between measurability and weak measurability is given by the following result, known as Pettis' theorem or Pettis measurability theorem. > Function f is almost surely separably valued (or essentially separably > valued) if there exists a subset N ⊆ X with μ(N) = 0 such that f(X \ N) ⊆ B > is separable. > A function f : X -> B defined on a measure space (X, Σ, μ) and taking > values in a Banach space B is (strongly) measurable (with respect to Σ and > the Borel algebra on B) if and only if it is both weakly measurable and > almost surely separably valued. In the case that B is separable, since any subset of a separable Banach space is itself separable, one can take N above to be empty, and it follows that the notions of weak and strong measurability agree when B is separable.
|
|
A more distant relation is P. barnardi, easily separable by the heavier sculpture and striking colour pattern.
|
|
The winner names are engraved around the trophy base, which is separable from the trophy's main body.
|
|
The Furstenberg integers are separable and metrizable, but incomplete. By Urysohn's metrization theorem, they are regular and Hausdorff.
|
|
However, it is sometimes argued that non-separable Hilbert spaces are also important in quantum field theory, roughly because the systems in the theory possess an infinite number of degrees of freedom and any infinite Hilbert tensor product (of spaces of dimension greater than one) is non-separable. For instance, a bosonic field can be naturally thought of as an element of a tensor product whose factors represent harmonic oscillators at each point of space. From this perspective, the natural state space of a boson might seem to be a non-separable space. However, it is only a small separable subspace of the full tensor product that can contain physically meaningful fields (on which the observables can be defined).
|
|
With respect to either σ or σ0, D is a separable space. Thus, Skorokhod space is a Polish space.
|
|
Many of the variations are separable only on tail and wing lengths and these vary with overlap across populations.
|
|
Most spaces used in physics are separable, and since these are all isomorphic to each other, one often refers to any infinite-dimensional separable Hilbert space as "the Hilbert space" or just "Hilbert space". defines a Hilbert space via a countable Hilbert basis, which amounts to an isometric isomorphism with l2. The convention still persists in most rigorous treatments of quantum mechanics; see for instance . Even in quantum field theory, most of the Hilbert spaces are in fact separable, as stipulated by the Wightman axioms.
|
|
In terms of quantum channels, a separable state can be created from any other state using local actions and classical communication while an entangled state cannot. When the state spaces are infinite-dimensional, density matrices are replaced by positive trace class operators with trace 1, and a state is separable if it can be approximated, in trace norm, by states of the above form. If there is only a single non-zero p_k, then the state is called simply separable (or it is called a "product state").
|
|
For example, the lower limit topology on the real line is first-countable, separable, and Lindelöf, but not second-countable. For metric spaces, however, the properties of being second-countable, separable, and Lindelöf are all equivalent.Willard, theorem 16.11, p. 112 Therefore, the lower limit topology on the real line is not metrizable.
|
|
If U is Urysohn universal and X is any separable metric space, then there exists an isometric embedding f:X → U. (Other spaces share this property: for instance, the space l∞ of all bounded real sequences with the supremum norm admits isometric embeddings of all separable metric spaces ("Fréchet embedding"), as does the space C[0,1] of all continuous functions [0,1]→R, again with the supremum norm, a result due to Stefan Banach.) Furthermore, every isometry between finite subsets of U extends to an isometry of U onto itself. This kind of "homogeneity" actually characterizes Urysohn universal spaces: A separable complete metric space that contains an isometric image of every separable metric space is Urysohn universal if and only if it is homogeneous in this sense.
|
|
Applying his version of the test to the cheerleader uniforms, he found that the design was not physically separable. Further, picturing the design separately would reveal a cheerleader uniform "coextensive with that design and cut", so the design and useful article were not conceptually separable either.Star Athletica, slip op. at 11 (Breyer, J., dissenting).
|
|
A separable metric space is completely metrizable if and only if the second player has a winning strategy in this game. A second characterization follows from Alexandrov's theorem. It states that a separable metric space is completely metrizable if and only if it is a G_\delta subset of its completion in the original metric.
|
|
DBSCAN can find non-linearly separable clusters. This dataset cannot be adequately clustered with k-means or Gaussian Mixture EM clustering.
|
|
Kelley, Problem 6.L, p. 208 A topological space homeomorphic to a separable complete metric space is called a Polish space.
|
|
The word "layer" indicates that the software is modular—it is front-end software, separable from an integrated library system (ILS).
|
|
The most interesting results of Maurice Lévy's thesis are the reconstruction of a separable interaction from a phase shiftA. Martin et M.Gourdin., « Exact determination of a phenomenogical separable interaction », Nuovo Cimento, 11 (1959), p. 670 and an original demonstration of Levinson's theorem.A. Martin, « On the validity of the Levinson Theorem for non local interactions », Nuovo Cimento, 7, ( 1958), p.
|
|
After reproduction the best chromosome and the worst chromosome in the offspring are found out. The designed filter has non- separable numerator and separable denominator transfer function.A. Mazinani, M. Ahmadi, M. Shridhar and R. S. Lashkari, “A novel approach to the design of 2-D recursive digital filters”, Journal of the Franklin Institute, Pergamon Press Ltd, vol. 329, no.
|
|
This is possible for simple PDEs, which are called separable partial differential equations, and the domain is generally a rectangle (a product of intervals). Separable PDEs correspond to diagonal matrices – thinking of "the value for fixed " as a coordinate, each coordinate can be understood separately. This generalizes to the method of characteristics, and is also used in integral transforms.
|
|
Independent component analysis (ICA) is directed to similar problems as principal component analysis, but finds additively separable components rather than successive approximations.
|
|
In mathematics, the Haran diamond theorem gives a general sufficient condition for a separable extension of a Hilbertian field to be Hilbertian.
|
|
Yet the Melanau language have retained much of its authenticity making it separable from Malay language despite heavy influence from Malay language itself.
|
|
The top of the hindwing is speckled yellow with red spots. It is only convincingly separable from Platysphinx piabilis by examining the genitalia.
|
|
In functional analysis, the Borel graph theorem is generalization of the closed graph theorem that was proven by L. Schwartz. The Borel graph theorem shows that the closed graph theorem is valid for linear maps defined on and valued in most spaces encountered in analysis. Recall that a topological space is called a Polish space if it is a separable complete metrizable space and that a Souslin space is the continuous image of a Polish space. The weak dual of a separable Fréchet space and the strong dual of a separable Fréchet–Montel space are Souslin spaces.
|
|
Breyer's approach to the problem was to interpret what "identified separately" meant in the context of the statute. His reading was that, to be separable, the design features needed to be either physically separable from the article while leaving the utilitarian object functional or else the design features needed to be conceivably separable without conjuring a picture of the utilitarian object in someone's mind. He returned to Mazer v. Stein and applied his reasoning to two lamps, one with a Siamese cat statuette for a pole and one with a brass rod pole and a cat statuette attached elsewhere on its base.
|
|
In quantum information theory, an entanglement witness is a functional which distinguishes a specific entangled state from separable ones. Entanglement witnesses can be linear or nonlinear functionals of the density matrix. If linear, then they can also be viewed as observables for which the expectation value of the entangled state is strictly outside the range of possible expectation values of any separable state.
|
|
Examples are on in carry on, get on, etc., over in take over, fall over, and so on. The equivalents in Dutch and German are separable prefixes, which also often have the same form as prepositions: for example, Dutch aanbieden and German anbieten (both meaning "to offer") contain the separable prefix aan/an, which is also a preposition meaning "on" or "to".
|
|
In field theory, a subfield of algebra, a separable extension is an algebraic field extension E\supseteq F such that for every \alpha\in E, the minimal polynomial of \alpha over F is a separable polynomial (i.e., its formal derivative is not zero; see below for other equivalent definitions).Isaacs, p. 281 Otherwise, the extension is said to be inseparable.
|
|
Advantages: 1\. The Fourier analysis is flexible as the signal is separable. 2.It preserves the phase components of every dimension unlike other spectral estimators.
|
|
But the imperatival character of this law is only felt in our feeling constrained to do some specific action, and is not separable from this.
|
|
Galois theory studies algebraic extensions of a field by studying the symmetry in the arithmetic operations of addition and multiplication. An important notion in this area is that of finite Galois extensions , which are, by definition, those that are separable and normal. The primitive element theorem shows that finite separable extensions are necessarily simple, i.e., of the form :, where is an irreducible polynomial (as above).
|
|
Any stochastic process with a countable index set already meets the separability conditions, so discrete-time stochastic processes are always separable. A theorem by Doob, sometimes known as Doob's separability theorem, says that any real-valued continuous-time stochastic process has a separable modification. Versions of this theorem also exist for more general stochastic processes with index sets and state spaces other than the real line.
|
|
Every algebraic extension of a field of characteristic zero is separable, and every algebraic extension of a finite field is separable.Isaacs, Theorem 18.11, p. 281 It follows that most extensions that are considered in mathematics are separable. Nevertheless, the concept of separability is important, as the existence of inseparable extensions is the main obstacle for extending many theorems proved in characteristic zero to non-zero characteristic.
|
|
The Borel graph theorem, proved by L. Schwartz, shows that the closed graph theorem is valid for linear maps defined on and valued in most spaces encountered in analysis. Recall that a topological space is called a Polish space if it is a separable complete metrizable space and that a Souslin space is the continuous image of a Polish space. The weak dual of a separable Fréchet space and the strong dual of a separable Fréchet-Montel space are Souslin spaces. Also, the space of distributions and all Lp-spaces over open subsets of Euclidean space as well as many other spaces that occur in analysis are Souslin spaces.
|
|
Later he considered unitary representations of general separable locally compact groups and, in particular, gave a characterization for their being CCR groups or type I groups.
|
|
It is by no means true that a finite- dimensional manifold of dimension n is globally homeomorphic to Rn, or even an open subset of Rn. However, in an infinite-dimensional setting, it is possible to classify “well-behaved” Banach manifolds up to homeomorphism quite nicely. A 1969 theorem of David Henderson states that every infinite-dimensional, separable, metric Banach manifold X can be embedded as an open subset of the infinite-dimensional, separable Hilbert space, H (up to linear isomorphism, there is only one such space, usually identified with \ell^2). In fact, Henderson's result is stronger: the same conclusion holds for any metric manifold modeled on a separable infinite-dimensional Fréchet space. The embedding homeomorphism can be used as a global chart for X. Thus, in the infinite-dimensional, separable, metric case, the “only” Banach manifolds are the open subsets of Hilbert space.
|
|
It is by no means true that a finite-dimensional manifold of dimension n is globally homeomorphic to Rn, or even an open subset of Rn. However, in an infinite- dimensional setting, it is possible to classify “well-behaved” Fréchet manifolds up to homeomorphism quite nicely. A 1969 theorem of David Henderson states that every infinite-dimensional, separable, metric Fréchet manifold X can be embedded as an open subset of the infinite-dimensional, separable Hilbert space, H (up to linear isomorphism, there is only one such space). The embedding homeomorphism can be used as a global chart for X. Thus, in the infinite-dimensional, separable, metric case, up to homeomorphism, the “only” topological Fréchet manifolds are the open subsets of the separable infinite- dimensional Hilbert space. But in the case of differentiable or smooth Fréchet manifolds (up to the appropriate notion of diffeomorphism) this fails.
|
|
In functional analysis, an abelian von Neumann algebra is a von Neumann algebra of operators on a Hilbert space in which all elements commute. The prototypical example of an abelian von Neumann algebra is the algebra L∞(X, μ) for μ a σ-finite measure on X realized as an algebra of operators on the Hilbert space L2(X, μ) as follows: Each f ∈ L∞(X, μ) is identified with the multiplication operator : \psi \mapsto f \psi. Of particular importance are the abelian von Neumann algebras on separable Hilbert spaces, particularly since they are completely classifiable by simple invariants. Though there is a theory for von Neumann algebras on non-separable Hilbert spaces (and indeed much of the general theory still holds in that case) the theory is considerably simpler for algebras on separable spaces and most applications to other areas of mathematics or physics only use separable Hilbert spaces.
|
|
Separable polynomials occur frequently in Galois theory. For example, let P be an irreducible polynomial with integer coefficients and p be a prime number which does not divide the leading coefficient of P. Let Q be the polynomial over the finite field with p elements, which is obtained by reducing modulo p the coefficients of P. Then, if Q is separable (which is the case for every p but a finite number) then the degrees of the irreducible factors of Q are the lengths of the cycles of some permutation of the Galois group of P. Another example: P being as above, a resolvent R for a group G is a polynomial whose coefficients are polynomials in the coefficients of P, which provides some information on the Galois group of P. More precisely, if R is separable and has a rational root then the Galois group of P is contained in G. For example, if D is the discriminant of P then X^2-D is a resolvent for the alternating group. This resolvent is always separable (assuming the characteristic is not 2) if P is irreducible, but most resolvents are not always separable.
|
|
For example, the phrase, "we two" is followed by, "must be twain", meaning must be separate. Also, "Our two loves" is followed by "separable spite".Vendler (1997).
|
|
If L/K is separable, then each root appears only once in the product (though the exponent, the degree [L:K(α)], may still be greater than 1).
|
|
Every real, separable Banach space is isometrically isomorphic to a closed subspace of , the space of all continuous functions from the unit interval into the real line.
|
|
A separable DWT does not fully capture the same. In order to overcome these difficulties, a method of wavelet transform called Complex wavelet transform (CWT) was developed.
|
|
This technique was later generalized to algorithms for finding longest common patterns of separable permutations;. however, the longest common pattern problem is NP-complete for arbitrary permutations..
|
|
Many German verbs have a separable prefix that changes the meaning of the root verb, but that does not always remain attached to the root verb. German sentence structure normally places verbs in second position or final position. For separable prefix verbs, the prefix always appears in final position. If a particular sentence's structure places the entire verb in final position then the prefix and root verb appear together.
|
|
This property is interesting in the case of locally compact topological groups, since locally compact compactly generated topological groups can be approximated by locally compact, separable metric factor groups of G. More precisely, for a sequence :Un of open identity neighborhoods, there exists a normal subgroup N contained in the intersection of that sequence, such that :G/N is locally compact metric separable (the Kakutani-Kodaira-Montgomery-Zippin theorem).
|
|
Multidimensional variants of the various DCT types follow straightforwardly from the one-dimensional definitions: they are simply a separable product (equivalently, a composition) of DCTs along each dimension.
|
|
He turned quickly out the light. = separable phrasal verb. b. He ran unexpectedly into his cousin = inseparable phrasal verb. c. He stared intently at the target = prepositional verb.
|
|
The criterion reads as follows: If ρ is a separable mixed state acting on H, then the range of ρ is spanned by a set of product vectors.
|
|
Let K be a non- archimedean local field, let Ks denote a separable closure of K, and let GK = Gal(Ks/K) be the absolute Galois group of K.
|
|
The Urysohn universal space is a certain metric space that contains all separable metric spaces in a particularly nice manner. This mathematics concept is due to Pavel Samuilovich Urysohn.
|
|
Every Fréchet lattice is a locally convex vector lattice. The set of all weak order units of a separable Fréchet lattice is a dense subset of its positive cone.
|
|
Any ring R with elements a and b satisfying ab = 1, but ba different from 1, is a separable extension over the subring S generated by 1 and bRa.
|
|
Non-convex penalties - Penalties can be constructed such that A is constrained to be a graph Laplacian, or that A has low rank factorization. However these penalties are not convex, and the analysis of the barrier method proposed by Ciliberto et al. does not go through in these cases. Non-separable kernels - Separable kernels are limited, in particular they do not account for structures in the interaction space between the input and output domains jointly.
|
|
Single layer perceptrons are only capable of learning linearly separable patterns. For a classification task with some step activation function a single node will have a single line dividing the data points forming the patterns. More nodes can create more dividing lines, but those lines must somehow be combined to form more complex classifications. A second layer of perceptrons, or even linear nodes, are sufficient to solve a lot of otherwise non-separable problems.
|
|
They backed up their conjecture by showing that the pair production of charged black holes in a background magnetic field leads to entangled black holes, but also, after Wick rotation, to a wormhole. This conjecture sits uncomfortably with the linearity of quantum mechanics. An entangled state is a linear superposition of separable states. Presumably, separable states are not connected by any wormholes, but yet a superposition of such states is connected by a wormhole.
|
|
Let E/F be a separable extension of finite degree. Then E=F(\alpha) for some \alpha\in E; that is, the extension is simple and \alpha is a primitive element.
|
|
A is separable if it is a projective module over A^e; thus, the A^e-projective dimension of A, sometimes called the bidimension of A, measures the failure of separability.
|
|
Indeed, this condition is necessary since the multiplication mapping \mu : A \otimes_K A \rightarrow A arising in the definition above is a A-A-bimodule epimorphism, which is split as an A-K- bimodule map by the right inverse mapping A \rightarrow A \otimes_K A given by a \mapsto a \otimes 1 . The converse can be proven by a judicious use of the separability idempotent (similarly to the proof of Maschke's theorem, applying its components within and without the splitting maps). Equivalently, the relative Hochschild cohomology groups H^n(R,S;M) of (R,S) in any coefficient bimodule M is zero for n > 0. Examples of separable extensions are many including first separable algebras where R = separable algebra and S = 1 times the ground field.
|
|
The Vitali covering theorem is not valid in infinite-dimensional settings. The first result in this direction was given by David Preiss in 1979:. there exists a Gaussian measure γ on an (infinite-dimensional) separable Hilbert space H so that the Vitali covering theorem fails for (H, Borel(H), γ). This result was strengthened in 2003 by Jaroslav Tišer: the Vitali covering theorem in fact fails for every infinite-dimensional Gaussian measure on any (infinite- dimensional) separable Hilbert space..
|
|
If a sentence places the verb in second position then only the root verb will appear in second position; the separated prefix remains at the end of the sentence. For example, the separable verb anfangen ("to start") consists of the separable prefix an and the root fangen: :Root verb in second position: Ich fange die Arbeit an. ("I start the work.") :Root verb in final position: Morgens trinke ich heiße Schokolade, weil ich dann die Arbeit anfange.
|
|
The speaker has accepted that he must be alone, because he sees no way they can be together. In our two loves there is but one respect, / Though in our lives a separable spite, :When it comes to their compassion there is only one matter: love. But in reality, there is a "separable spite" that will keep them apart. Which, though it alter not love's sole effect, / Yet doth it steal sweet hours from love's delight.
|
|
For symmetric additively separable hedonic games (those that satisfy v_i(j) = v_j(i) for all i,j\in N), there always exists a Nash-stable coalition structure by a potential function argument. In particular, coalition structures that maximize social welfare are Nash-stable. A similar argument shows that a Nash-stable coalition structure always exists in the more general class of subset-neutral hedonic games. However, there are examples of symmetric additively separable hedonic games that have empty core.
|
|
Separable verbs challenge theories of sentence structure because when they are separated, it is not evident how the compositionality of meaning should be understood. The separation of such verbs is called tmesis.
|
|
In quantum mechanics, in particular quantum information, the Range criterion is a necessary condition that a state must satisfy in order to be separable. In other words, it is a separability criterion.
|
|
Tensor products are used to study extensions of the places of an A-field to places of a finite separable extension of the field, with the more complicated inseparable case postponed to later.
|
|
There are ferrocenophanes which are optically active because of their configuration. Some of the optically active ferrocenophane derivatives are separable into their enantiomers (due to their rigid conformation), for example by chiral resolution.
|
|
Biswas-Diener has written that courage consists of two separable processes: managing the emotion of fear and “boosting the willingness to act”. He suggests that courage consists of skills that can be learned.
|
|
Lu in 1996 as a result on work on groupoids in Poisson geometry (later shown equivalent in nontrivial way to a construction of Takeuchi from the 1970s and another by Xu around the year 2000). They may be loosely thought of as Hopf algebras over a noncommutative base ring, where weak Hopf algebras become Hopf algebras over a separable algebra. It is a theorem that a Hopf algebroid satisfying a finite projectivity condition over a separable algebra is a weak Hopf algebra, and conversely a weak Hopf algebra H is a Hopf algebroid over its separable subalgebra HL. The antipode axioms have been changed by G. Böhm and K. Szlachányi (J. Algebra) in 2004 for tensor categorical reasons and to accommodate examples associated to depth two Frobenius algebra extensions.
|
|
A structure that satisfies all axioms for Boolean algebras except the two distributivity axioms is called an orthocomplemented lattice. Orthocomplemented lattices arise naturally in quantum logic as lattices of closed subspaces for separable Hilbert spaces.
|
|
Indeed, the compact operators on an infinite- dimensional separable Hilbert space form a maximal ideal, so the quotient algebra, known as the Calkin algebra, is simple. More generally, the compact operators form an operator ideal.
|
|
Electrical utilities use silicone grease to lubricate separable elbows on lines that must endure high temperatures. Silicone greases generally have an operating temperature range of approximately with some high-temperature versions extending this range slightly.
|
|
21 and any finitely generated infinite field is Hilbertian. There are several results on the permanence criteria of Hilbertian fields. Notably Hilbertianity is preserved under finite separable extensionsFried & Jarden (2008) p.224 and abelian extensions.
|
|
The Maxover algorithm (Wendemuth, 1995) is "robust" in the sense that it will converge regardless of (prior) knowledge of linear separability of the data set. In the linearly separable case, it will solve the training problem – if desired, even with optimal stability (maximum margin between the classes). For non-separable data sets, it will return a solution with a small number of misclassifications. In all cases, the algorithm gradually approaches the solution in the course of learning, without memorizing previous states and without stochastic jumps.
|
|
Chandrasekhar–Page equations describe the wave function of the spin- massive particles, that resulted by seeking a separable solution to the Dirac equation in Kerr metric or Kerr–Newman metric. In 1976, Subrahmanyan Chandrasekhar showed that a separable solution can be obtained from the Dirac equation in Kerr metric. Later, Don Page extended this work to Kerr-Newman metric, that is applicable to charged black holes. In his paper, Page notices that N. Toop also derived his results independently, as informed to him by Chandrasekhar.
|
|
If the problem is not originally linearly separable, the kernel trick can be used to turn it into a linearly separable one, by increasing the number of dimensions. Thus a general hypersurface in a small dimension space is turned into a hyperplane in a space with much larger dimensions. Neural networks try to learn the decision boundary which minimizes the empirical error, while support vector machines try to learn the decision boundary which maximizes the empirical margin between the decision boundary and data points.
|
|
Proposition 1. So uniruledness does not imply that the Kodaira dimension is −∞ in positive characteristic. A variety X is separably uniruled if there is a variety Y with a dominant separable rational map Y × P1 – → X which does not factor through the projection to Y. ("Separable" means that the derivative is surjective at some point; this would be automatic for a dominant rational map in characteristic zero.) A separably uniruled variety has Kodaira dimension −∞. The converse is true in dimension 2, but not in higher dimensions.
|
|
Hence S is not metrizable (since any compact metric space is separable); however, it is first countable. Also, S is connected but not path connected, nor is it locally path connected. Its fundamental group is trivial.
|
|
Box splines provide a flexible framework for designing such non-separable reconstruction FIR filters that can be geometrically tailored for each lattice.A. Entezari. Optimal sampling lattices and trivariate box splines. [Vancouver, BC.]: Simon Fraser University, 2007. .
|
|
Females and first-year males are brownish, somewhat like winter males but with a blurry stripe across the pale cheek patch. It is separable from the ruddy duck by its all-black face and larger size.
|
|
The frieze with the signing Bandini stands on the rear fins, looking aluminum separable, the flying cut on dashboard decentralized, on the body, chassis and engine over. The front corner lights come from a Volvo 480 ES.
|
|
In general, P(X) is separable if and only if it is square-free over any field that contains K, which holds if and only if P(X) is coprime to its formal derivative D P(X).
|
|
In nonzero characteristic , the discriminant is zero if and only if the polynomial is not square-free or it has an irreducible factor which is not separable (i.e., the irreducible factor is a polynomial in x^p).
|
|
Convergence is to global optimality for separable data sets and to local optimality for non-separable data sets. The Voted Perceptron (Freund and Schapire, 1999), is a variant using multiple weighted perceptrons. The algorithm starts a new perceptron every time an example is wrongly classified, initializing the weights vector with the final weights of the last perceptron. Each perceptron will also be given another weight corresponding to how many examples do they correctly classify before wrongly classifying one, and at the end the output will be a weighted vote on all perceptrons.
|
|
An LF-space that is the inductive limit of a countable sequence of separable spaces is separable. LF spaces are distinguished and their strong duals are bornological and barrelled (a result due to Alexander Grothendieck). If is the strict inductive limit of an increasing sequence of Fréchet space then a subset of is bounded in if and only if there exists some such that is a bounded subset of . A linear map from an LF-space into another TVS is continuous if and only if it is sequentially continuous.
|
|
In the present context, the family of separable states is a convex set in the space of trace class operators. If ρ is an entangled state (thus lying outside the convex set), then by theorem above, there is a functional f separating ρ from the separable states. It is this functional f, or its identification as an operator, that we call an entanglement witness. There is more than one hyperplane separating a closed convex set from a point lying outside of it, so for an entangled state there is more than one entanglement witness.
|
|
In mathematics, the structure theorem for Gaussian measures shows that the abstract Wiener space construction is essentially the only way to obtain a strictly positive Gaussian measure on a separable Banach space. It was proved in the 1970s by Kallianpur-Sato-Stefan and Dudley-Feldman-le Cam. There is the earlier result due to H. Satô (1969) H. Satô, Gaussian Measure on a Banach Space and Abstract Wiener Measure, 1969. which proves that "any Gaussian measure on a separable Banach space is an abstract Wiener measure in the sense of L. Gross".
|
|
The proof of BCT1 for arbitrary complete metric spaces requires some form of the axiom of choice; and in fact BCT1 is equivalent over ZF to the axiom of dependent choice, a weak form of the axiom of choice. A restricted form of the Baire category theorem, in which the complete metric space is also assumed to be separable, is provable in ZF with no additional choice principles. This restricted form applies in particular to the real line, the Baire space ωω, the Cantor space 2ω, and a separable Hilbert space such as .
|
|
Since the Banach–Alaoglu theorem is usually proven via Tychonoff's theorem, it relies on the ZFC axiomatic framework, and in particular the axiom of choice. Most mainstream functional analysis also relies on ZFC. However, the theorem does not rely upon the axiom of choice in the separable case (see below): in this case one actually has a constructive proof. In the non-separable case, the Ultrafilter Lemma, which is strictly weaker than the axiom of choice, suffices for the proof of the Banach-Alaoglu theorem, and is in fact equivalent to it.
|
|
The method of preliminary beamforming for reconfigurable arrays was proposed to reduce the number of A/D converters and the front-end complexities. To improve the imaging resolution, separable beamforming for SAU 3D imaging was used to decompose the 2D beamforming as a series of 1-D array processing, which was shown to produce images with comparable quality as the non-separable method. A better performance of these methods and devices will be achieved as the technology is improving in terms of higher computation speed and smaller size.
|
|
The implementation of complex oriented dual tree structure is done as follows: Two separable 2-D DWTs are implemented in parallel using the filterbank structure as in the previous section. Then, the appropriate sum and difference of different subbands (LL, LH, HL, HH) give oriented wavelets, a total of 6 in all. The figure shows the Fourier support of all 6 oriented wavelets obtained by a 2-D real oriented dual tree CWT Similarly, in 3-D, 4 separable 3-D DWTs in parallel are needed and a total of 28 oriented wavelets are obtained.
|
|
The rollers are stabilized and restrained by a flange on the inner ring, against which their large end slides, which stops the rollers from popping out due to the "pumpkin seed effect" of their conical shape. The larger the half angles of these cones the larger the axial force that the bearing can sustain. Tapered roller bearings are separable into a cone assembly and a cup. The non-separable cone assembly consists of the inner ring, the rollers, and a cage that retains and evenly spaces the rollers.
|
|
In quantum mechanics, a product state, or simply separable state, is a special type of separable state in which there are neither classical nor quantum correlations. Precisely, it is a joint state of two systems which can be expressed as : \rho = \rho_1 \otimes \rho_2 , where \rho_1 and \rho_2 are states of the respective systems. This is a more restrictive condition than mere separability, : \rho = \sum_k p_k \rho^k_1 \otimes \rho^k_2 . Category:Quantum mechanics One property of the product state is that in terms of entropy, : S(\rho) = S(\rho_1) + S(\rho_2).
|
|
Then E=F(\alpha) for some \alpha\in E. The corollary applies to algebraic number fields, i.e. finite extensions of the rational numbers Q, since Q has characteristic 0 and therefore every finite extension over Q is separable.
|
|
For a list of the particles that occur with particle phrasal verbs, see Jurafsky and Martin (2000:319). These verbs can be transitive or intransitive. If they are transitive, they are separable. ::a. They brought that up twice.
|
|
Both and correspond to the HH subband of two different separable 2-D DWTs. This wavelet is oriented at . Similarly, by considering , a wavelet oriented at is obtained. To obtain 4 more oriented real wavelets, , , and are considered.
|
|
If X is a compact separable space, then the space of finite signed Baire measures is the dual of the real Banach space of all continuous real-valued functions on X, by the Riesz–Markov–Kakutani representation theorem.
|
|
It closely resembles Nycteola revayana and is separable only by genitalic characters.The moth flies in two generations from mid-June to September and from March to April depending on the location. The larvae feed on Salix and Populus species.
|
|
The forewing of the females is broader, less acuminate, darker and more reddish than in males. The hindwings are more heavily spotted with red. It is separable from Platysphinx phyllis and Platysphinx piabilis only convincingly by examining the genitalia.
|
|
The forewing of the females is broader, less acuminate, darker and more reddish than in males. The hindwings are more heavily spotted with red. It is separable from Platysphinx stigmatica and Platysphinx piabilis only convincingly by examining the genitalia.
|
|
Notably, using non-separable filters leads to more parameters in design, and consequently better filters.J. Kovacevic and M. Vetterli, "Nonseparable two- and three-dimensional wavelets," IEEE Transactions on Signal Processing, vol. 43, no. 5, pp. 1269–1273, May 1995.
|
|
Volker 1989, pp.160. Many of the distinguishing characteristics of Standard German verbs, such as separable prefixes, second- and third-person stem change and the strong/weak distinction, are not present in Unserdeutsch.Volker 1982, pp.37.Volker 1989, pp.160.
|
|
When a prefix can be used both separably and inseparably, there are cases where the same verb can have different meanings depending on whether its prefix is separable or inseparable (an equivalent example in English would be take over and overtake).
|
|
However, they are conceptually separable. Matter represents what is changeable about the substance—what is potentially something else. For example, bronze matter is potentially a statue, or also potentially a cymbal. Matter must be understood as the matter of something.
|
|
We see that the problem quickly becomes intractable, even for low dimensions. Thus more sophisticated formulations are required. The separability problem is a subject of current research. A separability criterion is a necessary condition a state must satisfy to be separable.
|
|
Some authors have raised the island fence lizard to the rank of a species, i.e., Sceloporus becki. However, recent work in molecular systematics has suggested four clades and 11 genetically separable populations, and the subspecies will probably have to be redefined.
|
|
It can be shown that if minimal polynomial of k linear operator L is separable then L has Jordan-Chevalley decomposition and that if this polynomial is product of distinct irreducible polynomials in k[X], then L is semisimple over k.
|
|
His internal and genuine love proceeds from the beauty he views in his passion for himself and for his lover.Leishman, J. B. Themes and Variations in Shakespeare's Sonnets. London: Hutchinson, 1961. Print. It is separable and inseparable, with time and timeless.
|
|
The definition depends on whether one is working in discrete or continuous time. We will see that for CRRA utility, the two approaches yield the same answer. The below functional forms assume that utility from consumption is time additively separable.
|
|
Note that if the measure spaces (X, μ) is a standard measure space (that is X − N is a standard Borel space for some null set N and μ is a σ-finite measure) then L2(X, μ) is separable.
|
|
Many objects that arise in number theory are naturally Galois representations. For example, if L is a Galois extension of a number field K, the ring of integers OL of L is a Galois module over OK for the Galois group of L/K (see Hilbert–Speiser theorem). If K is a local field, the multiplicative group of its separable closure is a module for the absolute Galois group of K and its study leads to local class field theory. For global class field theory, the union of the idele class groups of all finite separable extensions of K is used instead.
|
|
Quantum mechanics may be modelled on a projective Hilbert space, and the categorical product of two such spaces is the Segre embedding. In the bipartite case, a quantum state is separable if and only if it lies in the image of the Segre embedding. Jon Magne Leinaas, Jan Myrheim and Eirik Ovrum in their paper "Geometrical aspects of entanglement""Geometrical aspects of entanglement", Physical Review A 74, 012313 (2006) describe the problem and study the geometry of the separable states as a subset of the general state matrices. This subset have some intersection with the subset of states holding Peres-Horodecki criterion.
|
|
For the construction of such a stochastic process, it is assumed that the sample functions of the stochastic process belong to some suitable function space, which is usually the Skorokhod space consisting of all right- continuous functions with left limits. This approach is now more used than the separability assumption, but such a stochastic process based on this approach will be automatically separable. Although less used, the separability assumption is considered more general because every stochastic process has a separable version. It is also used when it is not possible to construct a stochastic process in a Skorokhod space.
|
|
The complexification of a simple Euclidean Jordan algebra is a simple complex Jordan algebra which is also separable, i.e. its trace form is non-degenerate. Conversely, using the existence of a real form of the Lie algebra of the structure group, it can be shown that every complex separable simple Jordan algebra is the complexification of a simple Euclidean Jordan algebra. To verify that the complexification of a simple Euclidean Jordan algebra E has no ideals, note that if F is an ideal in EC then so too is F⊥, the orthogonal complement for the trace norm.
|
|
Examine the case where an image of size X\times Y is being passed through a separable filter of size J\times K. The image itself is not separable. If the result is calculated using the direct convolution approach without exploiting the separability of the filter, this will require approximately XYJK multiplications and additions. If the separability of the filter is taken into account, the filtering can be performed in two steps. The first step will have XYJ multiplications and additions and the second step will have XYK, resulting in a total of XYJ+XYK or XY(J+K) multiplications and additions.
|
|
In native words, the word stem is stressed, except verbs with a separable prefix where that prefix is stressed. In loan words, there is – in comparison to standard German – a preference for initial stress, for instance Bernese German ('casino'), ('chalet') vs. standard German , .
|
|
Branchlets downy at first, later become smooth, brown tinged with red, lenticular, finally they become darker and the papery outer layer becomes easily separable. ; Wood: Pale brown; light, soft, close-grained but weak. Specific gravity, 0.5451; weight of cu. ft., 33.97 lbs.
|
|
The two types of couplings are fifth wheel coupling and automatic. In some applications, no separable coupling is fitted, and the trailer is bolted to the tractor unit, using a bearing, and rocker feet as are used under a fifth wheel skid plate.
|
|
Gibson believed that the environment and animals are not separable items. He stated that without the environment animals cannot survive and without animals there is no environment. The environment is what we perceive at any given moment. All animals are able to perceive.
|
|
The winter range in northern Australia overlaps with that of wintering barn swallow (Hirundo rustica), but the latter is readily separable by its blue breast band. Welcome swallows readily breed close to human habitation. Swallows are a commonly found on wires, posts and other perches.
|
|
Homomorphic filtering is sometimes used for image enhancement. It simultaneously normalizes the brightness across an image and increases contrast. Here homomorphic filtering is used to remove multiplicative noise. Illumination and reflectance are not separable, but their approximate locations in the frequency domain may be located.
|
|
Copyright prevents nonfunctional items from being copied. To show copyright infringement, the plaintiff must show the infringing item was copied from the original. The copyrighted artistic expression must either have no substantial practical utility (e.g. a statue) or be separable from the useful substrate (e.g.
|
|
With the spread of the Internet and the ability to copy and distribute electronic data at no cost, the arguments for open access gained new importance. The fixed cost of producing the article is separable from the minimal marginal cost of the online distribution.
|
|
Let denote the coordinate functionals which assign to every in the coordinate of in the above expansion. They are called biorthogonal functionals. When the basis vectors have norm , the coordinate functionals have norm in the dual of . Most classical separable spaces have explicit bases.
|
|
The simplest approach to design a multi- dimensional filter banks is to cascade 1D filter banks in the form of a tree structure where the decimation matrix is diagonal and data is processed in each dimension separately. Such systems are referred to as separable systems.
|
|
A metric space is separable space if it has a countable dense subset. Typical examples are the real numbers or any Euclidean space. For metric spaces (but not for general topological spaces) separability is equivalent to second-countability and also to the Lindelöf property.
|
|
In mathematics, in the areas of topology and functional analysis, the Anderson–Kadec theorem states that any two infinite-dimensional, separable Banach spaces, or, more generally, Fréchet spaces, are homeomorphic as topological spaces. The theorem was proved by Mikhail Kadets (1966) and Richard Davis Anderson.
|
|
Moreover, except for complete graphs, equals the minimum of over all nonadjacent pairs of vertices . -connectivity is also called biconnectivity and -connectivity is also called triconnectivity. A graph which is connected but not -connected is sometimes called separable. Analogous concepts can be defined for edges.
|
|
Windowing is a process where an index limited sequence has its maximum energy concentrated in a finite frequency interval. This can be extended to an N-dimension where the N-D window has the limited support and maximum concentration of energy in a separable or non-separable N-D passband. The design of an N-dimensional window particularly a 2-D window finds applications in various fields such as spectral estimation of multidimensional signals, design of circularly symmetric and quadrantally symmetric non-recursive 2D filters, design of optimal convolution functions, image enhancement so as to reduce the effects of data-dependent processing artifacts, optical apodization and antenna array design.
|
|
The above last two inequalities together with lower bounds for ρ can be seen as quantum Fréchet inequalities, that is as the quantum analogous of the classical Fréchet probabilistic bounds, that hold for separable quantum states. The upper bounds are the previous ones I \otimes \rho_1 \geq \rho, \rho_2 \otimes I \geq \rho, and the lower bounds are the obvious constraint \rho \geq 0 together with \rho \geq I \otimes \rho_1 + \rho_2 \otimes I -I , where I are identity matrices of suitable dimensions. The lower bounds have been obtained in. These bounds are satisfied by separable density matrices, while entangled states can violate them.
|
|
One approach for avoiding mathematical construction issues of stochastic processes, proposed by Joseph Doob, is to assume that the stochastic process is separable. Separability ensures that infinite-dimensional distributions determine the properties of sample functions by requiring that sample functions are essentially determined by their values on a dense countable set of points in the index set. Furthermore, if a stochastic process is separable, then functionals of an uncountable number of points of the index set are measurable and their probabilities can be studied. Another approach is possible, originally developed by Anatoliy Skorokhod and Andrei Kolmogorov, for a continuous-time stochastic process with any metric space as its state space.
|
|
Each of these is called a subband. The subband with all low pass (LLL...) gives the approximation coefficients and all the rest give the detail coefficients at that level. For example, for and a signal of size , a separable DWT can be implemented as follows: The figure depicts 3-D separable DWT procedure by applying 1-D DWT for each dimension and splitting the data into chunks to obtain wavelets for different subbands Applying the 1-D DWT analysis filterbank in dimension , it is now split into two chunks of size . Applying 1-D DWT in dimension, each of these chunks is split into two more chunks of .
|
|
Similarly there is a strictly Henselian ring generated by A, called the strict Henselization of A. The strict Henselization is not quite universal: it is unique, but only up to non-unique isomorphism. More precisely it depends on the choice of a separable algebraic closure of the residue field of A, and automorphisms of this separable algebraic closure correspond to automorphisms of the corresponding strict Henselization. For example, a strict Henselization of the field of p-adic numbers is given by the maximal unramified extension, generated by all roots of unity of order prime to p. It is not "universal" as it has non-trivial automorphisms.
|
|
Though seemingly consistent with the idea of gene–environment interaction, Pinker argues it is nonetheless an absurd position since empirical evidence shows ancestry has no effect on language acquisition — environmental effects are often separable from genetic ones.Pinker, Steven. "Why nature & nurture won't go away." Daedalus 133, no.
|
|
Tribe Amblyoponini (Hymenoptera). Bull Mus Comp Zool 122: 143–230. discussed separable characters for Xymmer (as a junior synonym under the subgenus Stigmatomma) for the first time since Santschi's original description. Brown regarded Stigmatomma and its related names as junior synonyms of Amblyopone at that time.
|
|
Adaptive coordinate descent is an improvement of the coordinate descent algorithm to non-separable optimization by the use of adaptive encoding. Nikolaus Hansen. "Adaptive Encoding: How to Render Search Coordinate System Invariant". Parallel Problem Solving from Nature - PPSN X, Sep 2008, Dortmund, Germany. pp.205-214, 2008.
|
|
However any uncountable discrete space is first-countable but not second-countable. Second-countability implies certain other topological properties. Specifically, every second-countable space is separable (has a countable dense subset) and Lindelöf (every open cover has a countable subcover). The reverse implications do not hold.
|
|
The Review speculated that "these dicta imply that the independently existing work can have the shape and look of the article, evoke the same concepts, and even perform the same function and still be separable," and therefore be copyrightable. Indeed, a 2018 district court case, Silvertop Assocs.
|
|
Justice Breyer, joined by Justice Kennedy, dissented. While he agreed with much of the majority's reasoning, he disagreed with the framing and application of the majority's test and concluded the design was not separable from the uniform's useful article.Star Athletica, slip op. at 1 (Breyer, J., dissenting).
|
|
The TRM-800's frequency response ranges 10Hz to 40.000 Hz ±1 dB with T.H.D. less than 0.1% at rated output. Its preamplifier and main amplifier were separable for multi-channel amplifier systems. The amp has internal circuit breakers which prevent it from clipping or overheating.
|
|
This gives a general picture, and indeed a way of developing Galois theory (along lines exploited in Grothendieck's Galois theory). It can be shown that for separable extensions the radical is always {0}; therefore the Galois theory case is the semisimple one, of products of fields alone.
|
|
The efficiency of VEGAS depends on the validity of this assumption. It is most efficient when the peaks of the integrand are well-localized. If an integrand can be rewritten in a form which is approximately separable this will increase the efficiency of integration with VEGAS.
|
|
Some of her early work involved properties and consequences of lifting. Lifting theory, which had started with the pioneering papers of John von Neumann and later Dorothy Maharam, came into its own in the 1960s and 1970s with the work of the Ionescu Tulceas and provided the definitive treatment for the representation theory of linear operators arising in probability, the process of disintegration of measures. Their Ergebnisse monograph from 1969 became a standard reference in this area. By applying a lifting to a stochastic process, the Ionescu Tulceas obtained a ‘separable’ process; this gives a rapid proof of Joseph Leo Doob's theorem concerning the existence of a separable modification of a stochastic process (also a ‘canonical’ way of obtaining the separable modification). Furthermore, by applying a lifting to a ‘weakly’ measurable function with values in a weakly compact set of a Banach space, one obtains a strongly measurable function; this gives a one line proof of Phillips's classical theorem (also a ‘canonical’ way of obtaining the strongly measurable version).
|
|
The problem of determining if a pair of sets is linearly separable and finding a separating hyperplane if they are, arises in several areas. In statistics and machine learning, classifying certain types of data is a problem for which good algorithms exist that are based on this concept.
|
|
English has many phrasal or compound verb forms that are somewhat analogous to separable verbs. However, in English the preposition or verbal particle is either an invariable prefix (e.g. understand) or is always a separate word (e.g. give up), without the possibility of grammatically conditioned alternations between the two.
|
|
The forewing of the females is broader, less acuminate, darker and more reddish than in males. The hindwings are more heavily spotted with red. It is separable from Platysphinx phyllis and Platysphinx stigmatica only convincingly by examining the genitalia. The larvae feed on the leaves of Pterocarpus angolensis.
|
|
Urysohn proved that an Urysohn universal space exists, and that any two Urysohn universal spaces are isometric. This can be seen as follows. Take (X,d),(X',d'), two Urysohn spaces. These are separable, so fix in the respective spaces countable dense subsets (x_n)_n, (x'_n)_n.
|
|
In mathematics—specifically, in functional analysis—a weakly measurable function taking values in a Banach space is a function whose composition with any element of the dual space is a measurable function in the usual (strong) sense. For separable spaces, the notions of weak and strong measurability agree.
|
|
More generally, a point is an element of any set with an underlying topological structure; e.g. an element of a metric space or a topological group is also a "point". ;Point of closure: See Closure. ;Polish: A space is Polish if it is separable and completely metrizable, i.e.
|
|
Example of 2-D Slices of 3-D Synthetic Aperture Ultrasound Imaging From Field- II Simulation M. Yang, R. Sampson, S. Wei, T. F. Wenisch, and C. Chakrabarti, "Separable Beamforming for 3D Medical Ultrasound Imaging," IEEE Transactions on Signal Processing, vol. 63, no. 2, pp. 279-290, 2015.
|
|
Non-separable wavelets are multi-dimensional wavelets that are not directly implemented as tensor products of wavelets on some lower-dimensional space. They have been studied since 1992.J. Kovacevic and M. Vetterli, "Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for Rn," IEEE Trans. Inf. Theory, vol.
|
|
A system with more than d constants of motion is called superintegrable and a system with constants is called maximally superintegrable. Since the solution of the Hamilton–Jacobi equation in one coordinate system can yield only d constants of motion, superintegrable systems must be separable in more than one coordinate system. The Kepler problem is maximally superintegrable, since it has three degrees of freedom () and five independent constant of motion; its Hamilton–Jacobi equation is separable in both spherical coordinates and parabolic coordinates, as described below. Maximally superintegrable systems follow closed, one- dimensional orbits in phase space, since the orbit is the intersection of the phase-space isosurfaces of their constants of motion.
|
|
The Atkinson–Stiglitz theorem states that if non-linear taxes on earnings are available as policy tool, differential taxation of first- and second period consumption is not optimal if all consumers have preferences weakly separable between consumption and labor. Furthermore, consumers need to have homogeneous subutility functions of consumption. When applied to capital income taxation, the Atkinson–Stiglitz theorem argues that since present and future consumption are equally complementary to leisure due to weakly separable preferences (and hence there is no Corlett–Hague motive for capital income taxation), capital income taxes do not alleviate the tax distortions caused by labor income taxation while additionally distorting capital income. Thus, capital income taxation, i.e.
|
|
In vóórkomen and other verbs with a stressed prefix, the prefix is separable and separates as kom voor in the first-person singular present, with the past participle vóórgekomen. On the other hand, verbs with an unstressed prefix are not separable: voorkómen becomes voorkóm in the first-person singular present, and voorkómen in the past participle, without the past participle prefix ge-. Dutch has a strong stress accent like other Germanic languages, and it uses stress timing because of its relatively complex syllable structure. It has a preference for trochaic rhythm, with relatively stronger and weaker stress alternating between syllables in such a way that syllables with stronger stress are produced at a more or less constant pace.
|
|
This is easy and standard (uses the fact that the trace defines a non-degenerate bilinear form.) Let A be a finitely generated algebra over a field k that is an integral domain with field of fractions K. If L is a finite extension of K, then the integral closure A' of A in L is a finitely generated A-module and is also a finitely generated k-algebra. The result is due to Noether and can be shown using the Noether normalization lemma as follows. It is clear that it is enough to show the assertion when L/K is either separable or purely inseparable. The separable case is noted above; thus, assume L/K is purely inseparable.
|
|
Every group G may be made into a topological group by taking as a basis of open neighbourhoods of the identity, the collection of all normal subgroups of finite index in G. The resulting topology is called the profinite topology on G. A group is residually finite if, and only if, its profinite topology is Hausdorff. A group whose cyclic subgroups are closed in the profinite topology is said to be \Pi_C\,. Groups, each of whose finitely generated subgroups are closed in the profinite topology are called subgroup separable (also LERF, for locally extended residually finite). A group in which every conjugacy class is closed in the profinite topology is called conjugacy separable.
|
|
The equations below assume a beam with a circular cross-section at all values of ; this can be seen by noting that a single transverse dimension, , appears. Beams with elliptical cross-sections, or with waists at different positions in for the two transverse dimensions (astigmatic beams) can also be described as Gaussian beams, but with distinct values of and of the location for the two transverse dimensions and . Arbitrary solutions of the paraxial Helmholtz equation can be expressed as combinations of Hermite–Gaussian modes (whose amplitude profiles are separable in and using Cartesian coordinates) or similarly as combinations of Laguerre–Gaussian modes (whose amplitude profiles are separable in and using cylindrical coordinates).Siegman, p. 642.
|
|
When n = 0, the differential equation is linear. When n = 1, it is separable. In these cases, standard techniques for solving equations of those forms can be applied. For n eq 0 and n eq 1, the substitution u = y^{1-n} reduces any Bernoulli equation to a linear differential equation.
|
|
Another non-separable Hilbert space models the state of an infinite collection of particles in an unbounded region of space. An orthonormal basis of the space is indexed by the density of the particles, a continuous parameter, and since the set of possible densities is uncountable, the basis is not countable.
|
|
Indeed, this fungus is very closely related to A. flavus and is often misidentified as the latter. However, the two species are separable based on morphological features. A. parasiticus also exhibits physiological differences from A. flavus such as the inability to produce cyclopiazonic acid and the production of aflatoxin G.
|
|
A measurable space is said to be "standard Borel" if there exists a metric on that makes it a complete separable metric space in such a way that is then the Borel σ-algebra.Mackey, G.W. (1957): Borel structure in groups and their duals. Trans. Am. Math. Soc., 85, 134-165.
|
|
The first reported example of linkage isomerism had the formula [Co(NH3)5(NO2)]Cl2. The cationic cobalt complex exists in two separable linkage isomers. In the yellow-coloured isomer, the nitro ligand is bound through nitrogen. In the red linkage isomer, the nitrito is bound through one oxygen atom.
|
|
However, Choanephora and Blakeslea are considered to be distinct genera and can be distinguishable by the spore wall and its separation from the sporangiole wall. Species of Choanephora have highly adherent sporangiole wall in contrast to Blakeslea species where the sporangiole wall is readily separable from the underlying spore at maturity.
|
|
Equivalently, combine each input block with a key bit, and map the result through a 5→4 bit S-box. ## Mix adjacent 4-bit blocks using a maximum distance separable code over GF(24). ## Permute 4-bit blocks so that they will be adjacent to different blocks in following rounds.
|
|
Hence, Cdc4 is a protein "with separable but complementary functions in control of cell proliferation and differentiation". This evokes the assumption -beyond regulating cell cycle progression- Cdc4 as a tumor suppressor protein may extend its ability to directly regulate tissue differentiation. However, its concrete role in diseases is still to be elucidated.
|
|
Special Ordered Sets of type 2 are typically used to model non-linear functions of a variable in a linear model. They are the natural extension of the concepts of Separable Programming, but when embedded in a Branch and Bound code enable truly global optima to be found, and not just local optima.
|
|
The only two specimens of the Limestone Leaf Warbler, which have been directly compared with a series of P.ricketti are marginally colder yellow below a more greyish tinge above, and show marginally greyer lateral crown-stripes than P. ricketti. The Limestone Leaf Warbler is easily separable from P. cantator by its yellow belly”.
|
|
His historical account of the expedition included a description of platinum as being neither separable nor calcinable. Ulloa also anticipated the discovery of platinum mines. After publishing the report in 1748, Ulloa did not continue to investigate the new metal. In 1758, he was sent to superintend mercury mining operations in Huancavelica.
|
|
An effective Polish space is a complete separable metric space that has a computable presentation. Such spaces are studied in both effective descriptive set theory and in constructive analysis. In particular, standard examples of Polish spaces such as the real line, the Cantor set and the Baire space are all effective Polish spaces.
|
|
The Pileus is 1.4–3.5 cm in diameter and conic to convex to broadly convex then becoming flat in age. It is not usually umbonate. The pileus is deep chestnut brown and hygrophanous, fading to yellowish brown or grayish white when dry. The surface is viscid when moist from the separable gelatinous pellicle.
|
|
Many different methods and solutions developed to solve the problem, broadly defined as either separable, simultaneous solutions. Each type of solution has specific advantages and disadvantages as well as formulations and applications to the problem. A common theme throughout all of the methods is the common use of quaternions to represent rotations.
|
|
Females are also similar, but are separable by the pattern on their wings. Furthermore, the forewing upperside is more uniform in colour and the ground colour is grey with darker grey and black markings. The forewing and hindwing undersides are grey and the hindwing upperside is grey with darker grey and black markings.
|
|
The cap is (1)3–7(10) cm broad. Convex to obtusely campanulate with an incurved margin at first, rarely becoming plane, and often are umbonate or with a slight depression in the center. It is viscid when moist from a separable gelatinous pellicle. The margin is slightly translucent-striate when moist.
|
|
Stellaria neglecta forms part of a complex that also includes S. media and S. pallida. The last of these is generally separable on morphological grounds, but there is no clear-cut morphological distinction between S. neglecta and S. media, which are easily confused; neglecta was formerly treated as a subspecies of S. media.
|
|
In the limit, for a given n and d, the number of rows t in the smallest d-separable t\times n matrix will tend to be smaller than the number of rows t in the smallest d-disjunct t\times n matrix. However, if the matrix is to be used for practical testing, some algorithm is needed that can "decode" a test result (that is, a boolean sum such as 111100) into the indices of the defective items (that is, the unique set of columns that produce that boolean sum). For arbitrary d-disjunct matrices, polynomial-time decoding algorithms are known; the naïve algorithm is O(nt). For arbitrary d-separable but non-d-disjunct matrices, the best known decoding algorithms are exponential-time.
|
|
The vector x is an eigenvector of the matrix A. Every operator on a non- trivial complex finite dimensional vector space has an eigenvector, solving the invariant subspace problem for these spaces. In the field of mathematics known as functional analysis, the invariant subspace problem is a partially unresolved problem asking whether every bounded operator on a complex Banach space sends some non-trivial closed subspace to itself. Many variants of the problem have been solved, by restricting the class of bounded operators considered or by specifying a particular class of Banach spaces. The problem is still open for separable Hilbert spaces (in other words, all the examples found of operators with no non-trivial invariant subspaces act on Banach spaces which are not separable Hilbert spaces).
|
|
A distance-hereditary graph. In graph theory, a branch of discrete mathematics, a distance-hereditary graph (also called a completely separable graph). is a graph in which the distances in any connected induced subgraph are the same as they are in the original graph. Thus, any induced subgraph inherits the distances of the larger graph.
|
|
The MTL problem can be cast within the context of RKHSvv (a complete inner product space of vector-valued functions equipped with a reproducing kernel). In particular, recent focus has been on cases where task structure can be identified via a separable kernel, described below. The presentation here derives from Ciliberto et al., 2015.
|
|
The mouth parts of Lepidoptera mainly consist of the sucking kind; this part is known as the proboscis or 'haustellum'. The proboscis consists of two tubes held together by hooks and separable for cleaning. The proboscis contains muscles for operating. Each tube is inwardly concave, thus forming a central tube up which moisture is sucked.
|
|
Tmesis of prefixed verbs (whereby the prefix is separated from the simple verb) was an original feature of the Ancient Greek language, common in Homer (and later poetry), but not used in Attic prose. Such separable verbs are also part of the normal grammatical usage of some modern languages, such as Dutch and German.
|
|
In mathematical logic, an effective Polish space is a complete separable metric space that has a computable presentation. Such spaces are studied in effective descriptive set theory and in constructive analysis. In particular, standard examples of Polish spaces such as the real line, the Cantor set and the Baire space are all effective Polish spaces.
|
|
As it turns out, uniformly distributed measures are very rigid objects. On any "decent" metric space, the uniformly distributed measures form a one-parameter linearly dependent family: Let μ and ν be uniformly distributed Borel regular measures on a separable metric space (X, d). Then there is a constant c such that μ = cν.
|
|
The symmetric Tsirelson space S(T) is polynomially reflexive and it has the approximation property. As with T, it is reflexive and no ℓ p space can be embedded into it. Since it is symmetric, it can be defined even on an uncountable supporting set, giving an example of non-separable polynomially reflexive Banach space.
|
|
Krummenacher, J., Grubert, A., & Müller, H. J. (2010). Inter-trial and redundant-signals effects in visual search and discrimination tasks: Separable pre-attentive and post-selective effects. Vision Research, 50(14), 1382-1395. When a stimulus is presented consecutively, the stimulus is perceived at a faster rate than if different stimuli are presented consecutively.
|
|
The trophy is modeled over lotus flower, a symbolically important aquatic Asian plant. Five petals of the lotus symbolize the five sub-confederations under the AFC. The winning countries' names are engraved around the trophy base, which is separable from the trophy's main body. This trophy has a handle on each side, unlike its predecessor.
|
|
Number is either singular or plural in declension. The Colognian conjugation system has a few hundred individual types of grammatical conjugations, which mark verbs to distinguish person, number, voice, aspect, tense, mood, modality, etc. Colognian basic verbs are classified as strong, weak, or irregular. Independently, there are composite verbs, which are classified as either separable or inseparable.
|
|
In quantum information theory, the reduction criterion is a necessary condition a mixed state must satisfy in order for it to be separable. In other words, the reduction criterion is a separability criterion. It was first proved and independently formulated in 1999. Violation of the reduction criterion is closely related to the distillability of the state in question.
|
|
Strictly finer than the manifold topology. It is therefore Hausdorff, separable but not locally compact. A base for the topology is sets of the form Y^+(p,U) \cup Y^-(p,U) \cup p for some point p \in M and some convex normal neighbourhood U \subset M. (Y^\pm denote the chronological past and future).
|
|
Demonology is the study of demons or beliefs about demons. They may be human, or nonhuman, separable souls, or discarnate spirits which have never inhabited a body. A sharp distinction is often drawn between these two classes, notably by the Melanesians, several African groups, and others. The Islamic jinn, for example, are not reducible to modified human souls.
|
|
Any locally convex space having the extension property is injective. If is an injective Banach space, then for every Banach space , every continuous linear operator from a vector subspace of into has a continuous linear extension to all of . In 1953, Alexander Grothendieck that any Banach space with the extension property is either finite-dimensional or else not separable.
|
|
A morphism of schemes f:X \to Y is called étale if it is flat and unramfied. These are the algebro-geometric analogue of covering spaces. The two main examples to think of are covering spaces and finite separable field extensions. Examples in the first case can be constructed by looking at branched coverings and restricting to the unramified locus.
|
|
The seed's hard shell is only separable from the kernel when dry. In general, 100 kg of dry seeds (12–15% water) yields 27 kg to 29 kg of kernels, which must be further dried to prevent deterioration during storage. These kernels then yield 40% to 42% oil. A single Murumuru palm produces about 11 kg of dry seeds.
|
|
Zygaena minos is a member of the family Zygaenidae. It is found in most of Europe, except Ireland, Great Britain, the Benelux, the Iberian Peninsula and Norway.Fauna Europaea It is very similar to Zygaena purpuralis with which it forms a species complex and only separable by genital preparation or by the larval foodplant. The wingspan is 33–37 mm.
|
|
Uniquely in this group, it and the related T. hatinhensis appear to be parapatric, T. ebenus showing what appears to be signs of intergradation with T. hatinhensis are known,Duckworth, J. W., Salter, R. E., and Khounboline, K. (eds). 1999 Wildlife in Lao P.D.R: 1999 status report. Vientiane: IUCN, WCS and CPAWM. and genetically the two barely are separable.
|
|
In field theory, the primitive element theorem or Artin's theorem on primitive elements is a result characterizing the finite degree field extensions that possess a primitive element, or simple extensions. It says in that a finite extension is simple if and only if there are only finitely many intermediate fields. In particular, finite separable extensions are simple , more general.
|
|
In measure theory Prokhorov's theorem relates tightness of measures to relative compactness (and hence weak convergence) in the space of probability measures. It is credited to the Soviet mathematician Yuri Vasilyevich Prokhorov, who considered probability measures on complete separable metric spaces. The term "Prokhorov’s theorem" is also applied to later generalizations to either the direct or the inverse statements.
|
|
The cap is buff-brown to dingy orangish-brown and pale ochraceous when dry. It is smooth, hygrophanous, and slightly translucent-striate when moist but not viscid and without a separable gelatinous pellicle. The flesh is whitish to cream-colored, bruising blue when injured. Spores are purple-brown, ellipsoid, slightly flattened, and thick-walled, with a distinct germ pore.
|
|
In fact, even a single layer of Uranium atoms does not meet the Weak Phase Object Approximation. Linear imaging theory is still used, however, because it has some computational advantages. In Linear imaging theory, the Fourier coefficients for the image plane wavefunction are separable. This greatly reduces computational complexity, allowing for faster computer simulations of HRTEM images.
|
|
In topology, the long line (or Alexandroff line) is a topological space somewhat similar to the real line, but in a certain way "longer". It behaves locally just like the real line, but has different large-scale properties (e.g., it is neither Lindelöf nor separable). Therefore, it serves as one of the basic counterexamples of topology.
|
|
The cap is typically 7-15 mm in diameter, almost convex to conic in shape, umbonate with a small papilla. The cap is viscid and has a separable pellicle. It is a reddish-brown color when moist, but becomes lighter brown when dry. The stipe is 4.0-6.5 cm high × 1.5 cm thick, equal or slightly bulbous.
|
|
Liquid-liquid extractions can be carried out on digital microfluidic device by taking advantage of immiscible liquids.9 Two droplets, one containing the analyte in aqueous phase, and the other an immiscible ionic liquid are present on the electrode array. The two droplets are mixed and the ionic liquid extracts the analyte, and the droplets are easily separable.
|
|
Simultaneous solutions are based on solving for both and at the same time (rather than basing the solution of one part off of the other as in separable solutions), propagation of error is significantly reduced.Algo Li, et al. "Simultaneous robot-world and hand-eye calibration using dual-quaternions and Kronecker product." International Journal of the Physical Sciences Vol.
|
|
Productive exchanges are interdependent and this high degree of nonseparability generates the strongest emotions. Reciprocal exchanges are separable which reduces the perceptions of shared responsibility. The exchange produces little emotional response, but individuals instead express emotions in response to the asymmetrical transaction. Generalized exchanges do not occur directly, but interdependence is still high and coordination between partners is difficult.
|
|
Image texturization is an application of multidimensional AM-FM modulation. In this method, the image (2-D signal) is expressed into its special frequencies and amplitude estimates. The signal is represented as a product of 2 FM functions (using the independent frequencies), making is separable. Using the instantaneous frequency, the image can be represented topologically to illustrate its texture.
|
|
Every infinite-dimensional normed space is a barrelled space that is not a Montel space. In particular, every infinite-dimensional Banach space is not a Montel space. There exist Montel spaces that are not separable and there exist Montel spaces that are not complete. There exist Montel spaces having closed vector subspaces that are not Montel spaces.
|
|
Furthermore, Kongtrül states: > The ultimate truth is the primordial wisdom of emptiness free of > elaborations. Primordial wisdom is there in its very nature and is present > within the impure, mistaken consciousness. Even while consciousness is > temporarily stained, it remains in the wisdom nature. The defilements are > separable and can be abandoned because they are not the true nature.
|
|
Treatment of pure 17c with lithium tetramethylpiperidide and (±)-camphorsulfonyl oxaziridine gave separable α-hydroxyketones 18c (88%) and 18t (8%) in addition to some recovered starting material (3%). Reduction of pure ketone 18c using Red-Al followed by basic work-up resulted in epimerization to give the required trans-fused diol 19 in 88% yield. Scheme 2.
|
|
It was launched on 18 October 1947 from the Kapustin Yar test site The first V-2 rocket was transported to the Kapustin Yar test site and launched on 18 October 1947. It flew 206.7 km and deviated left for 30 km. The R-1A was tested, a variant with a separable warhead later in 1947.
|
|
Every finite topological space is compact since any open cover must already be finite. Indeed, compact spaces are often thought of as a generalization of finite spaces since they share many of the same properties. Every finite topological space is also second-countable (there are only finitely many open sets) and separable (since the space itself is countable).
|
|
Chalcides mionecton, the mionecton skink or Morocco cylindrical skink, is a species of skink in the family Scincidae. It is found only in Morocco. There are two subspecies: Genetic data suggest that these should be considered separate species, but they are not separable using external morphological characteristics. Its natural habitats are sandy shores, arable land, pastureland, and rural gardens.
|
|
The grey crowned crane is closely related to the black crowned crane, and the two species have sometimes been treated as the same species. The two are separable on the basis of genetic evidence, calls, plumage and bare parts, and all authorities treat them as different species today. There are two subspecies. The East African B. r.
|
|
A ring homomorphism (of unital, but not necessarily commutative rings) :K \to A is called separable (or a separable extension) if the multiplication map :\mu : A \otimes_K A \to A, a \otimes b \mapsto ab admits a section :\sigma: A \to A \otimes_K A by means of a homomorphism σ of A-A-bimodules. Such a section σ is determined by its value :p := \sigma(1) = \sum a_i \otimes b_i σ(1). The condition that σ is a section of μ is equivalent to :\sum a_i b_i = 1 and the condition to be an homomorphism of A-A-bimodules is equivalent to the following requirement for any a in A: :\sum a a_i \otimes b_i = \sum a_i \otimes b_i a. Such an element p is called a separability idempotent, since it satisfies p^2 = p.
|
|
Therefore, implementing the LQG controller may be problematic if the dimension of the system state is large. The reduced-order LQG problem (fixed-order LQG problem) overcomes this by fixing a-priori the number of states of the LQG controller. This problem is more difficult to solve because it is no longer separable. Also the solution is no longer unique.
|
|
Psychologist, 25(9), 664-667. Others have evaluated different types of in-vehicle notifications (i.e., auditory icons, speech commands) designed for task management in autonomous trucks for their relevance to separable neural mechanisms; this serves as an effective method to clarify often conflicting findings drawn from behavioral results alone.Glatz, C., Krupenia, S. S., Bülthoff, H. H., & Chuang, L. L. (2018, April).
|
|
In 1839 Carl Gustav Mosander, an assistant of Berzelius, separated ceria by heating the nitrate and dissolving the product in nitric acid. He called the oxide of the soluble salt lanthana. It took him three more years to separate the lanthana further into didymia and pure lanthana. Didymia, although not further separable by Mosander's techniques, was in fact still a mixture of oxides.
|
|
Making components within systems separable also assists in being able to dismantle materials quickly and efficiently. This can be achieved by using mechanical fasteners such as bolts to connect parts. Allowing physical access to the fasteners is another needed aspect of this design. Also, it is important to use standardized materials and assemble them in a consistent manner throughout the project.
|
|
The Seldon- Griswold Manufacturing Company was founded in Erie, Pennsylvania, in 1865 by Matthew Griswold (born 6 June 1833) and his cousins, the brothers J.C. and Samuel Selden. The company made separable butt hinges and other light hardware products at a building called the "Butt Factory" beside the Erie Extension Canal. Other products were stovepipe dampers, thimbles, and other stove furniture.
|
|
A world manifold is a four-dimensional orientable real smooth manifold. It is assumed to be a Hausdorff and second countable topological space. Consequently, it is a locally compact space which is a union of a countable number of compact subsets, a separable space, a paracompact and completely regular space. Being paracompact, a world manifold admits a partition of unity by smooth functions.
|
|
However, AES70 is designed to work with virtually any media transport scheme, as the application requires. AES70's parts are separable and may be used independently. For example, a device may implement AES70 connection management, but use other means for operational control and monitoring. AES70 is termed an "architecture" because it provides the basis for definition of multiple control protocols.
|
|
There exist distinguished Banach spaces spaces that are not semi- reflexive. The strong dual of a distinguished Banach space is not necessarily separable; l^{1} is such a space. The strong dual of a distinguished Fréchet space is not necessarily metrizable. There exists a distinguished semi- reflexive non-reflexive non-quasibarrelled Mackey space X whose strong dual is a non-reflexive Banach space.
|
|
Phenyl-hydrazine is used to prepare indoles by the Fischer indole synthesis, which are intermediates in the synthesis of various dyes and pharmaceuticals. Phenylhydrazine is used to form phenylhydrazones of natural mixtures of simple sugars in order to render the differing sugars easily separable from each other. This molecule is also used to induce acute hemolytic anemia in animal models.
|
|
The problem of deciding whether a state is separable in general is sometimes called the separability problem in quantum information theory. It is considered to be a difficult problem. It has been shown to be NP-hard.Gurvits, L., Classical deterministic complexity of Edmonds’ problem and quantum entanglement, in Proceedings of the 35th ACM Symposium on Theory of Computing, ACM Press, New York, 2003.
|
|
The efficiency of VEGAS depends on the validity of this assumption. It is most efficient when the peaks of the integrand are well-localized. If an integrand can be rewritten in a form which is approximately separable this will increase the efficiency of integration with VEGAS. VEGAS incorporates a number of additional features, and combines both stratified sampling and importance sampling.
|
|
100 (2): 313–330. . What is more, even among those who endorse a spiritual/theistic worldview, these salutary associations appear to be better explained by humanity/civility rather than endorsing a faith in a supernatural being.Schuurmans-Stekhoven, J. B. (2013). “As a Shepherd Divideth his Sheep from the Goats”: Does the Daily Spiritual Experiences Scale Encapsulate Separable Theistic and Civility Components?.
|
|
The strictly positive values \alpha_i in the Schmidt decomposition of w are its Schmidt coefficients. The number of Schmidt coefficients of w, counted with multiplicity, is called its Schmidt rank, or Schmidt number. If w can be expressed as a product :u \otimes v then w is called a separable state. Otherwise, w is said to be an entangled state.
|
|
Idioms possess varying degrees of mobility. Whereas some idioms are used only in a routine form, others can undergo syntactic modifications such as passivization, raising constructions, and clefting, demonstrating separable constituencies within the idiom. Mobile idioms, allowing such movement, maintain their idiomatic meaning where fixed idioms do not: ;Mobile: I spilled the beans on our project. → The beans were spilled on our project.
|
|
Breyer also criticized what he considered vagueness in the majority's test. He thought that, under it, "virtually any industrial design" could be considered separable as soon as it was thought of in terms of art, whether via giving it a picture frame or merely calling the object art like a Marcel Duchamp series.Star Athletica, slip op. at 6-7 (Breyer, J., dissenting).
|
|
Tisis mesozosta is a moth in the family Lecithoceridae. It is found in Taiwan and Anhui, Fujian, Jiangxi, Hainan and Yunnan provinces of China.Lecithoceridae (Lepidoptera) of Taiwan (II): Subfamily Lecithocerinae: Genus Lecithocera Herrich-Schäffer and Its Allies The wingspan is 19–21 mm. Adults are easily separable from other species of the genus Tisis by the characteristic marking on the forewings.
|
|
The real numbers are locally compact but not compact. There are various properties that uniquely specify them; for instance, all unbounded, connected, and separable order topologies are necessarily homeomorphic to the reals. Every nonnegative real number has a square root in R, although no negative number does. This shows that the order on R is determined by its algebraic structure.
|
|
Following a review of the genus Craspedia, Joy Everett and Andrew Doust named C. variabilis as a new species, along with C. paludicola, C. canens and C. haplorrhiza. They describe C. variabilis as "a complex species with several forms, some of which may be separable on further work". The specific epithet (variabilis) refers to the number of different forms across its wide distribution.
|
|
The crust-like fruit bodies of this species are soft and readily separable from the substrate. The colour of the margin ranges from white to pinkish tan to purplish, while the pore surface is pink to reddish orange. Pores are circular or angular and number two to three per millimetre. C. excelsa has a monomitic hyphal system, with only generative hyphae.
|
|
In mathematics, a polynomial P(X) over a given field K is separable if its roots are distinct in an algebraic closure of K, that is, the number of distinct roots is equal to the degree of the polynomial.S. Lang, Algebra, p. 178 This concept is closely related to square-free polynomial. If K is a perfect field then the two concepts coincide.
|
|
Results show that the spatial and temporal distribution of aftershocks is separable into a dependence on space and a dependence on time. And more recently, through the application of a fractional solution of the reactive differential equation, a double power law model shows the number density decay in several possible ways, among which is a particular case the Utsu-Omori Law.
|
|
Since this schwa almost always corresponds to the digraph "er" ending a word or a separable syllable prefix of Standard German orthography, most users of Rheinische Dokumenta positionally print "er", or "e̩r", respectively, for increased readability in an attempt of courtesy towards their readers who read German more fluently than Rheinische Dokumenta. From the standpoint of phonological writing, this is incorrect.
|
|
300, 1-3 (2005), 1–15. Permutations whose decomposition by skew and direct sums into a maximal number of parts, that is, can be built up from the permutations (1), are called separable permutations;Kitaev (2011) p.57 they arise in the study of sortability theory, and can also be characterized as permutations avoiding the permutation patterns 2413 and 3142.
|
|
Two datasets are linearly separable if their convex hulls do not intersect. The method may be formulated as a feedforward neural network with weights that are trained via linear programming. Comparisons between neural networks trained with the MSM versus backpropagation show MSM is better able to classify data.Neural Network Training via Linear Programing, Advances in Optimization and Parallel Computing, 1992, p.
|
|
In operator theory, particularly the study of PDEs, operators are particularly easy to understand and PDEs easy to solve if the operator is diagonal with respect to the basis with which one is working; this corresponds to a separable partial differential equation. Therefore, a key technique to understanding operators is a change of coordinates—in the language of operators, an integral transform—which changes the basis to an eigenbasis of eigenfunctions: which makes the equation separable. An important example of this is the Fourier transform, which diagonalizes constant coefficient differentiation operators (or more generally translation invariant operators), such as the Laplacian operator, say, in the heat equation. Especially easy are multiplication operators, which are defined as multiplication by (the values of) a fixed function–the values of the function at each point correspond to the diagonal entries of a matrix.
|
|
For such an extension, being normal and separable means that all zeros of are contained in and that has only simple zeros. The latter condition is always satisfied if has characteristic 0. For a finite Galois extension, the Galois group is the group of field automorphisms of that are trivial on (i.e., the bijections that preserve addition and multiplication and that send elements of to themselves).
|
|
The \alpha-perceptron further used a pre-processing layer of fixed random weights, with thresholded output units. This enabled the perceptron to classify analogue patterns, by projecting them into a binary space. In fact, for a projection space of sufficiently high dimension, patterns can become linearly separable. Another way to solve nonlinear problems without using multiple layers is to use higher order networks (sigma-pi unit).
|
|
Suppose there is a team of n > 1 risk neutral agents whose preference functions are strictly concave and increasing, and also additively separable in money and effort. Then, under an incentive system that distributes exactly the output among the team members, any Nash equilibrium is Pareto inefficient. RasmusenEric Rasmusen, "Moral Hazard in Risk-Averse Teams", The RAND Journal of Economics 18, no. 3 (1987), pp. 428–435.
|
|
Date taken from contents page of Complete sonatas and variations for cello and piano: from the Breitkopf & Härtel complete works edition. Courier Corporation, 1990. Lockwood also discerns a precedent set by Mozart involving formal structure: an Introduzione; i.e. Beethoven's scene forms a separable initial section of an opera having some degree of integrity of both plot and harmonic plan; Lockwood calls the Introduzione a "miniplay".
|
|
Fridell RA, Valera L, Qiu D, Kirk MJ, Wang C, Gao M. Intragenic complementation of hepatitis C virus NS5A RNA replication- defective alleles. J Virol. 2013;87(4):2320-2329. doi:10.1128/JVI.02861-12 On the bases of pairwise complementation tests between different NS5A mutant alleles, they identified three complementation groups that were considered to define three distinct and genetically separable functions of NS5A in RNA replication.
|
|
All three genera are noted for the pterostigmal region lacking a basal cross vein and instead being diffuse. Necroraphidia and Styporaphidia are separable by the cross veins in the pterostigma, with only one being found in Necroraphidia while Styporaphidia has two. The forewing of Ororaphidia is notably larger at and also displays distinct shapes to both the pterostigmal cross vein and second radial cell.
|
|
The Delta-compactness theorem of T. C. Lim states that if (X,d) is an asymptotically complete metric space, then every bounded sequence in X has a Delta-convergent subsequence. The Delta- compactness theorem is similar to the Banach–Alaoglu theorem for weak convergence but, unlike the Banach-Alaoglu theorem (in the non-separable case) its proof does not depend on the Axiom of Choice.
|
|
In plan the wing has a constant chord central section occupying about half the span, with separable straight tapered outer panels. The centre section trailing edges carries air brakes. Its fuselage is similar to that of the Aviamilano CPV1 with a wooden structure and ovoid cross-section. As before, the rear part is plywood skinned, but the forward part is covered with glass fibre.
|
|
Cysts with two or more wall layers that define a cavity are termed cavate. Excystment usually results in loss of part of, or an opening in, the cyst wall, termed archeopyle, the shape and position of which may indicate the position and/or shape of one or more thecal plates. Transmission electron microscopy (TEM) studies (e.g.) suggest that endophragm and periphragm are not morphologically separable.
|
|
The R-12 is a single-stage rocket with a separable single reentry vehicle. In the integrated fuel tanks the oxidizer was put forward of the fuel tank, separated by an intermediate plate. During flight this allowed the oxidizer from the lower unit to be spent first, improving in-flight stabilization. The propulsion system consists of four liquid propellant rocket motors with a common turbo pump unit.
|
|
The RSM-54 missile (3M37, R-29RM, or SS-N-23 according to the NATO classification) is a liquid-propellant, three-stage missile with separable heads (it carries four or ten warheads depending on the modification). It has a range of 8300 km, a CEP of 500 m, and a launching mass of 40.3 tons. It is 14.8 m long and 1.9 m in diameter.
|
|
Justice Clarence Thomas delivered the majority opinion, which was joined by Chief Justice John Roberts and Justices Alito, Sotomayor, and Kagan. The Court defined its task as "whether the lines, chevrons, and colorful shapes appearing on the surface of [Varsity Brands'] cheerleading uniforms are eligible for copyright restriction as separable features of the design of those cheerleading uniforms."Star Athletica, slip op. at 4.
|
|
When it was elsewhere on the base, it could be physically separable and was therefore copyrightable as a figurine. When the cat was the pole, it couldn't be physically separated, but it could be conceptually separated from the context of the lamp without conjuring the idea of a lamp and was therefore copyrightable as a figurine.Star Athletica, slip op. at 2-4 (Breyer, J., dissenting).
|
|
The continuum hypothesis can neither be proved nor be disproved; it is independent from the axioms of set theory. As a topological space, the real numbers are separable. This is because the set of rationals, which is countable, is dense in the real numbers. The irrational numbers are also dense in the real numbers, however they are uncountable and have the same cardinality as the reals.
|
|
In species of Lepidoptera, it consists of two tubes held together by hooks and separable for cleaning. Each tube is inwardly concave, thus forming a central tube through which moisture is sucked. Suction is effected through the contraction and expansion of a sac in the head. The proboscis is coiled under the head when the insect is at rest, and is extended only when feeding.
|
|
Psilocybe strictipes has a farinaceous smell and taste. Pleurocystidia are absent and its lageniform cheilocystidia are 21-45 by 7-10 µm. The cap is 5 to 30 mm across, conic to campanulate to convex, smooth, and translucent-striate near the margin, often with a low umbo. It is walnut brown to dark rusty brown, with a smooth surface and a separable gelatinous pellicle.
|
|
Diamantane can be nitrated by treatment with nitronium tetrafluoroborate (in nitrile-free nitromethane) to give a mixture of two isomeric nitrodiamantanes. :400px Chlorination with aluminium chloride and acetyl chloride yields equal amounts of 1- and 4-chlorodiamantane, whereas use of chlorosulfonic acid yields mainly the 1-chloro isomer. Hydrolysis of the chlorides yield the corresponding alcohols, which are separable by column chromatography over alumina.
|
|
A distinction is that semicollared may show a white second wing bar, but many individuals are not separable in the field. Semicollared flycatchers are birds of belts of deciduous woodlands, especially oak and hornbeam, in mountainous areas. They build an open nest in a native tree-holes and old nests of woodpeckers, also the species can occupy nest- boxes. The clutch size is 4-7 eggs.
|
|
Gamma1 is a blue-white star of spectral type B2III and apparent magnitude 4.3. The two pairs are separated by 41 arcseconds, easily separable in binoculars. Parallax measurements give a distance of 1,116 light-years, meaning that they are at least 12,000 AU apart. Further afield are 7.3-magnitude Gamma Velorum C and 9.4-magnitude Gamma Velorum D, lying 62 and 93 arcseconds south-southeast from Gamma2.
|
|
Thus, the results of the late 1980s appeared to vindicate the West German supply-side revolution. Tax rate reductions had led to greater vitality and revenues. Although the cumulative public-sector deficit had gone above the DM1 trillion level, the public sector was growing more slowly than before. The year 1989 was the last year of the West German economy as a separate and separable institution.
|
|
Schuurmans-Stekhoven, J. B. (2013). “As a shepherd divideth his sheep from the goats”: Does the Daily Spiritual Experiences Scale encapsulate separable theistic and civility components? Social Indicators Research, 110(1), 131-146.doi:10.1007/s11205-011-9920-8 In Research on Aging, Idler and other working group members reported results of in-depth analyses of data from administering the BMMRS in the 1998 General Social Survey.
|
|
Common examples of Polish spaces are the real line, any separable Banach space, the Cantor space, and the Baire space. Additionally, some spaces that are not complete metric spaces in the usual metric may be Polish; e.g., the open interval (0, 1) is Polish. Between any two uncountable Polish spaces, there is a Borel isomorphism; that is, a bijection that preserves the Borel structure.
|
|
A Radon space, named after Johann Radon, is a topological space such that every Borel probability measure on M is inner regular. Since a probability measure is globally finite, and hence a locally finite measure, every probability measure on a Radon space is also a Radon measure. In particular a separable complete metric space (M, d) is a Radon space. Every Suslin space is Radon.
|
|
However, in Swiss German as in some other southern German dialects, springen – besides meaning "to jump" – also means "to run". This term/concept also is used as a separable verb, i.e., rumspringen (to jump around) / er springt rum (he jumps around). In Pennsylvania German, the prefix rum is a contraction of herum – a development which is also all but general to spoken standard German.
|
|
In general, it begins with a special word, a 'subordinating conjunction' or a relative pronoun, setting it into relation with the encompassing sentence. 2\. The verb is, without separation, sent to the place where the first part of a separable verb would be in a main clause, i. e. at the end of the sentence. :Ich nehme den früheren Flug, damit ich heute noch ankomme.
|
|
The Peres–Horodecki criterion is a necessary condition, for the joint density matrix \rho of two quantum mechanical systems A and B, to be separable. It is also called the PPT criterion, for positive partial transpose. In the 2x2 and 2x3 dimensional cases the condition is also sufficient. It is used to decide the separability of mixed states, where the Schmidt decomposition does not apply.
|
|
The mole is essentially a count of particles. Usually the particles counted are chemically identical entities, individually distinct. For example, a solution may contain a certain number of dissolved molecules that are more or less independent of each other. However, in a solid the constituent particles are fixed and bound in a lattice arrangement, yet they may be separable without losing their chemical identity.
|
|
The cartridge has size and shape similar to real cartridges but can be screwed separable. It is made with machined brass multi-piece consisting of a simulated primer, base, piston and the "bullet". The plastic cap is plugged inside and sit on a piston which helps to keep the pressure of exploded gas to provide the blowback force. The blowback performance is much improved and cleanup is also easier.
|
|
This species is about with red legs, black bill, and a blackish iris. The breeding adult spectacled guillemot is distinctive, mostly plumaged dull sooty-black except for conspicuous white "spectacles" on the face In adult non-breeding plumage, the underparts are white, uniformly tipped very pale grey-brown. Transitional birds are like breeding adults, except the underparts are scaled with white. Sexes are alike, but juveniles are separable from adults.
|
|
Todorcevic proved that under PFA there are no S-spaces. This means that every regular T_1 hereditarily separable space is Lindelöf. For some time, it was believed the L-space problem would have a similar solution (that its existence would be independent of ZFC). Todorcevic showed that there is a model of set theory with Martin's axiom where there is an L-space but there are no S-spaces.
|
|
In mathematics, an affine algebraic group is said to be diagonalizable if it is isomorphic to a subgroup of Dn, the group of diagonal matrices. A diagonalizable group defined over k is said to split over k or k-split if the isomorphism is defined over k. This coincides with the usual notion of split for an algebraic group. Every diagonalizable group splits over the separable closure ks of k.
|
|
Let K be a non-archimedean local field, let Ks denote a separable closure of K, let GK = Gal(Ks/K) be the absolute Galois group of K, and let Hi(K, M) denote the group cohomology of GK with coefficients in M. Since the cohomological dimension of GK is two, Hi(K, M) = 0 for i ≥ 3\. Therefore, the Euler characteristic only involves the groups with i = 0, 1, 2\.
|
|
In 315 BCE, Theophrastus presented his classification of minerals in his treatise On Stones. His classification was influenced by the ideas of his teachers Plato and Aristotle. Theophrastus classified minerals as stones, earths or metals. Georgius Agricola's classification of minerals in his book De Natura Fossilium, published in 1546, divided minerals into three types of substance: simple (stones, earths, metals, and congealed juices), compound (intimately mixed) and composite (separable).
|
|
A topological space with a countable dense subset is called separable. A topological space is a Baire space if and only if the intersection of countably many dense open sets is always dense. A topological space is called resolvable if it is the union of two disjoint dense subsets. More generally, a topological space is called κ-resolvable for a cardinal κ if it contains κ pairwise disjoint dense sets.
|
|
Five bats are used to symbolise the "Five Blessings": longevity, wealth, health, love of virtue and peaceful death. The bat is sacred in Tonga and is often considered the physical manifestation of a separable soul. In the Zapotec civilisation of Mesoamerica, the bat god presided over corn and fertility. Zapotec bat god, Oaxaca, 350–500 CE The Weird Sisters in Shakespeare's Macbeth used the fur of a bat in their brew.
|
|
The domain of the wave function is configuration space, an abstract object quite different from ordinary physical spacetime. At a single "point" of configuration space, the wave function collects probabilistic information about several distinct particles, that respectively have physically space-like separation. So the wave function is said to supply a non-separable representation. This reflects a feature of the quantum world that was recognized by Einstein as early as 1905.
|
|
One half of an n-bit key is used as the actual encryption key and the other half of the n-bit key is used to modify the encryption algorithm (key-dependent S-boxes). Twofish borrows some elements from other designs; for example, the pseudo-Hadamard transform (PHT) from the SAFER family of ciphers. Twofish has a Feistel structure like DES. Twofish also employs a Maximum Distance Separable matrix.
|
|
The principle of compositionality is hence understood in terms of catenae. The catena is the basic meaning-bearing unit, not the constituent. The four Hungarian examples from above are analyzed in terms of catenae as follows: ::Separable verbs trees 2' The particle le is separated from its verb when the negation appears (trees b-d). Despite this fact, the particle still forms a catena with its verb in all four trees.
|
|
In general, the smaller forms occur in coastal mountains, intermediate birds in the Andes, and large, darker, forms breed on the tepuis. The largest of the tepui subspecies, Z. c. perezchincillae, has grey underparts, and the rufous collar extends as a black band of freckles across the breast. This form might be separable as a distinct species, or it might just be a particularly distinct population due to genetic bottleneck effects.
|
|
Using the isomorphism between entanglement witnesses and non-completely positive maps, it was shown (by the Horodecki's) that Theorem A mixed state \sigma \in L(H_A) \otimes L(H_B) is separable if for every positive map Λ from bounded operators on H_B to bounded operators on H_A, the operator (I_A \otimes \Lambda)(\sigma) is positive, where I_A is the identity map on \; L (H_A), the bounded operators on H_A.
|
|
This moth is typical of the genus, featuring a mottled brown pattern with cross lines. In most specimens white patches occur at the forewing tip, and at the wing shoulder, hence the species epithet pallidiplaga ("pale area"). In the most well marked specimens white colouration extends onto the first half of the abdomen as well. Duller specimens are similar to other genus members, and may not be separable without dissection.
|
|
The wing was built in three separable parts for ease of transport, with a rectangular centre section and slightly straight tapered outer panels with rounded tips, carrying slotted ailerons. All three panels were fabric- covered. Its rectangular cross-section fuselage was built of spruce and was ply covered. The cockpit opening was a simple rectangular uncovered cut out in the top of the fuselage in front of the wing leading edge.
|
|
The types of fleshy fruits are berries, pomes, and drupes. In berries, the entire pericarp is fleshy but this excludes the exocarp which acts as more as a skin. There are berries that are known as pepo, a type of berry with an inseparable rind, or hesperidium, which has a separable rind. An example of a pepo is the cucumber and a lemon would be an example of a hesperidium.
|
|
The Galois group of a polynomial of degree n is S_n or a proper subgroup of that. If a polynomial is separable and irreducible, then the corresponding Galois group is a transitive subgroup. Transitive subgroups of S_n form a directed graph: one group can be a subgroup of several groups. One resolvent can tell if the Galois group of a polynomial is a (not necessarily proper) subgroup of given group.
|
|
The first example by Enflo of a space failing the approximation property was at the same time the first example of a separable Banach space without a Schauder basis.see Robert C. James characterized reflexivity in Banach spaces with a basis: the space with a Schauder basis is reflexive if and only if the basis is both shrinking and boundedly complete.see R.C. James, "Bases and reflexivity of Banach spaces". Ann. of Math.
|
|
In the 19th century, philologists devised a now classic classification of languages according to their morphology. Some languages are isolating, and have little to no morphology; others are agglutinative whose words tend to have many easily separable morphemes; others yet are inflectional or fusional because their inflectional morphemes are "fused" together. That leads to one bound morpheme conveying multiple pieces of information. A standard example of an isolating language is Chinese.
|
|
In the Pauline view, Jesus, obedient to the point of death (Philippians 2:8) died "at the right time" (Romans 4:25) based on the plan of God. For Paul the "power of the cross" is not separable from the Resurrection of Jesus. However, the belief in the redemptive nature of Jesus' death predates the Pauline letters and goes back to the earliest days of Christianity and the Jerusalem church.
|
|
Donald A. Martin (1975) proved that for any set A, all Borel subsets of Aω are determined. Because the original proof was quite complicated, Martin published a shorter proof in 1982 that did not require as much technical machinery. In his review of Martin's paper, Drake describes the second proof as "surprisingly straightforward." The field of descriptive set theory studies properties of Polish spaces (essentially, complete separable metric spaces).
|
|
Artin–Schreier theory is the special case when A is the additive group of the separable closure of a field k of positive characteristic p, G is the Galois group, π is the Frobenius map minus the identity, and C the finite field of order p. Taking A to be a ring of truncated Witt vectors gives Witt's generalization of Artin–Schreier theory to extensions of exponent dividing pn.
|
|
307 "The impact of Hoeffding (1948) is overwhelming at the present time and is very likely to continue in the years to come". Note that the theory of U-statistics is not limited toSen (1992), p306 the case of independent and identically-distributed random variables or to scalar random- variables.Borovskikh's last chapter discusses U-statistics for exchangeable random elements taking values in a vector space (separable Banach space).
|
|
Episodes will often feature extra jokes and sequences as Easter eggs, accessible only by clicking certain objects on the screen during the cartoon. As of August 14, 2017, 207 Strong Bad Emails have been released on the website (with another six exclusive to DVD releases), separable into distinct eras by Strong Bad's different computers; the Tandy 400, the Compy 386, the Lappy 486, the Compé, and his current computer, the Lappier.
|
|
The Millennium problem requires the proposed Yang-Mills theory to satisfy the Wightman axioms or similarly stringent axioms. There are four axioms: ;W0 (assumptions of relativistic quantum mechanics) Quantum mechanics is described according to von Neumann; in particular, the pure states are given by the rays, i.e. the one-dimensional subspaces, of some separable complex Hilbert space. The Wightman axioms require that the Poincaré group acts unitarily on the Hilbert space.
|
|
Every layered permutation is an involution. They are exactly the 231-avoiding involutions, and they are also exactly the 312-avoiding involutions. The layered permutations are a subset of the stack- sortable permutations, which forbid the pattern 231 but not the pattern 312. Like the stack-sortable permutations, they are also a subset of the separable permutations, the permutations formed by recursive combinations of direct and skew sums.
|
|
The DC intra prediction mode generates a mean value by averaging reference samples and can be used for flat surfaces. The planar prediction mode in HEVC supports all block sizes defined in HEVC while the planar prediction mode in H.264/MPEG-4 AVC is limited to a block size of 16x16 pixels. The intra prediction modes use data from neighboring prediction blocks that have been previously decoded from within the same picture. ;Motion compensation For the interpolation of fractional luma sample positions HEVC uses separable application of one- dimensional half-sample interpolation with an 8-tap filter or quarter-sample interpolation with a 7-tap filter while, in comparison, H.264/MPEG-4 AVC uses a two-stage process that first derives values at half-sample positions using separable one-dimensional 6-tap interpolation followed by integer rounding and then applies linear interpolation between values at nearby half-sample positions to generate values at quarter-sample positions.
|
|
This is actually the first metal zipper that was made and it consisted of scoops of a special Y-shaped wire that were punched, nibbed and clamped onto a cloth tape to produce two facing rows that created a continuous zipper chain. 1923 saw Sundback's Separable Fastener's first use on a rubber boots. It then started being referred to as the "Zipper" from the "zip" sound produced when this device is used.
|
|
The insect in Europe and the Middle East has been described as C. cupressi, the one in Africa as C. cupressivora while the one in North America has been described as C. sabinae. These species are not separable using morphological characters alone, and a determination as to whether they are valid species awaits molecular evidence. Meanwhile, the CABI Invasive Species Compendium includes them all under C. cupressi "sensu lato" (in the broadest sense).
|
|
Reverse-phase analysis of another peak present in both venoms resolved a toxin that had an N-terminus identical to N. christyi short-chain neurotoxin 1. These fractions also contained toxins readily separable from the short-chain isotoxin by preparative reverse-phase chromatography. Amino acid sequencing of the first 28 residues indicated that both toxins were long-chain neurotoxins with identical N-termini. The LD50 of long-chain neurotoxins 2 from N. a.
|
|
A system of imprimitivity (U, π) of (G,X) on a separable Hilbert space H is irreducible if and only if the only closed subspaces invariant under all the operators Ug and π(A) for g and element of G and A a Borel subset of X are H or {0}. If (U, π) is irreducible, then π is homogeneous. Moreover, the corresponding measure on X as per the previous theorem is ergodic.
|
|
Historically, these sentences were proved in reverse order. In 1957, James had proved the reflexivity criterion for separable Banach spaces and 1964 for general Banach spaces. Since the reflexivity is equivalent to the weak compactness of the unit sphere, Victor L. Klee reformulated this as a compactness criterion for the unit sphere in 1962 and assumes that this criterion characterizes any weakly compact quantities. This was then actually proved by RC James in 1964.
|
|
DNA-DNA hybridisation studies have suggested that the two frogmouth groups may not be as closely related as previously thought, and that the Asian species may be separable as a new family, the Batrachostomidae. Although frogmouths are traditionally included in the order Caprimulgiformes, another study has cast doubt on their placement within that order, and they may be distinct enough to warrant an order of their own, Podargiformes, as Gregory Mathews proposed in 1918.
|
|
Reverse-phase analysis of another peak present in both venoms resolved a toxin that had an N-terminus identical to N. christyi short-chain neurotoxin 1. These fractions also contained toxins readily separable from the short-chain isotoxin by preparative reverse-phase chromatography. Amino-acid sequencing of the first 28 residues indicated that both toxins were long-chain neurotoxins with identical N-termini. The LD50 of long-chain neurotoxins 2 from N. a.
|
|
Adetomyrma aureocuprea, only known from males, is easily separable from the other Adetomyrma males by the yellowish body color, no mesoscutal notaulus, poorly developed subpetiolar process, lack of posterodorsal projection or lobe on the paramere, short hairs on the compound eye, and vestigial parapsidal line. The males of Adetomyrma aureocuprea display remarkable morphological variation in, for example, the size of the eye and ocelli, head shape, mesonotal shape, petiolar shape, and hairs on body surface.
|
|
Hilary Ann Priestley is a British mathematician. She is a professor at the University of Oxford and a Fellow of St Anne's College, Oxford, where she has been Tutor in Mathematics since 1972. Hilary Priestley introduced ordered separable topological spaces; such topological spaces are now usually called Priestley spaces in her honour. The term "Priestley duality" is also used for her application of these spaces in the representation theory of distributive lattices.
|
|
However, the statute had a severability clause,California Civil Code § 1746.5. so the court went through the severability test set forth in Hotel Employees & Rest. Employees Int'l Union v. Davis. The court held that the definition for "violent video game" is grammatically and functionally separable because, as an alternative definition of "violent video game", it can be removed from the Act without affecting the wording or function of the Act's other provisions.
|
|
Thus it was argued for further investigations of the Siau tarsier to see if it was taxonomically separable from T. sangirensis. The Sangihe Islands are known for their critically endangered avifauna, and concerns about the conservation status of the Siau Island tarsier grew before its formal description. The Siau Island tarsier was selected for the list of "The World's 25 Most Endangered Primates" by the IUCN Species Survival Commission, Primate Specialist Group.
|
|
Although both body and platform chassis are each made from similar pressed steel panels welded together, they were often bolted as the final two units and so may still be separable after construction. Achieving sufficient rigidity is difficult with a pure platform and so they are usually extended vertically with some form of box or tube section. This can be either a perimeter frame (e.g. Renault 4) or a central spine (e.g.
|
|
Formally speaking, this embedding was first introduced by Kuratowski,Kuratowski, C. (1935) "Quelques problèmes concernant les espaces métriques non-separables" (Some problems concerning non-separable metric spaces), Fundamenta Mathematicae 25: pp. 534–545. but a very close variation of this embedding appears already in the paper of FréchetFréchet M. (1906) "Sur quelques points du calcul fonctionnel", Rendiconti del Circolo Matematico di Palermo 22: 1–74. where he first introduces the notion of metric space.
|
|
Finite dimensional Banach spaces are homeomorphic as topological spaces, if and only if they have the same dimension as real vector spaces. Anderson–Kadec theorem (1965–66) proves that any two infinite-dimensional separable Banach spaces are homeomorphic as topological spaces. Kadec's theorem was extended by Torunczyk, who proved that any two Banach spaces are homeomorphic if and only if they have the same density character, the minimum cardinality of a dense subset.
|
|
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.
|
|
Liquid nitrogen being poured Nitrogen is the chemical element with atomic number 7, the symbol N and atomic mass 14.00674 u. Elemental nitrogen is a colorless, odorless, tasteless and mostly inert diatomic gas at standard conditions, constituting 78.08% by volume of Earth's atmosphere. The element nitrogen was discovered as a separable component of air, by Scottish physician Daniel Rutherford, in 1772. It occurs naturally in form of two isotopes: nitrogen-14 and nitrogen-15.
|
|
Ornstein noted that "Most techniques of meditation do not exist as solitary practices but are only artificially separable from an entire system of practice and belief."Robert Ornstein (1972) [1971], in: Naranjo and Orenstein, On the Psychology of Meditation. New York: Viking. For instance, while monks meditate as part of their everyday lives, they also engage the codified rules and live together in monasteries in specific cultural settings that go along with their meditative practices.
|
|
Hex-splines are the generalization of B-splines for 2-D hexagonal lattices. Similarly, in 3-D and higher dimensions, Voronoi splines provide a generalization of B-splines that can be used to design non- separable FIR filters which are geometrically tailored for any lattice, including optimal lattices. Explicit construction of ideal low-pass filters (i.e., sinc functions) generalized to optimal lattices is possible by studying the geometric properties of Brillouin zones (i.e.
|
|
Haruka uses a separable blade as her weapon, and specializes in charm magic. After a witch brings up memories of her painful past, where she wished to erase her sister from existence, she succumbs to her despair and becomes a witch herself. ; :One of the Yunagi magical girls, a positive-thinking girl who is classmates with Suzune. She wants to become friends with Suzune, even after finding out that she is a magical girl killer.
|
|
It takes the form of , where A and B are two systems, usually a robot base and a camera, and and are unknown transformation matrices. A highly studied special case of the problem occurs where , taking the form of the problem . Solutions to the problem take the forms of several types of methods, including separable closed-form solutions, simultaneous closed-form solutions, and iterative solutions.Mili I. Shah, Roger D. Eastman, Tsai Hong Hong.
|
|
French (1997) proposed a pseudo-recurrent backpropagation network (see Figure 2). In this model the network is separated into two functionally distinct but interacting sub-networks. This model is biologically inspired and is based on research from McClelland et al. (1995) McClelland and colleagues suggested that the hippocampus and neocortex act as separable but complementary memory systems, with the hippocampus for short term memory storage and the neocortex for long term memory storage.
|
|
There are numerous characterizations that tell when a second-countable topological space is metrizable, such as Urysohn's metrization theorem. The problem of determining whether a metrizable space is completely metrizable is more difficult. Topological spaces such as the open unit interval (0,1) can be given both complete metrics and incomplete metrics generating their topology. There is a characterization of complete separable metric spaces in terms of a game known as the strong Choquet game.
|
|
Kernel matrix defines the proximity of the input information. For example, in Gaussian Radial basis function, determines the dot product of the inputs in a higher-dimensional space, called feature space. It is believed that the data become more linearly separable in the feature space, and hence, linear algorithms can be applied on the data with a higher success. The kernel matrix can thus be analyzed in order to find the optimal number of clusters .
|
|
He also showed that even bound entanglement (when used in conjunction with a single pair of free entangled particles) can lead to quantum teleportation with a fidelity impossible to achieve with only separable states. Paweł Horodecki was educated in Poland, receiving an M.Sc from the University of Gdańsk (1995) and a Ph.D (with honours) from the Gdańsk University of Technology (1999) and a habilitation (with honours) from the University of Gdańsk (2004).
|
|
The dual tree hypercomplex wavelet transform (HWT) developed in consists of a standard DWT tensor and wavelets obtained from combining the 1-D Hilbert transform of these wavelets along the n-coordinates. In particular a 2-D HWT consists of the standard 2-D separable DWT tensor and three additional components: For the 2-D case, this is named dual tree quaternion wavelet transform (QWT). The total redundancy in M-D is tight frame.
|
|
Several conditions have been identified that guarantee the existence of a core coalition structure. This is the case in particular for hedonic games with the common ranking property, with the top coalition property, with top or bottom responsiveness, with descending separable preferences, and with dichotomous preferences. Moreover, common ranking property has been shown to guarantee the existence of a coalition structure which is core stable, individually stable and Pareto optimal at the same time.
|
|
Despite the close proximity with similar fossils, Hindeodus is easily determinable and readily separable by its large cusp. The wide distribution, clear derivation, and easy identifiability of Hindeodus makes it the ideal index fossil, which is why the International Commission on Stratigraphy (ICS) has assigned the First Appearance Datum of Hindeodus parvus as the defining biological marker for the start of the Induan, 252.2 ± 0.5 million years ago, the first stage of the Triassic.
|
|
Moreover, the Hahn–Banach theorem implies the Banach–Tarski paradox. For separable Banach spaces, D. K. Brown and S. G. Simpson proved that the Hahn–Banach theorem follows from WKL0, a weak subsystem of second-order arithmetic that takes a form of Kőnig's lemma restricted to binary trees as an axiom. In fact, they prove that under a weak set of assumptions, the two are equivalent, an example of reverse mathematics. Source of citation.
|
|
A newer model, stylistically and structurally similar to the original Moulton design, was manufactured by Bridgestone. Known as the Bridgestone Moulton, it was built in Japan and those sold in the UK were assembled in England at the Moulton factory. Like the original Moulton, the AM, and the APB before it, it was available in separable and rigid performance versions. Though similar in appearance to the original design, it was a contemporary performance bicycle with advanced design and components.
|
|
Many popular amino acid synthesis routes, such as the Strecker Synthesis, result in a mixture of R and S enantiomers. This mixture can be purified by (I) acylating the amine using an anhydride and then (II) selectively deacylating only the L enantiomer using hog kidney acylase. These enzymes are typically extremely selective for one enantiomer leading to very large differences in rate, allowing for selective deacylation. Finally the two products are now separable by classical techniques, such as chromatography.
|
|
The notions of unibranch and geometrically unibranch points are used in some theorems in algebraic geometry. For example, there is the following result: Theorem Let X and Y be two integral locally noetherian schemes and f \colon X \to Y a proper dominant morphism. Denote their function fields by K(X) and K(Y), respectively. Suppose that the algebraic closure of K(Y) in K(X) has separable degree n and that y \in Y is unibranch.
|
|
In mathematics, a Hilbert manifold is a manifold modeled on Hilbert spaces. Thus it is a separable Hausdorff space in which each point has a neighbourhood homeomorphic to an infinite dimensional Hilbert space. The concept of a Hilbert manifold provides a possibility of extending the theory of manifolds to infinite-dimensional setting. Analogously to the finite-dimensional situation, one can define a differentiable Hilbert manifold by considering a maximal atlas in which the transition maps are differentiable.
|
|
In 1972, Per Enflo constructed a separable Banach space that lacks the approximation property and a Schauder basis.Enflo's "sensation" is discussed on page 287 in Introductions to Enflo's solution were written by Halmos, by Johnson, by Kwapień, by Lindenstrauss and Tzafriri, by Nedevski and Trojanski, and by Singer. In 1972, Mazur awarded a live goose to Enflo in a ceremony at the Stefan Banach Center in Warsaw; the "goose reward" ceremony was broadcast throughout Poland.Kałuża, Saxe, Eggleton, Mauldin.
|
|
This secondary calcification and basis are also colored purple, and serve to halt further enlargement of shell size. As calcification proceeds, outer parts of the animal are raised off substrate, showing convex, saucer-shaped side view. Opercular plates are unusual in being completely fused on each side, with no trace left of scutal/tergal articulation, except in youngest individuals. Where scutum and tergum are separable, they are equal in size, and colored deep violet, with tergum darker than scutum.
|
|
At the southern end of the crown asterism are the stars Eta¹ and Eta² Coronae Australis, which form an optical double. Of magnitude 5.1 and 5.5, they are separable with the naked eye and are both white. Kappa Coronae Australis is an easily resolved optical double—the components are of apparent magnitudes 6.3 and 5.6 and are about 1000 and 150 light years away respectively. They appear at an angle of 359 degrees, separated by 21.6 arcseconds.
|
|
The discrete is inconstant, isolated and unpervading, mutable, supporting, mergent, conjunct and with an agent. The un-discrete is constant, field-like, pervasive, immutable, non-supporting, non-mergent, separable and independent of an agent.Samkhya karika by Iswara Krishna, Henry Colebrooke (Translator), Oxford University Press, pages 39-44 Both discrete and un- discrete, describes Karika in verse 11, are simultaneously imbued with three qualities, and these qualities (Guṇa) are objective, common, prolific, do not discriminate and are innate.
|
|
Phrasal verbs are represented in many languages by compound verbs. As a class, particle phrasal verbs belong to the same category as the separable verbs of other Germanic languages. For example in Dutch, de lamp aansteken (to light the lamp) becomes, in a principal clause, ik steek de lamp aan (I light the lamp on). Similarly, in German, das Licht einschalten (to switch on the light) becomes ich schalte das Licht ein (I switch the light on).
|
|
One page of the 11-page appendix to Justice Ginsburg's opinion, which highlighted that the designs were registered with the U.S. Copyright Office as "2-dimensional artwork" Justice Ginsburg wrote an opinion concurring in judgement--the cheerleading uniform designs were separable-- without joining in the majority's reasoning. The copyrights were not registered for the useful articles of clothing, emphasized Ginsburg. The registrations were for pictoral and graphical works that were then reproduced on the clothing.Star Athletica, LLC v.
|
|
In this type of estimation, we select the multidimensional signal to be a separable function. Because of this property we will be able to view the Fourier analysis taking place in multiple dimensions successively. A time delay in the magnitude squaring operation will help us process the Fourier transformation in each dimension. A Discrete time Multidimensional Fourier transform is applied along each dimension and in the end a maximum entropy estimator is applied and the magnitude is squared.
|
|
The quantum mechanical wavefunctions and energies (eigenvalues) are found by solving the Schrödinger equation with this Hamiltonian. Due to the spherical symmetry of the system, it is natural to use spherical coordinates r, \theta and \phi. When this is done, the time-independent Schrödinger equation for the system is separable, allowing the angular problems to be dealt with easily, and leaving an ordinary differential equation in r to determine the energies for the particular potential V(r) under discussion.
|
|
Removing fins from a missile also reduces the structural mass, so the payload weight or missile range can be increased. Without the fins and associated drag, the missile can be more responsive to changes in trajectory. Iranian sources cite an improved guidance system on the missile, and analysts note that adjusting the missile's in- flight trajectory without fins requires a highly responsive guidance system. The Qiam 1's accuracy is also improved with the addition of a separable warhead.
|
|
Its origins are not fully known. Most historians recognize the Tambralinga Kingdom of Chinese records as a precursor of Nakhon Si Thammarat. The town chronicles of this time are hardly separable from legend, but they do tell of an abandonment and refounding of the town, which would explain the break in history between Tambralinga and Nakhon Si Thammarat. References to a country named Poling appear in Chinese chronicles from the Tang dynasty period down to the early Ming dynasty.
|
|
An integral transform may transform the PDE to a simpler one, in particular, a separable PDE. This corresponds to diagonalizing an operator. An important example of this is Fourier analysis, which diagonalizes the heat equation using the eigenbasis of sinusoidal waves. If the domain is finite or periodic, an infinite sum of solutions such as a Fourier series is appropriate, but an integral of solutions such as a Fourier integral is generally required for infinite domains.
|
|
A Gaussian blur effect is typically generated by convolving an image with an FIR kernel of Gaussian values. In practice, it is best to take advantage of the Gaussian blur’s separable property by dividing the process into two passes. In the first pass, a one-dimensional kernel is used to blur the image in only the horizontal or vertical direction. In the second pass, the same one-dimensional kernel is used to blur in the remaining direction.
|
|
Given the equation , it is possible to decompose the equation into a purely rotational and translational part; methods utilizing this are referred to as separable methods. Where represents a 3×3 rotation matrix and a 3×1 translation vector, the equation can be broken into two parts:Amy Tabb, Khalil Yousef. "Solving the Robot-World Hand-Eye(s) Calibration Problem with Iterative Methods." Machine Vision and Applications, August 2017, Volume 28, Issue 5-6, pp 569-590.
|
|
The solvent must alter the relative volatility by a wide enough margin for a successful result. The quantity, cost and availability of the solvent should be considered. The solvent should be easily separable from the bottom product, and should not react chemically with the components or the mixture, or cause corrosion in the equipment. A classic example to be cited here is the separation of an azeotropic mixture of benzene and cyclohexane, where aniline is one suitable solvent.
|
|
Hurtado, Lord Jesus Christ, pg. 20 Furthermore, Bousset also relied on a distinction between "Palestinian" and "Hellenistic" for his studies on early Christology that, though was widely accepted in his day, has now been rejected by modern scholars as being simplistic. The relationship between Palestinian Judaism and Hellenistic Judaism is considered to be complex, with varying influences between the two concepts in different communities rather than clearly separable layers by which study on early Christology can be conducted.Marshall, Howard.
|
|
The Faddeev equations are the most often used non- perturbative formulations of the quantum-mechanical three-body problem. Unlike the three body problem in classical mechanics, the quantum three body problem is uniformly soluble. In nuclear physics, the off the energy shell nucleon- nucleon interaction has been studied by analyzing (n,2n) and (p,2p) reactions on deuterium targets, using the Faddeev Equations. The nucleon-nucleon interaction is expanded (approximated) as a series of separable potentials.
|
|
The Fokas method gives rise to a novel spectral collocation method occurring in Fourier space. Recent work has extended the method and demonstrated a number of its advantages; it avoids the computation of singular integrals encountered in more traditional boundary based approaches, it is fast and easy to code up, it can be used for separable PDEs where no Green's function is known analytically and it can be made to converge exponentially with the correct choice of basis functions.
|
|
The discrete wavelet transform is extended to the multidimensional case using the tensor product of well known 1-D wavelets. In 2-D for example, the tensor product space for 2-D is decomposed into four tensor product vector spaces as } This leads to the concept of multidimensional separable DWT similar in principle to the multidimensional DFT. gives the approximation coefficients and other subbands: low-high (LH) subband, high-low (HL) subband, high-high (HH) subband, give detail coefficients.
|
|
Dual tree CWT in 1-D uses 2 real DWTs, where the first one gives the real part of CWT and the second DWT gives the imaginary part of the CWT. M-D dual tree CWT is analyzed in terms of tensor products. However, it is possible to implement M-D CWTs efficiently using separable M-D DWTs and considering sum and difference of subbands obtained. Additionally, these wavelets tend to be oriented in specific directions.
|
|
As Levinson points out, there is evidence that supports the emergence of BCTs through physical objects and words used to signify simultaneous properties such as lightness. As such, these terms do not cohere as a unique, separable semantic domain denoting hue (see Bornstein for this criterion). Over time, though, and through processes of semantic change, such a domain can emerge. In response to work by Levinson and Lyons, Kay dubs this perspective the Emergence Hypothesis (EH).
|
|
In addition, attachment does not seem to fail in the early childhood of autistics. This suggests that emotion is a component of social cognition that is separable from mentalizing. Lombardo and Cohen updated the theory and pinpointed some additional factors that play an important part in ToM of autistic people. They highlighted that the middle cingulate cortex which is outside the traditional mentalizing region was underactive in autistic patients, while the rest of ToM activation was normal.
|
|
One environmental issue is to prevent noxious materials leaching from spent shale into the water supply. The oil shale processing is accompanied by the formation of process waters and waste waters containing phenols, tar and several other products, heavily separable and toxic to the environment. A 2008 programmatic environmental impact statement issued by the United States Bureau of Land Management stated that surface mining and retort operations produce of waste water per of processed oil shale.
|
|
A special case of the quantum mechanical three-body problem is the hydrogen molecule ion, . Two of the three bodies are nuclei and the third is a fast moving electron. The two nuclei are 1800 times heavier than the electron and thus modeled as fixed centers. It is well known that the Schrödinger wave equation is separable in Prolate spheroidal coordinates and can be decoupled into two ordinary differential equations coupled by the energy eigenvalue and a separation constant.
|
|
According to behavioral momentum theory, there are two separable factors that independently govern the rate with which a discriminated operant occurs and the persistence of that response in the face of disruptions such as punishment, extinction, or the differential reinforcement of alternative behaviors. (see Nevin & Grace, 2000, for a review). First, the positive contingency between the response and a reinforcing consequence controls response rates (i.e., a response–reinforcer relation) by shaping a particular pattern of responding.
|
|
Kosmos 1792 was a Soviet reconnaissance satellite which was launched in 1986. A Yantar-4K2 satellite, it operated for almost two months before being deorbited and recovered. Launched at 10:59 UTC on November 13, 1986 using a Soyuz-U rocket flying from the Baikonur Cosmodrome, Kosmos 1792 was operated in low Earth orbit until it was recovered on January 5, 1987. In addition to the main spacecraft, two separable film capsules were also returned during the satellite's mission.
|
|
In some cases, m-D signals and systems can be simplified into single dimension signal processing methods, if the considered systems are separable. Typically, multidimensional signal processing is directly associated with digital signal processing because its complexity warrants the use of computer modelling and computation. A multidimensional signal is similar to a single dimensional signal as far as manipulations that can be performed, such as sampling, Fourier analysis, and filtering. The actual computations of these manipulations grow with the number of dimensions.
|
|
The uma is the centre of social, religious, and political life and it is here where every village member of egalitarian Mentawai society is able to contribute meetings about matters affecting the community. Like many Indonesians, Mentawaians believe in a separable soul that leaves the body upon death becoming a ghost. To protect themselves from these spirits, fetish sticks are placed by the entrances of the log wall that surrounds and fortifies the village and forms a stockade for cattle.
|
|
Psilocybe weilii caps range from (2)3 to 6(8.5) cm in diameter and are obtusely conic to convex to campanulate. The margin is incurved or inrolled when young, becoming irregularly lobulated then straight with age. Psilocybe weilii are subumbonate, hygrophanous, glabrous, and subviscid when moist from the separable gelatinous pellicle. It is translucent-striate at the margin, and purple brown or chestnut brown to dark brown, fading to buff or straw yellow as it dries, with the center remaining blackish brown.
|
|
To motivate the (conjectural) motivic Galois group, fix a field k and consider the functor :finite separable extensions K of k → non- empty finite sets with a (continuous) transitive action of the absolute Galois group of k which maps K to the (finite) set of embeddings of K into an algebraic closure of k. In Galois theory this functor is shown to be an equivalence of categories. Notice that fields are 0-dimensional. Motives of this kind are called Artin motives.
|
|
The legs, as with many swifts, are very short, preventing the birds from perching, but allowing them to cling to vertical surfaces. The flight is mainly gliding due to very long primary feathers and small breast muscles. Aerodramus swiftlets, depending on species, weigh 8–35 grammes (0.28–1.23 oz) and are 9–16 centimetres (0.28–1.23 in) long. These swiftlets are very similar, and where several species occur, such as Borneo, New Guinea and the Philippines, may not be separable in the field.
|
|
The complex wavelet transform (CWT) is a complex-valued extension to the standard discrete wavelet transform (DWT). It is a two-dimensional wavelet transform which provides multiresolution, sparse representation, and useful characterization of the structure of an image. Further, it purveys a high degree of shift-invariance in its magnitude, which was investigated in. However, a drawback to this transform is that it exhibits 2^{d} (where d is the dimension of the signal being transformed) redundancy compared to a separable (DWT).
|
|
In separable problems, perceptron training can also aim at finding the largest separating margin between the classes. The so-called perceptron of optimal stability can be determined by means of iterative training and optimization schemes, such as the Min-Over algorithm (Krauth and Mezard, 1987) or the AdaTron (Anlauf and Biehl, 1989)). AdaTron uses the fact that the corresponding quadratic optimization problem is convex. The perceptron of optimal stability, together with the kernel trick, are the conceptual foundations of the support vector machine.
|
|
This meant, though, that the issue of the antiquity of man was not separable from other debates of the period, on geology and foundations of scientific archaeology. The first strong scientific arguments for the antiquity of man as very different from accepted biblical chronology were certainly also strongly controverted. Those who found the conclusion unacceptable could be expected to examine the whole train of reasoning for weak points. This can be seen, for example, in the Systematic Theology of Charles Hodge (1871–3).
|
|
Craske's research views fear and anxiety as separable constructs and explores how anxiety can stem from fear and be treated through fear extinction. One of her main goals has been to find effective treatments for anxiety, including methods of reducing panic attacks. Craske has develop a series of a computer- assisted therapy programs for treating anxiety disorders that are designed to help therapists and their clients. Craske's and her colleagues have focused on emotion regulation in clients, using focused breathing to promote mindfulness.
|
|
Finite geometry has contributed to coding theory, such as the Goppa code, so the field is supported by computer science. In the preface of the 1991 text Hirschfeld summarizes the status of Galois geometry, mentioning maximum distance separable code, mathematics journals publishing finite geometry, and conferences on combinatorics featuring Galois geometry. Colleague Joseph A. Thas is coauthor of General Galois Geometries on PG(n,q) where n ≥ 4. Hirschfeld was cited as the ultimate editor of Design Theory (1986).. 2nd ed.
|
|
Sundback finally solved the pulling-apart problem in 1913, with his invention of the first version not based on the hook-and-eye principle, the "Hookless Fastener No. 1". He increased the number of fastening elements from four per inch to ten or eleven. His invention had two facing rows of teeth that pulled into a single piece by the slider, and increased the opening for the teeth guided by the slider. The patent for the "Separable Fastener" was issued in 1917.
|
|
A tooth cannot rise up off the nib below it enough to break free, and its nib on top cannot drop out of the dimple in the tooth above it. for the "Separable Fastener" was issued in 1917. The name zipper was created in 1923 by B.F. Goodrich, who used the device on their new boots. Initially, boots and tobacco pouches were the primary use for zippers; it took another twenty years before they caught on in the fashion industry.
|
|
The double-pointed cofinite topology is the cofinite topology with every point doubled; that is, it is the topological product of the cofinite topology with the indiscrete topology on a two-element set. It is not T0 or T1, since the points of the doublet are topologically indistinguishable. It is, however, R0 since the topologically distinguishable points are separable. An example of a countable double-pointed cofinite topology is the set of even and odd integers, with a topology that groups them together.
|
|
In mechanistic or pre-quantum science, particles are seen as individual entities that interact only in a mechanistic sense. In quantum mechanics, particles such as electrons can become entangled so that a measurement on one instantly affects the state of the other. In quantum social science, people are similarly entangled, whether through shared institutions such as language, or (according to some interpretations) through actual physical processes. An implication is that people are never completely separable, but are entangled elements of society.
|
|
The first "separable coupon ticket" was patented by John Michael Lyons of Moncton, New Brunswick on June 5, 1882. The ticket showed the issuing station, the destination, and a consecutive number for reference. The lower half of the ticket was given to the passenger, while the upper half, with a hole at the top, was inserted into a brass sleeve and then attached to the baggage by a strap.Mario Theriault, Great Maritime Inventions 1833–1950, Goose Lane Editions, 2001, p. 63.
|
|
At each point in the image, the result of the Sobel–Feldman operator is either the corresponding gradient vector or the norm of this vector. The Sobel–Feldman operator is based on convolving the image with a small, separable, and integer-valued filter in the horizontal and vertical directions and is therefore relatively inexpensive in terms of computations. On the other hand, the gradient approximation that it produces is relatively crude, in particular for high-frequency variations in the image.
|
|
The two main questions which the theory of SSA attempts to answer are: (a) what time series components can be separated by SSA, and (b) how to choose the window length L and make proper grouping for extraction of a desirable component. Many theoretical results can be found in Golyandina et al. (2001, Ch. 1 and 6). Trend (which is defined as a slowly varying component of the time series), periodic components and noise are asymptotically separable as N\rightarrow \infty.
|
|
The Borel graph theorem states: An improvement upon this theorem, proved by A. Martineau, uses K-analytic spaces. :Definition: A topological space is called a if it is the countable intersection of countable unions of compact sets. :Definition: A Hausdorff topological space is called K-analytic if it is the continuous image of a space (that is, if there is a space and a continuous map of onto ). Every compact set is K-analytic so that there are non-separable K-analytic spaces.
|
|
In quantum chemistry, the potential energy surfaces are obtained within the adiabatic or Born–Oppenheimer approximation. This corresponds to a representation of the molecular wave function where the variables corresponding to the molecular geometry and the electronic degrees of freedom are separated. The non separable terms are due to the nuclear kinetic energy terms in the molecular Hamiltonian and are said to couple the potential energy surfaces. In the neighbourhood of an avoided crossing or conical intersection, these terms cannot be neglected.
|
|
The CFSP sees the North Atlantic Treaty Organisation (NATO) as responsible for the territorial defence of Europe and reconciliation. However, since 1999, the European Union is responsible for implementing missions such as peacekeeping and policing of treaties. A phrase often used to describe the relationship between the EU forces and NATO is "separable, but not separate". The same forces and capabilities form the basis of both EU and NATO efforts, but portions can be allocated to the European Union if necessary.
|
|
Bolin, I. (2006). Growing up in a culture of respect: Child rearing in highland Peru. Austin: University of Texas Press p. 43 Two-year-olds in the Chillihuani community frequently get their own food and drink, and those of herding families participate in herding and caring for the animals.Bolin, I. (2006). Growing up in a culture of respect: Child rearing in highland Peru. Austin: University of Texas Press p. 43, 48 In this community, work and play are not two separable things (i.e.
|
|
In linguistics, an affix is a morpheme that is attached to a word stem to form a new word or word form. Affixes may be derivational, like English -ness and pre-, or inflectional, like English plural -s and past tense -ed. They are bound morphemes by definition; prefixes and suffixes may be separable affixes. Affixation is the linguistic process that speakers use to form different words by adding morphemes at the beginning (prefixation), the middle (infixation) or the end (suffixation) of words.
|
|
In 1934 and 1935, Paul Horst, the owner of negotiable bonds, detached negotiable interest coupons prior to their due date and gave them as a gift to his son. His son thus collected the interest coupons at maturity. A coupon bond holder owns two independent and separable rights: (1) the right to receive at maturity the principal amount of the bond, and (2) the right to receive interim payments of interest on the investment of the amounts specified by the coupons.
|
|
Part 4 is titled Separable Functions of Men and Computers in the Anticipated Symbiotic Association. Licklider in the first passage of this part makes reference to the SAGE System. The text continues to identify ways in which theoretically active computers would function in ways including; to interpolate, extrapolate, convert static equations or logical statements into dynamic models (see also conceptual models).The part concludes with a statement of the functioning of a potential computer as performing diagnosis, pattern-matching, and relevance-recognizing.
|
|
Despite the enormous ecological importance of the myrtle family in Australia (e.g. Eucalyptus, Corymbia, Angophora, Melaleuca, Callistemon, Rhodamnia, Gossia), only one species of Eugenia, E. reinwardtiana, occurs on that continent. The genus also is represented in Africa south of the Sahara, but it is relatively species-poor on that continent. In the past some botanists included the morphologically similar Old World genus Syzygium in Eugenia, but research by Rudolf Schmid in the early 1970s convinced most botanists that the genera are easily separable.
|
|
In mathematics, particularly topology, a cosmic space is any topological space that is a continuous image of some separable metric space. Equivalently (for regular T1 spaces but not in general), a space is cosmic if and only if it has a countable network; namely a countable collection of subsets of the space such that any open set is the union of a subcollection of these sets. Cosmic spaces have several interesting properties. There are a number of unsolved problems about them.
|
|
The wavelets generated by the separable DWT procedure are highly shift variant. A small shift in the input signal changes the wavelet coefficients to a large extent. Also, these wavelets are almost equal in their magnitude in all directions and thus do not reflect the orientation or directivity that could be present in the multidimensional signal. For example, there could be an edge discontinuity in an image or an object moving smoothly along a straight line in the space-time 4D dimension.
|
|
Consider the integer multi-commodity flow problem of routing k types of integer commodities from m suppliers to n consumers subject to supply, consumption, and capacity constraints, so as to minimize the sum of linear or congestion-dependent convex costs on the arcs. Then for every fixed k and m, the Graver basis of the defining system can be computed and the resulting separable-convex objective function minimized in time which is polynomial in the variable number n of consumers and in the rest of the data.
|
|
Satsumas usually have 10 to 12 easily separable segments with tough membranes. The flesh is particularly delicate, and cannot withstand the effects of careless handling. Coloring of the fruit is often dependent on climate; Satsumas grown in humid areas may be ripe while the skin is still green while those grown in areas with cool night temperatures may see a brilliant reddish orange skin at peak. Satsumas are cold-hardy, and when planted in colder locations, the fruit becomes sweeter from the colder temperatures.
|
|
An abstract Wiener space is a mathematical object in measure theory, used to construct a "decent", strictly positive and locally finite measure on an infinite-dimensional vector space. Wiener's original construction only applied to the space of real-valued continuous paths on the unit interval, known as classical Wiener space. Leonard Gross provided the generalization to the case of a general separable Banach space. The notion of a Banach space itself was discovered independently by both Wiener and Stefan Banach at around the same time.
|
|
Hubbell plug and receptacle as advertised in the 1906 Hubbell catalog An early American electrical plug and socket was invented by Harvey Hubbell and patented in 1904. Hubbell's first design was a socket which screwed into a lampholder (like the early lampholder plugs), but with a separable plug with pins () or blades (US patent 774251). The 1906 Hubbell catalog shows the blade plug with a flush mounting socket for use in wall or floor. Other manufacturers adopted the Hubbell pattern, and by 1915 they were widespread.
|
|
Leonardo Fibonacci, the Italian mathematician who introduced the Hindu–Arabic numeral system invented between the 1st and 4th centuries by Indian mathematicians, to the Western World. Mathematics has no generally accepted definition. Aristotle defined mathematics as "the science of quantity" and this definition prevailed until the 18th century. However, Aristotle also noted a focus on quantity alone may not distinguish mathematics from sciences like physics; in his view, abstraction and studying quantity as a property "separable in thought" from real instances set mathematics apart.
|
|
Vol II. p.508-527Dieudonne, J. History of Functional Analysis Chapter VIII. Section 2. A notable example of a result which had to wait for the development and dissemination of general locally convex spaces (amongst other notions and results, like nets, the product topology and Tychonoff's theorem) to be proven in its full generality, is the Banach–Alaoglu theorem which Stefan Banach first established in 1932 by an elementary diagonal argument for the case of separable normed spacesBanach, S. Theory of linear operations p.75.
|
|
It took ten more years until neural network research experienced a resurgence in the 1980s. This text was reprinted in 1987 as "Perceptrons - Expanded Edition" where some errors in the original text are shown and corrected. The kernel perceptron algorithm was already introduced in 1964 by Aizerman et al. Margin bounds guarantees were given for the Perceptron algorithm in the general non-separable case first by Freund and Schapire (1998), and more recently by Mohri and Rostamizadeh (2013) who extend previous results and give new L1 bounds.
|
|
The basis problem was posed by Stefan Banach in his book, Theory of Linear Operators. Banach asked whether every separable Banach space has a Schauder basis. A Schauder basis or countable basis is similar to the usual (Hamel) basis of a vector space; the difference is that for Hamel bases we use linear combinations that are finite sums, while for Schauder bases they may be infinite sums. This makes Schauder bases more suitable for the analysis of infinite-dimensional topological vector spaces including Banach spaces.
|
|
From the one-to-one correspondence between positive maps and entanglement witnesses, we have that a state ρ is entangled if and only if there exists a positive map Φ such that :(I \otimes \Phi)(\rho) is not positive. Therefore, if ρ is separable, then for all positive map Φ, :(I \otimes \Phi)(\rho) \geq 0. Thus every positive, but not completely positive, map Φ gives rise to a necessary condition for separability in this way. The reduction criterion is a particular example of this.
|
|
This group is intended to contain the operculated species of Pleurotomida which are so characteristic of the archibenthal region. They are distinctly contrasted with the coarse, spotted or maculated shallow-water species of Pleuroma proper, by their thin, white, delicately sculptured shells. They are apart from Drillia by having no subtubular projection of the anal notch when adult and no thick varix to mark their maturity. They are separable from the archibenthal Drillias also by their larger shells, longer siphonal canal, and more inflated habit.
|
|
The Dialectic of Spontaneity and Organisation was the central feature of Luxemburg's political philosophy, wherein spontaneity is a grassroots approach to organising a party-oriented class struggle. She argued that spontaneity and organisation, are not separable or separate activities, but different moments of one political process as one does not exist without the other. These beliefs arose from her view that class struggle evolves from an elementary, spontaneous state to a higher level:In a Revolutionary Hour: What Next?. Collected Works (1: 2). p. 554.
|
|
It is a thread made of mercerized cotton, composed of six strands that are only loosely twisted together and easily separable. While there are other manufacturers, the two most-commonly used (and oldest) brands are DMC and Anchor, both of which have been manufacturing embroidery floss since the 1800s. Other materials used are pearl (or perle) cotton, Danish flower thread, silk and Rayon. Different wool threads, metallic threads or other novelty threads are also used, sometimes for the whole work, but often for accents and embellishments.
|
|
The members of the team were Georgios Siviloglou, John Broky, Aristide Dogariu, and Demetrios Christodoulides. In one-dimension, the Airy beam is the only exactly shape-preserving accelerating solution to the free- particle Schrödinger equation (or 2D paraxial wave equation). However, in two dimensions (or 3D paraxial systems), two separable solutions are possible: two-dimensional Airy beams and accelerating parabolic beams. Furthermore, it has been shown that any function on the real line can be mapped to an accelerating beam with a different transverse shape.
|
|
The more borings/ cores that are taken, the more accurate the map will be. Based on depth to bedrock reported in water well observations, the electrical conductivity of bedrock appears largely separable from that of the overlying glacial sediments due to the higher conductivity of the shale present in some soils. In one study done in Denmark, a series of braided buried valleys were found anywhere from 10 m to 300 m below the surface using drilling/boring.He, X. , Sonnenborg, T. , Jørgensen, F. , & Jensen, K. (2017).
|
|
The linear attenuation coefficients can hence be expanded as In contrast-enhanced imaging, high-atomic-number contrast agents with K absorption edges in the diagnostic energy range may be present in the body. K-edge energies are material specific, which means that the energy dependence of the photo-electric effect is no longer separable from the material properties, and an additional term can be added to Eq. () according to where a_K and f_K are the material coefficient and energy dependency of contrast- agent material K.
|
|
An explosion of interest and activity in open access journals has occurred since the 1990s, largely due to the widespread availability of Internet access. It is now possible to publish a scholarly article and also make it instantly accessible anywhere in the world where there are computers and Internet connections. The fixed cost of producing the article is separable from the minimal marginal cost of the online distribution. These new possibilities emerged at a time when the traditional, print-based scholarly journals system was in a crisis.
|
|
Of course in one-dimensional systems, resonances are shape resonances. In a system with more than one degree of freedom, this definition makes sense only if the separable model, which supposes the two groups of degrees of freedom uncoupled, is a meaningful approximation. When the coupling becomes large, the situation is much less clear. In the case of atomic and molecular electronic structure problems, it is well known that the self- consistent field (SCF) approximation is relevant at least as a starting point of more elaborate methods.
|
|
The relationship between measurability and weak measurability is given by the following result, known as Pettis' theorem or Pettis measurability theorem. > A function f is said to be almost surely separably valued (or essentially > separably valued) if there exists a subset N ⊆ X with μ(N) = 0 such that f(X > \ N) ⊆ B is separable. > Theorem (Pettis, 1938). A function f : X → B defined on a measure space (X, > Σ, μ) and taking values in a Banach space B is (strongly) measurable (that > equals a.e.
|
|
With this clue we can construct an example: :P(X) = Xp − T with K the field of rational functions in the indeterminate T over the finite field with p elements. Here one can prove directly that P(X) is irreducible, and not separable. This is actually a typical example of why inseparability matters; in geometric terms P represents the mapping on the projective line over the finite field, taking co-ordinates to their pth power. Such mappings are fundamental to the algebraic geometry of finite fields.
|
|
In topology, the split interval is a space that results from splitting each interior point in a closed interval into two adjacent points. It may be defined as the lexicographic product [0, 1] × {0, 1} without the isolated edge points, (0,1) and (1,0), equipped with the order topology. It is also known as the Alexandrov double arrow space or two arrows space. The split interval is compact Hausdorff, and it is hereditarily Lindelöf and hereditarily separable, but it is not metrizable; its metrizable subspaces are all countable.
|
|
The C3 optimisation algorithm was originally designed for simulation-based optimisation but it can be used for global optimisation problems in general.Glorieux E., Svensson B., Danielsson F., Lennartson B.: "Constructive cooperative coevolution for large-scale global optimisation", Journal of Heuristics, 2017. Its strength over other optimisation algorithms, specifically cooperative coevolution, is that it is better able to handle non-separable optimisation problems.Glorieux E., Danielsson F., Svensson B., Lennartson B.: "Constructive cooperative coevolutionary optimisation for interacting production stations", International Journal of Advanced Manufacturing Technology, 2015.
|
|
Governor Hunter's philosophy was that "the true Interests of the People and Government are the same, I mean A Government of Laws. No other deserves the Name, and are never Separated or Separable but in Imagination by Men of Craft." Hunter was succeeded as Governor by Pieter Schuyler as acting governor from 1719 to 1720 and finally by William Burnet, whose post as Comptroller of Customs was given to Hunter in exchange. Hunter was then Governor of Jamaica from 1727 until his death on 31 March 1734.
|
|
He built his first instrument as a 25 cm by 2.5 cm hollow wooden cylinder, which he later refined to comprise three detachable parts. The refined design featured a funnel-shaped cavity to augment the sound, separable from the body of the stethoscope. His clinical work allowed him to follow chest patients from bedside to the autopsy table. He was therefore able to correlate sounds captured by his new instruments with specific pathological changes in the chest, in effect pioneering a new non- invasive diagnostic tool.
|
|
Every contractible space is simply connected. ;Coproduct topology: If {Xi} is a collection of spaces and X is the (set-theoretic) disjoint union of {Xi}, then the coproduct topology (or disjoint union topology, topological sum of the Xi) on X is the finest topology for which all the injection maps are continuous. ;Cosmic space: A continuous image of some separable metric space. ;Countable chain condition: A space X satisfies the countable chain condition if every family of non-empty, pairswise disjoint open sets is countable.
|
|
It satisfies e(w/v) ≤ [L : K] (the degree of the extension L/K). The relative degree of w over v is defined to be f(w/v) = [Rw/mw : Rv/mv] (the degree of the extension of residue fields). It is also less than or equal to the degree of L/K. When L/K is separable, the ramification index of w over v is defined to be e(w/v)pi, where pi is the inseparable degree of the extension Rw/mw over Rv/mv.
|
|
There have long been differing opinions as to how mushrooms which were assigned to genus Lepista (sometimes also placed in genus Clitocybe) should be classified. The fungi in question all have a white or slightly pink/yellow spore print, finely warty spores, and easily separable gills. In 1981 Jörg H. Raithelhuber identified as separate a subgroup having very crowded strongly decurrent gills and spores which are oval in section to almost spherical, including Lepista flaccida and Lepista gilva. He proposed this subgroup as a new genus Paralepista.
|
|
In the Rice et al. article, classism is defined as the belief that all members of a certain social class possess certain characteristics inherent to that class. Many of the interviewees found it hard to recall specific experiences of classism, but nevertheless experienced being generally "looked down upon". Non-white first generation college students in the study would sometimes refer to their experiences using racial or ethnic terms interchangeably with class terms, showing that dimensions of their identities are not separable from one another.
|
|
These verses, it is argued, indicate that death is only a period or form of slumber. Adventists teach that the resurrection of the righteous will take place shortly after the second coming of Jesus, as described in Revelation 20:4–6 that follows Revelation 19:11–16, whereas the resurrection of the wicked will occur after the millennium, as described in Revelation 20:5 and 20:12–13 that follow Revelation 20:4 and 6–7, though Revelation 20:12–13 and 15 actually describe a mixture of saved and condemned people being raised from the dead and judged. Adventists reject the traditional doctrine of hell as a state of everlasting conscious torment, believing instead that the wicked will be permanently destroyed after the millennium by the lake of fire, which is called 'the second death' in Revelation 20:14. Those Adventist doctrines about death and hell reflect an underlying belief in: (a) conditional immortality (or conditionalism), as opposed to the immortality of the soul; and (b) the monistic nature of human beings, in which the soul is not separable from the body, as opposed to bipartite or tripartite conceptions, in which the soul is separable.
|
|
The Prewitt operator is used in image processing, particularly within edge detection algorithms. Technically, it is a discrete differentiation operator, computing an approximation of the gradient of the image intensity function. At each point in the image, the result of the Prewitt operator is either the corresponding gradient vector or the norm of this vector. The Prewitt operator is based on convolving the image with a small, separable, and integer valued filter in horizontal and vertical directions and is therefore relatively inexpensive in terms of computations like Sobel and Kayyali operators.
|
|
It prohibited the use of hard metal other than soft metal (hardness measured by Brinell scale (10/500) 91 HB or less) like zinc alloy in main parts of metal modelguns. The metal model handguns must have completely sealed barrel and added a hardened steel rod molded inside softer metal barrel to prevent attempts of modification and making it pass-through. Front of cylinder chamber of revolvers must be blocked. The barrel and frame of metal model handguns must not be separable to prevent the interchange of the barrel.
|
|
This new regulation prohibits further production of many full metal model handguns with separable barrel and slide. The ASGK manage the safety approval and the SMG (Safe Model Gun) mark replaced the SM mark on the metal models to identify the models meeting the new regulation. However, the new law did not apply to modelgun made in plastics and so it also stimulated the production of more plastic modelguns by various manufacturers. The modelgun makers imposed some voluntary industrial restraints (self- regulation) to the plastic modelguns to prevent modification and for easy identification as modelgun.
|
|
In order to ensure at least k keys must be compromised before every shared key can be computed by an attacker, identifiers must be k-linearly independent: all sets of k randomly selected user identifiers must be linearly independent. Otherwise, a group of malicious users can compute the key of any other member whose identifier is linearly dependent to theirs. To ensure this property, the identifiers shall be preferably chosen from a MDS- Code matrix (maximum distance separable error correction code matrix). The rows of the MDS-Matrix would be the identifiers of the users.
|
|
When walking, the male carries its tail in an upward-curving train. Juveniles are separable from adults at close range. They are similar to the adult female, but can be distinguished by: (1) the richer and more uniform rufous-brown colouring on the chin, throat and foreneck, and brighter red-brown wash on the forehead and forecrown; (2) the slightly paler upperbody; (3) the softer, downy texture of the rump, lower belly and vent feathers; and, most importantly, (4) the tail feathers (excluding the central pair of medians) are distinctly narrower, more tapered and pointed.
|
|
More exactly, it was a separable question, whether an end user might violate copyright in their copying of the material and whether the making of temporary copies to allow that user to view the material was itself a breach of copyright. An end user viewing the material was not of itself a copyright-breaching act (as mere viewing is not a copyright breach), therefore automated temporary copies for technical reasons, used to facilitate and enable that lawful act, were also to be deemed within the scope of EU law and lawful.
|
|
This muscle is categorised into five types according to morphology: the independent type, VI-type, VL-type, common type and two-belly type. The independent type of the tensor vastus intermedius, also the most frequent type, has its tendon lying between the vastus intermedius and the vastus lateralis. For the VI-type and the VL-type, the tendinous part of the muscle is integrated into the fascia of the vastus intermedius and the vastus lateralis respectively. For the common type, it has a non-separable origin between the intertrochanteric line and greater trochanter.
|
|
Internal beams vary in fabric from wood to steel. The load-bearing masonry on the perimeter of the building and the steel-framed structure in the core are fairly readily separable in the upper reaches of the building, though the edges of concrete floors do bear on the earlier masonry at the perimeter of the framed structure of the core. The panel walls contained in the 1917 frame are of brick. Floors in the perimeter building are generally suspended timber, joisted with added steel beams, while the framed core has reinforced concrete two-way slabs.
|
|
In 1958 Gillman was awarded a Guggenheim Fellowship, and he spent the next two years as a visiting member at the Institute for Advanced Study. He and former OEG colleague Nathan Fine defined remote points and showed that if the continuum hypothesis holds, then the real line (or any separable Tychonoff space that is not pseudocompact) has remote points. In 1960 he became chairman of the department of mathematics at the University of Rochester. He was active in recruiting top mathematicians to the department, including Arthur Harold Stone and his wife Dorothy Maharam.
|
|
The points x and y, separated by their respective neighbourhoods U and V. Points x and y in a topological space X can be separated by neighbourhoods if there exists a neighbourhood U of x and a neighbourhood V of y such that U and V are disjoint (U\cap V=\empty). X is a Hausdorff space if all distinct points in X are pairwise neighbourhood- separable. This condition is the third separation axiom (after T_0,T_1), which is why Hausdorff spaces are also called T_2 spaces. The name separated space is also used.
|
|
Laffer assumes that the government's revenue is a continuous function of the tax rate. However, in some theoretical models, the Laffer curve can be discontinuous, leading to an inability to devise a revenue-maximizing tax rate solution. Additionally, the Laffer curve depends on the assumption that tax revenue is used to provide a public good that is separable in utility and separate from labor supply, which may not be true in practice. The Laffer curve as presented is simplistic in that it assumes a single tax rate and a single labor supply.
|
|
Microsoft Corp. antitrust trial was whether Microsoft's Internet Explorer web browser was part of its Windows operating system or a separable piece of application software. As another example, the GNU/Linux naming controversy is, in part, due to disagreement about the relationship between the Linux kernel and the operating systems built over this kernel. In some types of embedded systems, the application software and the operating system software may be indistinguishable to the user, as in the case of software used to control a VCR, DVD player or microwave oven.
|
|
Therefore, in matters of the heart, courtly love wasn't always plausibly separable or indistinguishable from romantic love. However, by Eros, by Cupid's arrow, the object of a knight's affections may have resided elsewhere outside of his formal duties to his lady. In some instances, the lady was chosen, as in assigned to a knight by happenstance, whereby direct interaction may have been unlikely. As a princesse lointaine, she may have lived in a far away castle by which the chevalier could never, and would never have the chance to know her.
|
|
More precisely, fix a minimal normal subgroup A, which is either a π-group or a π'-group as G is π-separable. By induction there is a subgroup H of G containing A such that H/A is a Hall π-subgroup of G/A. If A is a π-group then H is a Hall π-subgroup of G. On the other hand, if A is a π'-group, then by the Schur–Zassenhaus theorem A has a complement in H, which is a Hall π-subgroup of G.
|
|
Pyrrhopyge is a Neotropical genus of firetips in the family Hesperiidae. Pyrrhopyge in Adalbert Seitz's Macrolepidoptera of the World This genus comprises very numerous, partly extremely similar species which are difficult to separate and perhaps neither are separable as distinct species. Nearly all are large, strong animals with black body and wings, often with a bronze-green or deep blue lustre, often spotted red on the head and abdomen. On the broad, mostly pointed forewings the discoidal runs very obliquely, the upper median vein rising somewhat behind the middle of the cell.
|
|
While our inferences sometimes are true and lead to successful action, it is also a fact that sometimes inference is wrong and leads to error. Truth then, state Charvaka, is not an unfailing character of inference, truth is merely an accident of inference, and one that is separable. We must be skeptics, question what we know by inference, question our epistemology. This epistemological proposition of Charvakas was influential among various schools of in Indian philosophies, by demonstrating a new way of thinking and re-evaluation of past doctrines.
|
|
The instars are separable by examining the posterior spiracles, or openings to the breathing system. The larvae use proteolytic enzymes in their excreta (as well as mechanical grinding by mouth hooks) to break down proteins on the livestock or corpse on which they are feeding. Blow flies are poikilothermic – the rate at which they grow and develop is highly dependent on temperature and species. Under room temperature (about 20 °C), the black blow fly Phormia regina can change from egg to pupa in 150–266 hours (six to 11 days).
|
|
The main idea of the median filter is to run through the signal entry by entry, replacing each entry with the median of neighboring entries. The pattern of neighbors is called the "window", which slides, entry by entry, over the entire signal. For one- dimensional signals, the most obvious window is just the first few preceding and following entries, whereas for two-dimensional (or higher-dimensional) data the window must include all entries within a given radius or ellipsoidal region (i.e. the median filter is not a separable filter).
|
|
Star Athletica, slip op. at 8-11. After applying this test to the cheerleading uniforms, the Court ruled in Varsity's favor that the designs were separable from the useful article and could be copyrighted.Star Athletica, slip op. at 10. The separability analysis started with the admittedly permissive first requirement, identifying the designs as separately identifiable "pictoral, graphical, or sculptural works." The design needed to be able to exist independently, and Thomas concluded that the design did when it appeared in other media, such as the two-dimensional drawings submitted to the Copyright Office.
|
|
Specifically, DNA/RNA store information that is processed by cells which then engage in intercellular communication to create the plane of existence called Life. Similarly, the brain and nervous system store and process information in animals which then engage in communication networks on the complex adaptive plane called Mind. Finally, linguistic storage and processing and communication between human beings generates the emergence of the Culture-Person plane of existence. The separable planes of existence or dimension of complexity argument is one of the most crucial aspects of the system.
|
|
Many have argued nature is hierarchically leveled; for example, a list of such levels might be subatomic particles, atoms, molecules, cells, organ structures, multi-celled organisms, consciousness, and society is common. The ToK System embraces a view of nature as levels, but adds the notion that there are also separable dimensions of complexity. The difference becomes particularly clear in the extension of the ToK System into the Periodic Table of Behavior. The Periodic Table of Behavior (PTB) shows that natural science can be arranged in terms of the four fundamental dimensions (i.e.
|
|
Robinson and Berridge's 1993 incentive-sensitization theory proposed that reward contains separable psychological components: wanting (incentive) and liking (pleasure). To explain increasing contact with a certain stimulus such as chocolate, there are two independent factors at work – our desire to have the chocolate (wanting) and the pleasure effect of the chocolate (liking). According to Robinson and Berridge, wanting and liking are two aspects of the same process, so rewards are usually wanted and liked to the same degree. However, wanting and liking also change independently under certain circumstances.
|
|
CORE-OM has 34 items all answered on the same five level frequency scale asking about the respondent's state over the last week. It was originally designed and developed in response to a research funding call from the UK Mental Health Foundation which required that the content must cover domains of well-being, problems, functioning and risk. These were seen as content domains, not as cleanly separable latent variables or factors, it was never envisaged that such a broad set of issues would show any neat population structure that would emerge in factor analysis.
|
|
Meprobamate is licensed for the short-term relief of anxiety, although whether the purported antianxiety effects of meprobamate are separable from its sedative effects is not known. Its effectiveness as a selective agent for the treatment of anxiety has not been proven in humans, and is not used as often as the benzodiazepines for this purpose. Meprobamate is available in 200- and 400-mg tablets for oral administration. It is also a component of the combination drug Equagesic (discontinued in the UK in 2002), acting as a muscle relaxant.
|
|
Other announcements made at the event included the unveiling by Samsung of the Wave and Wave Pro and NTTDOCOMO's F-04B, a separable phone that allows users to talk and view their phone at the same time. It is estimated that deals worth over of $US3.6 billion were signed at the tradeshow. The CommunicAsia Summit drew 650 participants and discussed topics including Mobile Value Added Services, Network Security, Getting in on the Cloud, Converged Device Management, Mobile Marketing & Profitability and New Revenue Opportunities. The keynote address was delivered by Josh Silverman, CEO of Skype.
|
|
Two copies of their construct yield six bright, separable colors. This, along with simplifications in color assignment, enabled them to observe the trajectories of each neuron over long distances. Specifically, they traced motor neurons from the antennal lobe to neuromuscular junctions, allowing them to identify the specific muscle targets of individual neurons. Ultimately, this technique provides the ability to efficaciously map the neuronal circuitry in Drosophila so that researchers are able to uncover more information about the brain structure of this invertebrate and how it relates to its ensuing behavior.
|
|
That finite fields are perfect follows a posteriori from their known structure. One can show that the tensor product of fields of L with itself over K for this example has nilpotent elements that are non-zero. This is another manifestation of inseparability: that is, the tensor product operation on fields need not produce a ring that is a product of fields (so, not a commutative semisimple ring). If P(x) is separable, and its roots form a group (a subgroup of the field K), then P(x) is an additive polynomial.
|
|
The most simple distinction between extrinsic and intrinsic motivation is the type of reasons or goals that lead to an action. While intrinsic motivation refers to doing something because it is inherently interesting or enjoyable and satisfying, extrinsic motivation, refers to doing something because it leads to a separable outcome. Extrinsic motivation thus contrasts with intrinsic motivation, which is doing an activity simply for the enjoyment of the activity itself, instead of for its instrumental value. Social psychological research has indicated that extrinsic rewards can lead to overjustification and a subsequent reduction in intrinsic motivation.
|
|
The notation (n,k,d)_q describes a block code over an alphabet \Sigma of size q, with a block length n, message length k, and distance d. If the block code is a linear block code, then the square brackets in the notation [n,k,d]_q are used to represent that fact. For binary codes with q=2, the index is sometimes dropped. For maximum distance separable codes, the distance is always d=n-k+1, but sometimes the precise distance is not known, non-trivial to prove or state, or not needed.
|
|
A third process for ore deposition is as an evaporite. A stringer lode is one in which the rock is so permeated by small veinlets that rather than mining the veins, the entire mass of ore and the enveined country rock is mined. It is so named because of the irregular branching of the veins into many anastomosing stringers, so that the ore is not separable from the country rock. One of largest silver lodes was the Comstock Lode in Nevada, although it is overshadowed by the more recently discovered Cannington Lode in Queensland, Australia.
|
|
The Convair X-11/SM-65A Atlas/Atlas A was the first full-scale prototype of the Atlas missile, first flying on 11 June 1957. It was a test model designed to verify the structure and propulsion system, and had no sustainer engine or separable stages. The first three Atlas A launches used an early Rocketdyne engine design with conical thrust chambers and only 135,000 pounds of thrust. By the fourth Atlas test, they were replaced by an improved engine design that had bell-shaped thrust chambers and 150,000 pounds of thrust.
|
|
To obtain the surface characteristic almost all measurements are subject to filtering. It is one of the most important topics when it comes to specifying and controlling surface attributes such as roughness, waviness, and form error. These components of the surface deviations must be distinctly separable in measurement to achieve a clear understanding between the surface supplier and the surface recipient as to the expected characteristics of the surface in question. Typically, either digital or analog filters are used to separate form error, waviness, and roughness resulting from a measurement.
|
|
In mathematics, a Tate module of an abelian group, named for John Tate, is a module constructed from an abelian group A. Often, this construction is made in the following situation: G is a commutative group scheme over a field K, Ks is the separable closure of K, and A = G(Ks) (the Ks-valued points of G). In this case, the Tate module of A is equipped with an action of the absolute Galois group of K, and it is referred to as the Tate module of G.
|
|
A flow battery may be used like a fuel cell (where the spent fuel is extracted and new fuel is added to the system) or like a rechargeable battery (where an electric power source drives regeneration of the fuel). While it has technical advantages over conventional rechargeables, such as potentially separable liquid tanks and near unlimited longevity, current implementations are comparatively less powerful and require more sophisticated electronics. The energy capacity is a function of the electrolyte volume and the power is a function of the surface area of the electrodes.
|
|
Baxter's law theoretically is applied to a variety of other industries where incumbent, vertically integrated, regulated monopolies control both monopoly segments and potentially competitive segments. Each industry is constructed as a large network for transporting its fundamental product (information, telecommunication) between any two feasible points of origin and destination. Moreover, each network is conceptually separable into several basic functions and various levels of layers. From the perspectives of enterprises, a monopolist in a regulated industry may face a price cap, or a rate of return type pricing scheme.
|
|
Tests done using mutagenic TSST-1 toxins indicated that the lethal and superantigenic properties are separable. When Lys-132 in TSST-O was changed to a Glu, the resulting mutant became completely lethal but non superantigenic. The same results, lethal but not superantigenic, were found for TSST-1 Gly16Val. Residues Gly16, Glu132,and Gln 136, located on the back of the back- side groove of the putative TCR binding region of TSST-1, it has been proposed that they are also a part of a second functionally lethal site in the TSST-1.
|
|
The utility of a linguistic framework constitutes issues that Carnap calls 'external' or 'pragmatic'. The distinction between 'internal' and 'external' arguments is not as obvious as it might appear. For example, discussion of the imaginary unit might be an internal question framed in the language of complex numbers about the correct usage of , or it be a question about the utility of complex numbers: whether there is any practical advantage in using . Clearly the question of utility is not completely separable from the way a linguistic framework is organized.
|
|
The hypothesis of the statement can be weakened a bit: a sequence in C(X) converges uniformly if it is equicontinuous and converges pointwise on a dense subset to some function on X (not assumed continuous). This weaker version is typically used to prove Arzelà–Ascoli theorem for separable compact spaces. Another consequence is that the limit of an equicontinuous pointwise convergent sequence of continuous functions on a metric space, or on a locally compact space, is continuous. (See below for an example.) In the above, the hypothesis of compactness of X cannot be relaxed.
|
|
An algebraic extension E\supseteq F is a purely inseparable extension if and only if for every \alpha\in E\setminus F, the minimal polynomial of \alpha over F is not a separable polynomial.Isaacs, p. 298 If F is any field, the trivial extension F\supseteq F is purely inseparable; for the field F to possess a non-trivial purely inseparable extension, it must be imperfect as outlined in the above section. Several equivalent and more concrete definitions for the notion of a purely inseparable extension are known.
|
|
It is sometimes convenient to think of the Hilbert cube as a metric space, indeed as a specific subset of a separable Hilbert space (i.e. a Hilbert space with a countably infinite Hilbert basis). For these purposes, it is best not to think of it as a product of copies of [0,1], but instead as :[0,1] × [0,1/2] × [0,1/3] × ···; as stated above, for topological properties, this makes no difference. That is, an element of the Hilbert cube is an infinite sequence :(xn) that satisfies :0 ≤ xn ≤ 1/n.
|
|
Chests of drawers often come in 5-, 6-, and 7-drawer varieties, with either a single or a double top drawer. The chest illustrated at right would be described as a '5 over 2 chest-on-chest', the latter term deriving from the fact that at one time it would have been made as 2 separable pieces. They are commonly made of wood, similar to many other kinds of furniture, but of course can be made of other materials. The inside of the drawers can be accessed by pulling them out at the front side.
|
|
Swern oxidation of alcohol 14 gave ketone 15. The next step set the final carbon- carbon bond between the B and C rings. This was achieved through a Chan rearrangement of 15 using lithium tetramethylpiperidide to give α-hydroxylactone 16 in 90% yield. The hydroxyl group was reductively removed using samarium(II) iodide to give an enol, and chromatography of this enol on silica gel gave the separable diastereomers cis 17c (77%) and trans 17t (15%), which could be recycled to 17c through treatment with potassium tert-butoxide.
|
|
In the mathematical discipline of general topology, a Polish space is a separable completely metrizable topological space; that is, a space homeomorphic to a complete metric space that has a countable dense subset. Polish spaces are so named because they were first extensively studied by Polish topologists and logicians—Sierpiński, Kuratowski, Tarski and others. However, Polish spaces are mostly studied today because they are the primary setting for descriptive set theory, including the study of Borel equivalence relations. Polish spaces are also a convenient setting for more advanced measure theory, in particular in probability theory.
|
|
Although Polish spaces are metrizable, they are not in and of themselves metric spaces; each Polish space admits many complete metrics giving rise to the same topology, but no one of these is singled out or distinguished. A Polish space with a distinguished complete metric is called a Polish metric space. An alternative approach, equivalent to the one given here, is first to define "Polish metric space" to mean "complete separable metric space", and then to define a "Polish space" as the topological space obtained from a Polish metric space by forgetting the metric.
|
|
They were sometimes called the Tenerife goldcrest, no matter which of the islands they lived on; however, a 2006 study of the vocalisations of these birds indicate that they actually comprise two subspecies of the Goldcrest that are separable on voice; R. r. teneriffae occurring on Tenerife and the newly described subspecies, R. r. ellenthalerae, occurring on the smaller islands of La Palma and El Hierro. The three goldcrest taxa on the Azores, Santa Maria goldcrest, Sao Miguel goldcrest and Western Azores goldcrest, represent recent colonisations from Europe, and are best treated as subspecies.
|
|
Two different Dawes Kingpin folding bicycles, an original and a later version, in folded state. The company's response to the 1960s passion for "unisex" small wheeled "shopping" bicycles was the step-framed "Newpin", with single-speed and three-speed Sturmey-Archer enclosed hub gearing systems. These were offered in both a fixed frame and separable two piece frame. It was later renamed as the "Kingpin", Newpin initially being used for the fixed frame version, and offered in a folding frame version that went through a number of developments, and is still in production .
|
|
An elementary Frobenioid is a generalization of the Frobenioid of a commutative monoid, given by a sort of semidirect product of the monoid of positive integers by a family Φ of commutative monoids over a base category D. In applications the category D is sometimes the category of models of finite separable extensions of a global field, and Φ corresponds to the line bundles on these models, and the action of a positive integers n in N is given by taking the nth power of a line bundle.
|
|
Kleiner Werder is the name of an island and its associated group (aka the Kleine Werder) of uninhabited and not clearly geographically separable German islands in the Baltic Sea that belong to the state of Mecklenburg-Western Pomerania. The individual island elements are only separated from one another by shallow water channels that occasionally dry out. Their highest points lie no more than one metre above sea level. The Kleiner Werder lies off the mainland east of the peninsula of Großer Werder and west of the likewise uninhabited island of Bock.
|
|
Additionally, switching costs to competitors play a role because customers may fear that the vendor may discontinue the product or go out of business. These authors suggest that the price of software should be based on its consumer surplus. Pricing strategies can be used to gain the most revenue such as product bundling, forming separable modules, and price discrimination with product variants and target groups. (2004) Calculations of consumer surplus is one way that software firms can keep track of their perception by customers in an integrative way.
|
|
The length of the penis is small and it has as an angular bend, the tip is not enlarged. The larger size of the Vespadelus darlingtoni distinguishes it from others of the genus, the forearm length being greater than 33 mm, in particular the similar species V. pumilus (eastern forest bat). The richly coloured chocolate wattled species Chalinolobus morio is separable by the absence of that species lobe at the lower lip and raised fur between the eyes. A single birth during November and December is usual for the species.
|
|
Spinalis dorsi, the medial continuation of the sacrospinalis, is scarcely separable as a distinct muscle. It is situated at the medial side of the longissimus dorsi, and is intimately blended with it; it arises by three or four tendons from the spinous processes of the first two lumbar and the last two thoracic vertebrae: these, uniting, form a small muscle which is inserted by separate tendons into the spinous processes of the upper thoracic vertebrae, the number varying from four to eight. It is intimately united with the semispinalis dorsi, situated beneath it.
|
|
The first multipartite entanglement measure that is neither a direct generalization nor an easy combination of bipartite measures was introduced by Coffman et al. and called tangle. Definition [tangle]: :\; \tau(A : B : C) = \tau(A : BC) - \tau(AB) - \tau(AC) , where the \; 2-tangles on the right-hand-side are the squares of concurrence. The tangle measure is permutationally invariant; it vanishes on all states that are separable under any cut; it is nonzero, for example, on the GHZ-state; it can be thought to be zero for states that are 3-entangled (i.e.
|
|
One of Fayz Kashani's most well known contributions to Islamic philosophy is his discourse on the archetypal images. Borrowing heavily from Platonic ideas of universals and particulars, Fayz seeks to articulate the relationship between the spiritual and material worlds and how their interaction fulfills divine will. From the beginning of creation, God entrusted Spirits to govern matter. However, because both spiritual and material substances possess distinct and separable essences, the power of the spiritual world alone is insufficient to establish a connection between the spiritual and the material.
|
|
Small wheels may be welcome in indoor locations where large wheels are not Small-wheel bicycles are adult bicycles that have wheels of 20 inch nominal diameter or less, which is smaller than the 26", 27.5", 29" or 700c sizes common on most full-sized adult bikes. While many folding bicycles are small- wheel bicycles, not all small-wheel bicycles can fold. Some small-wheel bicycles neither fold nor separate, such as the Moulton, which comes in both fixed-frame and separable-frame versions. While BMX bikes also have 20" wheels, they are not normally categorised as "small-wheel bikes".
|
|
716–727 Sometimes, more than one of these advantages compound together, thereby increasing the efficiency by 50% in terms of computation and storage when compared to rectangular sampling. Despite of all these advantages of hexagonal sampling over the rectangular sampling, its application has been limited because of its inability to result in the orthogonal rows and columns that can be transformed independently as is done with rectangular samples. For this reason, an efficient FFT with a separable Fourier kernel has been developed by utilizing the so-called array set addressing (ASA) scheme and is termed hexagonal fast Fourier transform.
|
|
In functional analysis, the Calkin algebra, named after John Williams Calkin, is the quotient of B(H), the ring of bounded linear operators on a separable infinite-dimensional Hilbert space H, by the ideal K(H) of compact operators. Here the addition in B(H) is addition of operators and the multiplication in B(H) is composition of operators; it is easy to verify that these operations make B(H) into a ring. When scalar multiplication is also included, B(H) becomes in fact an algebra over the same field over which H is a Hilbert space.
|
|
The cartridge can be made in full length (or very close to) as the real one. The recent models of Tanaka, Kokusai, Elan and HWS even make their cartridge's "bullet" portion screw separable and in silver or copper color so that they look very realistic lead / copper bullet cartridge. There are also some aftermarket cap-firing cartridges produced by Mulberry Field, B.W.C., C-Tec / Malugo and Tanio Koba for some selected compatible models of modelgun. Many of them are even designed to accommodate double or triple caps in their cartridge for enhanced blowback, sound and muzzle flash effect.
|
|
For fields that are not algebraically closed (or not separably closed), the absolute Galois group is fundamentally important: extending the case of finite Galois extensions outlined above, this group governs all finite separable extensions of . By elementary means, the group can be shown to be the Prüfer group, the profinite completion of . This statement subsumes the fact that the only algebraic extensions of are the fields for , and that the Galois groups of these finite extensions are given by :. A description in terms of generators and relations is also known for the Galois groups of -adic number fields (finite extensions of ).
|
|
Similarly, we can show that L^2(X;H), denoting the space of square integrable functions X\to H, is isomorphic to L^2(X)\otimes H if this space is separable. The isomorphism maps f(x)\otimes\phi\in L^2(X)\otimes H to f(x)\phi\in L^2(X;H) We can combine this with the previous example and conclude that L^2(X)\otimes L^2(Y) and L^2(X\times Y) are both isomorphic to L^2(X;L^2(Y)). Tensor products of Hilbert spaces arise often in quantum mechanics.
|
|
The use of biocatalysis to obtain enantiopure compounds can be divided into two different methods: # Kinetic resolution of a racemic mixture # Biocatalyzed asymmetric synthesis In kinetic resolution of a racemic mixture, the presence of a chiral object (the enzyme) converts one of the stereoisomers of the reactant into its product at a greater reaction rate than for the other reactant stereoisomer. The stereochemical mixture has now been transformed into a mixture of two different compounds, making them separable by normal methodology. Scheme 1. Kinetic resolution Biocatalyzed kinetic resolution is utilized extensively in the purification of racemic mixtures of synthetic amino acids.
|
|
A major concern was that cable operators were not motivated to provide efficient security access mechanisms to equipment competitors. To address this, the FCC directed that by January 1, 2005, that cable operators must use the same separable access device available to third-parties and they were banned from providing equipment with an integrated security access mechanism. This rule is usually referred to as the "integration ban", and was unsuccessfully challenged in the courts and petitions to the FCC by the cable operators. The deadline was shifted forward twice until it went into effect on July 1, 2007.
|
|
The pocket algorithm with ratchet (Gallant, 1990) solves the stability problem of perceptron learning by keeping the best solution seen so far "in its pocket". The pocket algorithm then returns the solution in the pocket, rather than the last solution. It can be used also for non-separable data sets, where the aim is to find a perceptron with a small number of misclassifications. However, these solutions appear purely stochastically and hence the pocket algorithm neither approaches them gradually in the course of learning, nor are they guaranteed to show up within a given number of learning steps.
|
|
Czech grammar, like that of other Slavic languages, is fusional; its nouns, verbs, and adjectives are inflected by phonological processes to modify their meanings and grammatical functions, and the easily separable affixes characteristic of agglutinative languages are limited. Czech inflects for case, gender and number in nouns and tense, aspect, mood, person and subject number and gender in verbs. Parts of speech include adjectives, adverbs, numbers, interrogative words, prepositions, conjunctions and interjections. Adverbs are primarily formed from adjectives by taking the final ý or í of the base form and replacing it with e, ě, or o.
|
|
For high energies and/or weak potential it can also be solved perturbatively by means of Born series. The method convenient also in the case of many-body physics, like in description of atomic, nuclear or molecular collisions is the method of R-matrix of Wigner and Eisenbud. Another class of methods is based on separable expansion of the potential or Green's operator like the method of continued fractions of Horáček and Sasakawa. Very important class of methods is based on variational principles, for example the Schwinger-Lanczos method combining the variational principle of Schwinger with Lanczos algorithm.
|
|
An MDS matrix (Maximum Distance Separable) is a matrix representing a function with certain diffusion properties that have useful applications in cryptography. Technically, an m×n matrix A over a finite field K is an MDS matrix if it is the transformation matrix of a linear transformation f(x)=Ax from Kn to Km such that no two different (m+n)-tuples of the form (x,f(x)) coincide in n or more components. Equivalently, the set of all (m+n)-tuples (x,f(x)) is an MDS code, i.e. a linear code that reaches the Singleton bound.
|
|
AN 37° flare connections are typically specified for military and aerospace applications. Fittings can be made from a large variety of materials. The “AN” standard (for Air Force / Navy) has been replaced by other military and aerospace standards, though in practice these fittings are still referred to as AN. Flared fittings are an alternative to solder-type joints that is mechanically separable and doesn’t require an open flame. Copper tube used for propane, liquefied petroleum gas, or natural gas may use flared brass fittings of single 45°-flare type, according to NFPA 54/ANSI. Z223.1 National Fuel Gas Code.
|
|
In Euclidean geometry, linear separability is a property of two sets of points. This is most easily visualized in two dimensions (the Euclidean plane) by thinking of one set of points as being colored blue and the other set of points as being colored red. These two sets are linearly separable if there exists at least one line in the plane with all of the blue points on one side of the line and all the red points on the other side. This idea immediately generalizes to higher-dimensional Euclidean spaces if the line is replaced by a hyperplane.
|
|
The reason for the error of Ishiwara, which was manifested in the calculation of the hydrogen atom, apparently was a superfluous averaging over the number of degrees of freedom (dividing by j before the sum). At the same time, his quantum condition, which differed from Sommerfeld's one in the presence of summation, allowed to obtain correct results regardless of the choice of coordinates. This was pointed out in 1917 by Einstein, who, not knowing about the work of the Japanese colleague, derived the same relation and showed that in the case of separable coordinates it gives the conditions of Wilson and Sommerfeld.
|
|
In a follow up work with Mohit Bhargava and Dipjyoti Majumdar, he shows that if voters beliefs are correlated, then it is possible to escape the impossibility of the GS theorem using this weaker notion of incentive compatibility. In his work with his coauthor Michel Le Breton, he studies a voting environment where voters vote on various dimensions but preferences of voters are separable across dimensions. Their work identifies conditions on environments such that every unanimous and non-manipulable (strategyproof) voting rule can be decomposed along each dimension. He has pursued this line of research in some of his other work.
|
|
In the 1950s the philosopher of language J. L. Austin introduced the term 'performative utterance' to make clear that 'to say something is to do something'.Austin (1962) Developing this idea, scholars have theorized on the relation of a spoken or written text to its broader context, that is to say everything outside the text itself. The question whether a performative is separable from the situation it emerged in is relevant when one addresses for example the status of individual intentions or speech as a resource of power. There are two main theoretical strands in research today.
|
|
Stochastic Network Optimization with Application to Communication and Queueing Systems, Morgan & Claypool, 2010. This is done by defining an appropriate set of virtual queues. It can also be used to produce time averaged solutions to convex optimization problems. M. J. Neely, "[Distributed and Secure Computation of Convex Programs over a Network of Connected Processors Distributed and Secure Computation of Convex Programs over a Network of Connected Processors]," DCDIS Conf, Guelph, Ontario, July 2005 S. Supittayapornpong and M. J. Neely, "Quality of Information Maximization for Wireless Networks via a Fully Separable Quadratic Policy," arXiv:1211.6162v2, Nov. 2012.
|
|
The adaptive coordinate descent approach gradually builds a transformation of the coordinate system such that the new coordinates are as decorrelated as possible with respect to the objective function. The adaptive coordinate descent was shown to be competitive to the state-of-the- art evolutionary algorithms and has the following invariance properties: # Invariance with respect to monotonous transformations of the function (scaling) # Invariance with respect to orthogonal transformations of the search space (rotation). CMA-like Adaptive Encoding Update (b) mostly based on principal component analysis (a) is used to extend the coordinate descent method (c) to the optimization of non-separable problems (d).
|
|
One placed the pilot under a separable, multi framed canopy; with the other the pilot after entry was surrounded by a demountable ply covering which filled the larger aperture, allowing his head to emerge from within an open, circular, collared hole. The interior was lit by glazing in the cover just in front of the seat. The Roma was an amphibian and had a single step, flying boat style hull with the step under mid-chord. Small stabilizing floats were mounted under the wings at about two-thirds span, each attached by two spanwise parallel pairs of V-struts.
|
|
The typical pigeons together with Streptopelia and the minor Nesoenas and Stigmatopelia lineages constitute the dominant evolutionary radiation of Columbidae in temperate Eurasia, though they also occur in tropical regions. The taxonomic status of some African pigeons presently placed here is in need of further study; they are smaller than the usual Columba (and hence often called "doves"), and differ in some other aspects. They might be separable as genus Aplopelia. That notwithstanding, the lineage of the typical pigeons probably diverged from its closest relatives in the Late Miocene, perhaps some 7-8 million years ago (Ma).
|
|
Articulated dump truck or dumper An articulated dumper is an all-wheel drive, off-road dump truck. It has a hinge between the cab and the dump box, but is distinct from a semi-trailer truck in that the power unit is a permanent fixture, not a separable vehicle. Steering is accomplished via hydraulic cylinders that pivot the entire tractor in relation to the trailer, rather than rack and pinion steering on the front axle as in a conventional dump truck. By this way of steering, the trailers wheels follow the same path as the front wheels.
|
|
Further, the definitions are volitionally separable because those sections were not of critical importance to the passage of the Act and the legislative body would have adopted the Act had it foreseen the partial invalidation of the statute. These definition sections were only included to avoid the possibility that a court would rule the terms unconstitutionally vague; the court found that the legislature would still have enacted the statute without this definition section. The court next went on to determine what level of scrutiny should be applied in reviewing the Act's prohibitions. The defendants insisted that the "variable obscenity" standard from Ginsberg v.
|
|
So the family of separable states is the closed convex hull of pure product states. We will make use of the following variant of Hahn–Banach theorem: Theorem Let S_1 and S_2 be disjoint convex closed sets in a real Banach space and one of them is compact, then there exists a bounded functional f separating the two sets. This is a generalization of the fact that, in real Euclidean space, given a convex set and a point outside, there always exists an affine subspace separating the two. The affine subspace manifests itself as the functional f.
|
|
Over time Applewhite also refined his identity in the group to encourage the belief that the "walk in" that was inhabiting his body was the same that had done so to Jesus 2,000 years ago. Similar to Nestorianism this belief stated that the personage of Jesus and the spirit of Jesus were separable. This meant that Jesus was simply the name of the body of an ordinary man that held no sacred properties that was taken over by an incorporeal sacred entity to deliver "next level" information. Another New Age belief Applewhite and Nettles adopted was the ancient astronaut hypothesis.
|
|
At the same time, considerations of construction of such an element receded: the theorem becomes an existence theorem. The following theorem of Artin then takes the place of the classical primitive element theorem. ;Theorem Let E/F be a finite degree field extension. Then E=F(\alpha) for some element \alpha\in E if and only if there exist only finitely many intermediate fields K with E\supseteq K\supseteq F. A corollary to the theorem is then the primitive element theorem in the more traditional sense (where separability was usually tacitly assumed): ;Corollary Let E/F be a finite degree separable extension.
|
|
The only Pairwise Stable network in the figure is the dark blue colored one since none of the players involved would benefit by deleting or creating a link. Jackson and Wolinsky showed that for homogeneous connection cost, the efficient network can only take one of three forms: a complete graph, a star or an empty graph depending on connection cost and benefits. Finding general analytical solutions for the efficient networks with heterogeneous costs can be intractable. However, for particular cost structures, such as Island- connection and Separable Heterogeneous connection costs, the efficient network can identified based on the heterogeneous connection costs and benefits.
|
|
Rudolf Steiner, who collaborated in a complete edition of Arthur Schopenhauer's work, wrote The Philosophy of Freedom, which focuses on the problem of free will. Steiner (1861–1925) initially divides this into the two aspects of freedom: freedom of thought and freedom of action. The controllable and uncontrollable aspects of decision making thereby are made logically separable, as pointed out in the introduction. This separation of will from action has a very long history, going back at least as far as Stoicism and the teachings of Chrysippus (279–206 BCE), who separated external antecedent causes from the internal disposition receiving this cause.
|
|
A Satake diagram is obtained from a Dynkin diagram by blackening some vertices, and connecting other vertices in pairs by arrows, according to certain rules. Suppose that G is an algebraic group defined over a field k, such as the reals. We let S be a maximal split torus in G, and take T to be a maximal torus containing S defined over the separable algebraic closure K of k. Then G(K) has a Dynkin diagram with respect to some choice of positive roots of T. This Dynkin diagram has a natural action of the Galois group of K/k.
|
|
An alternative term for ontological reductionism is fragmentalism, often used in a pejorative sense. Anti-realists use the term fragmentalism in arguments that the world does not exist of separable entities, instead consisting of wholes. For example, advocates of this idea claim that: > The linear deterministic approach to nature and technology promoted a > fragmented perception of reality, and a loss of the ability to foresee, to > adequately evaluate, in all their complexity, global crises in ecology, > civilization and education. The term fragmentalism is usually applied to reductionist modes of thought, often with the related pejorative term scientism.
|
|
In 1951, Bing proved that all hereditarily indecomposable arc-like continua are homeomorphic — this implies that Knaster's K, Moise's M, and Bing's B are all homeomorphic. Bing also proved that the pseudo-arc is typical among the continua in a Euclidean space of dimension at least 2 or an infinite-dimensional separable Hilbert space. Bing and F. Burton Jones constructed a decomposable planar continuum that admits an open map onto the circle, with each point preimage homeomorphic to the pseudo-arc, called the circle of pseudo-arcs. Bing and Jones also showed that it is homogeneous.
|
|
Although not widely accepted in linguistics, the term preverb is used in Caucasian (including all three families: Northwest Caucasian, Northeast Caucasian and Kartvelian), Caddoan, Athabaskan, and Algonquian linguistics to describe certain elements prefixed to verbs. In the context of Indo-European languages, the term is usually used for separable verb prefixes. Theoretically, any prefix could be called a preverbal element. However, in practice, the term preverb applies more narrowly in those families and refers to a prefixed element that is normally outside the premise of verbal morphology like locations of noun elements or, less often, noun elements themselves.
|
|
In practical terms, this means that theorems of algebra and combinatorics are restricted to countable structures, while theorems of analysis and topology are restricted to separable spaces. Many principles that imply the axiom of choice in their general form (such as "Every vector space has a basis") become provable in weak subsystems of second-order arithmetic when they are restricted. For example, "every field has an algebraic closure" is not provable in ZF set theory, but the restricted form "every countable field has an algebraic closure" is provable in RCA0, the weakest system typically employed in reverse mathematics.
|
|
The Principles of Quantum Mechanics, 4th edition, Oxford University Press, Oxford, p. ix: "For this reason I have chosen the symbolic method, introducing the representatives later merely as an aid to practical calculation." as unit vectors (called state vectors). Formally, these vectors are elements of a complex separable Hilbert space – variously called the state space or the associated Hilbert space of the system – that is well defined up to a complex number of norm 1 (the phase factor). In other words, the possible states are points in the projective space of a Hilbert space, usually called the complex projective space.
|
|
In the physical sciences, a phase is a region of space (a thermodynamic system), throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, magnetization and chemical composition. A simple description is that a phase is a region of material that is chemically uniform, physically distinct, and (often) mechanically separable. In a system consisting of ice and water in a glass jar, the ice cubes are one phase, the water is a second phase, and the humid air is a third phase over the ice and water.
|
|
Quantum systems may be measured by applying a series of yes-no questions. This set of questions can be understood to be chosen from an orthocomplemented lattice Q of propositions in quantum logic. The lattice is equivalent to the space of self-adjoint projections on a separable complex Hilbert space H. Consider a system in some state S, with the goal of determining whether it has some property E, where E is an element of the lattice of quantum yes-no questions. Measurement, in this context, means submitting the system to some procedure to determine whether the state satisfies the property.
|
|
The Unit developed original methods of solution and calculation of nonlinear problems of non-separable and cavitating flow around an airfoil near the free surface. Scientists also studied oscillating profile with a separation of the jets, the profiles' grating and the problems of electrochemical dimensional processing of metals. The obtained results were generally recognized, reflected in the number of special reports, books and monographs on the theory of jets and cavitation. The Unit of boundary value problems and the analog modeling laboratory (founded in 1976) made a great contribution to the theory of hydrodynamic design of objects with given properties.
|
|
In mathematics, constructive analysis is mathematical analysis done according to some principles of constructive mathematics. This contrasts with classical analysis, which (in this context) simply means analysis done according to the (more common) principles of classical mathematics. Generally speaking, constructive analysis can reproduce theorems of classical analysis, but only in application to separable spaces; also, some theorems may need to be approached by approximations. Furthermore, many classical theorems can be stated in ways that are logically equivalent according to classical logic, but not all of these forms will be valid in constructive analysis, which uses intuitionistic logic.
|
|
He later authored a seminal paper on the subject of coroutines, titled "Design of a Separable Transition-diagram Compiler", which included the first published explanation of the concept. In this paper, he proposed organizing a compiler as a set of coroutines, which allows using separate passes while debugging and then running a single pass compiler in production. Another famous paper is his 1958 proposal of an UNCOL, a Universal Computer Oriented Language, which attempted to provide a solution to economically produce compilers for new programming languages and computer architectures. Conway wrote an assembler for the Burroughs model 220 computer called SAVE.
|
|
When the abelian group A is the group of roots of unity in a separable closure Ks of K, the p-adic Tate module of A is sometimes referred to as the Tate module (where the choice of p and K are tacitly understood). It is a free rank one module over Zp with a linear action of the absolute Galois group GK of K. Thus, it is a Galois representation also referred to as the p-adic cyclotomic character of K. It can also be considered as the Tate module of the multiplicative group scheme Gm,K over K.
|
|
A multidimensional population translation experiment was utilized to determine the detection limits of an ARS device, Populations with small multidimensional separation, in this case aspirin and ibuprofen, were used to determine that tablets with a 0.08 mm difference in thickness, 0.0046 g mass difference, and a difference in density of 0.01658 g/mL were not separable by ARS. Using vitamin C and acetaminophen for the largest multidimensional separation, tablets with a thickness difference of 0.27 mm, 0.0756 g mass difference, and 0.01157 g/mL density difference in density were inseparable. Experimentally the dynamic range of ARS is a factor of ten.
|
|
On the other hand, there are Baire spaces (even separable metrizable ones) which are not Choquet spaces, so the converse fails. The strong Choquet game of X, G^s(X), is defined similarly, except that Player I chooses (x_0,U_0), then Player II chooses V_0, then Player I chooses (x_1,U_1), etc, such that x_i \in U_i, V_i for all i. A topological space X in which Player II has a winning strategy for G^s(X) is called a strong Choquet space. Every strong Choquet space is a Choquet space, although the converse does not hold.
|
|
Second-order arithmetic directly formalizes natural numbers and sets of natural numbers. However, it is able to formalize other mathematical objects indirectly via coding techniques, a fact which was first noticed by Weyl (Simpson 2009, p. 16). The integers, rational numbers, and real numbers can all be formalized in the subsystem RCA0, along with complete separable metric spaces and continuous functions between them (Simpson 2009, Chapter II). The research program of Reverse Mathematics uses these formalizations of mathematics in second-order arithmetic to study the set-existence axioms required to prove mathematical theorems (Simpson 2009, p. 32).
|
|
In experiments in 2012 and 2013, polarization correlation was created between photons that never coexisted in time. The authors claimed that this result was achieved by entanglement swapping between two pairs of entangled photons after measuring the polarization of one photon of the early pair, and that it proves that quantum non-locality applies not only to space but also to time. In three independent experiments in 2013 it was shown that classically communicated separable quantum states can be used to carry entangled states. The first loophole-free Bell test was held in TU Delft in 2015 confirming the violation of Bell inequality.
|
|
PCL consists in introducing a somatic adult or senescent cell nucleus or entire cell with enlarged membrane pores in an (activated) oocyte and to withdraw this treated cell before its de-differentiation and first cell division occurs. Thus, the progressive rejuvenation capability of the oocyte is used only temporarily in order to obtain a partial natural rejuvenation. PCL permits to envisage a chosen degree of partial rejuvenation in changing the duration of the introduction of the treated cell in the oocyte. Using PCL cell de- differentiation and its age reprogramming might be, at least partially, separable.
|
|
However, it is still NP-hard to find a Pareto optimal or socially optimal outcome. In particular, for hedonic games given by individually rational coalition lists, it is NP-complete to decide whether the game admits a core-stable, a Nash-stable, or an individually stable outcome. The same is true for anonymous games. For additively separable hedonic games, it is NP-complete to decide the existence of a Nash-stable or an individually stable outcome and complete for the second level of the polynomial hierarchy to decide whether there exists a core-stable outcome, even for symmetric additive preferences.
|
|
Martin Luther, in a sermon delivered in Torgau in 1533, stated that Christ descended into Hell. The Formula of Concord (a Lutheran confession) states, "we believe simply that the entire person, God and human being, descended to Hell after his burial, conquered the devil, destroyed the power of Hell, and took from the devil all his power" (Solid Declaration, Art. IX). Many attempts were made following Luther's death to systematize his theology of the descensus, whether Christ descended in victory or humiliation. For Luther, however, the defeat or "humiliation" of Christ is never fully separable from His victorious glorification.
|
|
The exact number of taxa involved is disputed, most of the "species" detected by the DNA barcoding study seem to be nothing more than morphs or incipient subspecies, coupled with a serious underestimation of variation. Still, two lineages appear to be well distinct and separable at least as subspecies: "CELT" has larvae with bold orange bands in the last instar, which were recorded only on Celtis iguanaea (Ulmaceae). "TRIGO" last-instar larvae have bold yellow bands and were found on the Malpighiales Trigonia (T. arborea, T. laevia and T. rugosa) and, apparently accidentally, on Licania arborea.
|
|
Anne's actions underscored that the Duke of Brittany's line of succession was governed by the Celtic nation's peculiar form of Semi-Salic Law rather than the strict Salic Law governing the Kingdom of France. Her actions also demonstrated that the Duke of Brittany and the King of France, at least at this time, remained distinct and separable titles. Charles VIII's successor, Louis XII, also married Anne of Brittany, and thus the title of Duke of Brittany jure uxoris was once again in the person of the king of France. In this marriage, however, Anne was allowed to use her title, and Louis enacted all official actions in Brittany in her name.
|
|
This class of buoyancy aid is known as a buoyancy control device or buoyancy compensator. A backplate and wing is an alternative configuration of scuba harness with a buoyancy compensation bladder known as a "wing" mounted behind the diver, sandwiched between the backplate and the cylinder or cylinders. Unlike stabilizer jackets, the backplate and wing is a modular system, in that it consists of separable components. This arrangement became popular with cave divers making long or deep dives, who needed to carry several extra cylinders, as it clears the front and sides of the diver for other equipment to be attached in the region where it is easily accessible.
|
|
Let be a prime power, and be the splitting field of the polynomial :P=X^q-X over the prime field . This means that is a finite field of lowest order, in which has distinct roots (the formal derivative of is , implying that , which in general implies that the splitting field is a separable extension of the original). The above identity shows that the sum and the product of two roots of are roots of , as well as the multiplicative inverse of a root of . In other words, the roots of form a field of order , which is equal to by the minimality of the splitting field.
|
|
For this reason, Planck's constant was often called the quantum of action. In order for the old quantum condition to make sense, the classical motion must be separable, meaning that there are separate coordinates q_i in terms of which the motion is periodic. The periods of the different motions do not have to be the same, they can even be incommensurate, but there must be a set of coordinates where the motion decomposes in a multi-periodic way. The motivation for the old quantum condition was the correspondence principle, complemented by the physical observation that the quantities which are quantized must be adiabatic invariants.
|
|
The trainset was articulated using shared Jacobs bogies to reduce weight, making the train operate as one integrated unit rather than as a separable locomotive and cars. The integrated-body-and-frame construction using aluminum reduced the required structural weight to a fraction of that for conventional body-on-frame railcars, and the trainset's total weight of was about the same as a single passenger coach of the time. The power car featured an elevated "turret cab" behind a nose featuring a large vertically- divided air intake grille formed by parabolic arches. On the roof of the cab were a headlamp and a vertical marker light.
|
|
"Household-production theory," as well as "cross-sectional evidence" ostensibly support a "non-time- separable utility function that admits greater inter-temporal substitution of leisure, something which is needed," according to the authors, "to explain aggregate movements in employment in an equilibrium model." For the K&P; model, monetary policy is irrelevant for economic fluctuations. The associated policy implications were clear: There is no need for any form of government intervention since, ostensibly, government policies aimed at stabilizing the business cycle are welfare-reducing. Since microfoundations are based on the preferences of decision-makers in the model, DSGE models feature a natural benchmark for evaluating the welfare effects of policy changes.
|
|
In mathematics, a pseudo-reductive group over a field k (sometimes called a k-reductive group) is a smooth connected affine algebraic group defined over k whose k-unipotent radical (i.e., largest smooth connected unipotent normal k-subgroup) is trivial. Over perfect fields these are the same as (connected) reductive groups, but over non-perfect fields Jacques Tits found some examples of pseudo-reductive groups that are not reductive. A pseudo-reductive k-group need not be reductive (since the formation of the k-unipotent radical does not generally commute with non-separable scalar extension on k, such as scalar extension to an algebraic closure of k).
|
|
R2-D2 and other astromech droids are constructed from unique parts, with a separate top, body and legs. The robots of Exo-Force, Mars Mission commander aliens and Bionicle miniatures have a design similar to the Star Wars Battle Droids, but with separate legs, movable hands, and a head affixed to a small torso. Hagrid, the half-giant character from the Harry Potter series, uses a larger minifigure body, with only the head being separable. Skeletons, usually found in Castle, Pirate, and Indiana Jones sets, use the standard minifigure head, but unique torsos, arms, and legs designed to resemble a skeletal structure; although different, these figure parts are still detachable.
|
|
This condition is also necessary over a field of characteristic 0 or, more generally, over a perfect field, because over such a field, every irreducible polynomial is separable, and thus coprime with its derivative. Over a field of characteristic 0, the quotient of f by its GCD with its derivative is the product of the a_i in the above square-free decomposition. Over a perfect field of non-zero characteristic , this quotient is the product of the a_i such that is not a multiple of . Further GCD computations and exact divisions allow computing the square-free factorization (see square-free factorization over a finite field).
|
|
In 1940, at the age of 58, he and his family fled Europe on the last voyage of the SS Washington, embarking on 1 June in Lisbon. He moved to the United States, giving the prestigious Oliver Wendell Holmes Lectures at Harvard Law School in 1942. He was supported by Roscoe Pound for a faculty position at Harvard but opposed by Lon Fuller on the Harvard faculty before becoming a full professor at the department of political science at the University of California, Berkeley in 1945. Kelsen was defending a position of the distinction of the philosophical definition of justice as it is separable from the application of positive law.
|
|
Medium- range missiles like the Soviet R-5, with a range, required ceramic composite heat shielding on separable reentry vehicles (it was no longer possible for the entire rocket structure to survive reentry). The first ICBMs, with ranges of , were only possible with the development of modern ablative heat shields and blunt-shaped vehicles. In the United States, this technology was pioneered by H. Julian Allen and A. J. Eggers Jr. of the National Advisory Committee for Aeronautics (NACA) at Ames Research Center.Boris Chertok, "Rockets and People", NASA History Series, 2006 In 1951, they made the counterintuitive discovery that a blunt shape (high drag) made the most effective heat shield.
|
|
Cross-domain interoperability exists when organizations or systems from different domains interact in information exchange, services, and/or goods to achieve their own or common goals. Interoperability is the method of systems working together (inter-operate). A domain in this instance is a community with its related infrastructure, bound by common purpose and interests, with consistent mutual interactions or rules of engagement that is separable from other communities by social, technical, linguistic, professional, legal or sovereignty related boundaries.Slater, T. "Cross-Domain Interoperability", Network Centric Operations Industry Consortium - NCOIC, 2013 The capability of cross-domain interoperability is becoming increasingly important as business and government operations become more global and interdependent.
|
|
Separable verbs challenge the understanding of meaning compositionality because when they are separated, the two parts do not form a constituent. Hence theories of syntax that assume that form–meaning correspondences should be understood in terms of syntactic constituents are faced with a difficulty, because it is not apparent what sort of syntactic unit the verb and its particle build. One prominent means of addressing this difficulty is via movement. One stipulates that languages like German and Dutch are actually SOV languages (as opposed to SVO) and that when separation occurs, the lexical verb has moved out of the clause-final position to a derived position further to the left, e.g.
|
|
The cyclotomic fields are examples. A cyclotomic extension, under either definition, is always abelian. If a field K contains a primitive n-th root of unity and the n-th root of an element of K is adjoined, the resulting Kummer extension is an abelian extension (if K has characteristic p we should say that p doesn't divide n, since otherwise this can fail even to be a separable extension). In general, however, the Galois groups of n-th roots of elements operate both on the n-th roots and on the roots of unity, giving a non-abelian Galois group as semi-direct product.
|
|
A compact semi-modular synthesiser A modular synthesizer has a case or frame into which arbitrary modules can be fitted; modules are usually connected together using patch cords and a system may include modules from different sources, as long as it fits the form factors of the case and uses the same electrical specifications. A semi-modular synthesizer on the other hand is a collection of modules from a single manufacturer that makes a cohesive product, an instrument. Modules may not be swapped out and usually a typical configuration has been pre-wired. The “modules” are typically not separable and may physically be parts of a contiguous circuit board.
|
|
Oxford: Blackwell. or that the mind and body are distinct and separable. Thus, it encompasses a set of views about the relationship between mind and matter, as well as between subject and object, and is contrasted with other positions, such as physicalism and enactivism, in the mind–body problem. Aristotle shared Plato's view of multiple souls and further elaborated a hierarchical arrangement, corresponding to the distinctive functions of plants, animals, and people: a nutritive soul of growth and metabolism that all three share; a perceptive soul of pain, pleasure, and desire that only people and other animals share; and the faculty of reason that is unique to people only.
|
|
The sheriff executed the order, whereupon, on June 29, 1888, Richardson instituted executory proceedings upon the mortgage of January 28, 1884, for the seizure and sale of the lands, as set forth in the next preceding case, the record of which was made part of the record in this case. The case was duly removed by said defendants into the circuit court of the United States upon the grounds that there was a separable controversy between them and the plaintiff, and that the suit involved a question under the bankrupt law of the United States as to the effect of the husband's discharge in bankruptcy upon the plaintiff's claim and mortgage.
|
|
Kraus is best known for her work in quantum information and especially in entanglement theory. Together with her coworkers she developed criteria to decide whether a quantum state is separable or entangled and showed how to construct optimal entanglement witnesses and studied the creation of entanglement by unitary quantum gates and dissipative processes. In 2010 she showed how to decide whether two pure quantum states of a many- particle system are equivalent to each other in terms of entanglement. More recently she introduced the notion of "maximally entangled sets" as a new concept generalizing maximally entangled states to the case of considering entanglement between more than two systems (multipartite entanglement).
|
|
The RTV-A-2 Hiroc (high-altitude rocket) was a product of the United States' first effort to develop an intercontinental ballistic missile (ICBM). The project was named MX-774. The project was canceled in 1947, but leftover funds were used to build and launch three of the planned 10 research vehicles designated RTV-A-2.Kennedy, Gregory P, “The Rockets and Missiles of White Sands Proving Ground 1945-1958,” Schiffer Military History, Atglen, PA, 2009 , p 63 The design included several innovations; the gimbaled thrust chambers provided guidance control, the internal gas pressure was used to support the airframe and the nose cap was separable.
|
|
Doing Deals: A Guide to Buying Land for Conservation (1995) Washington, DC: Land Trust Alliance In October 2002, Property and Environment Research Center published a report by Dominic P. Parker entitled Cost-Effective Strategies for Conserving Private Land. This paper identified numerous ways for operating land trusts more efficiently, pointing out that conservation easement and other tools for land preservation may be less costly than ownership. Sometimes the various rights associated with land ownership are separable. A preservationist organization may, for instance, buy only the extraction rights on a property with oil or minerals, and then rent those rights to extracters on the organization's terms.
|
|
Another kind with > pods the size of a hen's egg and resembling a cow's udder is called Niu-ju- > chiao 牛乳蕉 (cow's udder banana), and is slightly inferior to Yang-chiao- > chiao. A third kind is the size of a lotus rootstock; the pods are six to > seven inches in length, squarish in shape, not sweet, and considered the > most inferior. The stem is separable into fibers, and when treated with > lime, can be woven into thin cloth, called Chiao-ko 蕉葛 (banana linen). > Although the cloth is soft and good and yellowish-white in color, it is not > comparable to the reddish linen.
|
|
The VEGAS algorithm approximates the exact distribution by making a number of passes over the integration region which creates the histogram of the function f. Each histogram is used to define a sampling distribution for the next pass. Asymptotically this procedure converges to the desired distribution.Lepage, 1978 In order to avoid the number of histogram bins growing like Kd, the probability distribution is approximated by a separable function: :g(x_1, x_2, \ldots) = g_1(x_1) g_2(x_2) \ldots so that the number of bins required is only Kd. This is equivalent to locating the peaks of the function from the projections of the integrand onto the coordinate axes.
|
|
The proneural genes also have an important role in the development of distinct types of sensory organs, namely chordotonal organs (proprioceptorsthat detect mechanical and sound vibrations) and external sensory organs. Members of achaete-scute complex, such as achaete and scute, as well as ‘’atonal’’ and ‘’daughterless’’ confer to ectodermal cells the ability to become sensory mother cells (SMCs). In the development of sensory organs there are two main phases: determination and differentiation that may not be mechanistically separable. Proneural proteins are involved in both processes, through the activation of the downstream “differentiating genes” that in turn regulate the induction of sensory-organ-subtype characteristics.
|
|
It can be shown that there is no analogue of Lebesgue measure on an infinite-dimensional vector space. Even so, it is possible to define Gaussian measures on infinite-dimensional spaces, the main example being the abstract Wiener space construction. A Borel measure γ on a separable Banach space E is said to be a non-degenerate (centered) Gaussian measure if, for every linear functional L ∈ E∗ except L = 0, the push-forward measure L∗(γ) is a non- degenerate (centered) Gaussian measure on R in the sense defined above. For example, classical Wiener measure on the space of continuous paths is a Gaussian measure.
|
|
'In Lacan's seminars of the late 1950s and early 1960s, the evolving concept of the objet (petit) a is viewed in the matheme of phantasy as the object of desire sought in the other...a deliberate departure from British Object Relations psychoanalysis'.Mary Jacobus, The Poetics of Psychoanalysis (Oxford 2005) p. 26n In 1957, in his Seminar Les formations de l'inconscient, Lacan introduces the concept of objet petit a as the (Kleinian) imaginary part-object, an element which is imagined as separable from the rest of the body. In the Seminar Le transfert (1960–1961) he articulates objet a with the term agalma (Greek, an ornament).
|
|
In queueing theory, a discipline within the mathematical theory of probability, mean value analysis (MVA) is a recursive technique for computing expected queue lengths, waiting time at queueing nodes and throughput in equilibrium for a closed separable system of queues. The first approximate techniques were published independently by Schweitzer and Bard, followed later by an exact version by Lavenberg and Reiser published in 1980. It is based on the arrival theorem, which states that when one customer in an M-customer closed system arrives at a service facility he/she observes the rest of the system to be in the equilibrium state for a system with M − 1 customers.
|
|
Metalinguistic awareness refers to the understanding that language is a system of communication, bound to rules, and forms the basis for the ability to discuss different ways to use language (Baten, Hofman, & Loeys, 2011). In other words, it is the ability to consciously analyze language and its sub- parts, to know how they operate and how they are incorporated into the wider language system (Beceren, 2010). An individual with such ability is aware that linguistic forms and structure can interact and be manipulated to produce a vast variety of meanings. Words are only arbitrarily and symbolically associated with their referents, and are separable from them.
|
|
Conversely, if the mental abstractions were not a true understanding, then 'what is understood otherwise than the thing is false'. His solution to this problem was to state that the mind is able to separate in thought what is not necessarily separable in reality. He cites the human mind's ability to abstract from concrete particulars as an instance of this. This, according to Boethius, avoids the problem of Platonic universals being out there in the real world, but also the problem of them being purely constructs of the mind in that universals are simply the mind thinking of particulars in an abstract, universal way.
|
|
The real numbers form a metric space: the distance between x and y is defined as the absolute value . By virtue of being a totally ordered set, they also carry an order topology; the topology arising from the metric and the one arising from the order are identical, but yield different presentations for the topology—in the order topology as ordered intervals, in the metric topology as epsilon-balls. The Dedekind cuts construction uses the order topology presentation, while the Cauchy sequences construction uses the metric topology presentation. The reals are a contractible (hence connected and simply connected), separable and complete metric space of Hausdorff dimension 1\.
|
|
Convergent cross mapping (CCM) is a statistical test for a cause-and-effect relationship between two time series variables that, like the Granger causality test, seeks to resolve the problem that correlation does not imply causation. While Granger causality is best suited for purely stochastic systems where the influences of the causal variables are separable (independent of each other), CCM is based on the theory of dynamical systems and can be applied to systems where causal variables have synergistic effects. The fundamental idea of this test was first published by Cenys et al. in 1991 and used in a series of statistical approaches (see for example,).
|
|
However, they do seem to prefer areas where disturbance is relatively low while breeding. They may also roost on mudflats, sandbars, beaches, reefs, jetties and pilings. The species became first known to occur in New Zealand from a specimen shot at Jerusalem in 1890 and small numbers of subfossil bones, the first found at Lake Grassmere in 1947, followed by records of other stray individuals. The bones were later described as a new (sub)species, Pelecanus (conspicillatus) novaezealandiae (Scarlett, 1966: "New Zealand pelican") as they appeared to be larger, but Worthy (1998), reviewing new material, determined that they were not separable from the Australian population.
|
|
So, for example, some people who have a negative perception of and attitude toward Muslims may also show this toward non-Muslim immigrants, either as a whole or certain group (such as, for example, Eastern Europeans, sub-Saharan Africans, or Roma), whereas others would not. Nigel Farage, for example, is anti-EU and in favor of crackdowns on immigration from Eastern Europe, but is favourable to immigration from Islamic Commonwealth countries such as Nigeria and Pakistan. In the United States, where immigrants from Latin America and Asia dominate and Muslims are a comparatively small fraction, xenophobia and Islamophobia may be more easily separable. Classism is another overlapping factor in some nations.
|
|
This is regularly done using Bell's theorem, but in this situation the theorem is used as an entanglement witness, a dividing line between entangled quantum states and separable quantum states, and is as such not as sensitive to the problems described here. In October 2015, scientists from the Kavli Institute of Nanoscience reported that the Quantum nonlocality phenomenon is supported at the 96% confidence level based on a "loophole-free Bell test" study. These results were confirmed by two studies with statistical significance over 5 standard deviations which were published in December 2015. However, Alain Aspect writes that No experiment can be said to be totally loophole-free.
|
|
Gideon Sundback increased the number of fastening elements from four per inch (about one every 6.4 mm) to ten or eleven (around every 2.5 mm), introduced two facing rows of teeth that pulled into a single piece by the slider, and increased the opening for the teeth guided by the slider. The patent for the "Separable Fastener" was issued in 1917. Gideon Sundback also created the manufacturing machine for the new device. The "S-L" or "scrapless" machine took a special Y-shaped wire and cut scoops from it, then punched the scoop dimple and nib, and clamped each scoop on a cloth tape to produce a continuous zipper chain.
|
|
Suppose that G is a profinite group acting on a module A with a surjective homomorphism π from the G-module A to itself. Suppose also that G acts trivially on the kernel C of π and that the first cohomology group H1(G,A) is trivial. Then the exact sequence of group cohomology shows that there is an isomorphism between AG/π(AG) and Hom(G,C). Kummer theory is the special case of this when A is the multiplicative group of the separable closure of a field k, G is the Galois group, π is the nth power map, and C the group of nth roots of unity.
|
|
This genus belongs to a group of genera allied to Lepiota with a white spore print, free (or almost free) gills, stipe easily separable from the cap and having a partial veil. Amongst the Agaricaceae it is characterized by the white spore powder, cap skin microscopically an epithelium with rounded cells, and a brownish cap and stipe, with brown scales. The name comes from the Greek "echinos" (ἐχῖνος) meaning a hedgehog or sea-urchin and "derma" (δέρμα) meaning skin, referring to the spiny cap surface. The noun "derma" is neuter and therefore if the species name is an adjective, it needs to take the neuter ending (example: Echinoderma asperum).
|
|
In practice, when computing a discrete approximation of the Gaussian function, pixels at a distance of more than 3σ have a small enough influence to be considered effectively zero. Thus contributions from pixels outside that range can be ignored. Typically, an image processing program need only calculate a matrix with dimensions \lceil6\sigma\rceil × \lceil6\sigma\rceil (where \lceil \cdot \rceil is the ceiling function) to ensure a result sufficiently close to that obtained by the entire Gaussian distribution. In addition to being circularly symmetric, the Gaussian blur can be applied to a two-dimensional image as two independent one-dimensional calculations, and so is termed separable filter.
|
|
Since the 1970s, sequential quadratic programming (SQP) and interior point methods (IPM) have had increasing attention, in part because they more easily use sparse matrix subroutines from numerical software libraries, and in part because IPMs have proven complexity results via the theory of self-concordant functions. The augmented Lagrangian method was rejuvenated by the optimization systems LANCELOT and AMPL, which allowed sparse matrix techniques to be used on seemingly dense but "partially separable" problems. The method is still useful for some problems., chapter 17 Around 2007, there was a resurgence of augmented Lagrangian methods in fields such as total-variation denoising and compressed sensing.
|
|
The VEGAS algorithm approximates the exact distribution by making a number of passes over the integration region while histogramming the function f. Each histogram is used to define a sampling distribution for the next pass. Asymptotically this procedure converges to the desired distribution. In order to avoid the number of histogram bins growing like K^d with dimension d the probability distribution is approximated by a separable function: g(x_1, x_2, \ldots) = g_1(x_1) g_2(x_2) \cdots so that the number of bins required is only Kd. This is equivalent to locating the peaks of the function from the projections of the integrand onto the coordinate axes.
|
|
In general, the integral closure of a noetherian domain of dimension at most 2 is noetherian; Nagata gave an example of dimension 3 noetherian domain whose integral closure is not noetherian. A nicer statement is this: the integral closure of a noetherian domain is a Krull domain (Mori–Nagata theorem). Nagata also gave an example of dimension 1 noetherian local domain such that the integral closure is not finite over that domain. Let A be a noetherian integrally closed domain with field of fractions K. If L/K is a finite separable extension, then the integral closure A' of A in L is a finitely generated A-module.
|
|
The zu-infinitive has nothing to do with the gerundive, although it is created in a similar way. One simply puts the preposition zu before the bare infinitive, before the permanent prefix, but after the separable prefix. :zu lesen ‘to read’ :Ich lerne zu lesen ‘I learn to read’ :zu verlassen ‘to leave’ :Ich habe beschlossen, dich zu verlassen ‘I've decided to leave you’ :wegzuwerfen ‘to throw away’ :Ich habe beschlossen, das Buch wegzuwerfen ‘I've decided to throw away the book’ The zu-infinitive extended with um expresses purpose (in order to, for the purpose of). The subject of the main clause and the infinitive must be identical.
|
|
Iranian sources cite an improved guidance system on the missile, and analysts note that adjusting the missile's in-flight trajectory without fins requires a highly responsive guidance system. The Qiam 1's accuracy is also improved with the addition of a separable warhead--since only the warhead needs to survive re-entry most missiles have structurally weak bodies which can cause an attached warhead to tumble as the body breaks apart. Attachments visible in pictures of the warhead may show antennas for controlling the missile's trajectory by radio. The shape of the warhead on the Qiam 1 resembles that used on Iran's Shahab-3.
|
|
The MCE is used for mission planning, command and control, and image processing and dissemination; an LRE for controlling launch and recovery; and associated ground support equipment. The LRE provides precision Differential GPS corrections for navigational accuracy during takeoff and landings, while precision coded GPS supplemented with an inertial navigation system is used during mission execution. By having separable elements in the ground segment, the MCE and the LRE can operate in geographically separate locations, and the MCE can be deployed with the supported command's primary exploitation site. Both ground segments are contained in military shelters with external antennas for line-of-sight and satellite communications with the air vehicles.
|
|
Illinois Central 121 (IC #121) was a diesel streamliner built in 1936 by Pullman-Standard and powered by Electro-Motive Corporation, which was used by the Illinois Central Railroad on the Green Diamond. Its fixed five-car consist was also the end of an era; the popularity of the early streamliners was their undoing, because the trains could not be lengthened or shortened to handle varying loads. It was the last streamliner built with the power car articulated with the train; future streamliners featured a matched but separable locomotive.The train was painted in a two-tone green livery, "Cypress Green" on the nose and below the window sills with "Cedar Green" above, separated by an aluminum strip.
|
|
This is not true, though the Moulton design paved the way for such designs and various Moultons over the years have been made in separable versions allowing relatively easy dismantling for transportation or storage. Mass-appeal versions such as the Standard and Deluxe were complemented by Speed versions used in competition. Thus although Moultons are often included in the folding bicycle category along with small wheel folders, small wheel bicycles would be a more technically correct term covering all such bicycles. In August 2008, Alex Moulton announced the creation of a new company called Moulton Bicycle, in collaboration with British bicycle manufacturer Pashley Cycles which had manufactured certain Moulton designs under licence since 1992.
|
|
The M-10003 through M-10006 represented the final development of the custom streamlined trainset on the Union Pacific. They followed the cab/booster unit concept pioneered with the M-10002 trainset. As totally separable and interchangeable cab/booster power sets, they set the path that EMC was to follow with introduction of their E series locomotive sets the following year. Union Pacific was able to maintain daily service on the Chicago-Denver run for seventeen years by dedicating three locomotive sets to that service and re- purposing power units from M-10001 and M-10004 (three total) to provide additional power and keep at least two of the locomotive sets in running condition at any given time.
|
|
Tanselle, G.T. (1998). Texts and artifacts in the electronic era. 21stC, 3.2. Further, the Modern Language Association's Committee on the Future of the Print Record structured its "Statement on the Significance of Primary Records" on the inherent theoretical ideology that there is a need to preserve as many copies of a printed edition as is possible as texts and their textual settings are, quite simply, not separable, just as the artifactual characteristics of texts are as relevant and varied as the texts themselves (in the report mentioned herewith, G. Thomas Tanselle suggests that presently existing book stacks need not be abandoned with emerging technologies; rather they serve as vitally important original (primary) sources for future study).
|
|
A diagram of the Shuttle- Derived Heavy Lift Launch Vehicle, Block I configuration The HLV was proposed to be a vehicle at liftoff with two 4-segment Space Shuttle Solid Rocket Boosters weighing about providing a total thrust of at sea level and the Space Shuttle External Tank weighing about fueled. The side-mounted carrier was to include a Shuttle-derived 'boattail' carrying the three Space Shuttle Main Engines and other propulsion elements. A diameter payload carrier with a separable fairing weighing would take up the space usually occupied by the rest of the orbiter. The basic vehicle would not have an upper stage, requiring the payload to perform orbit circularization and possibly trans- lunar injection burns.
|
|
In 1914, Friedrich Dahl provisionally united all these descriptions under G. westringi, noting that further research across the region was needed to clarify the status of different forms. In 1911, Embrik Strand briefly named a species, G. wogeonis, from Vokeo in the Schouten Islands (Papua New Guinea), writing that it was separable from G. westringi by shorter spines and smaller sigilla. Apparently based on this comment, Dahl also provisionally synonymized G. wogeonis with G. westringi, without specific comment. However, in 1915, Strand published a more detailed description and an illustration of G. wogeonis that depicted a small-spined, reddish-colored, less elongate form quite unlike any other description of taxa included by Dahl in G. westringi.
|
|
A species assigned to a monotypic genus of Thylacinidae, most closely resembling the genus Wabulacinus yet separable from a Wabulacinus–Thylacinus clade as a sister group of those thylacinids. The size and form of the animal is estimated to have been that of a smaller dog breed and inhabited the Riversleigh area with similar sized thylacinids. The discovered existence of multiple phylogenies in early Miocene Riversleigh fauna, each presumably specialised to an ecological niche, strongly supported a revised conception of the family's evolutionary history from a monophyletic group of taxa with a narrow range of adaptations and trophic levels. Specimens referred to Ngamalacinus timmulvaneyi have been obtained at the Inabeyence and Camel Sputum sites at Riversleigh.
|
|
In 2000, Dernburg started up her laboratory at Lawrence Berkeley National Laboratory and the University of California, Berkeley to continue investigating chromosome organization and dynamics, focusing on meiosis using the nematode worm Caenorhabditis elegans as a model organism. Her laboratory has contributed to the community's understanding of how chromosomes find and pair with the appropriate homolog during meiosis, which is essential for proper chromosome segregation and ensuring the appropriate chromosome copy number in daughter cells. Her group has worked to understand how special regions of chromosomes, known as pairing centers, promote homologous chromosome pairing, synapsis, and segregation in the worm. In 2005, they published a study demonstrating how pairing centers perform two separable functions during meiosis.
|
|
Sidemount diver pushing a cylinder in front A backplate and wing is an alternative configuration of scuba harness with a buoyancy compensation bladder known as a "wing" mounted behind the diver, sandwiched between the backplate and the cylinder or cylinders. Unlike stabilizer jackets, the backplate and wing is a modular system, in that it consists of separable components. This arrangement became popular with cave divers making long or deep dives, who needed to carry several extra cylinders, as it clears the front and sides of the diver for other equipment to be attached in the region where it is easily accessible. This additional equipment is usually suspended from the harness or carried in pockets on the exposure suit.
|
|
HEVC has improved precision due to the longer interpolation filter and the elimination of the intermediate rounding error. For 4:2:0 video, the chroma samples are interpolated with separable one-dimensional 4-tap filtering to generate eighth-sample precision, while in comparison H.264/MPEG-4 AVC uses only a 2-tap bilinear filter (also with eighth-sample precision). As in H.264/MPEG-4 AVC, weighted prediction in HEVC can be used either with uni-prediction (in which a single prediction value is used) or bi-prediction (in which the prediction values from two prediction blocks are combined). ;Motion vector prediction HEVC defines a signed 16-bit range for both horizontal and vertical motion vectors (MVs).
|
|
Operating room productivity is the quantity and quality of output (typically surgical cases) from the surgical suite in contrast to the amount of input required (such as physicians and nurses and equipment for example). Many institutions believe that productivity (output/input) can be accomplished without sacrificing convenience (rapid access to open OR time such that a surgeon can book a case without having to wait) but these two aspects are not separable. Typically, the greater the operating room utilization, the less the convenience (able to book cases when desired) as defined by surgeons and patients. This is because as utilization goes up there is less available open staffed OR time available on short notice.
|
|
Accordingly, the reasoning that underlies the immediate appealability of the denial of absolute immunity indicates that the denial of qualified immunity should be similarly appealable under the "collateral order" doctrine; in each case, the district court's decision is effectively unreviewable on appeal from a final judgment. The denial of qualified immunity also meets the additional criteria for an appealable interlocutory order: it conclusively determines the disputed question, and it involves a claim of rights separable from, and collateral to, rights asserted in the action. P P. 524-530. :3. Petitioner is entitled to qualified immunity from suit for his authorization of the wiretap in question notwithstanding his actions violated the Fourth Amendment.
|
|
He then considered shoes painted by Vincent van Gogh and turned to the examples of Congress's intended targets of copyright in the amicus curiae brief filed by the Intellectual Property Professors. Breyer found that copyrighting those embellishments was not the same as copyrighting an entire cheerleading uniform design because those examples were conceptually separable while the uniform design was not. He reiterated that van Gogh could certainly have received a copyright to prevent people from reproducing his painting, but the request in Star Athletica was an injunction against reproducing uniforms and Breyer felt this decision would be equivalent to giving van Gogh a design copyright that could prevent others from producing those shoes.Star Athletica, slip op.
|
|
Using Zorn's lemma and the Gram–Schmidt process (or more simply well-ordering and transfinite recursion), one can show that every Hilbert space admits a basis, but not orthonormal base Linear Functional Analysis Authors: Rynne, Bryan, Youngson, M.A. page 79; furthermore, any two orthonormal bases of the same space have the same cardinality (this can be proven in a manner akin to that of the proof of the usual dimension theorem for vector spaces, with separate cases depending on whether the larger basis candidate is countable or not). A Hilbert space is separable if and only if it admits a countable orthonormal basis. (One can prove this last statement without using the axiom of choice).
|
|
" A common practice by the European cartographers of the time was to map unexplored areas as "blank spaces". This influenced the colonial powers as it sparked competition amongst them to explore and colonise these regions. Imperialists aggressively and passionately looked forward to filling these spaces for the glory of their respective countries. The Dictionary of Human Geography notes that cartography was used to empty 'undiscovered' lands of their Indigenous meaning and bring them into spatial existence via the imposition of "Western place-names and borders, [therefore] priming 'virgin' (putatively empty land, 'wilderness') for colonisation (thus sexualising colonial landscapes as domains of male penetration), reconfiguring alien space as absolute, quantifiable and separable (as property).
|
|
For Paul the "power of the cross" is not separable from the resurrection of Jesus. John Calvin supported the "agent of God" Christology and argued that in his trial in Pilate's Court Jesus could have successfully argued for his innocence, but instead submitted to crucifixion in obedience to the Father.The Reading and Preaching of the Scriptures by Hughes Oliphant Old 2002 page 125 This Christological theme continued into the 20th century, both in the Eastern and Western Churches. In the Eastern Church Sergei Bulgakov argued that the crucifixion of Jesus was "pre-eternally" determined by the Father before the creation of the world, to redeem humanity from the disgrace caused by the fall of Adam.
|
|
The larvae of a very few species feed on plants, but the majority are primary parasitoids on a huge range of arthropods at all stages of development. They are exceptional in that they are one of two hymenopteran families with some species that are known to parasitize Thysanoptera. Eulophids are found throughout the world in virtually all habitats (one is even aquatic, parasitising water-penny beetles). Eulophids are separable from most other Chalcidoidea by the possession of only four tarsomeres on each leg, a small, straight protibial spur (as opposed to the larger, curved one in most other chalcidoids), and by antennae with two to four funicle segments and at most 10 antennomeres.
|
|
Space tug missions, to disaggregate non-time-critical Mars logistics from crew, can reduce the costs by as much as 60% (if using advanced solar electric propulsion (ion engines)) and reduces overall mission risk by enabling on-site check-out of critical systems before the crew departs. Not only would the solar electric propulsion (SEP) technologies and designs be applied to future missions, but the ARRM spacecraft would be left in a stable orbit for reuse. The project has baselined any of multiple refueling capabilities; the asteroid-specific payload is at one end of the bus, for possible removal and replacement via future servicing, or as a separable spacecraft, leaving a qualified space tug in cislunar space.
|
|
When L/K is separable, the trace provides a duality theory via the trace form: the map from to K sending to Tr(xy) is a nondegenerate, symmetric, bilinear form called the trace form. An example of where this is used is in algebraic number theory in the theory of the different ideal. The trace form for a finite degree field extension L/K has non-negative signature for any field ordering of K. The converse, that every Witt equivalence class with non-negative signature contains a trace form, is true for algebraic number fields K.Lorenz (2008) p.38 If L/K is an inseparable extension, then the trace form is identically 0.
|
|
In mathematics, a Galois extension is an algebraic field extension E/F that is normal and separable; or equivalently, E/F is algebraic, and the field fixed by the automorphism group Aut(E/F) is precisely the base field F. The significance of being a Galois extension is that the extension has a Galois group and obeys the fundamental theorem of Galois theory. See the article Galois group for definitions of some of these terms and some examples. A result of Emil Artin allows one to construct Galois extensions as follows: If E is a given field, and G is a finite group of automorphisms of E with fixed field F, then E/F is a Galois extension.
|
|
Garth Dales and Robert M. Solovay proved in 1976 that Kaplansky's conjecture, namely that every algebra homomorphism from the Banach algebra C(X) (where X is some compact Hausdorff space) into any other Banach algebra must be continuous, is independent of ZFC. CH implies that for any infinite X there exists a discontinuous homomorphism into any Banach algebra. Consider the algebra B(H) of bounded linear operators on the infinite-dimensional separable Hilbert space H. The compact operators form a two-sided ideal in B(H). The question of whether this ideal is the sum of two properly smaller ideals is independent of ZFC, as was proved by Andreas Blass and Saharon Shelah in 1987.
|
|
By far, the most common bearing is the plain bearing, a bearing which uses surfaces in rubbing contact, often with a lubricant such as oil or graphite. A plain bearing may or may not be a discrete device. It may be nothing more than the bearing surface of a hole with a shaft passing through it, or of a planar surface that bears another (in these cases, not a discrete device); or it may be a layer of bearing metal either fused to the substrate (semi-discrete) or in the form of a separable sleeve (discrete). With suitable lubrication, plain bearings often give entirely acceptable accuracy, life, and friction at minimal cost.
|
|
Andy Magid 1980 Andy Roy Magid (born 4 May 1944 in Saint Paul, Minnesota)biographical information from American Men and Women of Science, Thomson Gale 2004 is an American mathematician. Magid received in 1966 from the University of California, Berkeley his bachelor's degree and in 1969 from Northwestern University his PhD under the direction of Daniel Zelinsky with thesis Separable Subalgebras of Commutative Algebras and Other Applications of the Boolean Spectrum. From 1969 to 1972 Magid was a Ritt Assistant Professor at Columbia University. At the University of Oklahoma he was from 1972 to 1974 an assistant professor, from 1974 to 1977 an associate professor, and from 1977 to 2012 a full professor, retiring as professor emeritus in 2012.
|
|
The wingspan is 10–13 mm. The forewings are yellowish white, speckled and mottled with olive-grey, becoming darker or more fuscous in certain spots, these are indistinctly separable from the profuse speckling which commences a little beyond the base, three are placed on the line of the fold at equal distances, the outer one being a little beyond the middle of the wing. There is also a small spot about the flexus, another beyond the end of the cell, and the speckling about the end of the termen is somewhat grouped, with intermediate pale spaces at and below the apex, it is also partly distributed through the pale whitish cinereous cilia. The hindwings are very pale bronzy grey.
|
|
In general topology, a remote point is a point p which belongs to the Stone–Čech compactification \beta X of a Tychonoff space X but which does not belong to the topological closure within \beta X of any nowhere dense subset of X. Let \R be the real line with the standard topology. In 1962, Nathan Fine and Leonard Gillman proved that, assuming the continuum hypothesis: Their proof works for any Tychonoff space which is separable and not pseudocompact. Chae and Smith proved that the existence of remote points is independent, in terms of Zermelo-Fraenkel set theory, of the continuum hypothesis for a class of topological spaces that includes metric spaces. Several other mathematical theorems have been proved concerning remote points.
|
|
The project was simulated the visionary system by how it starts to convert the signals to image(actually the edges and colors) and then recognizing the shapes to find a relation between brain's information and image. The Objective Visionary system actually is concentrating on the separable sections, this separation gives the application visionary system the excellence processing result, because with this method the system do not waste much time on processing non significant sections and signals. this operation in the Objective Vision project called objective processing and because the O.V. mission is focused on human visionary simulation, so the developer refers with Objective Vision. Scheme of the optic tract with image being decomposed on the way, up to simple cortical cells (simplified).
|
|
Mother Nature is surrounded by grottesche in this fresco detail from Villa d'Este. Renaissance grotesque motifs in assorted formats. Decorative panel showing the two separable elements of Grotesque: the elaborate acanthus leaf and candelabra type design and the hideous mask or face Since at least the 18th century Italy (in French and German as well as English), grotesque has come to be used as a general adjective for the strange, mysterious, magnificent, fantastic, hideous, ugly, incongruous, unpleasant, or disgusting, and thus is often used to describe weird shapes and distorted forms such as Halloween masks. In art, performance, and literature, however, grotesque may also refer to something that simultaneously invokes in an audience a feeling of uncomfortable bizarreness as well as sympathetic pity.
|
|
Writer Willy Ley asked Hohmann to contribute to an anthology of papers on spaceflight, "Die Möglichkeit der Weltraumfahrt" (The Possibility of Space Travel), published in 1928. Hohmann contributed a post about "Fahrtrouten, Fahrzeiten und Landungsmöglichkeiten" (Routes, Timetables, and Landing Options) where he proposed using a separable landing module to travel to the Moon, an idea that was later utilized in the Apollo lunar missions. Following the rise to power of the Nazi party, Hohmann distanced himself as much as possible from rocketry, wishing to play no part in the development of the rocket as a weapon. He died in an Essen hospital shortly before the end of World War II as a result of stress experienced during the intense Allied bombing of the city.
|
|
The properties of Bessel beams make them extremely useful for optical tweezing, as a narrow Bessel beam will maintain its required property of tight focus over a relatively long section of beam and even when partially occluded by the dielectric particles being tweezed. Similarly, particle manipulation with acoustical tweezers was achieved D. Baresch, J.L. Thomas, and R. Marchiano, Physical review letters, 2016, 116(2), 024301.with a Bessel beam that scatters and produces a radiation force resulting from the exchange of acoustic momentum between the wave-field and a particle placed along its path. The mathematical function which describes a Bessel beam is a solution of Bessel's differential equation, which itself arises from separable solutions to Laplace's equation and the Helmholtz equation in cylindrical coordinates.
|
|
A key approach within cognitive neuropsychology has been to use single case studies and dissociation as a means of testing theories of cognitive function. For example, if a theory states that reading and writing are simply different skills stemming from a single cognitive process, it should not be possible to find a person who, after brain injury, can write but not read or read but not write. This selective breakdown in skills suggests that different parts of the brain are specialized for the different processes and so the cognitive systems are separable. The philosopher Jerry Fodor has been particularly influential in cognitive neuropsychology, particularly with the idea that the mind, or at least certain parts of it, may be organised into independent modules.
|
|
For non-separable extensions, necessarily in characteristic p with p a prime number, then at least when the degree [L : K] is p, L / K has a primitive element, because there are no intermediate subfields. When [L : K] = p2, there may not be a primitive element (and therefore there are infinitely many intermediate fields). This happens, for example if K is :Fp(T, U), the field of rational functions in two indeterminates T and U over the finite field with p elements, and L is obtained from K by adjoining a p-th root of T, and of U. In fact one can see that for any α in L, the element αp lies in K, but a primitive element must have degree p2 over K.
|
|
In his widely cited article African (Black) Psychology: Issues and Synthesis, Kobi Kambon provides a general overview of his Africentric approach to studying the psychology of Black Americans. He argues that while most Black psychologists recognize the need for a Black psychology, some fail to consider that it might be an undertaking that is entirely separable from Western Psychology. Kambon suggests that to study Black psychology as contained within Western Psychology is to ignore African cultural and philosophical antecedents, thereby framing modern Black psychology as a set of mere reactions to Western culture and oppression. Kambon calls much of this work "Western psychology in blackface", referring to the psychologists involved as conceptually incarcerated thinkers, stuck within a Eurocentric framework of psychology.
|
|
Any topological vector space is an abelian topological group under addition, so the above conditions apply (although note that the above are written multiplicatively). Historically, definition 1(b) was the first reformulation of total boundedness for topological vector spaces; it dates to a 1935 paper of John von Neumann. This definition has the appealing property that, in a locally convex space endowed with the weak topology, the precompact sets are exactly the bounded sets. For seperable Banach spaces, there is a nice characterization of the precompact sets (in the norm topology) in terms of weakly convergent sequences of functionals: if is a separable Banach space, then is precompact if and only if every weakly convergent sequence of functionals converges uniformly on .
|
|
In a separable Banach space (X, +), the group operation moves any subset A ⊂ X to the translates A + x for any x ∈ X. When there is a probability measure μ on the σ-algebra of Borel subsets of X, such that for all x, μ(A + x) = 0, then A is a Haar null set. The term refers to the null invariance of the measures of translates, associating it with the complete invariance found with Haar measure. Some algebraic properties of topological groups have been related to the size of subsets and Haar null sets. Haar null sets have been used in Polish groups to show that when A is not a meagre set then A−1A contains an open neighborhood of the identity element.
|
|
Disquisitions of Matter and Spirit. p. 212 The ancient Greeks believed air, as opposed to solid earth, to be incorporeal, in so far as it is less resistant to movement; and the ancient Persians believed fire to be incorporeal in that every soul was said to be produced from it.Priestley, Joseph. Disquisitions of Matter and Spirit. p. 235 In modern philosophy, a distinction between the incorporeal and immaterial is not necessarily maintained: a body is described as incorporeal if it is not made out of matter. In the problem of universals, universals are separable from any particular embodiment in one sense, while in another, they seem inherent nonetheless. Aristotle offered a hylomorphic account of abstraction in contrast to Plato's world of Forms.
|
|
Thus the hero or helper may resort to the sword of light as the only effective weapon against this enemy. But often the sword is not enough, and the supernatural enemy has to be attacked on a single vulnerable spot. The weak spot, moreover, may be an external soul (motif index E710) concealed somewhere in the world at large (inside animals, etc.); or, as in the case of "The Young King Of Easaidh Ruadh", this external soul is encased within a nested series of animals."Separable soul, or external soul", Typically bound up with the quest for the sword of light is the quest for the "One Story" (' truth about women'), namely, the story of the faithless wife who transforms her husband into a wolf.
|
|
Cabless rear end of a Class 352 (right) in 'taxi' livery, coupled to a Talgo unit (left) With the Talgo II coaches having proved successful, and a new class of coaches--the Talgo III being introduced in the early 1960s--a new type of express locomotive was required to pull them. On 28 May 1962, the Board of Directors of RENFE placed an order for the locomotives needed, and the 2000-T series is born. Unlike the fixed formation Talgo II trains, the Talgo III was to have a locomotive which was separable from the coaches. Five locomotives were initially built by Krauss-Maffei, who gave the locomotives the internal designation ML 2400; in Spain they are placed in the class 2000-T.
|
|
In practice, this is usually the maximally-localized set, in which the Wannier function ϕR is localized around the point R and rapidly goes to zero away from R. For the one-dimensional case, it has been proved by Kohn that there is always a unique choice that gives these properties (subject to certain symmetries). This consequently applies to any separable potential in higher dimensions; the general conditions are not established, and are the subject of ongoing research. A Pipek-Mezey style localization scheme has also been recently proposed for obtaining Wannier functions. Contrary to the maximally localized Wannier functions (which are an application of the Foster-Boys scheme to crystalline systems), the Pipek-Mezey Wannier functions do not mix σ and π orbitals.
|
|
Declarative sentences use V2 word order: the finite verb is preceded by one and only one constituent (unlike in English, this need not be the subject); in Germanic tradition, the position occupied by this constituent is referred to as the Vorfeld 'prefield'. Coordinating conjunctions like und 'and' or aber 'but' precede both the prefield and the finite verb, and so do topicalised elements (similarly to the 'that' in English 'That I don't know'). The prefield is often used to convey emphasis. : : : : Non-finite verbs as well as separable particles are placed at the end of the sentence: : : : In the midfield (the part of the clause between the position of the finite verb and that of the clause-final verb cluster), German word order is highly variable.
|
|
The substance of value as labour then becomes apparent (and is theoretically demonstrated) only in the analysis of the production of commodities "by means of commodities" (including the commodity labour-power). Some Western Marxists do not find this Unoist approach very satisfactory however, among other things because (1) a "form" is a form "of" something, the form that a content takes, hence form and content are not really separable, and (2) Marx claims that the formation of product values is an outcome of both the "economy of labour-time" and "the economy of trade" working in tandem.See Simon Clarke, "The Basic Theory of Capitalism: A Critical Review of Itoh and the Uno School", in: Capital & Class, Vol. 13, No. 1, March 1989, pp.
|
|
Distinguishing inclusion and participation. Paper presented at the Public Management Research Conference, Columbus, Ohio, October 2007 Sometimes "50/50" means that process and outcome are equally important, in other words that the effects of a process on community building are as important as the task completion. Sometimes it means that ideally 50% of the people involved in a process have participated in prior, related processes and 50% are newcomers, such that each policy-making effort acknowledges past conversations or decisions yet remains open to new ideas that may alter the previous consensus. From the perspective of the 50/50 rule, things like process and outcome or task and community are not in a trade-off relationship, and indeed are not even separable.
|
|
The birds formerly considered to be the resident Indian subspecies are now considered a separate species, the Indian spotted eagle (Clanga hastata), quite distinct and readily separable by morphological, behavioral, ecological, and DNA sequence data. The European taxon is actually closer to the greater spotted eagle; their common ancestor seems to have diverged around the middle Pliocene, perhaps some 3.6 million years ago, from the ancestors of the Indian birds. The "proto-spotted eagle" probably lived in the general region of Afghanistan, being split into a northern and a southern lineage when both glaciers and deserts advanced in Central Asia as the last ice age began. The northern lineage subsequently separated into the eastern (greater) and western (lesser) species of today, probably around the Pliocene-Pleistocene boundary not quite 2 million years ago.
|
|
Invariance Invariance is the property of perception whereby simple geometrical objects are recognized independent of rotation, translation, and scale; as well as several other variations such as elastic deformations, different lighting, and different component features. For example, the objects in A in the figure are all immediately recognized as the same basic shape, which are immediately distinguishable from the forms in B. They are even recognized despite perspective and elastic deformations as in C, and when depicted using different graphic elements as in D. Computational theories of vision, such as those by David Marr, have provided alternate explanations of how perceived objects are classified. Emergence, reification, multistability, and invariance are not necessarily separable modules to model individually, but they could be different aspects of a single unified dynamic mechanism.
|
|
This unique, dynamical representation of an old systems, allows researchers to apply techniques and hardware developed for CNN to better understand important CA. Furthermore, the continuous state space of CNN processors, with slight modifications that have no equivalent in Cellular Automata, creates emergent behavior never seen before. Any information processing platform that allows the construction of arbitrary Boolean functions is called universal, and as result, this class CNN processors are commonly referred to as universal CNN processors. The original CNN processors can only perform linearly separable Boolean functions. This is essentially the same problem Marvin Minsky introduced with respect to the perceptions of the first neural networks In either case, by translating functions from digital logic or look-up table domains into the CNN domain, some functions can be considerably simplified.
|
|
More formally, a support-vector machine constructs a hyperplane or set of hyperplanes in a high- or infinite-dimensional space, which can be used for classification, regression, or other tasks like outliers detection. Intuitively, a good separation is achieved by the hyperplane that has the largest distance to the nearest training-data point of any class (so-called functional margin), since in general the larger the margin, the lower the generalization error of the classifier. Kernel machine Whereas the original problem may be stated in a finite-dimensional space, it often happens that the sets to discriminate are not linearly separable in that space. For this reason, it was proposed that the original finite-dimensional space be mapped into a much higher-dimensional space, presumably making the separation easier in that space.
|
|
An extension L which is a splitting field for a set of polynomials p(X) over K is called a normal extension of K. Given an algebraically closed field A containing K, there is a unique splitting field L of p between K and A, generated by the roots of p. If K is a subfield of the complex numbers, the existence is immediate. On the other hand, the existence of algebraic closures in general is often proved by 'passing to the limit' from the splitting field result, which therefore requires an independent proof to avoid circular reasoning. Given a separable extension K′ of K, a Galois closure L of K′ is a type of splitting field, and also a Galois extension of K containing K′ that is minimal, in an obvious sense.
|
|
For example, turn off has a meaning unrelated to turn in Turn off the television set and the light. Many English phrasal verbs are separable, in the sense that if they are transitive then the object is placed between the core verb and the particle if the object is a pronoun (and optionally if it is a short noun phrase, but not if it is a long noun phrase as in the example above). For example: :Turn off the light OR Turn the light off (optional tmesis) :Turn it off (mandatory tmesis) This intervention of the object in the middle of the phrasal verb can be viewed as a form of tmesis even though the semantic unit being separated is written as two words even when not separated.
|
|
In physics, horror vacui, or plenism (), commonly stated as "nature abhors a vacuum", is a postulate attributed to Aristotle, who articulated a belief, later criticized by the atomism of Epicurus and Lucretius, that nature contains no vacuums because the denser surrounding material continuum would immediately fill the rarity of an incipient void. He also argued against the void in a more abstract sense (as "separable"), for example, that by definition a void, itself, is nothing, and following Plato, nothing cannot rightly be said to exist. Furthermore, insofar as it would be featureless, it could neither be encountered by the senses, nor could its supposition lend additional explanatory power. Hero of Alexandria challenged the theory in the first century CE, but his attempts to create an artificial vacuum failed.
|
|
Theorem. Let X be a Polish space, that is, a topological space such that there is a metric d on X that defines the topology of X and that makes X a complete separable metric space. Then X as a Borel space is Borel isomorphic to one of (1) R, (2) Z or (3) a finite space. (This result is reminiscent of Maharam's theorem.) It follows that a standard Borel space is characterized up to isomorphism by its cardinality, and that any uncountable standard Borel space has the cardinality of the continuum. Borel isomorphisms on standard Borel spaces are analogous to homeomorphisms on topological spaces: both are bijective and closed under composition, and a homeomorphism and its inverse are both continuous, instead of both being only Borel measurable.
|
|
The MOVIE index is a neuroscience-based model for predicting the perceptual quality of a (possibly compressed or otherwise distorted) motion picture or video against a pristine reference video. Thus, the MOVIE index is a full-reference metric. The MOVIE model is quite different from many other models since it uses neuroscience-based models of how the human brain processes visual signals at various stages along the visual pathway, including the lateral geniculate nucleus, primary visual cortex, and in the motion-sensitive extrastriate cortex visual area MT. Spatial MOVIE operates by processing spatial and temporal motion picture information in an approximately separable manner. A prediction of the spatial (frame) quality of a video is found by calculating a space-time frequency decomposition of both reference and test (distorted) videos using a Gabor filter bank.
|
|
ATOM not treat the system as a 'flat' configuration, but as a 'spatial', taken from several points of view - as separate, although reciprocally incorporated 'sectional views' (reflections), depending on separable criteria of decomposition. It is assumed that these cuts may be many, but so far succeeded established only four criteria (sectional views and structures): # The first sectional view considers the system as the structure of all processes occurring in system: S1 = . # The second sectional view refers to the structure of all the resources participating in the system (materials and products [M], people [H], equipment and tools [E], information resources [D], capital and financial resources (free financial resources) [F] ): S2 = . # The third sectional view reflects the hierarchical structure of all organizational units (primary, auxiliary and informational) that make up the ergo- transformational system: S3 = .
|
|
Let (fn) be a sequence of M-valued measurable functions, where M is a separable metric space, on some measure space (X,Σ,μ), and suppose there is a measurable subset A ⊆ X, with finite μ-measure, such that (fn) converges μ-almost everywhere on A to a limit function f. The following result holds: for every ε > 0, there exists a measurable subset B of A such that μ(B) < ε, and (fn) converges to f uniformly on the relative complement A \ B. Here, μ(B) denotes the μ-measure of B. In words, the theorem says that pointwise convergence almost everywhere on A implies the apparently much stronger uniform convergence everywhere except on some subset B of arbitrarily small measure. This type of convergence is also called almost uniform convergence.
|
|
Illustration of an adult and a juvenile by Joseph Smit (1875) The Indian spotted eagle was earlier considered as the resident of eastern subspecies of the lesser spotted eagle but has proven quite distinct and readily separable by morphological, behavioral, ecological and DNA sequence data. The Indian lineage seems to have diverged around the middle Pliocene, perhaps some 3.6 million years ago,The estimate in Väli (2006) is certainly incorrect; it uses a molecular clock that is appropriate for small passerines with half the generation times of eagles. from the common ancestor of the lesser and greater spotted eagles. The "proto- spotted eagle" probably lived in the general region of Afghanistan, being split into a northern and a southern lineage when both glaciers and deserts advanced in Central Asia as the last ice age began.
|
|
In algebra, the Jacobson–Bourbaki theorem is a theorem used to extend Galois theory to field extensions that need not be separable. It was introduced by for commutative fields and extended to non-commutative fields by , and who credited the result to unpublished work by Nicolas Bourbaki. The extension of Galois theory to normal extensions is called the Jacobson–Bourbaki correspondence, which replaces the correspondence between some subfields of a field and some subgroups of a Galois group by a correspondence between some sub division rings of a division ring and some subalgebras of an algebra. The Jacobson–Bourbaki theorem implies both the usual Galois correspondence for subfields of a Galois extension, and Jacobson's Galois correspondence for subfields of a purely inseparable extension of exponent at most 1.
|
|
These hardness results extend to games given by hedonic coalition nets. While Nash- and individually stable outcomes are guaranteed to exist for symmetric additively separable hedonic games, finding one can still be hard if the valuations v_i(j) are given in binary; the problem is PLS- complete. For the stable marriage problem, a core-stable outcome can be found in polynomial time using the deferred acceptance algorithm; for the stable roommates problem, the existence of a core-stable outcome can be decided in polynomial time if preferences are strict, but the problem is NP-complete if preference ties are allowed. Hedonic games with preferences based on the worst player behave very similarly to stable roommates problems with respect to the core, but there are hardness results for other solution concepts.
|
|
The Big Five was a series of biological weapons developed by the United States Army Chemical Corps' Special Operations Division (SOD) at Fort Detrick Biological Warfare Laboratory (BWL) for use by special forces. These weapons were developed in the 1950s and 1960s, and were eventually destroyed when the United States unilaterally ended its offensive biological warfare program. The weapons were - M1 Biodart (E1) A 7.62mm rifle cartridge with a sabot surrounding a flechette with exterior grooves filled with either botulinum toxin A (XR), saxitoxin (TZ), or possibly a combination of the two. There were 4,450 filled and 5,315 unfilled M1s in the arsenal at the time of its destruction. M2 Separable Bullet (E2) A 7.62mm rifle cartridge with a hollow metal bullet containing dry-type botulinum toxin A (XR), or a simulant.
|
|
The latter practice illustrates the Imperial genius as innate to its holder but separable from him as a focus of respect and cult, formally consistent with cult to the personification of ideas and ideals such as Fortune (Fortuna), peace (Pax) or victory (Victoria) et al. in conjunction with the genius of the Emperor, Senate or Roman people; Julius Caesar had showed his affinity with the virtue of clemency (Clementia), a personal quality associated with his divine ancestor and patron goddess Venus. Priests typically and respectfully identified their function by manifesting the appearance and other properties of their deus. The duties of Imperial priests were both religious and magistral: they included the provision of approved Imperial portraits, statues and sacrifice, the institution of regular calendrical cult and the inauguration of public works, Imperial games (state ludi) and munera to authorised models.
|
|
Other work, with Hugh Catts and colleagues, examined overlapping language profiles of children identified with dyslexia and those identified with SLI; their research identified a high rate of comorbidity between these developmental disorders. In another study, they compared the language development trajectories of 8th graders identified as having impairments in either reading comprehension or decoding skills, which include the ability to recognize the basic sounds that make up words and map sounds onto letters. At kindergarten, 2nd, and 4th grade, the children with poor reading comprehension had shown deficits in linguistic comprehension whereas the children with poor decoding skills had shown deficits in phonological processing. The distinct patterns of impaired skills in the two groups provided support for the simple view of reading, which proposes that reading is dependent on separable skills of decoding and linguistic comprehension.
|
|
Single-layer perceptrons are only capable of learning linearly separable patterns; in 1969 in a famous monograph entitled Perceptrons, Marvin Minsky and Seymour Papert showed that it was impossible for a single-layer perceptron network to learn an XOR function (nonetheless, it was known that multi-layer perceptrons are capable of producing any possible boolean function). Although a single threshold unit is quite limited in its computational power, it has been shown that networks of parallel threshold units can approximate any continuous function from a compact interval of the real numbers into the interval [-1,1]. This result can be found in Peter Auer, Harald Burgsteiner and Wolfgang Maass "A learning rule for very simple universal approximators consisting of a single layer of perceptrons". A single-layer neural network can compute a continuous output instead of a step function.
|
|
For finite dimensional H, this group would be a complex general linear group and not at all contractible. In fact it is homotopy equivalent to its maximal compact subgroup, the unitary group U of H. The proof that the complex general linear group and unitary group have the same homotopy type is by the Gram-Schmidt process, or through the matrix polar decomposition, and carries over to the infinite-dimensional case of separable Hilbert space, basically because the space of upper triangular matrices is contractible as can be seen quite explicitly. The underlying phenomenon is that passing to infinitely many dimensions causes much of the topological complexity of the unitary groups to vanish; but see the section on Bott's unitary group, where the passage to infinity is more constrained, and the resulting group has non-trivial homotopy groups.
|
|
Gomphidius subroseus, family Gomphidiaceae The order Boletales originally was erected to describe boletes, but based on micromorphological and molecular phylogenetic characteristics, a large number of nonbolete species have recently been established to belong to this group, as well. The order also includes some gilled mushrooms, in the families Gomphidiaceae, Serpulaceae, Tapinellaceae, Hygrophoropsidaceae, and Paxillaceae, which often have the same flesh texture as the boletes, spore-bearing tissue which is also easily separable from the cap, and similar microscopic characteristics of spores and cystidia. Taxonomic studies using secondary metabolites and later molecular phylogenetic evidence moved several physically dissimilar groups into Boletales, including the Sclerodermataceae (earthballs) and the Rhizopogonaceae (false truffles). Phylogenetic analyses shows the Sclerodermataceae, Boletinellaceae and Gyroporaceae appear to form a discrete group within the Boletales, and together with the Pisolithaceae, and the Astraceae, are grouped under the suborder Sclerodermatineae.
|
|
Consider the optimized case where a row of signal data can fit entirely within the processor's cache. This particular processor would be able to access the data row-wise efficiently, but not column-wise since different data operands in the same column would lie on different cache lines. In order to take advantage of the way in which memory is accessed, it is more efficient to transpose the data set and then axis it row-wise rather than attempt to access it column-wise. The algorithm then becomes: # Separate the separable two-dimensional signal h(n_1,n_2) into two one-dimensional signals h_1(n_1) and h_2(n_2) # Perform row-wise convolution on the horizontal components of the signal x(n_1,n_2) using h_1(n_1) to obtain g(n_1,n_2) # Transpose the vertical components of the signal g(n_1,n_2) resulting from Step 2.
|
|
This follows as K(α) is K-isomorphic to K(β) by irreducibility of the minimal polynomial, and any isomorphism of fields F and F that maps polynomial p to p can be extended to an isomorphism of the splitting fields of p over F and p over F, respectively. In summary, the conjugate elements of α are found, in any normal extension L of K that contains K(α), as the set of elements g(α) for g in Aut(L/K). The number of repeats in that list of each element is the separable degree [L:K(α)]sep. A theorem of Kronecker states that if α is a nonzero algebraic integer such that α and all of its conjugates in the complex numbers have absolute value at most 1, then α is a root of unity.
|
|
Another criticism of Cardona's work has come from Szemerényi: his review of Cardona's Haplology in Indo- European centers primarily on the volume's thinness of "substance", as well as its physical thinness. As far as the "substance" of the volume goes, Szemerényi starts straight away by singling out Cardona's dictum that "haplology is not essentially separable from regular sound change amenable to formulation in terms of what are called sound laws". The majority of the review goes on to criticize this thesis as untenable because of its insensitivity to an essential difference between what Szemerényi contends are two different types of sound change governing the realization of haplology: 1) regular group-changes and 2) irregular (sporadic) group-changes. The former, Szemerényi specifies, "cover general[ized] rules of assimilation and dissimilation", for instance the dissimilation of the sequence l-l to l-r in Latin.
|
|
The most significant change was the switch from fully bonded construction to the use of bolt fasteners to attach the fibreglass body to the backbone steel frame. While reducing the torsional and flexural stiffneses somewhat, the use of a separable body was welcomed by the automotive insurance industry as it greatly reduced the complexity and cost of making repairs to the vehicle. Early examples of the S2 were externally almost identical to the S1 with the exception of the new windows. From early 1969, secondary front indicator lamp nacelles were added between the headlights, and larger door handles were used in place of the S1's push-button items. During 1968 a number of Europas (and Elans) were produced bearing black-and-silver Lotus badges on the nose and steering wheel in place of the customary yellow- and-green ones.
|
|
"Am I copyrightable?" The Harvard Law Review felt Star Athletica was an important step towards removing subjectivity from the tests in this area of the law, such as by removing the framing problem that changed the outcome of the analysis based on how the usefulness of the article was defined, evidenced by Judge McKeague. However, the Review worried that the decision may not fully resolve conflicting lower court rulings because the conflicting majority and dissent were both based on close readings of the statute without enough clearly differentiating examples in the majority to completely discredit the alternative view. A potential contradiction in Thomas's majority opinion may not help on that front that perception; specifically, the assertion that surface designs are "inherently separable" from useful articles without being useful articles themselves and the assertion that other clothing bearing the design do not conjure the original useful article.
|
|
The name of the press comes from Leavis' self-positioning as a literary critic upholding a minority – rather than a mass culture – stance; against an "anything goes" pluralism. Leavis wrote that > The potentialities of human experience in any age are realised by only a > tiny minority, and the important poet is important because he belongs to > this (and has also, of course, the power of communication) ... Almost all of > us live by routine, and are not fully aware of what we feel; or, if that > seems paradoxical, we do not express to ourselves an account of our > possibilities of experience ... The poet is unusually sensitive, unusually > aware, more sincere and more himself than the ordinary man can be. He knows > what he feels and knows what he is interested in. He is a poet because his > interest in his experience is not separable from his interest in words.
|
|
Separators have been used as part of data compression algorithms for representing planar graphs and other separable graphs using a small number of bits. The basic principle of these algorithms is to choose a number k and repeatedly subdivide the given planar graph using separators into O(n/k) subgraphs of size at most k, with O(n/√k) vertices in the separators. With an appropriate choice of k (at most proportional to the logarithm of n) the number of non-isomorphic k-vertex planar subgraphs is significantly less than the number of subgraphs in the decomposition, so the graph can be compressed by constructing a table of all the possible non-isomorphic subgraphs and representing each subgraph in the separator decomposition by its index into the table. The remainder of the graph, formed by the separator vertices, may be represented explicitly or by using a recursive version of the same data structure.
|
|
One theory posed to explain these phenomena proposes that the brain has separable neural "premotor" or "agency" systems for managing the process of transforming intentions into overt action. An anteromedial frontal premotor system is engaged in the process of directing exploratory actions based on "internal" drive by releasing or reducing inhibitory control over such actions. A recent paper reporting on neuronal unit recording in the medial frontal cortex in human subjects showed a clear pre-activation of neurons identified in this area up to several hundred milliseconds prior to the onset of an overt self- generated finger movement and the authors were able to develop a computational model whereby volition emerges once a change in internally generated firing rate of neuronal assemblies in this part of the brain crossed a threshold. Damage to this anteromedial premotor system produces disinhibition and release of such exploratory and object acquisition actions which then occur autonomously.
|
|
The utility of this observation is that although in general not every polynomial of degree n in R[x] has n roots counting multiplicity (this is the maximum, by the above theorem), we may pass to field extensions in which this is true (namely, algebraic closures). Once we do, we may uncover a multiple root that was not a root at all simply over R. For example, if R is the field with three elements, the polynomial :f(x)\,=\,x^6 + 1 has no roots in R; however, its formal derivative is zero since 3 = 0 in R and in any extension of R, so when we pass to the algebraic closure it has a multiple root that could not have been detected by factorization in R itself. Thus, formal differentiation allows an effective notion of multiplicity. This is important in Galois theory, where the distinction is made between separable field extensions (defined by polynomials with no multiple roots) and inseparable ones.
|
|
There is also difficulty with trying to determine whether the common sense is truly separable from the individual sense perceptions and from imagination, in anything other than a conceptual way as a capability. Aristotle never fully spells out the relationship between the common sense and the imaginative faculty (, ), although the two clearly work together in animals, and not only humans, for example in order to enable a perception of time. They may even be the same. Despite hints by Aristotle himself that they were united, early commentators such as Alexander of Aphrodisias and Al-Farabi felt they were distinct, but later, Avicenna emphasized the link, influencing future authors including Christian philosophers.. argues that Aristotle used the term "common sense" both to discuss the individual senses when these act as a unity, which Gregorić calls "the perceptual capacity of the soul", or the higher level "sensory capacity of the soul" that represents the senses and the imagination working as a unity.
|
|
However the courts overturned these decisions in two leading cases. In Re Brumark Investments Ltd[2001] UKPC 28 the Privy Council advised that a charge in favour of Westpac bank that purported to separate uncollected debts (where a charge was said to be fixed) and the proceeds (where the charge was said to be floating) could not be deemed separable: the distinction made no commercial sense because the only value in uncollected debts are the proceeds, and so the charge would have to be the same over both.[2001] UKPC 28, [46] In Re Spectrum Plus Ltd,[2005] UKHL 41 the House of Lords finally decided that because the hallmark of a floating charge is that a company is free to deal with the charged assets in the ordinary course of business, any charge purported to be "fixed" over book debts kept in any account except one which a bank restricts the use of, must be in substance a floating charge.
|
|
Of > course, to make possible such constancy it is also necessary that this > content be organized, not only through relatively fixed association but also > with the aid of the rules of logic, and of our basic categories of space, > time, causality, universality, etc. ... there will be a strong background of > recurrent, stable, and separable features, against which the transitory and > changing aspects of the unbroken flow of experience will be seen as fleeting > impressions that tend to be arranged and ordered mainly in terms of the vast > totality of the relatively static and fragmented content of [memories]. Bohm also claimed that "as with consciousness, each moment has a certain explicate order, and in addition it enfolds all the others, though in its own way. So the relationship of each moment in the whole to all the others is implied by its total content: the way in which it 'holds' all the others enfolded within it".
|
|
The B series test program took a considerable amount of delays and frustration, not in the least because the Atlas B was far more complicated than the prototype Atlas A, in fact the first launch would feature all hardware systems found on an operational Atlas, including the sustainer engine, separable booster section, guidance computer, Azusa tracking system, detachable nose cone, and more. The first flight article missile, 3B, was originally planned for launch in May 1958, but the date was set back by endless hardware difficulties, both with the missile itself and the newly opened LC-11. In addition, Atlas 3B could not be cleared for flight until a successful firing run of Missile 2B was performed at the Sycamore Canyon test stand, which was also experiencing nonstop technical issues. The launch of a third Soviet satellite in April also put further pressure on program planners. Finally, on July 19, Missile 3B was launched.
|
|
Although it was important to her because she believed fashion designers deserved to restrict their valuable designs with copyright, she didn't think it would change things for designers because it was based on the language of the preexisting statute. On March 31, 2017, Puma sued Forever 21 for a number of alleged violations of Puma's intellectual property rights. Puma based the copyright infringement portion of their case on the nine-day-old precedent and said that various Forever 21 shoes included copyrighted elements of similar Puma products. Forever 21, a supplier of knock-offs, had been sued for copyright infringement in the past, but this was among the first times that a company used the argument that, in the case of Puma's Fenty Fur Slides, their "wide plush fur strap extending to the base of the sandal" was capable of being represented in another tangible medium, and therefore covered by copyright as separable from the shoe itself.
|
|
The full text (using a slightly different translation to the book) is as follows: :Among Prerogative Instances I will put in the fourteenth place Instances of the Fingerpost, borrowing the term from the fingerposts which are set up where roads part, to indicate the several directions. These I also call Decisive and Judicial, and in some cases, Oracular and Commanding Instances. I explain them thus. When in the investigation of any nature the understanding is so balanced as to be uncertain to which of two or more natures the cause of the nature in question should be assigned on account of the frequent and ordinary concurrence of many natures, instances of the fingerpost show the union of one of the natures with the nature in question to be sure and indissoluble, of the other to be varied and separable; and thus the question is decided, and the former nature is admitted as the cause, while the latter is dismissed and rejected.
|
|
However, it is still not clear whether lower-order control processors are differentially affected by impairments in higher-order control when between-level interactions are required to complete a task, or whether there are feedback influences of lower-level on higher-level control (Bedre, Hoffman, Cooney & D'Esposito 2009). Botvinik (2008) found that all existing models of hierarchically structured behavior share at least one general assumption – that the hierarchical, part–whole organization of human action is mirrored in the internal or neural representations underlying it. Specifically, the assumption is that there exist representations not only of low-level motor behaviors, but also separable representations of higher-level behavioral units. The latest crop of models provides new insights, but also poses new or refined questions for empirical research, including how abstract action representations emerge through learning, how they interact with different modes of action control, and how they sort out within the prefrontal cortex (PFC).
|
|
The Floridian population, which occurs approximately south of Tampa, is separated as the nominate subspecies Anas fulvigula fulvigula and is occasionally called the Florida mottled duck or Florida mallard. It differs from the other subspecies, the Gulf Coast mottled duck (A. f. maculosa) (etymology: maculosa, Latin for "the mottled one"), by being somewhat lighter in color and less heavily marked; while both subspecies are intermediate between female mallards and American black ducks, the Florida mottled duck is closer to the former and the Gulf Coast mottled duck closer to the latter in appearance; this is mainly recognizable in the lighter head being quite clearly separated from the darker breast in Gulf Coast mottled ducks, but much less so in Florida mottled ducks. As the subspecies' ranges do not overlap, these birds can only be confused with female mallards and American black ducks however; particularly female American black ducks are often only reliably separable by their dark purple speculum from mottled ducks in the field.
|
|
The reverence of the Amesha Spenta and the Yazatas has been frequently attacked by non- Zoroastrian sources for its polytheist nature, not only in modern times but also the Sassanid era. While the "worship of the elements" was a repeated accusation during the 4th and 5th centuries, Christian missionaries (such as John Wilson) in 19th-century India specifically targeted the immanence of the Amesha Spenta as indicative of (in their view) a Zoroastrian polytheistic tradition worthy of attack. pp. 182ff. A frequent target for criticism was the Zoroastrian credo in which the adherent declares, "I profess to be a worshiper of Mazda, follower of the teachings of Zoroaster,... one who praises and reveres the Amesha Spenta" (the Fravaraneh, Yasna 12.1). Some modern Zoroastrian theologians, especially those identifying with the Reformist school of thought, believe that ethereal spirit and physical manifestation are not separable in any sense and that a reverence of any of Ahura Mazda's creations is ultimately a worship of the Creator.
|
|
The beginning of the essential declaration of belief for Christians, the Nicene Creed (somewhat equivalent to Maimonides' 13 principles of Faith), starts with the Shema influenced declaration that "We Believe in One God..." Like Judaism, Christianity asserts the absolute monotheism of God. Unlike the Zohar, Christianity interprets the coming of the Messiah as the arrival of the true immanence of God. Like the Zohar the Messiah is believed to be the bringer of Divine Light: "The Light (the Messiah) shineth in the Darkness and the Darkness has never put it out", yet the Light, although being God, is separable within God since no one has seen God in flesh: "for no man has seen God..." (John 1). It is through the belief that Jesus Christ is the Messiah, since God had vindicated him by raising him from the dead, that Christians believe that Jesus is paradoxically and substantially God, despite God's simple undivided unity.
|
|
In orbit around the orange subgiant star HD 177830 is one of the earliest exoplanets to be detected. A jovian-mass planet, it orbits in an eccentric orbit with a period of 390 days. A second planet closer to the star was discovered in 2011. Visible to the naked eye are HD 173416, a yellow giant hosting a planet over twice the mass of Jupiter discovered in 2009; and HD 176051, a low-mass binary star containing another high-mass planet. Just short of naked-eye visibility is HD 178911, a triple system consisting of a close binary and a visually separable sunlike star. The sunlike star has a planet with over 6 Jupiter masses discovered in 2001, the second found in a triple system after that of 16 Cygni. One of the most-studied exoplanets in the night sky is TrES-1b, in orbit around the star GSC 02652-01324. Detected from a transit of its parent star, the planet has around 3/4 the mass of Jupiter, yet orbits its parent star in only three days.
|
|
Given a base scheme S, an algebraic torus over S is defined to be a group scheme over S that is fpqc locally isomorphic to a finite product of copies of the multiplicative group scheme Gm/S over S. In other words, there exists a faithfully flat map X → S such that any point in X has a quasi- compact open neighborhood U whose image is an open affine subscheme of S, such that base change to U yields a finite product of copies of GL1,U = Gm/U. One particularly important case is when S is the spectrum of a field K, making a torus over S an algebraic group whose extension to some finite separable extension L is a finite product of copies of Gm/L. In general, the multiplicity of this product (i.e., the dimension of the scheme) is called the rank of the torus, and it is a locally constant function on S. Most notions defined for tori over fields carry to this more general setting.
|
|
With family cat Fred about 1966 The Born rule states that an observable property of a quantum system is defined by a Hermitian operator on a separable Hilbert space, that the only observable values of the property are the eigenvalues of the operator, and that the probability of the system being observed in a particular eigenvalue is the square of the absolute value of the complex number obtained by projecting the state vector (a point in the Hilbert space) onto the corresponding eigenvector. George Mackey had asked whether Born's rule is a necessary consequence of a particular set of axioms for quantum mechanics, and more specifically whether every measure on the lattice of projections of a Hilbert space can be defined by a positive operator with unit trace. Though Richard Kadison proved this was false for two-dimensional Hilbert spaces, Gleason's theorem (published 1957) shows it to be true for higher dimensions. Gleason's theorem implies the nonexistence of certain types of hidden variable theories for quantum mechanics, strengthening a previous argument of John von Neumann.
|
|
Ahmadis universally concur in the belief that Ghulam Ahmad was both the promised Mahdi and Messiah foretold by Muhammad to appear in the end times, and that his prophetic qualities were neither independent nor separable from those of Muhammad. What this entailed theologically, however, became an issue of contention within the early Ahmadiyya movement. Muhammad Ali held that the type of prophecy described by Ghulam Ahmad in reference to himself did not make him a prophet in the technical sense of the word as used in Islamic terminology, amounted to nothing more than sainthood (walāya) and that Islamic mystics preceding Ghulam Ahmad had similarly described experiences of prophecy within Islam in the context of their relationship with Muhammad."The Issue of Khatam-un-Nabiyyin", The Lahore Ahmadiyya Movement Unlike the majority Muslim belief which expects the physical return of Jesus, the Lahore Ahmadiyya affirm the absolute cessation of prophethood, and believe that no prophet can appear after Muhammad, neither a past one like Jesus, nor a new one.
|
|
In physics, the no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state, a statement which has profound implications in the field of quantum computing among others. The theorem is an evolution of the 1970 no-go theorem authored by James Park, in which he demonstrates that a non-disturbing measurement scheme which is both simple and perfect cannot exist (the same result would be independently derived in 1982 by Wootters and Zurek as well as Dieks the same year). One should note that the aforementioned theorems do not preclude the state of one system becoming entangled with the state of another as cloning specifically refers to the creation of a separable state with identical factors. For example, one might use the controlled NOT gate and the Walsh–Hadamard gate to entangle two qubits without violating the no-cloning theorem as no well-defined state may be defined in terms of a subsystem of an entangled state.
|
|
The Atkinson–Stiglitz theorem is a theorem of public economics which states "that, where the utility function is separable between labor and all commodities, no indirect taxes need be employed" if non-linear income taxation can be used by the government and was developed in a seminal article by Joseph Stiglitz and Anthony Atkinson in 1976. The Atkinson–Stiglitz theorem is generally considered to be one of the most important theoretical results in public economics and spawned a broad literature which delimited the conditions under which the theorem holds, e.g. Saez (2002) which showed that the Atkinson–Stiglitz theorem does not hold if households have heterogeneous rather than homogeneous preferences. In practice the Atkinson–Stiglitz theorem has often been invoked in the debate on optimal capital income taxation: Because capital income taxation can be interpreted as the taxation of future consumption in excess of the taxation of present consumption, the theorem implies that governments should abstain from capital income taxation if non- linear income taxation is an option since capital income taxation would not improve equity by comparison to the non-linear income tax, while additionally distorting savings.
|
|
He also denied that pleasure is the sole good, maintaining instead (with T.H. Green) that experiences are good as wholes and that pleasure is not, strictly speaking, a separable element within such wholes. Disagreeing with G.E. Moore that the "naturalistic fallacy" is really a fallacy, he gave an entirely naturalistic analysis of goodness, holding that an experience is intrinsically good to the degree that it (a) fulfills an impulse or drive and (b) generates a feeling- tone of satisfaction attendant upon such fulfillment. He regarded the first of these factors as by far the more important and held that the major intrinsic goods of human experience answer to the basic drives of human nature; he maintained that these two factors together provide not merely a criterion for but the actual meaning of intrinsic goodness. (He defined all other ethical terms, including "right", in terms of intrinsic goodness, a right act, for example, being that act which tends to produce the greatest amount of intrinsic goodness under the relevant circumstances.) The little that Blanshard wrote on political theory (mainly in Reason and Goodness) owed much to Green and Bosanquet.
|
|
The church, true to her commission, has always asserted the unity and indissolubility of marriage, the relative rights and duties of husband, wife, and children; she has also maintained that, the natural contract in marriage having been raised to the dignity of a sacrament, these two are henceforth one and the same thing so that there cannot be a marriage contract amongst Christians which is not a sacrament. Hence, while admitting the right of civil authority to regulate the civil concerns and consequences of marriage, the church has always claimed exclusive authority over the marriage contract and its essentials, since it is a sacrament. The encyclical shows by the light of history that for centuries the church exercised, and the civil power admitted, that authority. But human weakness and wilfulness began to throw off the bridle of Christian discipline in family life; civil rulers began to disown the authority of the church over the marriage tie; and rationalism sought to sustain them by establishing the principle that the marriage contract is not a sacrament at all, or at least that the natural contract and the sacrament are separable and distinct things.
|
|
For a phenomenology undertaken within the natural attitude, meaning does not inherently accrue to an object as a thing-in-itself, is not an "add- on" to the object (a label), and is not separable from the object as constituted by the intending subject in the act of meaning constitution. For phenomenology, the meaning and the object (in its "materiality") are co- constituted in the intending of the object by the subject—phenomenologically speaking there are only meaningful objects. There is no such thing as a neutrally valued object, or a meaningless object, and the notion of an object as "nonsense" is itself a meaningful determination - as the existentialists would say, we are condemned to meaning. Note that, because we as observers have already been born into an already-existing social world that is already pre-interpreted - through both social meanings and through architectural and business intentionality - and 'made meaningful-to-us' as an intersubjectively available "entity", any proposal that the subject is creating the object, or creating the meaning of the object as an individual achievement in a particular situation is a misrepresentation of what is actually taking place.
|
|
The following examples show how tensor products arise naturally. Given two measure spaces X and Y, with measures \mu and u respectively, one may look at L^2(X\times Y), the space of functions on X\times Y that are square integrable with respect to the product measure \mu\times u. If f is a square integrable function on X, and g is a square integrable function on Y, then we can define a function h on X\times Y by h(x,y)=f(x)g(y). The definition of the product measure ensures that all functions of this form are square integrable, so this defines a bilinear mapping L^2(X)\times L^2(Y)\to L^2(X\times Y). Linear combinations of functions of the form f(x)g(y) are also in L^2(X\times Y). It turns out that the set of linear combinations is in fact dense in L^2(X\times Y), if L^2(X) and L^2(Y) are separable. This shows that L^2(X)\otimes L^2(Y) is isomorphic to L^2(X\times Y), and it also explains why we need to take the completion in the construction of the Hilbert space tensor product.
|
|
Moreover, in characteristic 2 there are additional possibilities arising not from exceptional isogenies but rather from the fact that for simply connected type C (I.e., symplectic groups) there are roots that are divisible (by 2) in the weight lattice; this gives rise to examples whose root system (over a separable closure of the ground field) is non- reduced; such examples exist with a split maximal torus and an irreducible non-reduced root system of any positive rank over every imperfect field of characteristic 2. The classification in characteristic 3 is as complete as in larger characteristics, but in characteristic 2 the classification is most complete when [k:k^2]=2 (due to complications caused by the examples with a non-reduced root system, as well as phenomena related to certain regular degenerate quadratic forms that can only exist when [k:k^2]>2). Subsequent work of , building on additional material included in the second edition , completes the classification in characteristic 2 up to a controlled central extension by providing an exhaustive array of additional constructions that only exist when [k:k^2]>2 , ultimately resting on a notion of special orthogonal group attached to regular but degenerate and not fully defective quadratic spaces in characteristic 2.
|
|