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"congruence" Definitions
  1. (formal) agreement with something; the state of being similar to something and not in conflict with it synonym compatibility
  2. (geometry) the quality of having the same size and shape

600 Sentences With "congruence"

How to use congruence in a sentence? Find typical usage patterns (collocations)/phrases/context for "congruence" and check conjugation/comparative form for "congruence". Mastering all the usages of "congruence" from sentence examples published by news publications.

And finally, to validate what you are sensing, consider congruence.
It's the congruence of intelligent people bouncing ideas off each other.
It was the weird congruence in team philosophies that was striking.
Such congruence creates alpha waves in the brains — the neural resonance of relaxation.
I've seen enough congruence between what the two sides are trying to accomplish.
In fact, what mattered most to me was congruence between my mind and body.
More now, in these times that it seems there's no respect or congruence in anything.
At the close, there's a fugue-like absence where there should be congruence and meaning.
Through this exercise, I've noticed my left eye droops in congruence to my lack of sleep.
Yet the Holocaust has unavoidable international dimensions—lines of influence, circles of complicity, moments of congruence.
If anything, this recent food bank reveals a massive lack of congruence between National Action's varied tactics.
Obviously, there are left-wing extremists but there is no congruence between the far-left and the alt-right.
I'll address that in part 2, in which I discuss the congruence between presidents and the justices they appoint.
It's a very sound relationship that's based on the basic strategic congruence of views, about the world, about the region.
"Obviously, there are left-wing extremists, but there is no congruence between the far-left and the alt-right," Segal said.
This formal congruence between dance and sport still doesn't explain why Quevedo renders most of his diagrams in a maximalist aesthetic.
Nine of the 10 most nefarious offenders fall east of the Mississippi River — and the largest congruence is in the East Coast.
"It's a very sound relationship that's based on the basic strategic congruence of views, about the world, about the region," Lee said.
I stuck to my guns because think there's a congruence between Islamic values as Christian values, which the party is based on.
To find the congruence requires a long, and at times frustrating, journey, to what some call Mexico profundo—the country's ancient roots.
The route of travel could have been via the inland, coastal route or both — but the congruence of data favors the inland route.
Examining these periods of time, it became clear there was a congruence between periods of increased unemployment and more frequent episodes of school shootings.
The increasing congruence of ideology and partisanship has so sharpened the divide that 9 in 10 Democrats and Republicans now routinely back their party's nominee.
In that silence, as you uncover the points of congruence, so too do you uncover Halliday's beautiful argument about the pleasure and obligations of fiction.
Some Muslim Republicans see the GOP as a venue for preserving their values and norms, which are more in congruence with the Republican than Democratic Party.
It is the second 55 second snippet they have shared through the playlist, replacing the previous fragment yet maintaining stylistic congruence with its ambient-leaning tone.
It felt very much like a congruence that was allowing this sort of miraculous thing to happen," they continue, "even though, as I said, it was coincidence.
As such, both of their artistic practices are perverse in their simultaneous insistence on the utter ideals of abstraction and an absolute congruence between ideas and representations.
But as the play turns more serious in the last third, finally revealing what happened in New York, the congruence of form and function begins to fray.
We see a continuing focus on sectors that are a natural complement to what this region does well – technology, life sciences, and particularly, the congruence of the two.
And yet, because the discursive circuit is so furiously closed, there is a sense in which the show's boundaries come into congruence with those of the broader world.
But deposed Fox CEO Roger Ailes is a unique case because of the congruence between the gender ideals promoted on camera and the allegations about his behavior off camera.
Each scene has its own specific energy and tone, conjured by a happy congruence of skillfully vivid acting, naturalistic conversations and a cinematographer, Wyatt Garfield, with a clear grasp of mood.
It says something about the strange congruence between the libertarian moment and the politics of 2018 that the C.I.A. chief Paul filibustered five years ago, John Brennan, is now a furious Trump critic.
"I had gotten the idea about the mattresses around the same time, and I wasn't even that aware that there would be a congruence of the voice-over and the actions," Ms. Rainer said.
Ross Douthat Opinion Columnist In almost every opinion on the restaurant that famously refused to serve Sarah Huckabee Sanders, there is a too-neat congruence between the moral argument and the meta-political argument.
Byron Wien, vice chairman at Blackstone and a 50-year veteran of Wall Street, pointed out Wednesday there has been a "strong congruence" between the Federal Reserve's balance sheet expansion and the 's rise since 2009.
Alignment is the congruence of who you are, what you feel, and what you love on a deep and fundamental level with what you do, what you say, what you envision, and where you are going.
And as smart devices become more incorporated into our homes and workplaces via gadgets like smart speakers, TVs, and even doorbells, that congruence is going be a huge deciding factor for consumers in the years to come.
That win would line up the geographical congruence that is sometimes evident between state and winning movie: Sweet Home Alabama won in Alabama, Sleepless in Seattle won in Washington, and the very SoCal Clueless won in California.
The obvious barrier is organized labor and given Democrats' congruence with unions on many other issues and their reliance on union campaign contributions, as well as simple inertia, getting Democrats to embrace free trade will entail overcoming union opposition.
The production techniques used in execution videos produced in Libya were so similar to ones emerging from Syria that some experts theorized that the Islamic State must have dispatched a cameraman from Syria to Libya to achieve that congruence.
He sought a criticism that would be "less royal"; that is, less prone to unsupported authoritative pronouncements based on highly partial narratives of historical development (or what he called "drastic simplificatory strategies to reduce the hectic scene to congruence").
As Rogowski put it: High levels of ideological conflict lead partisan voters to make decisions that place increased emphasis on their partisan ties, and less emphasis on the relative degree of congruence between their policy views and the candidates' platforms.
But there is a curious congruence between the smiling nihilism of the 2016 Berlin Biennale and the aloof refusal of this year's: Neither offers enough of a positive vision of what an art exhibition, and what art itself, might actually be for.
Yiadom-Boakye often cites the unfashionable British painter Walter Sickert as an influence, and it is perhaps here that the congruence occurs: Virginia Woolf was also an admirer of Sickert, and published a monograph about him; Vanessa, her sister, illustrated the cover.
And are you able to really find a way to see the congruence in running our laws to protect competition and consumers with this new industry, these new industries, that operate and look very different from the old industries that were here before.
Then in the general election it was possible to argue that the latter groups only came around to Trump reluctantly, out of fear of contemporary liberalism's anticlerical streak, and that their relationship to his identitarian nationalism was transactional and didn't reflect any deep congruence.
In addition, the level of congruence between presidential approval and the House vote (for the president's party if approving, for the other party if disapproving) in both pre-election polls and the one postelection poll now available is the highest on record, over 90 percent.
For the broader dimensions of her traumatic life and fierce courage, readers might turn to Hayden Herrera's 1983 biography, "Frida," published before Fridamania attained its current frenzy — a phenomenon owing in no small part to her art's congruence with current ideas about gender politics and cultural identity.
But it took Crammed Discs schemer Vincent Kenis to alert me to the obvious: just as soukous's rippling polyrhythms once migrated south from Congo, there's a congruence between the modern Lusaka sound and the unforgiving attack of Kinshasa's 21st-century street bands—the much-missed Staff Benda Bilili and the self-renewing Konono No. 1.
The implicit argument behind the Gilens/Page paper, and of Gilens's book Affluence and Influence, is that in a democracy, there should be strong congruence between policy outcomes and the opinions of the American middle class — or, at the very least, between policy outcomes and the views of the American public as a whole.
It turns out that barbed congruence coincides with the congruence induced by early bisimilarity.
In number theory, a congruence of squares is a congruence commonly used in integer factorization algorithms.
The lattice Con(A) of all congruence relations on an algebra A is algebraic. John M. Howie described how semigroup theory illustrates congruence relations in universal algebra: :In a group a congruence is determined if we know a single congruence class, in particular if we know the normal subgroup which is the class containing the identity. Similarly, in a ring a congruence is determined if we know the ideal which is the congruence class containing the zero. In semigroups there is no such fortunate occurrence, and we are therefore faced with the necessity of studying congruences as such.
An important question regarding the algebraic structure of arithmetic groups is the congruence subgroup problem, which asks whether all subgroups of finite index are essentially congruence subgroups. Congruence subgroups of 2×2 matrices are fundamental objects in the classical theory of modular forms; the modern theory of automorphic forms makes a similar use of congruence subgroups in more general arithmetic groups.
In mathematics, the finite lattice representation problem, or finite congruence lattice problem, asks whether every finite lattice is isomorphic to the congruence lattice of some finite algebra.
The plane-triangle congruence theorem angle-angle-side (AAS) does not hold for spherical triangles. As in plane geometry, side-side-angle (SSA) does not imply congruence.
Washington, DC: Taylor & Francis. Resources and deficits co-exist, as conceptualized in the Resource-Congruence Model.Wong, P. T. P. (1993). Effective management of life stress: The resource-congruence model.
In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in the sense that algebraic operations done with equivalent elements will yield equivalent elements.Hungerford, Thomas W.. Algebra. Springer-Verlag, 1974, p. 27 Every congruence relation has a corresponding quotient structure, whose elements are the equivalence classes (or congruence classes) for the relation.
In 1954 Maltsev gave two other conditions that are equivalent to the one given above defining a congruence-permutable variety of algebras. This initiated the study of congruence-permutable varieties.
When a person's vocational interests match his or her work environment types, this is considered congruence. Congruence has been found to predict occupation and college major.Betz, N. (2008). Advances in vocational theories.
In universal algebra, a congruence-permutable algebra is an algebra whose congruences commute under composition. This symmetry has several equivalent characterizations, which lend to the analysis of such algebras. Many familiar varieties of algebras, such as the variety of groups, consist of congruence- permutable algebras, but some, like the variety of lattices, have members that are not congruence-permutable.
In the set of all group congruences on a semigroup S, the minimal element (for the partial order defined by inclusion of sets) need not be the smallest element. In the specific case in which S is an inverse semigroup σ is the smallest congruence on S such that S/σ is a group, that is, if τ is any other congruence on S with S/τ a group, then σ is contained in τ. The congruence σ is called the minimum group congruence on S. The minimum group congruence can be used to give a characterisation of E-unitary inverse semigroups (see below). A congruence ρ on an inverse semigroup S is called idempotent pure if :a\in S, e\in E(S), a\,\rho\,e\Longrightarrow a\in E(S).
Most classical varieties in abstract algebra, such as groups, rings, and Lie algebras are congruence-permutable. Any variety that contains a group operation is congruence-permutable, and the Maltcev term is xy^{-1}z.
This problem should not be confused with the congruence lattice problem.
Given an integer , called a modulus, two integers are said to be congruent modulo , if is a divisor of their difference (i.e., if there is an integer such that ). Congruence modulo is a congruence relation, meaning that it is an equivalence relation that is compatible with the operations of addition, subtraction, and multiplication. Congruence modulo is denoted: :a \equiv b \pmod n.
Like any congruence relation, congruence modulo is an equivalence relation, and the equivalence class of the integer , denoted by , is the set . This set, consisting of all the integers congruent to modulo , is called the congruence class, residue class, or simply residue of the integer modulo . When the modulus is known from the context, that residue may also be denoted .
Congruence and similarity are concepts that describe when two shapes have similar characteristics. In Euclidean geometry, similarity is used to describe objects that have the same shape, while congruence is used to describe objects that are the same in both size and shape. Hilbert, in his work on creating a more rigorous foundation for geometry, treated congruence as an undefined term whose properties are defined by axioms. Congruence and similarity are generalized in transformation geometry, which studies the properties of geometric objects that are preserved by different kinds of transformations.
In algebra, the congruence ideal of a surjective ring homomorphism f : B → C of commutative rings is the image under f of the annihilator of the kernel of f. It is called a congruence ideal because when B is a Hecke algebra and f is a homomorphism corresponding to a modular form, the congruence ideal describes congruences between the modular form of f and other modular forms.
The second congruence is proved similarly, by exchanging the subscripts 1 and 2.
Some representative Rindler observers (navy blue hyperbolic arcs) depicted using the Cartesian chart. The red lines at 45 degrees from the vertical represent the Rindler horizon; the Rindler coordinate system is only defined to the right of this boundary. As with any timelike congruence in any Lorentzian manifold, this congruence has a kinematic decomposition (see Raychaudhuri equation). In this case, the expansion and vorticity of the congruence of Rindler observers vanish.
If this congruence does not hold, then n cannot be prime. Provided GCD(n, Q) = 1 then testing for congruence () is equivalent to augmenting our Lucas test with a "base Q" Solovay–Strassen primality test. Additional congruence conditions that must be satisfied if n is prime are described in Section 6 of. If any of these conditions fails to hold, then we have proved that n is not prime.
The idea is generalized in universal algebra: A congruence relation on an algebra A is a subset of the direct product A × A that is both an equivalence relation on A and a subalgebra of A × A. The kernel of a homomorphism is always a congruence. Indeed, every congruence arises as a kernel. For a given congruence ~ on A, the set A/~ of equivalence classes can be given the structure of an algebra in a natural fashion, the quotient algebra. The function that maps every element of A to its equivalence class is a homomorphism, and the kernel of this homomorphism is ~.
Scriptural validity, to him, stems from its congruence with experiential truth and not vice versa.
A similar trick allows one to speak of kernels in ring theory as ideals instead of congruence relations, and in module theory as submodules instead of congruence relations. A more general situation where this trick is possible is with Omega-groups (in the general sense allowing operators with multiple arity). But this cannot be done with, for example, monoids, so the study of congruence relations plays a more central role in monoid theory.
It is a straightforward exercise to show that, under multiplication, the set of congruence classes modulo n that are coprime to n satisfy the axioms for an abelian group. Indeed, a is coprime to n if and only if . Integers in the same congruence class satisfy , hence one is coprime to n if and only if the other is. Thus the notion of congruence classes modulo n that are coprime to n is well-defined.
In mathematics, a congruence subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. A very simple example would be invertible 2 × 2 integer matrices of determinant 1, in which the off-diagonal entries are even. More generally, the notion of congruence subgroup can be defined for arithmetic subgroups of algebraic groups; that is, those for which we have a notion of 'integral structure' and can define reduction maps modulo an integer. The existence of congruence subgroups in an arithmetic group provides it with a wealth of subgroups, in particular it shows that the group is residually finite.
Then it fixes an m and tries values of i in the right- hand side of the congruence above, in the manner of trial multiplication. It tests to see if the congruence is satisfied for any value of j, using the precomputed values of \alpha^j.
At its roots, geometry consists of a notion of congruence between different objects in a space. In the late 19th century, notions of congruence were typically supplied by the action of a Lie group on space. Lie groups generally act quite rigidly, and so a Cartan geometry is a generalization of this notion of congruence to allow for curvature to be present. The flat Cartan geometries--those with zero curvature--are locally equivalent to homogeneous spaces, hence geometries in the sense of Klein.
The surface's Fuchsian group can be constructed as the principal congruence subgroup of the (2,3,7) triangle group in a suitable tower of principal congruence subgroups. Here the choices of quaternion algebra and Hurwitz quaternion order are described at the triangle group page. Choosing the ideal \langle 2 \rangle in the ring of integers, the corresponding principal congruence subgroup defines this surface of genus 7. Its systole is about 5.796, and the number of systolic loops is 126 according to R. Vogeler's calculations.
RV Coefficient and Congruence Coefficient. In Neil Salkind (Ed.), Encyclopedia of Measurement and Statistics. Thousand Oaks (CA): Sage.
The congruence coefficient is preferred to Pearson's r as a measure of factor similarity, because the latter may produce misleading results. The computation of the congruence coefficient is based on the deviations of factor loadings from zero, whereas r is based on the deviations from the mean of the factor loadings.
A lattice is called algebraic if it is complete and compactly generated. In 1963, Grätzer and Schmidt proved that every algebraic lattice is isomorphic to the congruence lattice of some algebra.G. Grätzer and E. T. Schmidt, Characterizations of congruence lattices of abstract algebras, Acta Sci. Math. (Szeged) 24 (1963), 34–59.
Therefore, spatial or structural congruence comes from not only combining the stimuli but is also determined by our understanding.
The definition of a congruence depends on the type of algebraic structure under consideration. Particular definitions of congruence can be made for groups, rings, vector spaces, modules, semigroups, lattices, and so forth. The common theme is that a congruence is an equivalence relation on an algebraic object that is compatible with the algebraic structure, in the sense that the operations are well-defined on the equivalence classes. For example, a group is an algebraic object consisting of a set together with a single binary operation, satisfying certain axioms. If G is a group with operation \ast, a congruence relation on G is an equivalence relation \equiv on the elements of G satisfying :g_1 \equiv g_2 \ \ \, and \ \ \, h_1 \equiv h_2 \implies g_1 \ast h_1 \equiv g_2 \ast h_2 for all g_1, g_2, h_1, h_2 \in G. For a congruence on a group, the equivalence class containing the identity element is always a normal subgroup, and the other equivalence classes are the cosets of this subgroup.
There is a definitive difference in mood congruence and mood dependence. Lewis and Critchley discuss the difference in these memory effects. Mood congruence is when one can match an emotion to a specific memory. Mood dependence, on the other hand, is the sorting of memory when mood at retrieval is the same as encoding.
For example, with perfect congruence the angle between the factor axes is 0 degrees, and the cosine of 0 is 1.
Viewed as a lattice the chain with three elements is not congruence-permutable and hence neither is the variety of lattices.
In mathematics, a congruence is an equivalence relation on the integers. The following sections list important or interesting prime-related congruences.
Both have similar storylines that fit into an overall chronology and appear to have been written in congruence with each other.
In multivariate statistics, the congruence coefficient is an index of the similarity between factors that have been derived in a factor analysis. It was introduced in 1948 by Cyril Burt who referred to it as unadjusted correlation. It is also called Tucker's congruence coefficient after Ledyard Tucker who popularized the technique. Its values range between -1 and +1.
In general relativity, a congruence (more properly, a congruence of curves) is the set of integral curves of a (nowhere vanishing) vector field in a four- dimensional Lorentzian manifold which is interpreted physically as a model of spacetime. Often this manifold will be taken to be an exact or approximate solution to the Einstein field equation.
Minimal algebra is an important concept in tame congruence theory, a theory that has been developed by Ralph McKenzie and David Hobby .
A plane that satisfies Hilbert's Incidence, Betweeness and Congruence axioms is called a Hilbert plane. Hilbert planes are models of absolute geometry.
This is among the oldest unsolved problems in universal algebra.Joel Berman. Congruence lattices of finite universal algebras. PhD thesis, University of Washington, 1970.
When people maintain stable images of themselves, other members of the organization can count on them to "be" the same person day in and day out and the identity negotiation process can unfold automatically. This may free people to devote their conscious attention to the work at hand, which may explain why researchers have found that groups characterized by high levels of congruence perform better (Swann et al., 2000). Also, just as demographic diversity tends to undermine group performance when congruence is low, diversity improves performance when congruence is high (Polzer, Milton, & Swann, 2003; Swann, Polzer, Seyle, & Ko, 2004).
Congruences are defined on inverse semigroups in exactly the same way as for any other semigroup: a congruence ρ is an equivalence relation that is compatible with semigroup multiplication, i.e., :a\,\rho\,b,\quad c\,\rho\,d\Longrightarrow ac\,\rho\,bd. Of particular interest is the relation \sigma, defined on an inverse semigroup S by :a\,\sigma\,b\Longleftrightarrow there exists a c\in S with c\leq a,b. It can be shown that σ is a congruence and, in fact, it is a group congruence, meaning that the factor semigroup S/σ is a group.
In general, Jónsson terms, more formally, a sequence of Jónsson terms, is a sequence of ternary terms satisfying certain related idenitities. One of the earliest Maltsev condition, a variety is congruence distributive if and only if it has a sequence of Jónsson terms. Originally proved in B. Jónsson, Algebras whose congruence lattices are distributive. Math. Scand., 21:110-121, 1967.
Quartic or biquadratic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x4 ≡ p (mod q) is solvable; the word "reciprocity" comes from the form of some of these theorems, in that they relate the solvability of the congruence x4 ≡ p (mod q) to that of x4 ≡ q (mod p).
402-403 It is their defined relationships that are discussed. Hilbert first enumerates the undefined concepts: point, line, plane, lying on (a relation between points and lines, points and planes, and lines and planes), betweenness, congruence of pairs of points (line segments), and congruence of angles. The axioms unify both the plane geometry and solid geometry of Euclid in a single system.
In: Besters-Dilger, J. et al. (eds.): Congruence in Contact-Induced Language Change: Language Families, Typological Resemblance, and Perceived Similarity. Berlin/Boston, 93-121.
Effective management of life stress: The resource-congruence model. Stress Medicine, 9, 51-60.Wong, P. T. P., Reker, G. T., & Peacock, E. (2006).
If A is played as a normal-play (last- playing winning) impartial game, then the congruence classes of A are in one- to-one correspondence with the nim values that occur in the play of the game (themselves determined by the Sprague–Grundy theorem). In misere play, the congruence classes form a commutative monoid, instead, and it has become known as a misere quotient.
The Supreme Court has held that Congress may do this only if the private remedies it enacts under Section 5 have "congruence and proportionality" to the constitutional wrongs which it seeks to redress.. Without the requisite congruence and proportionality, Congress cannot constitutionally authorize private litigants to recover money damages from the states, although such litigants can sue for equitable relief.See , 374 n.9 (2001) (citing ).
In mathematics, the congruence lattice problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of some other lattice. The problem was posed by Robert P. Dilworth, and for many years it was one of the most famous and long-standing open problems in lattice theory; it had a deep impact on the development of lattice theory itself. The conjecture that every distributive lattice is a congruence lattice is true for all distributive lattices with at most ℵ1 compact elements, but F. Wehrung provided a counterexample for distributive lattices with ℵ2 compact elements using a construction based on Kuratowski's free set theorem.
In a Euclidean system, congruence is fundamental; it is the counterpart of equality for numbers. In analytic geometry, congruence may be defined intuitively thus: two mappings of figures onto one Cartesian coordinate system are congruent if and only if, for any two points in the first mapping, the Euclidean distance between them is equal to the Euclidean distance between the corresponding points in the second mapping. A more formal definition states that two subsets A and B of Euclidean space Rn are called congruent if there exists an isometry f : Rn → Rn (an element of the Euclidean group E(n)) with f(A) = B. Congruence is an equivalence relation.
In 1973, Pierre Deligne and Michael Rapoport showed that the ring of modular forms is finitely generated when is a congruence subgroup of . In 2003, Lev Borisov and Paul Gunnells showed that the ring of modular forms is generated in weight at most 3 when \Gamma is the congruence subgroup \Gamma_1(N) of prime level in using the theory of toric modular forms. In 2014, Nadim Rustom extended the result of Borisov and Gunnells for \Gamma_1(N) to all levels and also demonstrated that the ring of modular forms for the congruence subgroup \Gamma_0(N) is generated in weight at most 6 for some levels . In 2015, John Voight and David Zureick-Brown generalized these results: they proved that the graded ring of modular forms of even weight for any congruence subgroup of is generated in weight at most 6 with relations generated in weight at most 12.
If f:A\, \rightarrow B is a homomorphism between two algebraic structures (such as homomorphism of groups, or a linear map between vector spaces), then the relation R defined by :a_1\, R\, a_2 if and only if f \left(a_1\right) = f\left(a_2\right) is a congruence relation. By the first isomorphism theorem, the image of A under f is a substructure of B isomorphic to the quotient of A by this congruence.
In Euclidean geometry, AAA (Angle-Angle-Angle) (or just AA, since in Euclidean geometry the angles of a triangle add up to 180°) does not provide information regarding the size of the two triangles and hence proves only similarity and not congruence in Euclidean space. However, in spherical geometry and hyperbolic geometry (where the sum of the angles of a triangle varies with size) AAA is sufficient for congruence on a given curvature of surface.
Despite the these disruptions in placement between these two studies, the overall integrity of "Clade 1" and "Clade 2" is in congruence with the clades established from the molecular data.
Such a full relation (obtained by combining partial relations) is called a cycle. Sometimes, forming a cycle from two partial relations leads directly to a congruence of squares, but rarely.
E.T. Schmidt, Zur Charakterisierung der Kongruenzverbände der Verbände, Mat. Casopis Sloven. Akad. Vied. 18 (1968), 3--20. F. Wehrung, A uniform refinement property for congruence lattices, Proc. Amer. Math. Soc.
To avoid complications arising from the presence of singularities, usually one requires the vector field to be nonvanishing. If we add more mathematical structure, our congruence may acquire new significance.
The triple bar symbol (U+2261, LaTeX \equiv) is often used to indicate an identity, a definition (which can also be represented by or ), or a congruence relation in modular arithmetic.
J. Moll. Stud. 67: 215–224.Oliverio M. M. Cervelli, and P. Mariottini. 2002. ITS2 rRNA evolution and its congruence with the phylogeny of muricid neogastropods (Caenogastropoda, Muricoidea) Mol. Phylogenet. Evol.
The genetic landscape of Buergeria robusta presents high congruence to the topography of Taiwan; populations on the eastern and western sides of the Central Mountain Range showed a prominent genetic divergence.
In mathematics, two square matrices A and B over a field are called congruent if there exists an invertible matrix P over the same field such that :PTAP = B where "T" denotes the matrix transpose. Matrix congruence is an equivalence relation. Matrix congruence arises when considering the effect of change of basis on the Gram matrix attached to a bilinear form or quadratic form on a finite-dimensional vector space: two matrices are congruent if and only if they represent the same bilinear form with respect to different bases. Note that Halmos defines congruence in terms of conjugate transpose (with respect to a complex inner product space) rather than transpose, but this definition has not been adopted by most other authors.
Julius Christian Johannes Zeller (24 June 1822, Mühlhausen am Neckar - 31 May 1899, Cannstatt) was a German mathematician. Originally trained in mathematics, geography and theology, in 1874 Zeller became Director of the Seminary in Markgröningen and a girls' orphanage. In 1882 he became a member of the Société Mathématique de France. The following year, on 16 March 1883, he delivered a short account of his congruence relation (Zeller's congruence), which was published in the society's journal.
Another research article examined the influence of different opinion climates in online forums (opinion congruence with the majority of forum participants vs. website source) and found personal opinion congruence was more influential than the online site in which the forum is situated in. Gonzenbach and Nekmat said it might be worth researching whether the factors in these studies or other factors cause people to be more comfortable when it comes to speaking their mind while online.
Wieferich primes can be defined by other equivalent congruences. If p is a Wieferich prime, one can multiply both sides of the congruence by 2 to get . Raising both sides of the congruence to the power p shows that a Wieferich prime also satisfies , and hence for all . The converse is also true: for some implies that the multiplicative order of 2 modulo p2 divides gcd, φ, that is, and thus p is a Wieferich prime.
The map :x \bmod N \mapsto (x \bmod n_1, \ldots, x\bmod n_k) maps congruence classes modulo to sequences of congruence classes modulo . The proof of uniqueness shows that this map is injective. As the domain and the codomain of this map have the same number of elements, the map is also surjective, which proves the existence of the solution. This proof is very simple but does not provide any direct way for computing a solution.
Goal congruence also plays a role in influencing the relationship between one's core self-evaluations and the satisfaction one has with one's job. The theory behind goal congruence argues that people who choose self-concordant (i.e., congruent) goals will be happier with the goals they pursue, be more likely to put in effort towards achieving these goals, and, consequently, will be more likely to attain their goals. Self-concordant goals include goals that focus on intrinsic factors.
Host switches have also been involved in the creation of new hosts with the close or same related genus, which would be apparent for congruence of the hosts and the parasitic birds.
The will of Charles II of Spain in 1700 was in congruence with the European powers that Louis XIV, despite his victories during the War of Spanish Succession, was unable to influence.
Political Representation and Policy Congruence in Modern Societies. Amsterdam: Pallas Publications (Amsterdam University Press)Hankiovsky, Olena / Anastasiya Salnykova (eds.) (2012). Gender, Politics and Society in Ukraine. Toronto: University of Toronto PressVatter, Adrian (2014).
Thus there is essentially no restriction on the shape of a congruence lattice of an algebra. The finite lattice representation problem asks whether the same is true for finite lattices and finite algebras. That is, does every finite lattice occur as the congruence lattice of a finite algebra? In 1980, Pálfy and Pudlák proved that this problem is equivalent to the problem of deciding whether every finite lattice occurs as an interval in the subgroup lattice of a finite group.
The Goldberg–Sachs theorem is a result in Einstein's theory of general relativity about vacuum solutions of the Einstein field equations relating the existence of a certain type of congruence with algebraic properties of the Weyl tensor. More precisely, the theorem states that a vacuum solution of the Einstein field equations will admit a shear-free null geodesic congruence if and only if the Weyl tensor is algebraically special. The theorem is often used when searching for algebraically special vacuum solutions.
The congruence lattice Con A of an algebra A is an algebraic lattice. The (∨,0)-semilattice of compact elements of Con A is denoted by Conc A, and it is sometimes called the congruence semilattice of A. Then Con A is isomorphic to the ideal lattice of Conc A. By using the classical equivalence between the category of all (∨,0)-semilattices and the category of all algebraic lattices (with suitable definitions of morphisms), as it is outlined here, we obtain the following semilattice-theoretical formulation of CLP. \---- Semilattice- theoretical formulation of CLP: Is every distributive (∨,0)-semilattice isomorphic to the congruence semilattice of some lattice? \---- Say that a distributive (∨,0)-semilattice is representable, if it is isomorphic to Conc L, for some lattice L. So CLP asks whether every distributive (∨,0)-semilattice is representable.
The contents of Professor John Stillwell's 1999 translation of the are as follows :Chapter 1. On the divisibility of numbers :Chapter 2. On the congruence of numbers :Chapter 3. On quadratic residues :Chapter 4.
In mathematics, a group is called boundedly generated if it can be expressed as a finite product of cyclic subgroups. The property of bounded generation is also closely related with the congruence subgroup problem (see ).
Generalizing the observational congruence of Guarded Commands into a lattice has led to Refinement Calculus. This has been mechanized in Formal Methods like B-Method that allow one to formally derive programs from their specifications.
Conversely, because finding square roots modulo a composite number turns out to be probabilistic polynomial-time equivalent to factoring that number, any integer factorization algorithm can be used efficiently to identify a congruence of squares.
Raoul Bricard (23 March 1870 – 26 November 1943) was a French engineer and a mathematician. He is best known for his work in geometry, especially descriptive geometry and scissors congruence, and kinematics, especially mechanical linkages.
In the humanistic approach, Carl Rogers identified a number of necessary and sufficient conditions that are required for therapeutic change to take place. These include the three core conditions: congruence, unconditional positive regard and empathy.
First, the kernel- as-an-ideal is the equivalence class of the neutral element eA under the kernel-as-a-congruence. For the converse direction, we need the notion of quotient in the Mal'cev algebra (which is division on either side for groups and subtraction for vector spaces, modules, and rings). Using this, elements a and b of A are equivalent under the kernel-as-a-congruence if and only if their quotient a/b is an element of the kernel-as-an-ideal.
Hilbert's axioms for plane geometry number 16, and include Transitivity of Congruence and a variant of the Axiom of Pasch. The only notion from intuitive geometry invoked in the remarks to Tarski's axioms is triangle. (Versions B and C of the Axiom of Euclid refer to "circle" and "angle," respectively.) Hilbert's axioms also require "ray," "angle," and the notion of a triangle "including" an angle. In addition to betweenness and congruence, Hilbert's axioms require a primitive binary relation "on," linking a point and a line.
Jacquet functors and unrefined minimal K-types, Commentarii Math.Helv. 71(1996), 98-121; with Allen Moy. [10]. On the congruence subgroup problem: Determination of the "Metaplectic Kernel", Inventiones Math. 71(1983), 21-42; with M.S.Raghunathan. [11].
Sikh ethics emphasize the congruence between spiritual development and everyday moral conduct. Its founder Guru Nanak summarized this perspective:Singh, Pashaura, and Louis E. Fenech. 2014. The Oxford Handbook of Sikh Studies. p. 234. Oxford University Press. .
467 pp. University of Texas, AustinBrochu, C. A. (2001). Congruence between physiology, phylogenetics, and the fossil record on crocodylian historical biogeography. In: G. Grigg, F. Seebacher, and C.E. Franklin (eds.), Crocodilian Biology and Evolution, 9–28.
There are no more than cosets, because . The coset is the congruence class of modulo . The subgroup is normal in , and so, can be used to form the quotient group the group of integers mod m.
The algorithm attempts to set up a congruence of squares modulo n (the integer to be factorized), which often leads to a factorization of n. The algorithm works in two phases: the data collection phase, where it collects information that may lead to a congruence of squares; and the data processing phase, where it puts all the data it has collected into a matrix and solves it to obtain a congruence of squares. The data collection phase can be easily parallelized to many processors, but the data processing phase requires large amounts of memory, and is difficult to parallelize efficiently over many nodes or if the processing nodes do not each have enough memory to store the whole matrix. The block Wiedemann algorithm can be used in the case of a few systems each capable of holding the matrix.
Informally, the reconstruction conjecture in graph theory says that graphs are determined uniquely by their subgraphs. It is due to KellyKelly, P. J., A congruence theorem for trees, Pacific J. Math. 7 (1957), 961-968. and Ulam.
Colton proved many results about refactorable numbers, showing that there were infinitely many and proving a variety of congruence restrictions on their distribution. Colton was only later alerted that Kennedy and Cooper had previously investigated the topic.
Generally, a congruence coefficient of 0.90 is interpreted as indicating a high degree of factor similarity, while a coefficient of 0.95 or higher indicates that the factors are virtually identical. Alternatively, a value in the range 0.85–0.94 has been seen as corresponding to a fair similarity, with values higher than 0.95 indicating that the factors can be considered to be equal. The congruence coefficient can also be defined as the cosine of the angle between factor axes based on the same set of variables (e.g., tests) obtained for two samples (see Cosine similarity).
To generalise this to universal algebra, normal subgroups need to be replaced by congruence relations. A congruence on an algebra A is an equivalence relation \Phi\subseteq A \times A that forms a subalgebra of A \times A considered as an algebra with componentwise operations. One can make the set of equivalence classes A/\Phi into an algebra of the same type by defining the operations via representatives; this will be well-defined since \Phi is a subalgebra of A \times A. The resulting structure is the quotient algebra.
The motivational relevance aspect of the appraisal of the process has been shown to influence the intensity of the experienced emotions so that when a situation is highly relevant to one's well-being, the situation elicits a more intense emotional response (Smith & Kirby, 2009). The second aspect of an individual's primary appraisal of a situation is the evaluation of motivational congruence. When evaluating the motivational congruence of a situation, an individual answers the question, "Is this situation congruent or incongruent (consistent or inconsistent) with my goals?" (Smith & Kirby, 2009).
This premise is consistent with Rogerian or person-centered approaches; it further connects with Rogerian thought by suggesting that the use of the theory should have congruence. Just as Rogers suggests that a person should have congruence between, their experience, awareness, and communication,Rogers, C.R. (1961) On Becoming a Person. Boston: Houghton Mifflin. pp. 61-62. Porter suggests that a psychometric test should communicate to the user in such a way that it heightens the awareness of the life-experience of the test-taker and becomes useful to the test-taker regarding making behavioral choices.
Secret sharing consists of recovering a secret S from a set of shares, each containing partial information about the secret. The Chinese remainder theorem (CRT) states that for a given system of simultaneous congruence equations, the solution is unique in some , with under some appropriate conditions on the congruences. Secret sharing can thus use the CRT to produce the shares presented in the congruence equations and the secret could be recovered by solving the system of congruences to get the unique solution, which will be the secret to recover.
A complex intervention will affect co-operative interactions over work (its congruence), and the normal pattern of outcomes of this work (its disposal). Therefore: a complex intervention is disposed to normalization if it confers an interactional advantage in flexibly accomplishing congruence and disposal of work. # Relational integration: This describes how knowledge and work is mediated and understood within the social networks of people around it. A complex intervention will affect not only the knowledge required by its users (its accountability), but also the ways that they understand the actions of people around them (its confidence).
Any triple of positive integers can serve as the side lengths of an integer triangle as long as it satisfies the triangle inequality: the longest side is shorter than the sum of the other two sides. Each such triple defines an integer triangle that is unique up to congruence. So the number of integer triangles (up to congruence) with perimeter p is the number of partitions of p into three positive parts that satisfy the triangle inequality. This is the integer closest to when p is even and to when p is odd.
Rogers (1957; 1959) stated that there are six necessary and sufficient conditions required for therapeutic change: # Therapist–client psychological contact: a relationship between client and therapist must exist, and it must be a relationship in which each person's perception of the other is important. # Client incongruence: that in- congruence exists between the client's experience and awareness. # Therapist congruence, or genuineness: the therapist is congruent within the therapeutic relationship. The therapist is deeply involved—they are not "acting"—and they can draw on their own experiences (self-disclosure) to facilitate the relationship.
Social psychologists have long made the distinction between ingroup favoritism and outgroup negativity, where outgroup negativity is the act of punishing or placing burdens upon the outgroup. Indeed, a significant body of research exists that attempts to identify the relationship between ingroup favoritism and outgroup negativity, as well as conditions that will lead to outgroup negativity. For example, Struch and Schwartz found support for the predictions of belief congruence theory. The belief congruence theory concerns itself with the degree of similarity in beliefs, attitudes, and values perceived to exist between individuals.
Several weaker substitutes have also been proposed as rigidity conditions, such as by Noether (1909) or Born (1910) himself. A modern alternative was given by Epp, Mann & McGrath.Epp, Mann & McGrath (2009) In contrast to the ordinary Born rigid congruence consisting of the "history of a spatial volume-filling set of points", they recover the six degrees of freedom of classical mechanics by using a quasilocal rigid frame by defining a congruence in terms of the "history of the set of points on the surface bounding a spatial volume".
Client-therapist congruence of expectations over the course of therapy. British Journal of Clinical Psychology, 26, 17-24.Vinokur, A., Schul, Y., & Caplan, R.D. (1987). Determinants of perceived social support: Interpersonal transactions, personal outlook, and transient affective states.
The decision problem for free theories is particularly important, as many theories can be reduced to it. Free theories can be solved by searching for common subexpressions to form the congruence closure. Solvers include satisfiability modulo theories solvers.
Oxford, UK: Wiley Blackwell.Wong, P. T. P. (2016). Chinese positive psychology revisited. International Journal of Existential Psychology and Psychotherapy, 6(1). Wong's main contribution to stress and coping research is the resource-congruence modelWong, P. T. P. (1993).
A symbol commonly used for congruence is an equals symbol with a tilde above it, ≅, corresponding to the Unicode character 'approximately equal to' (U+2245). In the UK, the three-bar equal sign ≡ (U+2261) is sometimes used.
American Journal of Botany 87 1300-08.Ferguson, C. J. and R. K. Jansen. (2002). A chloroplast DNA phylogeny of eastern Phlox (Polemoniaceae): implications of congruence and incongruence with the ITS phylogeny. American Journal of Botany 89 1324-35.
Besides, with an exception of 168432 and 21246792, no composites are known to hold for () with k = 2, much less k = 3. Thus the conjecture is considered likely because Wolstenholme's congruence seems over- constrained and artificial for composite numbers.
Pálfy and Pudlák. Congruence lattices of finite algebras and intervals in subgroup lattices of finite groups. Algebra Universalis 11(1), 22–27 (1980). DOI For an overview of the group theoretic approach to the problem, see Pálfy (1993)Péter Pál Pálfy.
1004, pp. 176–205. Springer, Berlin (1983). DOI Until it is answered, the theory of finite algebras is incomplete since, given a finite algebra, it is unknown whether there are, a priori, any restrictions on the shape of its congruence lattice.
Bhante Sujato, a contemporary scholar monk, argues that the remarkable congruence of the various recensions suggests that the Samyutta Nikaya/Saṃyukta Āgama was the only collection to be finalized in terms of both structure and content in the pre-sectarian period.
Correct usage of the system can allow for farmers to plant two crops a year, increasing food security and bringing in extra income.Niranjan Pant. "Indigenous Irrigation in South Bihar: A Case of Congruence of Boundaries." Economic and Political Weekly 33, no.
The navies of India and Sri Lanka with anti-submarine warfare corvettes INS Kamorta and INS Kiltan as well as offshore patrol vessel Sayura and training ship Gajabahu respectively begin a three-day exercise Slinex 2020 to highlight growing congruence.
In mathematics, a Mennicke symbol is a map from pairs of elements of a number field to an abelian group satisfying some identities found by . They were named by , who used them in their solution of the congruence subgroup problem.
In the theory of smooth manifolds, a congruence is the set of integral curves defined by a nonvanishing vector field defined on the manifold. Congruences are an important concept in general relativity, and are also important in parts of Riemannian geometry.
Zeller's congruence is an algorithm devised by Christian Zeller to calculate the day of the week for any Julian or Gregorian calendar date. It can be considered to be based on the conversion between Julian day and the calendar date.
PP waves provide a rare exception to this rule: if you have two PP waves sharing the same covariantly constant null vector (the same geodesic null congruence, i.e. the same wave vector field), with metric functions H_1, H_2 respectively, then H_1 + H_2 gives a third exact solution. Roger Penrose has observed that near a null geodesic, every Lorentzian spacetime looks like a plane wave. To show this, he used techniques imported from algebraic geometry to "blow up" the spacetime so that the given null geodesic becomes the covariantly constant null geodesic congruence of a plane wave.
Since modular arithmetic has such a wide range of applications, it is important to know how hard it is to solve a system of congruences. A linear system of congruences can be solved in polynomial time with a form of Gaussian elimination, for details see linear congruence theorem. Algorithms, such as Montgomery reduction, also exist to allow simple arithmetic operations, such as multiplication and exponentiation modulo , to be performed efficiently on large numbers. Some operations, like finding a discrete logarithm or a quadratic congruence appear to be as hard as integer factorization and thus are a starting point for cryptographic algorithms and encryption.
For example, consider the problem of finding all circles in the Euclidean plane up to congruence. Any circle can be described uniquely by giving three points, but many different sets of three points give the same circle: the correspondence is many-to-one. However, circles are uniquely parameterized by giving their center and radius: this is two real parameters and one positive real parameter. Since we are only interested in circles "up to congruence", we identify circles having different centers but the same radius, and so the radius alone suffices to parameterize the set of interest.
Earlier (1965) work of Michel Lazard, whose importance was not appreciated by the specialists in the field for about 20 years, had dealt with the case where K is the ring of p-adic integers and G is the pth congruence subgroup of .
It has been shown by Dain and Moreschi that a corresponding theorem will not hold in linearized gravity, that is, given a solution of the linearised Einstein field equations admitting a shear-free null congruence, then this solution need not be algebraically special.
Google Books. Online edn, November 2018. Pp. 119 In congruence with his previous works, Paine emphasizes the compatibility between individual rights and societal wellbeing. He fervently contends that crippling poverty undermines the rights of an individual, and consequently the legitimacy of government.
Various empirical inquiries have been aimed at measuring academic self-efficacy.Bong, M. (1997). Congruence of measurement specificity on relations between academic self-efficacy, effort, and achievement indexes. Paper presented at the Annual Meeting of the American Educational Research Association (Chicago, IL, March 24–28, 1997).
It can be used to study the similarity of extracted factors across different samples of, for example, test takers who have taken the same test.Lorenzo-Seva, U. & ten Berge, J.M.F. (2006). Tucker’s Congruence Coefficient as a Meaningful Index of Factor Similarity. Methodology, 2, 57–64.
In statistics and probability theory, the tilde means "is distributed as"; see random variable. A tilde can also be used to represent geometric similarity (e.g. , meaning triangle is similar to ). A triple tilde (≋) is often used to show congruence, an equivalence relation in geometry.
91, pp. 133-144. The following pluvial (rain) periods allowed the whipbirds on the western side to migrate east and take up areas near the Murray basin.Cracraft, J., 1986. Origin and evolution of continental biotas: speciation and historical congruence within the Australian avifauna. Evolution. Vol.
The cyclic group G = Z/3Z of congruence classes modulo 3 (see modular arithmetic) is simple. If H is a subgroup of this group, its order (the number of elements) must be a divisor of the order of G which is 3. Since 3 is prime, its only divisors are 1 and 3, so either H is G, or H is the trivial group. On the other hand, the group G = Z/12Z is not simple. The set H of congruence classes of 0, 4, and 8 modulo 12 is a subgroup of order 3, and it is a normal subgroup since any subgroup of an abelian group is normal.
In real algebraic geometry, Gudkov's conjecture, also called Gudkov’s congruence, (named after Dmitry Gudkov) was a conjecture, and is now a theorem, which states that an M-curve of even degree 2d obeys the congruence : p - n \equiv d^2\, (\\!\bmod 8), where p is the number of positive ovals and n the number of negative ovals of the M-curve. (Here, the term M-curve stands for "maximal curve"; it means a smooth algebraic curve over the reals whose genus is k-1, where k is the number of maximal components of the curve.) The theorem was proved by the combined works of Vladimir Arnold and Vladimir Rokhlin.
Karl Mahlburg is an American mathematician whose research interests lie in the areas of modular forms, partitions, combinatorics and number theory. He submitted a paper to Proceedings of the National Academy of Sciences (PNAS) entitled Partition Congruences and the Andrews-Garvan-Dyson Crank in 2005, and the paper won the PNAS first Paper of the Year prize. The paper extends a result first conjectured by Srinivasa Ramanujan and later detailed by Freeman Dyson, George Andrews, Frank Garvan, and Mahlburg's advisor Ken Ono called the crank having to do with congruence patterns in partitions. Until recently such congruence patterns were only known to occur for 5, 7, and 11.
In general relativity, a timelike congruence in a four-dimensional Lorentzian manifold can be interpreted as a family of world lines of certain ideal observers in our spacetime. In particular, a timelike geodesic congruence can be interpreted as a family of free-falling test particles. Null congruences are also important, particularly null geodesic congruences, which can be interpreted as a family of freely propagating light rays. Warning: the world line of a pulse of light moving in a fiber optic cable would not in general be a null geodesic, and light in the very early universe (the radiation-dominated epoch) was not freely propagating.
The two main hurdles to determining cospeciation using Fahrenholz's rule are instances of false congruence and false incongruence. False congruence occurs when parasite and host phylogenies mirror each other but not due to cospeciation, for instance, if the parasites were to colonize the hosts after the host species had diverged and congruent phylogenies resulted by chance, but this is unlikely. False incongruence, when cospeciation has occurred, but the phylogenies do not mirror each other, is more common, and can be caused by a number of factors; it might also appear to be present if parasites that are present on a host are not detected by the experimenter.
He believes that the late Christopher Hitchens committed this error by assuming that the drive for congruence is a defining feature of religion and that Daniel Dennett has done it by overlooking the fact that religious actions are dependent on the situation, just like other actions.
The functional similarity of the enzymes remains the strongest argument for divergent evolution. All three enzymes activate a C–H bond adjacent to a carbonyl group. The active sites are located at the carboxylic ends of the β strands. Such congruence is in favor of divergent evolution.
1709\. It is founded as a brotherhood La Purisima by the illustrious bishop Don Diego Camacho. 1805\. The first baptism certificate is recorded. 1869\. Huanusco municipality is declared by Governor Victoriano Zamora. 1918\. It is declared a free municipality, in congruence with the Constitution of 1917. 1935\.
This conjecture has been proven by E. Lindenstrauss in the case where S is compact and the \phi_j are additionally eigenfunctions for the Hecke operators on S. In the case of congruence covers of the modular some additional difficulties occur, which were dealt with by K. Soundararajan.
The totality of both narratives are however in congruence with the large scale movement of pastoralists from the plains into the forested areas, assimilation of forest-dwelling communities and wide-spread identity shift. A widespread trend across the region as the mutai of the 1830s dragged on.
The theorem was formulated in many ways before its modern form: Euler and Legendre did not have Gauss's congruence notation, nor did Gauss have the Legendre symbol. In this article p and q always refer to distinct positive odd primes, and x and y to unspecified integers.
Every algebraic lattice is isomorphic to the congruence lattice of some algebra. The lattice Sub V of all subspaces of a vector space V is certainly an algebraic lattice. As the next result shows, these algebraic lattices are difficult to represent. Theorem (Freese, Lampe, and Taylor 1979).
The orange and green quadrilaterals are congruent; the blue one is not congruent to them. Congruence between the orange and green ones is established by the facts that side BC corresponds to (in this case of congruence, equals in length) JK, CD corresponds to KL, DA corresponds to LI, and AB corresponds to IJ, while angle C corresponds to (equals) angle K, D corresponds to L, A corresponds to I, and B corresponds to J. In geometry, the tests for congruence and similarity involve comparing corresponding sides and corresponding angles of polygons. In these tests, each side and each angle in one polygon is paired with a side or angle in the second polygon, taking care to preserve the order of adjacency. For example, if one polygon has sequential sides a, b, c, d, and e and the other has sequential sides v, w, x, y, and z, and if b and w are corresponding sides, then side a (adjacent to b) must correspond to either v or x (both adjacent to w).
Suppose A is a set of impartial combinatorial games that is finitely-generated with respect to disjunctive sums and closed in both of the following senses: (1) Additive closure: If G and H are games in A, then their disjunctive sum G + H is also in A. (2) Hereditary closure: If G is a game in A and H is an option of G, then H is also in A. Next, define on A the indistinguishability congruence ≈ that relates two games G and H if for every choice of a game X in A, the two positions G+X and H+X have the same outcome (i.e., are either both first- player wins in best play of A, or alternatively are both second-player wins). One easily checks that ≈ is indeed a congruence on the set of all disjunctive position sums in A, and that this is true regardless of whether the game is played in normal or misere play. The totality of all the congruence classes form the indistinguishability quotient.
The quotients by congruence subgroups are of significant interest. Other important quotients are the triangle groups, which correspond geometrically to descending to a cylinder, quotienting the coordinate modulo , as . is the group of icosahedral symmetry, and the triangle group (and associated tiling) is the cover for all Hurwitz surfaces.
In Federal Court, judges have wide discretion to structure trials. Factors evaluated will include congruence of issues, complexity for the jury, and possible prejudice to any of the parties. American Federal Rules of Civil Procedure, Rule 42(b) allows the court to decide issues contained in separate trials.
Sauer, J., Darioly, A., Schmid Mast, M., Schmid, P. C., & Bischof, N. (2010). A multi-level approach of evaluating crew resource management training: A laboratory-based study examining communication skills as a function of team congruence. Ergonomics, 58(11), 1311–1324. Schmid, P. C., & Schmid Mast, M. (2010).
Potter and Kappeler (1996), in their introduction to Constructing Crime: Perspective on Making News And Social Problems wrote, "Public opinion and crime facts demonstrate no congruence. The reality of crime in the United States has been subverted to a constructed reality as ephemeral as swamp gas.", p. 2.
The totality of both narratives are however in congruence with the large scale movement of pastoralists from the plains into the forested areas, assimilation of forest-dwelling communities and wide-spread identity shift. A widespread trend across the region as the Mutai of the 19th-century dragged on.
More precisely, Gauss observed that if a+bi is a (Gaussian) prime and a–1+bi is divisible by 2+2i, then the number of solutions to the congruence 1=xx+yy+xxyy (mod a+bi), including x=∞, y=±i and x=±i, y=∞, is (a–1)2+b2.
US 431 leaves the congruence at Trinty Lane, leaving US 31W, US 41 to carry on. US 31W, US 41 then have a incomplete interchange with SR 155 and I-65. US 31W, US 41 split just north of Goodlettsville. US 31W has an interchange with I-65.
Where the branch length in coalescent units (T) is also written in an alternative form: the number of generations (t) divided by twice the effective population size (Ne). Pamilo and Nei also derived the probability of congruence for rooted trees of four and five taxa as well as a general upper bound on the probability of congruence for larger trees. Rosenberg followed up with equations used for the complete set of topologies (although the large number of distinct phylogenetic trees that becomes possible as the number of taxa increases makes these equations impractical unless the number of taxa is very limited). The phenomenon of hemiplasy is a natural extension of the basic idea underlying gene tree-species tree discordance.
Then there is at most one line in the plane, determined by a and A, that passes through A and does not intersect a. :V. Continuity # Axiom of Archimedes. If AB and CD are any segments then there exists a number n such that n segments CD constructed contiguously from A, along the ray from A through B, will pass beyond the point B. # Axiom of line completeness. An extension of a set of points on a line with its order and congruence relations that would preserve the relations existing among the original elements as well as the fundamental properties of line order and congruence that follows from Axioms I–III and from V-1 is impossible.
A congruence subgroup is (roughly) a subgroup of an arithmetic group defined by taking all matrices satisfying certain equations modulo an integer, for example the group of 2 by 2 integer matrices with diagonal (respectively off-diagonal) coefficients congruent to 1 (respectively 0) modulo a positive integer. These are always finite-index subgroups and the congruence subgroup problem roughly asks whether all subgroups are obtained in this way. The conjecture (usually attributed to Jean-Pierre Serre) is that this is true for (irreducible) arithmetic lattices in higher-rank groups and false in rank-one groups. It is still open in this generality but there are many results establishing it for specific lattices (in both its positive and negative cases).
A congruence θ of a join-semilattice S is monomial, if the θ-equivalence class of any element of S has a largest element. We say that θ is distributive, if it is a join, in the congruence lattice Con S of S, of monomial join- congruences of S. The following definition originates in Schmidt's 1968 work and was subsequently adjusted by Wehrung. Definition (weakly distributive homomorphisms). A homomorphism μ : S → T between join-semilattices S and T is weakly distributive, if for all a, b in S and all c in T such that μ(c)≤ a ∨ b, there are elements x and y of S such that c≤ x ∨ y, μ(x)≤ a, and μ(y)≤ b.
Every finite distributive lattice is isomorphic to the congruence lattice of some finite lattice. It is important to observe that the solution lattice found in Grätzer and Schmidt's proof is sectionally complemented, that is, it has a least element (true for any finite lattice) and for all elements a ≤ b there exists an element x with a ∨ x = b and a ∧ x = 0. It is also in that paper that CLP is first stated in published form, although it seems that the earliest attempts at CLP were made by Dilworth himself. Congruence lattices of finite lattices have been given an enormous amount of attention, for which a reference is Grätzer's 2005 monograph.
Describing the mutual motion of the test particles in a null geodesic congruence in a spacetime such as the Schwarzschild vacuum or FRW dust is a very important problem in general relativity. It is solved by defining certain kinematical quantities which completely describe how the integral curves in a congruence may converge (diverge) or twist about one another. It should be stressed that the kinematical decomposition we are about to describe is pure mathematics valid for any Lorentzian manifold. However, the physical interpretation in terms of test particles and tidal accelerations (for timelike geodesic congruences) or pencils of light rays (for null geodesic congruences) is valid only for general relativity (similar interpretations may be valid in closely related theories).
This constant spontaneity challenges MacGyver as well as his adversaries. Because MacGyver continues to operate in this manner, it is assumed the tactical advantage of spontaneity outweighs its disadvantages. This is observed by MacGyver's nemesis Murdoc. MacGyver demonstrates mood congruence, exhibiting grief in tragedy, fear in peril, and pain in suffering.
They also found that when in a happy mood, participants were quicker at identifying happy words than sad words. Such findings are in line with the emotion-congruence thesis. This research also makes the conclusion that our existing moods and emotions lead us to selectively perceive emotion-congruent objects and events.
In congruence with the findings of this research, Niedenthal et al. tested the anger superiority effect using a neural analysis of human faces in two different simulations in order to separate emotional and perceptual processes. They found that perceptual bias is causing a faster, more accurate identification of anger faces.
As another example of a closure operator used in algebra, if some algebra has universe A and X is a set of pairs of A, then the operator assigning to X the smallest congruence containing X is a finitary closure operator on A x A.Clifford Bergman, Universal Algebra, 2012, Section 2.4.
"Interspecific affinities within the genus Sminthopsis (Dasyuromorphia: Dasyuridae) based on morphology of the penis: congruence with other anatomical and molecular data." Journal of Mammalogy 88.6 (2007): 1381–1392. The only accessory sex glands marsupials possess are the prostate and bulbourethral glands. There are no ampullae, seminal vesicles or coagulating glands.
Rogers described the concepts of congruence and incongruence as important ideas in his theory. In proposition #6, he refers to the actualizing tendency. At the same time, he recognized the need for positive regard. In a fully congruent person, realizing their potential is not at the expense of experiencing positive regard.
Christine Baranski was nominated for the Primetime Emmy Award for Outstanding Guest Actress in a Comedy Series at the 62nd Primetime Emmy Awards for the episode, "The Maternal Congruence". Jim Parsons won the Primetime Emmy Award for Outstanding Lead Actor in a Comedy Series for the episode "The Pants Alternative".
Congruence covers of arithmetic surfaces are known to give rise to surfaces with large injectivity radius. Likewise the Ramanujan graphs constructed by Lubotzky—Phillips—Sarnak have large girth. It is in fact known that the Ramanujan property itself implies that the local girths of the graph are almost always large.
Mechanism of the base catalyzed alcoholysis of pentacoordinated phosphorus It can be understood from these experiments that the increased reactivity observed for hypervalent molecules, contrasted with analogous nonhypervalent compounds, can be attributed to the congruence of these species to the hypercoordinated activated states normally formed during the course of the reaction.
Though seemingly disparate, the totality of these narratives are in congruence with the large scale movement of pastoralists from the plains into the forested areas, assimilation of forest-dwelling communities and wide-spread identity shift. A widespread trend across the region as the Mutai of the 19th-century dragged on.
1999c), and despite Waddell et al. (2001) showing near total congruence of mtDNA-based and nuclear-based trees when such sequences were excluded, some authors continued to produce misleading trees (Arnason et al., 2002). A study investigating retrotransposon presence/absence data has claimed strong support for Euarchonta (Kriegs et al.
Spanish colonies and territories in the Caribbean basin (c. 1490 – c. 1660) In congruence with the colonialist activities of competing European imperial powers throughout the 15th – 19th centuries, the Spanish were equally engrossed in extending geopolitical power. The Caribbean basin functioned as a key geographic focal point for advancing Spanish imperialism.
It was presented in the context of a study of certain congruence properties of the partition function discovered by the Indian mathematical genius Srinivasa Ramanujan. A different concept, sharing the same name, is used in combinatorics, where the rank is taken to be the size of the Durfee square of the partition.
Voelkel, J. R. (1995). The music of the heavens: Kepler's harmonic astronomy. 1994. Physics Today, 48(6), 59–60. When Kepler uses the term "harmony" it is not strictly referring to the musical definition, but rather a broader definition encompassing congruence in Nature and the workings of both the celestial and terrestrial bodies.
"Study concerning the colors of tactile blocks for the visually handicapped -- Visibility for the visually handicapped and scenic congruence for those with ordinary sight and vision.". SEPT. The paving was first introduced in a street in Okayama city, Japan, in 1967. Its use gradually spread in Japan and then around the world.
In Hilbert's axioms, congruence is an equivalence relation on segments. One can thus define the length of a segment as its equivalence class. One must thus prove that this length satisfies properties that characterize nonnegative real numbers. It is what did Artin, with axioms that are not Hilbert's ones, but are equivalent.
It is the smallest base 10 Friedman number as it can be expressed by its own digits: 52. It is also a Cullen number. 25 is the smallest pseudoprime satisfying the congruence 7n = 7 mod n. 25 is the smallest aspiring number -- a composite non-sociable number whose aliquot sequence does not terminate.
Thus, objects that can be transformed into each other by rigid transformations, mirroring, and uniform scaling are similar. Similarity is preserved when one of the objects is uniformly scaled, while congruence is not. Thus, congruent objects are always geometrically similar, but similar objects may not be congruent, as they may have different size.
This theory also states that dissimilarity increases negative orientations towards others. When applied to racial discrimination, the belief congruence theory argues that the perceived dissimilarity of beliefs has more of an impact on racial discrimination than does race itself. Research finds evidence of in-group bias in police investigations and judicial decisions.
Avolio, B. J., Bass, B. M., & Jung, D. (1996). Construct validation of the multifactor leadership questionnaire MLQ-Form 5X (CLS Report 96-1). Binghamton: State University of New York, Center for Leadership Studies.Bass, B. M., & Yammarino, F. J. (1991). Congruence of self and others’ leadership ratings of naval officers for understanding successful performance.
The resource- congruence model of coping and the development of the Coping Schema Inventory. In P. T. P. Wong, & L. C. J. Wong (Eds.), Handbook of multicultural perspectives on stress and coping (pp. 223-283). New York, NY: Springer. and the Stress Appraisal Measure (SAM).Peacock, E. J., & Wong, P. T. P. (1990).
Hilbert discusses the existence of non-Euclidean geometry and non-Archimedean geometry > ...a geometry in which all the axioms of ordinary euclidean geometry hold, > and in particular all the congruence axioms except the one of the congruence > of triangles (or all except the theorem of the equality of the base angles > in the isosceles triangle), and in which, besides, the proposition that in > every triangle the sum of two sides is greater than the third is assumed as > a particular axiom.Hilbert, David, "Mathematische Probleme" Göttinger > Nachrichten, (1900), pp. 253–297, and in Archiv der Mathematik und Physik, > (3) 1 (1901), 44–63 and 213–237. Published in English translation by Dr. > Maby Winton Newson, Bulletin of the American Mathematical Society 8 (1902), > 437–479 .
The introduction of cultural factors are in congruence to necessary biological elements.Kimura, Doreen. (2004). Human sex differences in cognition, fact, not predicament. Sexualities, Evolution and Gender, 1, 45-53. doi:10.1080/14616660410001733597 An article published in the Review of Educational Research summarizes the history of the controversy around sex differences in variability of intelligence.
A vacuum metric, R_{ab}=0, is algebraically special if and only if it contains a shear-free null geodesic congruence; the tangent vector obeys k_{[a}C_{b]ijc}k^ik^j=0.; originally published in Acta Phys. Pol. 22, 13–23 (1962). This is the theorem originally stated by Goldberg and Sachs.
Congruence bias is the tendency of people to over-rely on testing their initial hypothesis (the most congruent one) while neglecting to test alternative hypotheses. That is, people rarely try experiments that could disprove their initial belief, but rather try to repeat their initial results. It is a special case of the confirmation bias.
There is a natural quotient functor from C to C/R which sends each morphism to its equivalence class. This functor is bijective on objects and surjective on Hom- sets (i.e. it is a full functor). Every functor F : C → D determines a congruence on C by saying f ~ g iff F(f) = F(g).
These pressures may lead people to feel forced into attempting to change their sexual orientation. Other researchers have found that social pressure plays a key role in a person's desire to change his or her sexuality.Beckstead, A. Gay is not me: Seeking Congruence Through Sexual Reorientation Therapy. (Unpublished master's thesis, University of Utah, 1999).
It follows that the Riemann surface in question can be taken to be :H/Γ with H the upper half-plane and Γ of finite index in the modular group, compactified by cusps. Since the modular group has non-congruence subgroups, it is not the conclusion that any such curve is a modular curve.
According to Gregory Halfond, such congruence was a particular quality of the Gallo-Roman church, in which the Roman aristocracy made up an important part of the leadership of the Gallo-Roman (and later the Frankish) church; continuity in this power nexus is indicated also by the continued use of Roman procedures in the councils.Halfond, Gregory I. (2009).
His father József Grätzer was famous in Hungary as the "Puzzle King" ("rejtvénykirály"). George Grätzer received his PhD from Eötvös Loránd University in 1960 under the supervision of László Fuchs. In 1963 Grätzer and Schmidt published their theorem on the characterization of congruence lattices of algebras. In 1963 Grätzer left Hungary and became a professor at Pennsylvania State University.
The three isoscelizers P1Q1, P2Q2, P3Q3 are continuously parallel-shifted such that the three triangles A'P2Q3, Q1B'P3, P1Q2C' are always congruent to each other until the triangle A'B'C' formed by the intersections of the isoscelizers reduces to a point. The point to which the triangle A'B'C' reduces to is called the Yff center of congruence of triangle ABC.
What follows will be based on the Unger translation. Hilbert's axiom system is constructed with six primitive notions: point, line, plane, betweenness, lies on (containment), and congruence. All points, lines, and planes in the following axioms are distinct unless otherwise stated. :I. Incidence # For every two points A and B there exists a line a that contains them both.
The mood congruence effect refers to the tendency of individuals to retrieve information more easily when it has the same emotional content as their current emotional state. For instance, being in a depressed mood increases the tendency to remember negative events (Drace, 2013). This effect has been demonstrated for explicit retrieval as well as implicit retrieval.
In string theory and supersymmetric gauge theory, the algebraic structure of the ring of modular forms can be used to study the structure of the Higgs vacua of four-dimensional gauge theories with N = 1 supersymmetry. The stabilizers of superpotentials in N = 4 supersymmetric Yang–Mills theory are rings of modular forms of the congruence subgroup of .
This concept alludes to the significance of congruence among emotions, appraisal, and cognitions. This particular article discusses the coping effect of appraisal and reappraisal, claiming reappraisal can act as an "adaptive strategy," while rumination is not (Verduyn et al. 2011). Both reappraisal (or initial cognitive appraisal) and rumination, however, can affect the duration of an emotional experience.
This generalization is commonly called satisfiability modulo theories. The question whether a sentence in propositional logic is satisfiable is a decidable problem. In general, the question whether sentences in first-order logic are satisfiable is not decidable. In universal algebra and equational theory, the methods of term rewriting, congruence closure and unification are used to attempt to decide satisfiability.
Les Théorèms de Jordan-Hölder et Schreier, La Revue Scientifique 85: 579–96, review by Oystein Ore: He also wrote "Algebra de relations de congruence".Annales Scientifiques de l'Ecole Normale Superieure. Toisime serie 64: 339–68 Investigation of binary relations was further pursued by his student Jacques Riguet. Châtelet also did research on number theory and group theory.
In some cases, one may consider as equal two mathematical objects that are only equivalent for the properties being considered. In geometry for instance, two geometric shapes are said to be equal when one may be moved to coincide with the other. The word congruence (and the associated symbol \cong) is also used for this kind of equality.
Cells that project from the lateral amygdala to the central amygdala allow for the initiation of an emotional response if a stimulus is deemed threatening. Cognitive Control. Evaluating a gamble and calculating its expected value requires a certain amount of cognitive control. Several brain areas are dedicated to monitoring the congruence between expected and actual outcomes.
Sydler was born in 1921 in Neuchâtel, Switzerland. He graduated from ETH Zürich in 1943 and received a doctorate in 1947. In 1950 he became a librarian at the ETH while continuing to publish mathematical papers in his spare time. In 1960 he received a prize of the Danish Academy of Sciences for his work on scissors congruence.
A uniform coloring allows identical sided polygons at a vertex to be colored differently, while still maintaining vertex-uniformity and transformational congruence between vertices. (Note: Some of the tiling images shown below are not color-uniform) In addition to the 11 convex uniform tilings, there are also 14 nonconvex tilings, using star polygons, and reverse orientation vertex configurations.
TrasiankaAlso transliterated trasyanka. (, ) refers to a mixed form of speech in which Belarusian and Russian elements and structures alternate arbitrarily.Hentschel, Gerd Belarusian and Russian in the Mixed Speech of Belarus. In Besters-Dilger, J. et al. (eds.): “Congruence in Contact-Induced Language Change: Language Families, Typological Resemblance, and Perceived Similarity.” Berlin, Boston: De Gruyter, 2014, 93-121.
They forage for pollen and nectar, which are then stored within nest pots. (cited in Oliveira-Abreu et al. 2014). The bee species, Geotrigona mombuca, is found within in the same subterranean habitat and has a similar foraging activity patterns above 22.0 °C. The biogeographical and foraging congruence suggest a possible common history between the two species.
Having less time outside of jobs can also lead to less congruence between parents in their child-rearing practices. Having less consistency can cause the child to become more inhibited and reserved. However, natural growth is comparable to slow parenting, advocated by well- informed and financially stable parents who wish their children to be more independent and imaginative.
According to Maasai tradition, the Uasin Gishu front conquered a group of people who occupied the Uasin Gishu plateau, this community is remembered as Senguer. Other Maasai traditions concur with this assertion, noting that the Loosekelai (i.e Sigerai/Siger) were attacked by an alliance of the Uasin Gishu and Siria communities. Finding congruence with Maasai traditions, are Kalenjin traditions.
Furthermore, multiple twin studies have also shown that homosexual traits displayed greater congruence in monozygotic (MZ) twins than dizygotic (DZ) twins displaying genetic contributions.Knafo, A., Iervolino, A. C., Plomin, R. (2005). Masculine girls and feminine boys: genetic and environmental contributions to atypical gender development in early childhood. Journal of Personality and Psychology. 88(2), 400-412.
A subsequent number contains a contribution On the Rev. J. G. MacVicar's Experiment on Vision, on the work of John Gibson Macvicar; and the Report of the Cheltenham meeting in 1856 of the British Association contains abstracts of papers communicated by him On the Polyhedron of Forces and On the Congruence nx ≡ n + 1 (mod. p.).
The general state of healthcare in Myanmar (also known as Burma) is poor. The military government of 1962-2011 spent anywhere from 0.5% to 3% of the country's GDP on healthcare. Healthcare in Myanmar is consistently ranked among the lowest in the world. In 2015, in congruence with a new democratic government, a series of healthcare reforms were enacted.
In mathematical physics, Kundt spacetimes are Lorentzian manifolds admitting a geodesic null congruence with vanishing optical scalars (expansion, twist and shear). A well known member of Kundt class is pp-wave. Ricci-flat Kundt spacetimes in arbitrary dimension are algebraically special. In four dimensions Ricci-flat Kundt metrics of Petrov type III and N are completely known.
Hence, due to the congruence and similar orientations, the ray directions and are the same (but not necessarily normal to the wavefronts, since the secondary wavefronts are not necessarily spherical). This construction can be repeated any number of times, giving a straight ray of any length. Thus a homogeneous medium admits rectilinear rays.De Witte, 1959 (p.
Since and implies , the set of classes coprime to n is closed under multiplication. Integer multiplication respects the congruence classes, that is, and implies . This implies that the multiplication is associative, commutative, and that the class of 1 is the unique multiplicative identity. Finally, given a, the multiplicative inverse of a modulo n is an integer x satisfying .
Along with a clearer understanding of the effect of mood on a person's information processing, the AIM also provides a guide by which researchers can design experiments to investigate the effect of sending persuasive messages to subjects. One important area of research involves the concept of 'mood congruence', or how the results of mood compare to the mood itself. It has been found that 'mood congruence' occurs when a person exhibits a positive relationship between his or her mood and a dependent variable; essentially, as the strength of the mood increases or decreases, so the performance measured by this variable increases or decreases correspondingly. Conversely, 'mood incongruence' occurs when a person exhibits a negative relationship between mood and the dependent variable; thus, as mood increases, performance decreases and vice versa.
The centroid of a triangle (where the three red segments meet) is equivariant under affine transformations: the centroid of a transformed triangle is the same point as the transformation of the centroid of the triangle. In the geometry of triangles, the area and perimeter of a triangle are invariants: translating or rotating a triangle does not change its area or perimeter. However, triangle centers such as the centroid, circumcenter, incenter and orthocenter are not invariant, because moving a triangle will also cause its centers to move. Instead, these centers are equivariant: applying any Euclidean congruence (a combination of a translation and rotation) to a triangle, and then constructing its center, produces the same point as constructing the center first, and then applying the same congruence to the center.
The SSA condition (side-side-angle) which specifies two sides and a non-included angle (also known as ASS, or angle-side-side) does not by itself prove congruence. In order to show congruence, additional information is required such as the measure of the corresponding angles and in some cases the lengths of the two pairs of corresponding sides. There are a few possible cases: If two triangles satisfy the SSA condition and the length of the side opposite the angle is greater than or equal to the length of the adjacent side (SSA, or long side-short side-angle), then the two triangles are congruent. The opposite side is sometimes longer when the corresponding angles are acute, but it is always longer when the corresponding angles are right or obtuse.
The geometrical construction for locating the Yff center of congruence has an interesting generalization. The generalisation begins with an arbitrary point P in the plane of a triangle ABC. Then points D, E, F are taken on the sides BC, CA, AB such that ∠BPD = ∠DPC, ∠CPE = ∠EPA, and ∠APF = ∠FPB. The generalization asserts that the lines AD, BE, CF are concurrent.
Kaplansky's theorem states that a prime p congruent to 1 modulo 16 is representable by both or none of x2 + 32y2 and x2 + 64y2, whereas a prime p congruent to 9 modulo 16 is representable by exactly one of these quadratic forms. This is remarkable since the primes represented by each of these forms individually are not describable by congruence conditions..
In light of the injuries, the Ukrainian Community Centre was used as a make-shift hospital. Members of the women's auxiliary operated the centre, before the Vancouver police threw tear gas into the first-aid centre.The strike, in congruence with other, similar West Coast strikes, led to the right to collective bargaining and the creation of International Longshore and Warehouse Union.
Many of the over 200 new symbols introduced by Leibniz are still in use today. Besides the differentials , and the integral sign ( ∫ ) already mentioned, he also introduced the colon (:) for division, the dot (⋅) for multiplication, the geometric signs for similar (~) and congruence (≅), the use of Recorde's equal sign (=) for proportions (replacing Oughtred's :: notation) and the double- suffix notation for determinants.
Based on their love of backcountry snowboarding and surfing, Chris and Jeremy began a collaboration to create a snowboard that captured the congruence of snowboarding and surfing. Born of Chris and Jeremy’s surf/design partnership was the well-received ‘storm chaser’- a swallowtail with a surfboard rocker and the ability for tight turns on groomers or in the deepest powder.
In number theory, a branch of mathematics, a Mirimanoff's congruence is one of a collection of expressions in modular arithmetic which, if they hold, entail the truth of Fermat's Last Theorem. Since the theorem has now been proven, these are now of mainly historical significance, though the Mirimanoff polynomials are interesting in their own right. The theorem is due to Dmitry Mirimanoff.
Attempts by international human rights to reform religious laws and codes of Islam has become the Islamist rallying platforms during political campaigns.A. SAJOO (1999), Islam and Human Rights: Congruence or Dichotomy, Temple International and Comparative Law Journal, vol. 4, pp. 23–34K. ALI (2003), Progressive Muslims and Islamic Jurisprudence: The Necessity for Critical Engagement with Marriage and Divorce Law, In: SAFI, O. (Ed.).
Intuitively, if the light rays are converging, this means that the light is moving backwards inside of the ball. If all the rays around the entire surface are converging, we say that there is a trapped null surface. More formally, if every null congruence orthogonal to a spacelike two-surface has negative expansion, then such surface is said to be trapped.
Stronger forms of Dirichlet's theorem state that for any such arithmetic progression, the sum of the reciprocals of the prime numbers in the progression diverges and that different such arithmetic progressions with the same modulus have approximately the same proportions of primes. Equivalently, the primes are evenly distributed (asymptotically) among the congruence classes modulo d containing a's coprime to d.
Qualitative psychological research is psychological research that employs qualitative methods. Qualitative research methodologies are oriented towards developing an understanding of the meaning and experience dimensions of human lives and their social worlds. Good qualitative research is characterized by congruence between the perspective that informs the research questions and the research methods used.Fossey, E., Harvey, C., McDermott, F., & Davidson, L. (2002).
The root of the word adaptation is apt, from the Latin aptus, meaning 'fitting or suited' (OED), a root meaning already used in the career construct of “aptitude”. The word adapt can be traced, through Latin and French, to aduptare, meaning “to fit.” The idea of fit (or congruence) remains the central construct in trait-and-factor or person-environment theory.
In 2012 the creators of Flatland: The Movie released an educational sequel film, Flatland 2: Sphereland based in part on Burger's Sphereland that dealt with the topics of curved spaces, symmetry and congruence, an expanding universe, and the multiverse. Actors Kristen Bell, Danny Pudi, Michael York, Tony Hale, Danica McKellar, and Kate Mulgrew provide voices for the 36-minute animated movie.
In fact, after n divisions, it can be proven that the remaining pile is divisible by n, a property made convenient use of by the creator of the problem. A formal way of stating the above argument is: The original pile of coconuts will be divided by 5 a total of 5 times with a remainder of 1, not considering the last division in the morning. Let N = number of coconuts in the original pile. Each division must leave the number of nuts in the same congruence class (mod 5). So, :N \equiv 4/5\cdot(N-1) (mod 5) (the –1 is the nut tossed to the monkey) :5N \equiv 4N - 4 (mod 5) :N \equiv -4 (mod 5) (–4 is the congruence class) So if we began in modulo class –4 nuts then we will remain in modulo class –4.
On the fields generated by the lengths of closed geodesics in locally symmetric spaces, preprint; with A.S.Rapinchuk. [20]. Developments on the congruence subgroup problem after the work of Bass, Milnor and Serre, In "Collected papers of John Milnor", vol.V, AMS (2010), 307-325; with A.S.Rapinchuk. [21]. Fake projective planes, Inventiones Math. 168(2007), 321-370, "Addendum", ibid, 182(2010), 213-227; with Sai-Kee Yeung. [22].
The rank of a partition, shown as its Young diagram In number theory and combinatorics rank of a partition of a positive integer is a certain integer associated with the partition. Dyson introduced the concept in a paper published in the journal Eureka. It was presented in the context of a study of certain congruence properties of the partition function discovered by the mathematician Srinivasa Ramanujan.
Unfortunately, the terminology concerning pp-waves, while fairly standard, is highly confusing and tends to promote misunderstanding. In any pp-wave spacetime, the covariantly constant vector field k always has identically vanishing optical scalars. Therefore, pp-waves belong to the Kundt class (the class of Lorentzian manifolds admitting a null congruence with vanishing optical scalars). Going in the other direction, pp-waves include several important special cases.
This heuristic predicts that the number of Wolstenholme primes between K and N is roughly ln ln N − ln ln K. The Wolstenholme condition has been checked up to 109, and the heuristic says that there should be roughly one Wolstenholme prime between 109 and 1024. A similar heuristic predicts that there are no "doubly Wolstenholme" primes, for which the congruence would hold modulo p5.
This phenomenon can best be described using the vocabulary of abstract algebra. The congruence classes relatively prime to the modulus are a group under multiplication, called the group of units of the ring Z/nZ, and the squares are a subgroup of it. Different nonresidues may belong to different cosets, and there is no simple rule that predicts which one their product will be in.
Only processes with a unique response to each input are needed in practice, so weak bi simulation is a congruence. # CBS subsystems are interfaced by translators; by mapping messages to silence, these can restrict hearing and hide speech. Reversing a translator turns its scope inside out. This permits a new specification for a communication link - the environment of each user should behave like the other user.
Person-centered therapy, also known as person-centered psychotherapy, person- centered counseling, client-centered therapy and Rogerian psychotherapy, is a form of psychotherapy developed by psychologist Carl Rogers beginning in the 1940s and extending into the 1980s. Person-centered therapy seeks to facilitate a client's self-actualizing tendency, "an inbuilt proclivity toward growth and fulfillment", via acceptance (unconditional positive regard), therapist congruence (genuineness), an empathic understanding.
We say that a (∨,0)-semilattice satisfies Schmidt's Condition, if it is isomorphic to the quotient of a generalized Boolean semilattice B under some distributive join- congruence of B. One of the deepest results about representability of (∨,0)-semilattices is the following. Theorem (Schmidt 1968). Any (∨,0)-semilattice satisfying Schmidt's Condition is representable. This raised the following problem, stated in the same paper. \---- Problem 1 (Schmidt 1968).
Scanlon, . Another limitation that the courts have read into Congressional power to abrogate is the "congruence and proportionality" test, first discussed in City of Boerne v. Flores, . Because the Fourteenth Amendment allows Congress to take "appropriate" action to enforce rights, the Court has determined that such action must be congruent and proportional to the deprivation of the right that the Congress is seeking to remedy.
In mathematics, Kronecker's congruence, introduced by Kronecker, states that : \Phi_p(x,y)\equiv (x-y^p)(x^p-y)\bmod p, where p is a prime and Φp(x,y) is the modular polynomial of order p, given by :\Phi_n(x,j) = \prod_\tau (x-j(\tau)) for j the elliptic modular function and τ running through classes of imaginary quadratic integers of discriminant n.
If harmonic Maass forms are interpreted as harmonic sections of the line bundle of modular forms of weight k equipped with the Petersson metric over the modular curve, then this differential operator can be viewed as a composition of the Hodge star operator and the antiholomorphic differential. The notion of harmonic Maass forms naturally generalizes to arbitrary congruence subgroups and (scalar and vector valued) multiplier systems.
The relations are given as a (finite) binary relation on . To form the quotient monoid, these relations are extended to monoid congruences as follows: First, one takes the symmetric closure of . This is then extended to a symmetric relation by defining if and only if = and = for some strings with . Finally, one takes the reflexive and transitive closure of , which then is a monoid congruence.
Since vector fields can be visualized as stream-lines of a stationary flow or as Faraday’s lines of force, a non-vanishing vector field in space generates a space-filling system of lines through each point, known to mathematicians as a congruence (i.e., a local foliation). Ricci’s vision filled Riemann’s n-dimensional manifold with n congruences orthogonal to each other, i.e., a local orthogonal grid.
These proportions might be written today as equations:A reason for using the notation above is that, for the ancient Greeks, a ratio is not a number or a geometrical object. We may think of ratio today as an equivalence class of pairs of geometrical objects. Also, equality for the Greeks is what we might today call congruence. In particular, distinct line segments may be equal.
Rogers' view of 'hidden' personality relates to the person one could be given the right circumstances within society. For an individual to be truly happy and for self-actualisation to be realised, the public and hidden selves must be as similar as possible. Rogers believed that when all aspects of a person's life, surroundings and thoughts are in harmony, thus the ideal state of congruence is reached.
In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective. "We shall find it convenient to use the word transformation in the special sense of a one-to-one correspondence P \to P' among all points in the plane (or in space), that is, a rule for associating pairs of points, with the understanding that each pair has a first member and a second member and that every point occurs as the first member of just one pair and also as the second member of just one pair... In particular, an isometry (or "congruent transformation," or "congruence") is a transformation which preserves length..." composition of two opposite isometries is a direct isometry. A reflection in a line is an opposite isometry, like or on the image. Translation is a direct isometry: a rigid motion.
In number theory, the Eichler–Shimura congruence relation expresses the local L-function of a modular curve at a prime p in terms of the eigenvalues of Hecke operators. It was introduced by and generalized by . Roughly speaking, it says that the correspondence on the modular curve inducing the Hecke operator Tp is congruent mod p to the sum of the Frobenius map Frob and its transpose Ver. In other words, :Tp = Frob + Ver as endomorphisms of the Jacobian J0(N)Fp of the modular curve X0N over the finite field Fp. The Eichler–Shimura congruence relation and its generalizations to Shimura varieties play a pivotal role in the Langlands program, by identifying a part of the Hasse–Weil zeta function of a modular curve or a more general modular variety, with the product of Mellin transforms of weight 2 modular forms or a product of analogous automorphic L-functions.
If a and v correspond to each other, then c corresponds to x, d corresponds to y, and e corresponds to z; hence the ith element of the sequence abcde corresponds to the ith element of the sequence vwxyz for i = 1, 2, 3, 4, 5\. On the other hand, if in addition to b corresponding to w we have c corresponding to v, then the ith element of abcde corresponds to the ith element of the reverse sequence xwvzy. Congruence tests look for all pairs of corresponding sides to be equal in length, though except in the case of the triangle this is not sufficient to establish congruence (as exemplified by a square and a rhombus that have the same side length). Similarity tests look at whether the ratios of the lengths of each pair of corresponding sides are equal, though again this is not sufficient.
If C is an additive category and we require the congruence relation ~ on C to be additive (i.e. if f1, f2, g1 and g2 are morphisms from X to Y with f1 ~ f2 and g1 ~g2, then f1 \+ f2 ~ g1 \+ g2), then the quotient category C/~ will also be additive, and the quotient functor C -> C/~ will be an additive functor. The concept of an additive congruence relation is equivalent to the concept of a two-sided ideal of morphisms: for any two objects X and Y we are given an additive subgroup I(X,Y) of HomC(X, Y) such that for all f ∈ I(X,Y), g ∈ HomC(Y, Z) and h∈ HomC(W, X), we have gf ∈ I(X,Z) and fh ∈ I(W,Y). Two morphisms in HomC(X, Y) are congruent iff their difference is in I(X,Y).
Only with hindsight did he realize the congruence and the logic behind them, as if all his previous studies had been driven by the same desire to make fully understandable what at first sight appeared obscure or confusing. In doing so, he relied on the readily observable background of common human experience, as he recounts in a reflection on his intellectual pursuits published in 2013, Cheminement d’un sinologue (A Sinologist's Journey).
Thus, it makes sense to speak of the quotient monoid M/(ker f). The first isomorphism theorem for monoids states that this quotient monoid is naturally isomorphic to the image of f (which is a submonoid of N),(for the congruence relation). This is very different in flavour from the above examples. In particular, the preimage of the identity element of N is not enough to determine the kernel of f.
New bone outgrowths, called "spurs" or osteophytes, can form on the margins of the joints, possibly in an attempt to improve the congruence of the articular cartilage surfaces in the absence of the menisci. The subchondral bone volume increases and becomes less mineralized (hypomineralization). All these changes can cause problems functioning. The pain in an osteoarthritic joint has been related to thickened synovium and to subchondral bone lesions.
Harmonices MundiThe full title is Ioannis Keppleri Harmonices mundi libri V (The Five Books of Johannes Kepler's The Harmony of the World). (Latin: The Harmony of the World, 1619) is a book by Johannes Kepler. In the work, written entirely in Latin, Kepler discusses harmony and congruence in geometrical forms and physical phenomena. The final section of the work relates his discovery of the so-called "third law of planetary motion".
This contrasts with the classical proofs by the criteria for congruence of triangles.Georges Glaeser – The crisis of geometry teaching The first systematic effort to use transformations as the foundation of geometry was made by Felix Klein in the 19th century, under the name Erlangen programme. For nearly a century this approach remained confined to mathematics research circles. In the 20th century efforts were made to exploit it for mathematical education.
He proved many congruences for these numbers, such as for primes . This congruence (and others like it that Ramanujan proved) inspired Jean-Pierre Serre (1954 Fields Medalist) to conjecture that there is a theory of Galois representations that "explains" these congruences and more generally all modular forms. is the first example of a modular form to be studied in this way. Deligne (in his Fields Medal-winning work) proved Serre's conjecture.
The embryo continues to develop in the egg prior to hatching. In the northernmost coastal region of New South Wales, the lizards have relatively long incubation periods (approximately 15 days), and the eggshells are thicker.Reeder, T. W. 2003. A phylogeny of the Australian Sphenomorphus group (Scincidae : Squamata) and the phylogenetic placement of the crocodile skinks (Tribolonotus): Bayesian approaches to assessing congruence and obtaining confidence in maximum likelihood inferred relationships.
Modulo 2, every integer is a quadratic residue. Modulo an odd prime number p there are (p + 1)/2 residues (including 0) and (p − 1)/2 nonresidues, by Euler's criterion. In this case, it is customary to consider 0 as a special case and work within the multiplicative group of nonzero elements of the field Z/pZ. (In other words, every congruence class except zero modulo p has a multiplicative inverse.
Karma (lit. "action") refers to the works one performs, which can occur either in congruence with or in opposition to Dharma – and thus, to Ṛta – and which are posited to stand in a causal relationship to the pains and pleasures one experiences in life.Myers (2001:184). The emergence of Karma as a central doctrine of the late Vedic and early Hindu tradition is due in part to the problem of theodicy.
The method of casting out nines offers a quick check of decimal arithmetic computations performed by hand. It is based on modular arithmetic modulo 9, and specifically on the crucial property that 10 ≡ 1 (mod 9). Arithmetic modulo 7 is used in algorithms that determine the day of the week for a given date. In particular, Zeller's congruence and the Doomsday algorithm make heavy use of modulo-7 arithmetic.
In S. Kitayama & D. Cohen (Eds.), Handbook of cultural psychology. (691–713). New York: Guilford. For example, the association between self-esteem and life satisfaction is much stronger in individualist culture than in collectivistic culture (Diener & Diener, 1995; Oishi, Diener, Lucas, & Suh, 1999). Diener and his colleagues also discovered a cultural congruence effect such that people are happier if their characteristics match the cultural norms (Fulmer et al.
Theorem (Funayama and Nakayama 1942). The congruence lattice of any lattice is distributive. This says that α ∧ (β ∨ γ) = (α ∧ β) ∨ (α ∧ γ), for any congruences α, β, and γ of a given lattice. The analogue of this result fails, for instance, for modules, as A\cap(B+C) eq(A\cap B)+(A\cap C), as a rule, for submodules A, B, C of a given module.
The method of coordinates (analytic geometry) was adopted by René Descartes in 1637. At that time, geometric theorems were treated as absolute objective truths knowable through intuition and reason, similar to objects of natural science; and axioms were treated as obvious implications of definitions. Two equivalence relations between geometric figures were used: congruence and similarity. Translations, rotations and reflections transform a figure into congruent figures; homotheties — into similar figures.
150px Michele Cipolla (28 October 1880, Palermo - 7 September 1947, Palermo) was an Italian mathematician, mainly specializing in number theory. He was a professor of Algebraic Analysis at the University of Catania and, later, the University of Palermo. He developed (among other things) a theory for sequences of sets and Cipolla's algorithm for finding square roots modulo a prime number. He also solved the problem of binomial congruence.
In traditional geometry, affine geometry is considered to be a study between Euclidean geometry and projective geometry. On the one hand, affine geometry is Euclidean geometry with congruence left out; on the other hand, affine geometry may be obtained from projective geometry by the designation of a particular line or plane to represent the points at infinity.H. S. M. Coxeter (1942). Non-Euclidean Geometry, University of Toronto Press, pp.
Studying cospeciation within plant-insect relationships, he proposed that species have a physiological range of conditions and environments. Over time, conserved traits within a parasitic species allows for survival in a range of conditions or environments. "Ecological fitting", as it is known, means more closely related parasites will share similar traits that pertain to surviving on a particular host. This provides explanation for the congruence of the host-parasite phylogenies.
Self-regulation has been conceptualized in proposed models by Tsui and Ashford (1994) as well as Wood and Bandura (1989). The models have some differences but agree on a fundamental sequence where individuals (a) regulate their attention and effort around self-set goals or assigned goals, (b) take action to achieve their goals, (c) obtain their goals or their performance strategy, if necessary, to maintain or enhance their progress toward their goals and (e) recommence the cycle. Tsui and Ashford (1994) describe the procedure as setting the goal, behaving, detecting a discrepancy, and lastly reducing any discrepancy. This process is vital in leader development because it can have both internal and external effects. As Sosik, Potosky, and Jung (2002) stated that, "individuals desire congruence between their own and others’ perceptions of their behavior, and, therefore, set and work toward goals to reduce perceptual discrepancies, gain congruence, and improve their effectiveness" (p. 212).
Repeated application of the Finsler–Hadwiger theorem can be used to prove Van Aubel's theorem, on the congruence and perpendicularity of segments through centers of four squares constructed on the sides of an arbitrary quadrilateral. Each pair of consecutive squares forms an instance of the theorem, and the two pairs of opposite Finsler–Hadwiger squares of those instances form another two instances of the theorem, having the same derived square., problem 15, pp. 25–26.
Synthetic proofs of geometric theorems make use of auxiliary constructs (such as helping lines) and concepts such as equality of sides or angles and similarity and congruence of triangles. Examples of such proofs can be found in the articles Butterfly theorem, Angle bisector theorem, Apollonius' theorem, British flag theorem, Ceva's theorem, Equal incircles theorem, Geometric mean theorem, Heron's formula, Isosceles triangle theorem, Law of cosines, and others that are linked to here.
The appraisal process is broken up into two different categories, primary appraisal and secondary appraisal (Lazarus, 1991). In a person's primary appraisal, he or she evaluates two aspects of a situation: the motivational relevance and the motivational congruence (Smith & Kirby, 2009). When evaluating motivational relevance, an individual answers the question, "How relevant is this situation to my needs?" Thus, the individual evaluates how important the situation is to his or her well-being.
After 1921 Cuschieri's political engagements continued to grow gradually. The rise to power of Benito Mussolini in Italy in 1922 made him, and many others in Malta, look to fascism with increasing fascination and appeal. Like many other Neo-Thomists, Cuschieri saw great congruence between the Scholastics' philosophical position and the Italian philosophy of fascism. By time, Cuschieri became an overt and avowed Fascist, and this was recognised both in Malta and in Italy.
This symbol (in US English) informally means "approximately", "about", or "around", such as "~30 minutes before", meaning "approximately 30 minutes before". It can mean "similar to", including "of the same order of magnitude as", such as: "" meaning that and are of the same order of magnitude. Another approximation symbol is the double tilde , meaning "approximately equal to". The tilde is also used to indicate congruence of shapes by placing it over an symbol, thus: .
Namely, in the ring of integers of the appropriate number field, the rational prime 13 splits as a product of three distinct prime ideals. The principal congruence subgroups defined by the triplet of primes produce Fuchsian groups corresponding to the first Hurwitz triplet. The sequence of allowable values for the genus of a Hurwitz surface begins :3, 7, 14, 17, 118, 129, 146, 385, 411, 474, 687, 769, 1009, 1025, 1459, 1537, 2091, ...
Such an observer will experience some interesting optical effects. If he looks into the oncoming wavefronts at distant galaxies which have already encountered the wave, he will see their images undistorted. This must be the case, since he cannot know the wave is coming until it reaches his location, for it is traveling at the speed of light. However, this can be confirmed by direct computation of the optical scalars of the null congruence \partial_v.
Keith Moxey, Peasants, Warriors, and Wives: Popular Imagery in the Reformation (U of Chicago Press, 2004). The course of the war also demonstrated the importance of a congruence of events: the new liberation ideology, the appearance within peasant ranks of charismatic and military-trained men like Müntzer and Gaismair, a set of grievances with specific economic and social origins, a challenged set of political relationships and a communal tradition of political and social discourse.
RFRA was seen disproportionate in its effects compared to its objective. Justice Kennedy wrote: Moreover, remedial or prophylactic legislation still had to show "congruence and proportionality" between the end it aimed to reach (that is, the violations it aimed to correct), and the means it chose to reach those ends--that is, the penalties or prohibitions it enacted to prevent or correct those violations. Because RFRA was not reasonably remedial or preventative, it was unconstitutional.
A special class of accelerated observers follow worldlines whose three curvatures are constant. These motions belong to the class of Born rigid motions, i.e., the motions at which the mutual distance of constituents of an accelerated body or congruence remains unchanged in its proper frame. Two examples are Rindler coordinates or Kottler-Møller coordinates for the proper reference frame of hyperbolic motion, and Born or Langevin coordinates in the case of uniform circular motion.
Behavioral Mimicry characteristic traits are noticed in body positioning and postures. These traits would fit into the dynamics noted between interacting individuals. Noted psychotherapist, Albert Scheflen (1964) believed that mimicry or postural congruence was an indicator of similarity in views or rules among interacting individuals in similar settings. (Chartrand and Bargh, 1999) focused on mimicry of specific mannerisms and confirmed that mimicry occurs spontaneously in dyadic interactions (Interpersonal Communications, Spitzburgh and Cupach, 2007).
Lee et al. supported the studies on that product involvement strengthens the effects of "endorser–product congruence on consumer responses" when the endorsers expertise is well related with product to create source credibility. Lee's finding also helps to understand celebrity endorsement as not only a peripheral cue but also a motivation for central route. Later in 1985, Bitner, Mary J., and Carl Obermiller expand this model theoretically in the field of marketing.
The course introduces concepts such as basic trigonometry, angles of elevation and depression, and methods of proving triangle congruence. Algebra II, advanced Algebra or intermediate algebra has a prerequisite of Algebra I. Historically, intermediate algebra has been a high school level course. The Common Core mathematical standards recognize both the sequential as well as the integrated approach to teaching high-school mathematics, which resulted in increased adoption of integrated math programs for high school.
Graumann & E.-D. Lantermann (Hrsg.), Ökologische Psychologie (S. 1-13). München: Psychologie Verlags Union. It deals, for example, with the concepts of ‘appropriation’ (Graumann), ‘behavior-setting analysis’ (Kaminski), ‘person-environment congruence’ (Fuhrer) and ‘control and loss of control’ (Fischer and Stephan). Additional subjects include ‘children and environment’ (Flade), ‘school learning environments’ (Linneweber), ‘museums’ (Klein), ‘working environments’ (Schmale), ‘office environments’ (Schaible-Rapp), ‘therapeutic environments’ (Welter), ‘the sick and disabled’ (Day) and ‘nursing homes’ (Saup).
Tarski's axiomatization is shorter than its rivals, in a sense Tarski and Givant (1999) make explicit. It is more concise than Pieri's because Pieri had only two primitive notions while Tarski introduced three: point, betweenness, and congruence. Such economy of primitive and defined notions means that Tarski's system is not very convenient for doing Euclidean geometry. Rather, Tarski designed his system to facilitate its analysis via the tools of mathematical logic, i.e.
Freda Adler coined synnomie as the opposite of anomie. Using Émile Durkheim's concept of social solidarity and collective consciousness, Adler defined synnomie as "a congruence of norms to the point of harmonious accommodation." Adler described societies in a synnomie state as "characterized by norm conformity, cohesion, intact social controls and norm integration." Social institutions such as the family, religion, and communities, largely serve as sources of norms and social control to maintain a synnomic society.
Social distance, as Ellis notes, concerns the extent to which individual learners can identify themselves with members of TL group and, thereby, can achieve contact with them. Psychological distance is the extent to which individual learners are at ease with their target-language learning task.Ellis (1994), p. 231 Schumann identifies eight factors that influence social distance: social dominance, integration pattern, enclosure, cohesiveness, size factor, cultural congruence, attitude factor, and intended length of residence.
Giuseppe Peano and Mario Pieri used the expression motion for the congruence of point pairs. Alessandro Padoa celebrated the reduction of primitive notions to merely point and motion in his report to the 1900 International Congress of Philosophy. It was at this congress that Bertrand Russell was exposed to continental logic through Peano. In his book Principles of Mathematics (1903), Russell considered a motion to be a Euclidean isometry that preserves orientation.
The smallest 5-Con triangles with integral sides. In geometry, two triangles are said to be 5-Con or almost congruent if they are not congruent triangles but they are similar triangles and share two side lengths (of non- corresponding sides). The 5-Con triangles are important examples for understanding the solution of triangles. Indeed, knowing three angles and two sides (but not their sequence) is not enough to determine a triangle up to congruence.
The symbol can be annotated to denote various sets, with varying usage amongst different authors: , or for the positive integers, or for non-negative integers, and for non-zero integers. Some authors use for non-zero integers, while others use it for non-negative integers, or for }. Additionally, is used to denote either the set of integers modulo (i.e., the set of congruence classes of integers), or the set of -adic integers.
Vanderscheuren, 2006, Montgomery, Het beschrijf, Vers Brussel, Brussels, Belgium where the painted cityscapes show in combination with a poem by Agnieszka Kuciak, a Polish poet and different interviews with local inhabitants. This congruence of systems of signs finalizes with a sculpture on Montgomery Square. He designs a very high lifeguard chair in stainless steel on a concrete slab in which one may read a poem of Kuciak.P; Smet, 2008, In Transit, 5 jaar visuele kunst in Brussel, p.
Euclidean geometry is geometry in its classical sense. As it models the space of the physical world, it is used in many scientific areas, such as mechanics, astronomy, crystallography, and many technical fields, such as engineering, architecture, geodesy, aerodynamics, and navigation. The mandatory educational curriculum of the majority of nations includes the study of Euclidean concepts such as points, lines, planes, angles, triangles, congruence, similarity, solid figures, circles, and analytic geometry.Schmidt, W., Houang, R., & Cogan, L. (2002).
Phylogeny based on the following works:Lavoué, S., Sullivan J. P., & Hopkins C. D. (2003): Phylogenetic utility of the first two introns of the S7 ribosomal protein gene in African electric fishes (Mormyroidea: Teleostei) and congruence with other molecular markers. Biological Journal of the Linnean Society. 78, 273-292. PDF Sullivan, J. P., Lavoué S., & Hopkins C. D. (2000): Molecular systematics of the African electric fishes (Mormyroidea: Teleostei) and a model for the evolution of their electric organs.
Animation showing the continuous shrinking of the Yff central triangle to the Yff center of congruence. The animation also shows the continuous expansion of the Yff central triangle until the three outer triangles reduce to points on the sides of the triangle. Let ABC be any triangle. Let P1Q1, P2Q2, P3Q3 be the isoscelizers of the angles A, B, C such that the triangle A'B'C' formed by them is the Yff central triangle of triangle ABC.
On the other hand, emotion-focused coping refers to one's ability to handle or adjust to the situation should the circumstances remain inconsistent with one's goals (Smith & Kirby, 2009). Again, the emotions people experience are influenced by how they perceive their ability to perform emotion-focused coping. The fourth component of secondary appraisal is one's future expectancy (Lazarus, 1991). Future expectancy refers to one's expectations of change in the motivational congruence of a situation (for any reason).
The preceding alternative calculus is an example of a Hilbert-style deduction system. In the case of propositional systems the axioms are terms built with logical connectives and the only inference rule is modus ponens. Equational logic as standardly used informally in high school algebra is a different kind of calculus from Hilbert systems. Its theorems are equations and its inference rules express the properties of equality, namely that it is a congruence on terms that admits substitution.
His research interests include: diversification of life, quality of the fossil record, shapes of phylogenies, age-clade congruence, mass extinctions, Triassic ecosystem evolution, basal diapsid phylogeny, basal archosaurs, and the origin of the dinosaurs. Benton has also been contributing in some documentaries. One of these was BBCs 2002 program The Day The Earth Nearly Died, which feature scientists and deals with the mysteries of the Permian extinction. In December 2010, Benton had a rhynchosaur (Bentonyx) named in his honour.
In modular arithmetic, the method of successive substitution is a method of solving problems of simultaneous congruences by using the definition of the congruence equation. It is commonly applied in cases where the conditions of the Chinese remainder theorem are not satisfied. There is also an unrelated numerical-analysis method of successive substitution, a randomized algorithm used for root finding, an application of fixed-point iteration. The method of successive substitution is also known as back substitution.
The "congruence and proportionality" requirement replaced the previous theory advanced in Katzenbach v. Morgan that the Equal Protection Clause is "a positive grant of legislative power authorizing Congress to exercise its discretion in determining the need for and nature of legislation to secure Fourteenth Amendment guarantees." Before the 1997 Boerne decision, Katzenbach v. Morgan was often interpreted as allowing Congress to go beyond, but not fall short of, the Court's interpretation of the Equal Protection Clause.
The pathogenic tendency of Sporisorium reilianum as illustrated above is to carry out its life cycle in congruence with the growth of either maize or sorghum as the host plant. For example, In place of ears of corn; plant-like sorus develop. The onset of this smut is sporadic and slowly progressive however disease severity is high. For example, a field of corn can have 10% infected with yield loss that has an 80% apparent infection rate.
The three components of primary appraisal are goal relevance, goal congruence, and type of ego-involvement. In the primary appraisal stage, an individual first evaluates an event in terms of personal goal relevanceOatley et al., 2006 If an event is deemed relevant to an individual's personal goals, an emotion is generated; if not, an emotion will not ensue. Then the individual appraises ongoing events to the extent that the event is congruent or incongruent with the individual's goals.
Primary Appraisal Components 1\. If there is goal relevance, then any emotion is possible, including love. 2\. If there is goal congruence, then only positive emotions are possible, including love. 3\. If the type of ego-involvement is desire for mutual appreciation, which is affirming to our ego-identity, then the emotion possibilities narrow to love (or at least liking); if to this is added sexual interest or passion, then love is romantic rather than companionate.
Within the progression of modulations different voices behave as though they are in different meters as different voices either prepare, result from, or resist meter changes, not in congruence with each other. This allows Carter to move smoothly between asynchronicity and synchronicity of voices. As musicologist Joseph Kerman summarizes, "Simultaneous speeds give Carter novel possibilities of texture; successive speeds give him novel possibilities of musical movement."Joseph Kerman, "American Music: The Columbia Series," Hudson Review 11 (Autumn 1958): 422.
An empirical research was done by Katholiki Georgiades, Michael H. Boyle, and Kelly A. Fife over the Emotional and Behavior Problems Among Adolescent Students, in specific immigrant students. They examined the relationship between immigrants and racial/ethnic congruence in school. They hypothesized that school belonging is the connection between the congruency and the emotional problems. Although their study was unable to find enough evidence to support their hypothesis they agree that school belonging will influence emotional behavioral problems.
Phylogeny based on the following works:Lavoué, S., Sullivan J. P., & Hopkins C. D. (2003): Phylogenetic utility of the first two introns of the S7 ribosomal protein gene in African electric fishes (Mormyroidea: Teleostei) and congruence with other molecular markers. Biological Journal of the Linnean Society. 78, 273-292. PDF Sullivan, J. P., Lavoué S., & Hopkins C. D. (2000): Molecular systematics of the African electric fishes (Mormyroidea: Teleostei) and a model for the evolution of their electric organs.
In its full generality, partitioning cryptanalysis works by dividing the sets of possible plaintexts and ciphertexts into efficiently-computable partitions such that the distribution of ciphertexts is significantly non-uniform when the plaintexts are chosen uniformly from a given block of the partition. Partitioning cryptanalysis has been shown to be more effective than linear cryptanalysis against variants of DES and CRYPTON. A specific partitioning attack called mod n cryptanalysis uses the congruence classes modulo some integer for partitions.
In § VI of the Disquisitiones ArithmeticaeGauss, DA, arts 329-334 Gauss discusses two factoring algorithms that use quadratic residues and the law of quadratic reciprocity. Several modern factorization algorithms (including Dixon's algorithm, the continued fraction method, the quadratic sieve, and the number field sieve) generate small quadratic residues (modulo the number being factorized) in an attempt to find a congruence of squares which will yield a factorization. The number field sieve is the fastest general-purpose factorization algorithm known.
High-commitment management firms are designed by their founders or transformational chief executives to achieve sustained high commitment from employees. The application of high-commitment management in firms today originated from an alignment of the employees’ and the firm's mission. Sociologists attribute this congruence as a product of performance and psychological collaboration between the firm and its employees. Since its initial developments, high commitment management has been driven by self- regulated behavior and performance-driven group dynamics.
More generally, for any e and d satisfying , the same conclusion follows from Carmichael's generalization of Euler's theorem, which states that for all m relatively prime to n. When m is not relatively prime to n, the argument just given is invalid. This is highly improbable (only a proportion of numbers have this property), but even in this case the desired congruence is still true. Either or , and these cases can be treated using the previous proof.
Though parasites have been thought to be specialized to a certain host species, it is common for a parasite to colonize a different host that was not previous colonized by the parasite species. If a "host switch" occurs after a cospeciation event, the presence of the parasite on other host species will disrupt any potential congruence in the two phylogenies. Coupled with extinction or independent speciation, phylogenetic comparisons can become complicated and entirely mask the cospeciation event.
The majority, in an opinion authored by Chief Justice William Rehnquist, began by reaffirming City of Boerne v. Flores (1997), which was the first case to set down the "congruence and proportionality" requirement for laws enacted under Section 5 of the Fourteenth Amendment. The Court stated that while "Congress' power to enforce' the [Fourteenth] Amendment includes the authority both to remedy and to deter violation of rights guaranteed thereunder by prohibiting a somewhat broader swath of conduct, including that which is not itself forbidden by the Amendment's text",538 U.S. at 727 (citations and internal quotation marks omitted). the remedies which Congress enacts to enforce the Amendment must not constitute "an attempt to substantively redefine the States' legal obligations."538 U.S. at 728 (citations and internal quotation marks omitted). To prevent Congress from doing this, the Court said, its case law required Section 5 legislation to "exhibit 'congruence and proportionality between the injury to be prevented or remedied and the means adopted to that end.'"538 U.S. at 728 (quoting City of Boerne v. Flores, 521 U.S. at 520).
Promotion refers to "the marketing communication used to make the offer known to potential customers and persuade them to investigate it further". May comprise elements such as: advertising, PR, direct marketing and sales promotion. Target marketing allows the marketer or sales team to customize their message to the targeted group of consumers in a focused manner. Research has shown that racial similarity, role congruence, labeling intensity of ethnic identification, shared knowledge and ethnic salience all promote positive effects on the target market.
We can prove by several means either proof theoretic (algebraic steps); or semantic (truth table, method of analytic tableaux, Venn diagram, Veitch diagram / Karnaugh map) known in propositional calculus that :\left(A \land \left( A \rightarrow B\right)\right) \rightarrow B holds. Since i-j \mid m, by the transitivity property of the divisibility relation, p \mid i-j \rightarrow p \mid m. Thus (as equality axioms postulate identity to be a congruence relation ) :p \mid m can be proven.
The collaboration between the older and more experienced Rantzau under the younger, less experienced Cadogan is an example of the congruence in Marlborough's multinational army. In 1709, Denmark re-entered the Great Northern War against Sweden and Rantzau returned to Denmark to participate as lieutenant-general in the invasion of Scania under Christian Detlev Reventlow. This led to the Battle of Helsingborg (1710). Just prior to the battle, Reventlow was taken ill and had to yield command to Jørgen Rantzau.
He brought hundreds of new attendees to Azusa, helping the previously struggling ministry grow. Three weeks after Garr's experience, he said God called on him to take Pentecostalism to India and China. In congruence with this, Garr was taken off of the editor list for the Burning Bush magazine and was denounced by other leaders of the Burning Bush movement. Before they arrived in India and China, however, the Garrs stopped in Danville to spread the Pentecostal message to their former congregations.
Scientists and philosophers often marvel at the congruence between nature and mathematics. In 1960 the Nobel Prize–winning physicist and mathematician Eugene Wigner wrote an article entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". He pointed out that "the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it.""The Unreasonable Effectiveness of Mathematics in the Natural Sciences," in Communications on Pure and Applied Mathematics, vol.
Two vectors of Rn are in the same congruence class modulo the subspace if and only if they are identical in the last n−m coordinates. The quotient space Rn/ Rm is isomorphic to Rn−m in an obvious manner. More generally, if V is an (internal) direct sum of subspaces U and W, :V=U\oplus W then the quotient space V/U is naturally isomorphic to W . An important example of a functional quotient space is a Lp space.
Like Mankind, the Macro Manuscript version of Wisdom bears a Latin inscription by the monk Thomas Hyngman and the phrase (translated), “Oh book, if anyone shall perhaps ask to whom you belong, you will say, “I belong above everything to Hyngham, a monk.” Eccles, pp. xxviii Similarities between this hand and the text of the play lead scholars to believe that Hyngman transcribed the play.Beadle, pp. 318 Close parallels between the Digby version and Macro version (including congruence of transcription errors).
The libertarian understanding of BI; ii. The identification of the community as a network; iii. The vision of the project as integrated pedagogical process. As we have said we do not deny that the methodology has influence on the results, but also reaffirm that the congruence between the object and its method is itself inseparable from the empirical definition, and determining not only the fulfilment of the purpose of the process or system, but the character and authenticity of the program or project.
Seminole reinforced the "sovereign immunity of states" doctrine, which makes it difficult to sue states for many things, especially civil rights violations. The Flores "congruence and proportionality" requirement prevents Congress from going too far in requiring states to comply with the Equal Protection Clause, which replaced the ratchet theory advanced in Katzenbach v. Morgan (1966). The ratchet theory held that Congress could ratchet up civil rights beyond what the Court had recognized, but that Congress could not ratchet down judicially recognized rights.
According to Slings, the use of the protreptic in Clitophon is a parody of protreptic literature, which is designed to cause a change in behavior of the listener. Whether or not Clitophon was paraphrasing, Socrates' speeches lack congruence in content with three unrelated exhortations, taking the pattern of the Platonic trichotomy of values. Clitophon employs this pattern with exhortative motifs seen in other dialogues. The beginning of the dialogue is the accusing protreptic seen in Plato's Apology at 29d9-e3.
The more general Ramanujan–Petersson conjecture for holomorphic cusp forms in the theory of elliptic modular forms for congruence subgroups has a similar formulation, with exponent where is the weight of the form. These results also follow from the Weil conjectures, except for the case , where it is a result of . The Ramanujan–Petersson conjecture for Maass forms is still open (as of 2016) because Deligne's method, which works well in the holomorphic case, does not work in the real analytic case.
Steuco preferred Plato to Aristotle and saw greater congruence between the former and Christianity than the latter philosopher. He held that philosophy works in harmony with religion and should lead to knowledge of God, and that truth flows from a single source, more ancient than the Greeks. Steuco was strongly influenced by Iamblichus's statement that knowledge of God is innate in all,Jamblichi De mysteriis liber, ed. Gustavus Parthey (Berlin), I, 3; 7-10 and also gave great importance to Hermes Trismegistus.
When an external, public phenomenon is experienced and carefully described (in words or measurements) by one individual, other individuals can see if their experiences of the phenomenon "fit" the description. If they do, a sense of congruence between one subject and another occurs. This is the basis for a definition of what is true that is agreed upon by the involved parties. If the description does not fit the experience of one or more of the parties involved, incongruence occurs instead.
Until 1968, Saudi Arabia used Arabic time, where clocks were set to 12 o'clock at sunset or when the call to prayer for the sunset prayer was heard. This was because the Islamic calendar defines sunset as marking the beginning of a new day. However this later conflicted with the introduction of western sun time, which defined, in congruence with Europe, the start of a new day to be midnight. With western sun time, clocks were set to six o'clock at sun set.
American Academy Elections, Notices of the American Mathematical Society, vol. 52 (2005), no. 7, p. 764 In 2005-6 He led in the Institute for Advanced Study in Princeton a year long program on "Pro-finite groups and the congruence subgroup problem". In 2006, he got an honorary degree from the University of Chicago for his contribution to Modern mathematics.Honorary Degrees University of Chicago In 2008 Lubotzky received the European Research Council (ERC) advanced grant for exceptional established research leaders.
Fresco of a Roman woman from Pompeii, c. 50 AD The word "beauty" is often used as a countable noun to describe a beautiful woman. The characterization of a person as “beautiful”, whether on an individual basis or by community consensus, is often based on some combination of inner beauty, which includes psychological factors such as personality, intelligence, grace, politeness, charisma, integrity, congruence and elegance, and outer beauty (i.e. physical attractiveness) which includes physical attributes which are valued on an aesthetic basis.
This vector consists of three stages which flow in chronological order, but are able to overlap. These stages are humanizing values, personalizing value, and developing congruence. The process of humanizing values encompasses the shift from a cold, stiff value system to one which is more balanced with the interests of others matched with the interests of the self. After this is established, the individual begins to assemble a core group of personal values which are firmly held, but the beliefs of others are considered and respected.
Moreover, the diamond crystal as a network in space has a strong isotropic property. Namely, for any two vertices x and y of the crystal net, and for any ordering of the edges adjacent to x and any ordering of the edges adjacent to y, there is a net-preserving congruence taking x to y and each x-edge to the similarly ordered y-edge. Another (hypothetical) crystal with this property is the Laves graph (also called the K4 crystal, (10,3)-a, or the diamond twin).
Mount Mary University students can participate in several student clubs and organizations, campus ministry activities, honor societies, and athletics teams. In congruence with the university's mission, Mount Mary also encourages students to participate in social justice and service learning activities on and off campus, as well as study abroad experiences. The student-run newspaper, Arches, is an award-winning publication. The newspaper won awards for general web excellence, sports reporting, graphics, and general reporting at the Wisconsin Newspaper Association's Collegiate Better Newspaper Contest in 2012.
The Honolulu Fire Department (HFD) operates their 44 Fire Stations on the Island of Oahu, and in and around Honolulu. Seven current or former stations are on the National Register of Historic Places, of which five are still in use today as fire stations. By the 1920s, the accepted style for most public architecture in Honolulu, Hawaii, was Spanish Mission Revival or, more broadly, Mediterranean Revival. Five fire stations built on Oahu between 1924 and 1932 illustrate this stylistic congruence, despite being designed by three different architects.
Gibberish, also called jibber-jabber or gobbledygook, is speech that is (or appears to be) nonsense. It may include speech sounds that are not actual words, or language games and specialized jargon that seems nonsensical to outsiders. "Gibberish" is also used as an imprecation to denigrate or tar ideas or opinions the user disagrees with or finds irksome, a rough equivalent of "nonsense", "folderol", or "claptrap". The implication is that the criticized expression or proposition lacks substance or congruence, as opposed to simply being a differing view.
There are also four tone markers that are sometimes used on vowels to avoid ambiguity in homophones, but this is generally uncommon. Gaj's alphabet has been adopted by the Serbian and Bosnian standards and that it has complete one-to-one congruence with Serbian Cyrillic, where the three digraphs map to Cyrillic letters џ, љ and њ, respectively. Rarely and non-standardly, digraph dj is used instead of đ (like it was previously) (Cyrillic ђ). Montenegrin variant additionally uses Ś and Ź to indicate dialectal pronunciation.
Mood- congruent memory has been demonstrated by the finding that emotional material is remembered more reliably in moods that match the emotional content of these memories. For example, when feeling depressed, it is quite typical for an individual to remember more of the negative events their past than of the positive events. Hence, the mood-congruence memory effect refers to better recall for information contained in experiences that match an individual's current emotional state. This effect has been found to occur for both happy and sad memories.
The spirit of pre- War American culture was one of expansionism and activism with an orientation toward business and enterprise. The extensive financial records and correspondence of the Volunteer Movement illustrate a congruence in style between business enterprise and the missions enterprise. American culture's shift toward scientific positivism during this era was reflected in the Student Volunteer Movement's emphasis on elaborate statistical evidence of its work. Practical aspects of the late nineteenth and early twentieth century also contributed to the rapid growth of Protestant missions.
Kernels allow defining quotient objects (also called quotient algebras in universal algebra, and cokernels in category theory). For many types of algebraic structure, the fundamental theorem on homomorphisms (or first isomorphism theorem) states that image of a homomorphism is isomorphic to the quotient by the kernel. The concept of a kernel has been extended to structures such that the inverse image of a single element is not sufficient for deciding whether an homomorphism is injective. In these cases, the kernel is a congruence relation.
Many communities that have adopted the ABC strategy of sex education have used this strategy of sex education in congruence with religious or ideological influences. In Malawi, religious leaders influence and emphasize the use this strategy However, in the United States, political ideologies influence the use of ABC strategy. For example, conservatism had previously taught young women that sex was about danger, not pleasure, focusing on an abstinence-only education program. Political ideologies have long been influences in the debate over sex education programs.
In cryptography, mod n cryptanalysis is an attack applicable to block and stream ciphers. It is a form of partitioning cryptanalysis that exploits unevenness in how the cipher operates over equivalence classes (congruence classes) modulo n. The method was first suggested in 1999 by John Kelsey, Bruce Schneier, and David Wagner and applied to RC5P (a variant of RC5) and M6 (a family of block ciphers used in the FireWire standard). These attacks used the properties of binary addition and bit rotation modulo a Fermat prime.
Relations with the same formal properties as similarity relations of sensations considered by Poincaré are nowadays, after Zeeman, called tolerance relations. A tolerance \tau on a set O is a relation \tau \subseteq O \times O that is reflexive and symmetric. In algebra, the term tolerance relation is also used in a narrow sense to denote reflexive and symmetric relations defined on universes of algebras that are also compatible with operations of a given algebra, i.e., they are generalizations of congruence relations (see e.g.,).
Marshall deputed a succession of ASI officers to survey the site. These included D. R. Bhandarkar (1911), R. D. Banerji (1919, 1922–1923), and M.S. Vats (1924). In 1923, on his second visit to Mohenjo-daro, Baneriji wrote to Marshall about the site, postulating an origin in "remote antiquity," and noting a congruence of some of its artifacts with those of Harappa. Later in 1923, Vats, also in correspondence with Marshall, noted the same more specifically about the seals and the script found at both sites.
However, Jesus Christ, as both man and the Second Person of the Holy Trinity, possessed complete congruence of His two wills, the divine and the human. Therefore, St Maximus reasoned, Christ was never in a state of ignorance regarding what he wanted, and so never engaged in gnomic willing. Aristotle, a major philosophical influence on Maximus, in comparing the works of Nature with those of a human worker, had also declared that any process of deliberation, far from indicating superior intellect, is a sign of our weakness.
Congruence is an example of an equivalence relation. The leftmost two triangles are congruent, while the third and fourth triangles are not congruent to any other triangle shown here. Thus, the first two triangles are in the same equivalence class, while the third and fourth triangles are each in their own equivalence class. In mathematics, when the elements of some set have a notion of equivalence (formalized as an equivalence relation) defined on them, then one may naturally split the set into equivalence classes.
Aside from entomology Colless was also very interested in the theory and philosophy of taxonomy and classification. Colless published 30 influential articles on the philosophical underpinnings and theory of taxonomy from 1966–1996. In total, he published 127 scientific papers and book chapters. His most citedDH Colless bibliography and perhaps most utilized contribution is entitled Congruence between morphometric and allozyme data for Menidia species: a reappraisal, in which he devised the calculation of the consensus fork index (CFI), which is sometimes referred to as Colless' index.
During severe episodes of mania or depression people with bipolar disorder may have psychotic symptoms, such as hallucinations or delusions.. When experiencing hallucinations or delusions, people with schizophrenia often seem to "lose touch" with reality. "Voices" are the most common type of hallucination in schizophrenia. In bipolar disorder, the psychotic symptoms tend to reflect the person's extreme depressed or elated mood (mood congruence). People with either disorder may have delusions of grandeur in which they believe they are a famous person or historical figure.
His departure was initially assumed to be related to the protests. However, unlike Wolfe, student protesters had not requested that he step down. His resignation was the congruence of several issues raised by administrators and faculty, who were displeased with his leadership style, dismissal of administrators, and management of several campus incidents of racism and graduate health insurance subsidies that were allowed to lapse under his leadership. The days after the resignation announcement resulted in some confusion, cancelled classes and reports of threats and suspicious activity.
The major problem with their congruence is that, at Planck scale (a fundamental small unit of length) lengths, general relativity predicts a smooth, flowing surface, while quantum mechanics predicts a random, warped surface, which are nowhere near compatible. Superstring theory resolves this issue, replacing the classical idea of point particles with strings. These strings have an average diameter of the Planck length, with extremely small variances, which completely ignores the quantum mechanical predictions of Planck-scale length dimensional warping. Also, these surfaces can be mapped as branes.
45 One of the first video game artists who contributed more shape and two dimensional characters was Shigeru Miyamoto, who created Mario and Donkey Kong. Starting in the early 1990s art requirements in video games were allowed to increase greatly because there was more room in the budget for art. Video game art began to be in 3D around 1994, before which it had mainly been 2D art design. This required the artist and programmer to work in congruence very carefully, in the beginning, due to the foreign nature of 3D in video games.
Between 1983 and 1985, Alexandra was managed by Bill Wyman of The Rolling Stones and created numerous pop songs and music videos for radio and MTV. Her "Dumped On", "Lust In The Jungle", and "Free As I Want To Be" music videos were shot on location in New Zealand, Hong Kong, Yugoslavia and Los Angeles. Alexandra's music video of Bruce Lee, "Feel The Heat", was revamped in congruence with the Academy of Motion Picture Arts and Sciences 40th Anniversary Celebration of Bruce Lee's breakout film, Enter the Dragon.
Regional synods had been held regularly in the Church of Gaul, more than thirty of them between 314 and 506.Halfond 2. The synods listed here (some of which are also referred to as "General synods of the German empire") mark a particularly Germanic development in the Western Church: to the usual regional or provincial councils, Germanic peoples added a traditional element from their systems of government, the idea of a national council, which was influenced by the Christian East. They also indicate a growing congruence between church and state.
Authenticity encapsulates the uniqueness of a team with descriptions corresponding to being uncompromising, radical or traditional. When teams are perceived as having human traits, the emotional connection between sports team and their sports fan is strengthened due to the ability to link their self-identity, with the team's identity, showing congruence with the brand's personality. Aspects that enable fan identification with a sports team are considered to be predictors of their consumption behaviour such as the continuation of support and participation in the team's activities even after long losing streaks.
Meaningfulness is considered to be related to the feeling of participation and motivation and to a perceived meaning of the work. The meaningfulness component has also been linked with Job control and with task significance. Job control implies that employees have more authority to make decisions concerning their work and the working process. Task significance involves "the experience of congruence between personal values and work activities, which is accompanied by strong feelings of identification with the attitudes, values or goals of the working tasks and feelings of motivation and involvement".
Contextual effects occur as a result of the degree of similarity between the encoding context and the retrieval context of an emotional dimension. The main findings are that the current mood we are in affects what is attended, encoded and ultimately retrieved, as reflected in two similar but subtly different effects: the mood congruence effect and mood-state dependent retrieval. Positive encoding contexts have been connected to activity in the right fusiform gyrus. Negative encoding contexts have been correlated to activity in the right amygdala (Lewis & Critchley, 2003).
If the femur head is dislocated, it should be reduced as soon as possible, to prevent damage to its blood supply. This is preferably done under anaesthesia, following which, leg is kept pulled by applying traction to prevent joint from dislocating. The final management depends on the size of the fragment(s), stability and congruence of the joint. In some cases traction for six to eight weeks may be the only treatment required; however, surgical fixation using screw(s) and plate(s) may be required if the injury is more complex.
The storm system responsible for the tornado outbreak resulted from the unusual congruence of a cold, dry system, originating in the Four Corners and a warm, moist system, moving north out of Texas. Complicating factors included daytime heating and a strong wind field favorable to the creation of circulating thunderstorms. On the second day, the stronger cold front limited discrete supercell activity and the risk of tornadoes decreased significantly. A squall line, however, produced high winds and rain along the river valleys, primarily those of the Mississippi and Ohio Rivers.
Gauss also considered a coarser notion of equivalence, with each coarse class called a genus of forms. Each genus is the union of a finite number of equivalence classes of the same discriminant, with the number of classes depending only on the discriminant. In the context of binary quadratic forms, genera can be defined either through congruence classes of numbers represented by forms or by genus characters defined on the set of forms. A third definition is a special case of the genus of a quadratic form in n variables.
Asymptotic phenomena for the systole of surfaces of large genus have been shown to be related to interesting ergodic phenomena, and to properties of congruence subgroups of arithmetic groups. Gromov's 1983 inequality for the homotopy systole implies, in particular, a uniform lower bound for the area of an aspherical surface in terms of its systole. Such a bound generalizes the inequalities of Loewner and Pu, albeit in a non-optimal fashion. Gromov's seminal 1983 paper also contains asymptotic bounds relating the systole and the area, which improve the uniform bound (valid in all dimensions).
But in 1997, in City of Boerne v. Flores, the Court limited congressional power to override state sovereign immunity using the Fourteenth Amendment, and for the first time required "congruence and proportionality" between the constitutional wrong and the congressionally enacted remedy to protect constitutional rights.521 U.S. 507, 520 (1997). Boerne held that it was the Court, and only the Court, that could determine what constituted a constitutional wrong, and that Congress could not permissibly increase the level of constitutional protection beyond that which the Court had recognized.
Catholic schools wanted to prove their legitimacy in comparison to public ones, and so they created Catholic teacher Certification. This was in congruence with the 1907 Seth Bill, which related the years of teaching experience to one’s certification. After continual urging by school inspectors, the Ontario Provincial government started to legitimately look into the certification of Catholic school teachers. Over the next 20 years, the issue was debated back and forth with the decision on 2 November 1907 by the Judicial Committee of the Privy Council to uphold that Catholic teachers needed certification.
Boerne is important for several reasons. One is that it introduced a completely new test for deciding whether Congress had exceeded its Section 5 powers: the "congruence and proportionality" test, a test that has proven to have great importance in the context of the Eleventh Amendment. Another reason was that it explicitly declared that the Court alone has the ability to state which rights are protected by the Fourteenth Amendment. Still another was that it had First Amendment consequences in that it spelled the end for any legislative attempts to overturn Employment Division v. Smith.
Integrative models assume that consumers process advertising information via two paths – both cognitive (thinking) and affective (feeling) simultaneously. These models seek to combine the type of purchase with the consumer's dominant mode of processing.Yoon,K., Laczniak, R.N., Muehling, D.D. and Reece, B.B., "A Revised Model of Advertising Processing: Extending the Dual Mediation Hypothesis," Journal of Current Issues & Research in Advertising, Vol. 17, no. 2, 1995, pp 53-67 Integrative models are based on research findings indicating that congruence between personality and the way a persuasive message is framed.
This assumes the existence of a notion of equivalence on both language A and language B. Typically, this can be a notion of equality of structured data or a notion of syntactically different yet semantically identical programs, such as structural congruence or structural equivalence. ; soundness : if two terms T_A^1 and T_A^2 are equivalent in A, then [T_A^1] and [T_A^2] are equivalent in B. ; completeness : if two terms [T_A^1] and [T_A^2] are equivalent in B, then T_A^1 and T_A^2 are equivalent in A.
An important precedent for Morrison was United States v. Harris (1883), which ruled that the Equal Protection Clause did not apply to a prison lynching because the state action doctrine applies Equal Protection only to state action, not private criminal acts. Since the ratchet principle was replaced with the "congruence and proportionality" principle by Flores, it was easier to revive older precedents for preventing Congress from going beyond what Court interpretations would allow. Critics such as Associate Justice John Paul Stevens accused the Court of judicial activism (i.e.
A related body of thought in psychotherapy started in the 1950s with Carl Rogers. Based also on the works of Abraham Maslow and his hierarchy of human needs, Rogers brought person-centered psychotherapy into mainstream focus. The primary requirement was that the client receive three core "conditions" from his counselor or therapist: unconditional positive regard, sometimes described as "prizing" the client's humanity; congruence [authenticity/genuineness/transparency]; and empathic understanding. This type of interaction was thought to enable clients to fully experience and express themselves, and thus develop according to their innate potential.
Decades of anthropological, sociological, and psychological research have established that "religious congruence" (the assumption that religious beliefs and values are tightly integrated in an individual's mind or that religious practices and behaviors follow directly from religious beliefs or that religious beliefs are chronologically linear and stable across different contexts) is actually rare. People's religious ideas are fragmented, loosely connected, and context- dependent, as in all other domains of culture and in life. The beliefs, affiliations, and behaviors of any individual are complex activities that have many sources including culture.
Waugh confirmed the autobiographical basis for the novel on several occasions; at the book's launch on 19 July 1957, to Robert Henriques in a letter of 15 August 1957 ("Mr Pinfold's experiences were almost exactly my own."),Amory (ed.), pp. 493–94 and to John Freeman in a Face to Face television interview in 1960.Stannard 1984, p. 517 As well as the congruence with real life of specific incidents in the book, Pinfold's age and his domestic and professional circumstances as revealed in the first chapter closely mirror Waugh's.
After the early unsatisfactory results of the two-component designs, most of the more recent designs feature three components, with a polyethylene meniscal bearing interposed between the two metal bone-anchored components. This meniscal bearing should allow full congruence at the articular surfaces in all joint positions in order to minimize wear and deformation of the components. Poor understanding of the functions of the structures guiding ankle motion in the natural joint (ligaments and articular surfaces), and poor restoration of these functions in the replaced joint may be responsible for the complications and revisions.
Bowlby instead posited that several lines of development were possible, the outcome of which depended on the interaction between the organism and the environment. In attachment this would mean that although a developing child has a propensity to form attachments, the nature of those attachments depends on the environment to which the child is exposed. From early in the development of attachment theory there was criticism of the theory's lack of congruence with various branches of psychoanalysis. Bowlby's decisions left him open to criticism from well-established thinkers working on similar problems.
His methods are still inspiring contemporary mathematicians: Boener and Sniatycki talked about the congruence of Lepage; not so long ago, Demeter Krupka, introduced--beside the eulerian forms which correspond to the classical equations of the calculus of variations of Euler--the so-called lepagian forms or equivalents of Lepage in equations of variations on fiber spaces. We also have Lepage to thank for interesting results concerning linear representations of the symplectic group, and more specifically Lepage's dissolution of an outer potency of the product of an even number of duplicates of a complex surface.
They are spacelike surfaces (topological spheres, tubes, etc.) with restricted bounds, their area tending to decrease locally along any possible future direction and with a dual definition with respect to the past. The trapped surface is a spacelike surface of co-dimension 2, in a Lorentzian spacetime. It follows that any normal vector can be expressed as a linear combination of two future directed null vectors, normalised by: k+ · k− = −2 The k+ vector is directed “outwards” and k− “inwards”. The set of all such vectors engenders one outgoing and one ingoing null congruence.
In number theory, a branch of mathematics, Dickson's conjecture is the conjecture stated by that for a finite set of linear forms , , ..., with , there are infinitely many positive integers for which they are all prime, unless there is a congruence condition preventing this . The case k = 1 is Dirichlet's theorem. Two other special cases are well-known conjectures: there are infinitely many twin primes (n and 2 + n are primes), and there are infinitely many Sophie Germain primes (n and 1 + 2n are primes). Dickson's conjecture is further extended by Schinzel's hypothesis H.
Greater Germanic Reich In the 1920s this originally innocent movement was usurped by nationalistic political forces in several European countries, first and foremost in Germany. It was during this decade that an unfortunate congruence with national socialist ideology was seen to take place; the vocabulary of German Volkskunde, words such as Volk (folk), Rasse (race), Stamm (tribe) and Erbe (heritage) mapped neatly into the political dogmas of Adolf Hitler and the Nazi party. The expressed goal of the National Socialists was to re-establish the purity of the Germanic, i.e. Nordic, tribes in Europe.
The apparent congruence between Gaitskell's economic policies and those of his Conservative successor as chancellor Rab Butler, who had retained and extended NHS charges, was sometimes labelled "Butskellism" by the press. This view was not shared by Gaitskell himself, and after Butler's emergency "Pots and Pans" budget in October 1955, in which he reversed tax cuts made prior to the Conservatives' re-election at the General Election earlier that year, he attacked him strongly for allegedly having misled the electorate. Gaitskell won further praise for his attacks on Butler.
The case of elliptic curves was worked out by Hasse in 1934. Since the genus is 1, the only possibilities for the matrix H are: H is zero, Hasse invariant 0, p-rank 0, the supersingular case; or H non-zero, Hasse invariant 1, p-rank 1, the ordinary case. Here there is a congruence formula saying that H is congruent modulo p to the number N of points on C over F, at least when q = p. Because of Hasse's theorem on elliptic curves, knowing N modulo p determines N for p ≥ 5.
In the texts, the king is called upon to transform into an akh in the Akhet. The akh, literally "effective being", was the resurrected form of the deceased, attained through individual action and ritual performance. If the deceased failed to complete the transformation, they became mutu, that is "the dead". The function of the texts, in congruence with all funerary literature, was to enable the reunion of the ruler's ba and ka leading to the transformation into an akh, and to secure eternal life among the gods in the sky.
The main focus of the book is on the specification of geometric data that will determine uniquely the shape of a three- dimensional convex polyhedron, up to some class of geometric transformations such as congruence or similarity. It considers both bounded polyhedra (convex hulls of finite sets of points) and unbounded polyhedra (intersections of finitely many half-spaces). The 1950 Russian edition of the book included 11 chapters. The first chapter covers the basic topological properties of polyhedra, including their topological equivalence to spheres (in the bounded case) and Euler's polyhedral formula.
If X and Y are algebraic structures of some fixed type (such as groups, rings, or vector spaces), and if the function f from X to Y is a homomorphism, then ker f is a congruence relation (that is an equivalence relation that is compatible with the algebraic structure), and the coimage of f is a quotient of X. The bijection between the coimage and the image of f is an isomorphism in the algebraic sense; this is the most general form of the first isomorphism theorem. See also Kernel (algebra).
More generally, one can use the adelic approach as a way of dealing with the whole family of congruence subgroups at once. From this point of view, an automorphic form over the group G(AF), for an algebraic group G and an algebraic number field F, is a complex- valued function on G(AF) that is left invariant under G(F) and satisfies certain smoothness and growth conditions. Poincaré first discovered automorphic forms as generalizations of trigonometric and elliptic functions. Through the Langlands conjectures automorphic forms play an important role in modern number theory.
A comparison between modern turtles and Proganochelys found that it was not likely that stem- turtles had differentiated into specialized ecologies such as open water swimmers or solely terrestrial turtles in the Late Triassic period. If this is the case, a freshwater habitat would be the most likely environment for Proganochelys to have lived in. On the other hand, it is noted that some believe Proganochelys were solely terrestrial. Shell bone histology of extant turtles revealed congruence with terrestrial turtles for the earliest basal turtles, including Proganochelys, taxa in one study.
In contrast to Nairne's findings of a survival advantage, it has been found that the superiority of survival processing can be explained by a congruity effect. The congruity effect means that people tend to be better at remembering items if they are congruent with the way they are processed. Congruence between the processing task and target words leads to deeper and more elaborate encoding, which is thought to explain the survival advantage. Butler and colleagues conducted three experiments to test this view; the first replicated Nairne's work and confirmed a survival recall advantage.
During the last years of Bronsart's time as president discontent arose over the repertoire of the concerts at the Tonkünstler-Versammlungen. In 1896, in Leipzig, for example, works by Alessandro Scarlatti, Pietro Antonio Locatelli, Johann Sebastian Bach, Georg Friedrich Händel and Friedrich II of Prussia as well as works by Brahms, Berlioz, Liszt and Wagner were performed. The works of historical styles met an increasing interest of that time in music of the Baroque or even earlier periods of music history. Performing these works was in congruence with the statutes of the ADMV.
Let V be an infinite-dimensional vector space over an uncountable field F. Then Con A isomorphic to Sub V implies that A has at least card F operations, for any algebra A. As V is infinite- dimensional, the largest element (unit) of Sub V is not compact. However innocuous it sounds, the compact unit assumption is essential in the statement of the result above, as demonstrated by the following result. Theorem (Lampe 1982). Every algebraic lattice with compact unit is isomorphic to the congruence lattice of some groupoid.
Maria Hoffmann-Ostenhof (née Bauer, born 1947) is an Austrian mathematician known for her work on the behavior of the Schrödinger equation, and particularly on its asymptotic analysis, nodal lines, and behavior near its singularities. Hoffmann-Ostenhof was born on 12 January 1947 in Vienna. She studied mathematics at the University of Vienna, with a year visiting the University of Zurich, and completed her Ph.D. in 1973 at the University of Vienna. Her dissertation, Über Kongruenzverbände universaler Algebren und binärer Systeme [On congruence relations of universal algebras and binary systems] was supervised by .
They hoped these precautions would prevent them contracting the disease. The mask was originally beaked with a purpose in congruence with the miasmatic theory of disease practiced at that time: the hollow beak allowed for the containment of flowers and other sweet-smelling substances designed to keep away the foul odors that were thought to spread infection. Those who wear the plague doctor mask often also wear the associated clothing of the plague doctor. The popularity of the Medico della peste among carnival celebrants can be seen as a memento mori.
Sometimes known as distraction or Mood Incongruent Recollection, this is one of the most common mood repair strategies. Normally people engage in thoughts of mood congruence, which are ones that are in harmony with their mood. Mood incongruent recollection is usually the forced consideration of memories not related to the current mood. The theory behind this thinking is that when the mind is engaged in a track of negative mood, the forced recall of positive memories will break the cycle and force the brain to reorient into a more positive state.
In 2009 Baranski began guest-starring in The Big Bang Theory as Dr. Beverly Hofstadter, a dispassionate psychiatrist and neuroscientist and mother of one of the protagonists, Leonard Hofstadter. She first appeared in the second- season episode "The Maternal Capacitance", for which she received an Emmy nomination. Due to the popularity of her first appearance, Baranski returned in the third season for the Christmas episode "The Maternal Congruence", receiving another Emmy nomination. She appeared in a total of 16 episodes during the show's run, earning 4 Emmy nominations for her recurring role.
He noted that every Euclidean congruence is an affine mapping, and each of these is a projective transformation; therefore the group of projectivities contains the group of affine maps, which in turn contains the group of Euclidean congruencies. The term motion, shorter than transformation, puts more emphasis on the adjectives: projective, affine, Euclidean. The context was thus expanded, so much that "In topology, the allowed movements are continuous invertible deformations that might be called elastic motions."Ari Ben-Menahem (2009) Historical Encyclopedia of the Natural and Mathematical Sciences, v.
According to the social learning theory (more recently expanded as social cognitive theory), behavioural change is determined by environmental, personal, and behavioural elements. Each factor affects each of the others. For example, in congruence with the principles of self-efficacy, an individual's thoughts affect their behaviour and an individual's characteristics elicit certain responses from the social environment. Likewise, an individual's environment affects the development of personal characteristics as well as the person's behavior, and an individual's behaviour may change their environment as well as the way the individual thinks or feels.
In semi-Riemannian geometry, the Bel decomposition, taken with respect to a specific timelike congruence, is a way of breaking up the Riemann tensor of a pseudo-Riemannian manifold into lower order tensors with properties similar to the electric field and magnetic field. Such a decomposition was partially described by Alphonse Matte in 1953 and by Lluis Bel in 1958. This decomposition is particularly important in general relativity. This is the case of four-dimensional Lorentzian manifolds, for which there are only three pieces with simple properties and individual physical interpretations.
Multimodal perception is how animals form coherent, valid, and robust perception by processing sensory stimuli from various modalities. Surrounded by multiple objects and receiving multiple sensory stimulations, the brain is faced with the decision of how to categorize the stimuli resulting from different objects or events in the physical world. The nervous system is thus responsible for whether to integrate or segregate certain groups of temporally coincident sensory signals based on the degree of spatial and structural congruence of those stimulations. Multimodal perception has been widely studied in cognitive science, behavioral science, and neuroscience.
Judge, Bono, Erez, and Locke (2005) found that goal congruence, or choosing self-concordant goals, partially mediates the relationship between core self-evaluations and job satisfaction. The authors explain that individuals with positive self-regard (i.e. high core self- evaluations) believe themselves to be capable and competent and will be less likely to be affected by external factors; thus, they will be more likely to choose self-concordant goals, which will lead to higher satisfaction. On the other hand, individuals with negative self- regard will be susceptible to external factors like anxiety and guilt.
The long-term effects of the Erlangen program can be seen all over pure mathematics (see tacit use at congruence (geometry), for example); and the idea of transformations and of synthesis using groups of symmetry has become standard in physics. When topology is routinely described in terms of properties invariant under homeomorphism, one can see the underlying idea in operation. The groups involved will be infinite-dimensional in almost all cases – and not Lie groups – but the philosophy is the same. Of course this mostly speaks to the pedagogical influence of Klein.
In mathematical logic, the Lindenbaum–Tarski algebra (or Lindenbaum algebra) of a logical theory T consists of the equivalence classes of sentences of the theory (i.e., the quotient, under the equivalence relation ~ defined such that p ~ q exactly when p and q are provably equivalent in T). That is, two sentences are equivalent if the theory T proves that each implies the other. The Lindenbaum–Tarski algebra is thus the quotient algebra obtained by factoring the algebra of formulas by this congruence relation. The algebra is named for logicians Adolf Lindenbaum and Alfred Tarski.
This was one of the Froebel gifts, a set of kindergarten activities designed in the early 19th century by Friedrich Fröbel. The book was also influenced by an earlier Indian geometry textbook, First Lessons in Geometry, by Bhimanakunte Hanumantha Rao (1855–1922). First Lessons drew inspiration from Fröbel's gifts in setting exercises based on paper-folding, and from the book Elementary Geometry: Congruent Figures by Olaus Henrici in using a definition of geometric congruence based on matching shapes to each other and well-suited for folding-based geometry. In turn, Geometric Exercises in Paper Folding inspired other works of mathematics.
Stephen Joseph Owen (April 21, 1898 – May 17, 1964) was an American football player and coach. He earned a place in the Pro Football Hall of Fame as head coach of the National Football League's New York Giants from 1930 to 1953. Owen's skill at designing defenses, his fundamentals-centered approach to the game and his innovative "A formation," a variation on the single-wing, also helped his offenses thrive and were key to his success. His personal style was memorable for the odd congruence of gravelly voice and easy disposition to go with his perpetual tobacco chewing.
Book VI, known only through translation from the Arabic, contains 33 propositions, the least of any book. It also has large lacunae, or gaps in the text, due to damage or corruption in the previous texts. The topic is relatively clear and uncontroversial. Preface 1 states that it is “equal and similar sections of cones.” Apollonius extends the concepts of congruence and similarity presented by Euclid for more elementary figures, such as triangles, quadrilaterals, to conic sections. Preface 6 mentions “sections and segments” that are “equal and unequal” as well as “similar and dissimilar,” and adds some constructional information.
The Rindler coordinate chart has a coordinate singularity at x = 0, where the metric tensor (expressed in the Rindler coordinates) has vanishing determinant. This happens because as x → 0 the acceleration of the Rindler observers diverges. As we can see from the figure illustrating the Rindler wedge, the locus x = 0 in the Rindler chart corresponds to the locus T2 = X2, X > 0 in the Cartesian chart, which consists of two null half-planes, each ruled by a null geodesic congruence. For the moment, we simply consider the Rindler horizon as the boundary of the Rindler coordinates.
In an essay he wrote in 1989, Doob came to believe a clear-cut definition of propaganda was neither possible nor desirable because of the complexity of issues related to behavior in society and differences in times and cultures. The essential ingredients of successful propaganda, for Doob, contained three elements: repetition, cultural congruence, and flattery. Utilizing these three components, if the target is known and objectives clear, then the right acts combined with the right words, at the right time, can carry tremendous leverage. Ultimately, Leonard W. Doob was no advocate for propaganda, like his contemporary, Edward Bernays was.
Although the original core techniques of NLP were therapeutic in orientation their generic nature enabled them to be applied to other fields. These applications include persuasion, sales, negotiation,Tosey P. & Mathison, J., "Fabulous Creatures of HRD: A Critical Natural History of Neuro-Linguistic Programming", University of Surrey Paper presented at the 8th International Conference on Human Resource Development Research & Practice across Europe, Oxford Brookes Business School, 26–28 June 2007 management training, sports,Ingalls, Joan S. (1988) "Cognition and athletic behavior: An investigation of the NLP principle of congruence." Dissertation Abstracts International. Vol 48(7-B), p. 2090.
This may be explained by mood congruence theory, as depressed individuals remember negatively charged memories during frequent negative moods. Depressed adults also tend to actively rehearse negative memories, which increases their retention period and vividness. Another explanation may be the tendency for individuals suffering from depression to separate themselves from their positive memories and focus more on evidence that supports their current negative self-image to keep it intact. Depressed adults also recall positive memories from an observer perspective rather than a field perspective, where they appear as a spectator rather than a participant in their own memory.
It is easy to see that ker f is an equivalence relation on A, and in fact a congruence relation. Thus, it makes sense to speak of the quotient algebra A/(ker f). The first isomorphism theorem in general universal algebra states that this quotient algebra is naturally isomorphic to the image of f (which is a subalgebra of B). Note that the definition of kernel here (as in the monoid example) doesn't depend on the algebraic structure; it is a purely set-theoretic concept. For more on this general concept, outside of abstract algebra, see kernel of a function.
The term and the ideas around co-opetition gained wide attention within the business community after the publication in 1996 of the book by Brandenberger and Nalebuff bearing the same title. Until today this remains the reference work for both researchers and practitioners alike. Giovanni Battista Dagnino and Giovanna Padula's conceptualized in their conference paper (2002) that, at inter- organisational level, coopetition occurs when companies interact with partial congruence of interests. They cooperate with each other to reach a higher value creation if compared to the value created without interaction and struggle to achieve competitive advantage.
In order to distinguish the two definitions, the graphs in which non-edges are required to be a non-unit distance apart may be called strict unit distance graphs.. The graph formed by removing one of the spokes from the wheel graph W7 is a subgraph of a unit distance graph, but is not a strict unit distance graph: there is only one way (up to congruence) to place the vertices at distinct locations such that adjacent vertices are a unit distance apart, and this placement also puts the two endpoints of the missing spoke at unit distance.
Sited adjacent to Housing and Development Board apartment blocks of the Marine Parade Housing Estate, the Marine Parade Community Building could be seen as an attempt to engage the wider community. The activities of the community building were planned to overlap and to coalesce, as a one-stop destination for the entire family. The rich congruence of the multiple programmes for the building is expressed architecturally as a collage of diverse elements. The building was designed by a local architectural firm, William Lim Associates, which adopted a postmodern pluralist approach, expressed through a multiplicity of materials and forms.
Research has shown that multisensory cues from an object may share certain semantic features, which may contribute to cross-modal binding of sensory information. Sinnett and his colleagues conducted an experiment using meaningful stimuli, and their findings showed that the Colavita effect continued to exist when using complex and meaningful stimuli were used. In addition, a study conducted by Laurienti and colleagues showed that, under certain conditions, responses to audiovisual stimuli can be affected by semantic congruence or incongruence. More specifically, their findings showed that participants responded faster to congruent auditory and visual stimuli than to incongruent stimuli.
He goes on to explain that these mental states were once experienced, rendering, by definition, their future spontaneous appearance into consciousness the act of remembering, though we may not always be aware of where or how we experienced this information the first time. Ebbinghaus also made the key note that these involuntary reproductions are not random or accidental; instead, "they are brought about through the instrumentality of other immediately present mental images," under the laws of association. This reflects congruence with Mace’s and Linton’s theory of involuntary memories as by-products of other memories, as discussed above.
It is important to note, however, that this is not a proper distance metric as it does not have the triangle inequality property—or, more formally, the Schwarz inequality—and it violates the coincidence axiom; to repair the triangle inequality property while maintaining the same ordering, it is necessary to convert to angular distance (see below). One advantage of cosine similarity is its low-complexity, especially for sparse vectors: only the non-zero dimensions need to be considered. Other names of cosine similarity are Orchini similarity and the Tucker coefficient of congruence; Ochiai similarity (see below) is cosine similarity applied to binary data.
Sergei Evdokimov was born in Leningrad (now Saint Petersburg, Russia), and graduated from Leningrad State University, Dept. of Mathematics and Mechanics, in 1973 (Honours Diploma). During his studies, he attended a seminar on modular forms and started to work in this area under the supervision of professor Anatoli N. Andrianov. After graduation, he continued research in the theory of modular forms, and in 1977 earned his PhD degree (Candidate of Sciences) from Leningrad Department of Steklov Mathematical Institute of USSR Academy of Sciences with the thesis "Euler products for congruence subgroups of the Siegel group of genus".
The congruence between the principles and methods is not only fundamental to achieving the goal, or only determinant of the degree of correspondence between the object and its primary concepts or theoretical, is the foundation that defines the process, or more precisely the principle that is indeed. Something that involves serious objections to a Basic Income unconditional initiatives within authoritarian regimes. A Basic Income can even exist within a weak democratic, authoritarian or populist, but not exactly under the responsibility of such a scheme, but as the product of free civil society initiative. Being the way, democratic self-management.
Thus Liszt's second piece, Au lac de Wallenstadt (By Lake Wallenstadt), with its evocation of rippling water, is accompanied by Byron's description of the still reflective surface of Lac Leman (stanza 68). Between the next few quotations there is greater congruence, however. Liszt's fifth piece, Orage (Storm), comes with Byron's equating of meteorological and emotional weathers from canto 96. The change of tone in the sixth piece, Vallée d’Obermann, is signalled by the transition of mood at the end of Byron's following stanza 97; and the peaceful beginning of stanza 98 accompanies the succeeding Eglogue (Eclogue).
In number theory, a Shimura variety is a higher-dimensional analogue of a modular curve that arises as a quotient variety of a Hermitian symmetric space by a congruence subgroup of a reductive algebraic group defined over Q. Shimura varieties are not algebraic varieties but are families of algebraic varieties. Shimura curves are the one-dimensional Shimura varieties. Hilbert modular surfaces and Siegel modular varieties are among the best known classes of Shimura varieties. Special instances of Shimura varieties were originally introduced by Goro Shimura in the course of his generalization of the complex multiplication theory.
For special types of hermitian symmetric domains and congruence subgroups Γ, algebraic varieties of the form Γ \ X = ShK(G,X) and their compactifications were introduced in a series of papers of Goro Shimura during the 1960s. Shimura's approach, later presented in his monograph, was largely phenomenological, pursuing the widest generalizations of the reciprocity law formulation of complex multiplication theory. In retrospect, the name "Shimura variety" was introduced by Deligne, who proceeded to isolate the abstract features that played a role in Shimura's theory. In Deligne's formulation, Shimura varieties are parameter spaces of certain types of Hodge structures.
A solar meridian indicates the length of days and nights, therefore reflecting the timing of the solstices. It was used as an instrument to check the congruence of the civil calendar with the solar year. Further archeological findings where a travertine pavement embedded with a line running north to south with Greek lettering in bronze with zodiac signs confirmed Pliny's writing. Also, the fact that the site was measured to be about a meter too high to be considered of Augustan date, therefore indicated that the instrument built under Augustus lost its accuracy and was renovated by Domitian.
Yasutaka Ihara (伊原 康隆, Ihara Yasutaka; born 1938, Tokyo Prefecture) is a Japanese mathematician, professor emeritus at the Research Institute for Mathematical Sciences, working on number theory who introduced Ihara's lemma and the Ihara zeta function. Ihara received his PhD at the University of Tokyo in 1967 with thesis Hecke polynomials as congruence zeta functions in elliptic modular case. In 1965/66 he was at the Institute for Advanced Study. He was a professor at the University of Tokyo and then at the Research Institute for Mathematical Science (RIMS) of the University of Kyōto.
The Corinthianesque capital between the second and third bays of the Cenacle is stylistically indicative of multiple geographical regions and chronological periods. This capital’s spiky leaves, which tightly adhere to the volume of the column before erupting into scrolls, are in congruence with common outputs of the 12th century sculpture workshop at the Temple site in Jerusalem in the last years before Saladin’s conquest in 1187.See Zehava Jacoby, "The Workshop of the Temple Area in Jerusalem in the Twelfth Century: its Origin, Evolution, and Impact", Zeitschrift für Kunstgeschichte, 45 Bd., H. 4 (1982), 325–394. Drilling is discussed on p. 362.
India and Japan, two of the largest and oldest democracies in Asia, having a high degree of congruence of political, economic and strategic interests, view each other as partners that have responsibility for, and are capable of, responding to global and regional challenges. India is the largest recipient of Japanese aid and both country have a special relationship official development assistance (ODA). As of 2017, bilateral trade between India and Japan stood at US$17.63 billion. The British occupiers of India and Japan were enemies during World War II, but political relations between the two nations have remained warm since India's independence.
Consumers construct their identities through their brand choices based on congruence between brand image and self-image. Thus, the meaning and value of a brand is not just its ability to express the self, but also its role in helping consumers create and build their self-identities. This is one of the main issues today that cause money hungry corporate officials to hinder other individuals hard work. Possessions can be used to satisfy psychological needs, such as actively creating one's self-concept, reinforcing and expressing self-identity, and allowing one to differentiate oneself and assert one's individuality.
Congruence of triangles is determined by specifying two sides and the angle between them (SAS), two angles and the side between them (ASA) or two angles and a corresponding adjacent side (AAS). Specifying two sides and an adjacent angle (SSA), however, can yield two distinct possible triangles unless the angle specified is a right angle. Triangles are congruent if they have all three sides equal (SSS), two sides and the angle between them equal (SAS), or two angles and a side equal (ASA) (Book I, propositions 4, 8, and 26). Triangles with three equal angles (AAA) are similar, but not necessarily congruent.
The restriction of this projective transformation to the midsphere is a Möbius transformation.. There is a unique way of performing this transformation so that the midsphere is the unit sphere and so that the centroid of the points of tangency is at the center of the sphere; this gives a representation of the given polyhedron that is unique up to congruence, the canonical polyhedron.. Alternatively, a transformed polyhedron that maximizes the minimum distance of a vertex from the midsphere can be found in linear time; the canonical polyhedron chosen in this way has maximal symmetry among all choices of the canonical polyhedron..
By the end of the 19th century, projective geometers were studying more general kinds of transformations on figures in projective space. Rather than the projective linear transformations which were normally regarded as giving the fundamental Kleinian geometry on projective space, they concerned themselves also with the higher degree birational transformations. This weaker notion of congruence would later lead members of the 20th century Italian school of algebraic geometry to classify algebraic surfaces up to birational isomorphism. The second early 19th century development, that of Abelian integrals, would lead Bernhard Riemann to the development of Riemann surfaces.
This feeling of congruence can set students on a path towards their future selves, and it can shape how they interpret experienced difficulty along the way. Two interpretations of experienced difficulty are highlighted. The first way to interpret experienced difficulty is that it reflects the importance of a task or of attaining a goal. Experienced difficulty in this case reflects that this is the path—as in the saying “no pain, no gain.” The second way to interpret experienced difficulty is that it reflects the possibility of succeeding in a task or of attaining a goal.
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations. By comparison, a quadrilateral with just one pair of parallel sides is a trapezoid in American English or a trapezium in British English.
In the mathematical theory of Riemann surfaces, the first Hurwitz triplet is a triple of distinct Hurwitz surfaces with the identical automorphism group of the lowest possible genus, namely 14 (genera 3 and 7 each admit a unique Hurwitz surface, respectively the Klein quartic and the Macbeath surface). The explanation for this phenomenon is arithmetic. Namely, in the ring of integers of the appropriate number field, the rational prime 13 splits as a product of three distinct prime ideals. The principal congruence subgroups defined by the triplet of primes produce Fuchsian groups corresponding to the triplet of Riemann surfaces.
European colonial empires in Africa increasingly opted for nationalization rather than previous policies of indirect rule and forced contracted or temporary labor. However, according to historian Peter A. Blitstein, the ultimate objectives of the British and French for Westernizing colonized and "detribalized" Africans remained unclear by the mid-twentieth century, as colonizers struggled to articulate how Africans could be brought into congruence with their visions of "modernity."Blitstein 2006, p. 291-292. Throughout post-independence Africa, two different types of African states emerged, according to scholar Mahmood Mamdani, which he terms as "the conservative and the radical" African states.
For example, the subdirect irreducibles in the variety generated by a finite linearly ordered Heyting algebra H must be just the nondegenerate quotients of H, namely all smaller linearly ordered nondegenerate Heyting algebras. The conditions cannot be dropped in general: for example, the variety of all Heyting algebras is generated by the set of its finite subdirectly irreducible algebras, but there exist subdirectly irreducible Heyting algebras of arbitrary (infinite) cardinality. There also exists a single finite algebra generating a (non- congruence-distributive) variety with arbitrarily large subdirect irreducibles.R. McKenzie, The residual bounds of finite algebras, Int.
The monks of Solesmes brought in their heaviest artillery in this battle, as indeed the academically sound 'Paleo' was intended to be a war-tank, meant to abolish once and for all the corrupted Pustet edition. On the evidence of congruence throughout various manuscripts (which were duly published in facsimile editions with ample editorial introductions) Solesmes was able to work out a practical reconstruction. This reconstructed chant was academically praised, but rejected by Rome until 1903, when Pope Leo XIII died. His successor, Pope Pius X, promptly accepted the Solesmes chant – now compiled as the Liber Usualis – as authoritative.
In this case, either n is prime or it is a Lucas pseudoprime. If congruence () is true, then n is likely to be prime (this justifies the term probable prime), but this does not prove that n is prime. As is the case with any other probabilistic primality test, if we perform additional Lucas tests with different D, P and Q, then unless one of the tests proves that n is composite, we gain more confidence that n is prime. Examples: If P = 3, Q = −1, and D = 13, the sequence of U's is : U0 = 0, U1 = 1, U2 = 3, U3 = 10, etc.
The second and third experiments controlled for the congruity effect, which was thought to be an underlying explanation for such a memory advantage. A survival scenario along with a robbery scenario were used to rate words instead of the original survival, moving or pleasantness categories. Butler found that, when the materials are controlled for with respect to congruence between type of processing (survival vs robbery scenario) and nature of materials (word lists), survival processing does not always produce superior recall; survival processing did not produce a recall advantage within the congruent conditions where congruity was controlled for.
Flores (1997), the majority stated, Congress was required to adhere to the Court's interpretation of the Fourteenth Amendment, including the Court's interpretation of the state-action doctrine. The "congruence and proportionality" requirement of Boerne did not allow Congress to exceed the Court's interpretation of the Fourteenth Amendment. Although it had been widely believed that section five of the Fourteenth Amendment was a "one-way ratchet," in which Congress could go beyond, but not fall short of, the Court's interpretation of the Equal Protection Clause,See, e.g., Stephen L. Carter, "The Morgan 'Power' and the Forced Reconsideration of Constitutional Decisions", 53 U. Chi.
These institutions are located in densely indigenous areas and, though they allow for diversity in enrollment, they are especially intended for the indigenous population. Founded on the principle of intercultural education, they aim to foster dialogue between different cultures and represent a way of responding to both the historical and more recent demands of indigenous peoples. In congruence with the recognition of diversity, Intercultural Universities do not propose a fixed approach to their educational activities. While assuring the respect of some basic principles, each university defines its curriculum according to the needs and potentials of the region in which it is located.
The treatment of pilon fractures depends on the extent of the injury. This includes the involvement of other bones such as the fibula and the talus, involvement of soft tissue, and the fracture pattern. Treatment strategies and fixation methods used include internal and external fixation, as well as staged approaches, with the aim of reducing the fracture, reconstructing the involved bones and restoration of articular surface congruence, with minimal insult to soft tissues. Appropriate wound management is important to reduce the high rate of infectious complications and secondary wound healing problems associated with open pilon fractures.
The Tonelli–Shanks algorithm (referred to by Shanks as the RESSOL algorithm) is used in modular arithmetic to solve for r in a congruence of the form r2 ≡ n (mod p), where p is a prime: that is, to find a square root of n modulo p. Tonelli–Shanks cannot be used for composite moduli: finding square roots modulo composite numbers is a computational problem equivalent to integer factorization.Oded Goldreich, Computational complexity: a conceptual perspective, Cambridge University Press, 2008, p. 588. An equivalent, but slightly more redundant version of this algorithm was developed by Alberto Tonelli in 1891.
The majority opinion stated that Congress, in enacting the ADA, had satisfied the requirement that it make clear its intention to abrogate state sovereign immunity and allow states to be sued for damages under the Fourteenth Amendment. However, the majority opinion also stated that part of the ADA to lack the "congruence and proportionality" required when Congress exercises its enforcement power under the Fourteenth Amendment, citing City of Boerne v. Flores (1997). Under the Equal Protection Clause, discrimination against people with disabilities is analyzed by "rational basis" scrutiny: if the discrimination has a rational basis, it is constitutional.
Random House () There have been attempts to bring the two into congruence, and the modern, cutting edge of science, especially in physics, seems to many observers to lend itself to a melding of religious experience and intersubjective verification of beliefs. Some scientists have described religious worldviews—generally of a mystical nature—consistent with their understanding of science: > There are two ways to live your life. One is as though nothing is a miracle. > The other is as though everything is a miracle ... Science without religion > is lame, religion without science is blind ... The religion of the future > will be a cosmic religion.
Dana's search for an architect to match her aspirations ended when she was introduced in 1902 to Frank Lloyd Wright, the rising leader of the new Prairie School movement of "organic architecture" which stressed congruence between the interior of a building and its surroundings. The Dana commission to plan the remodeling of the Lawrences' Italianate mansion was the largest Wright had received. Recognizing a kindred spirit in Mrs. Dana, he expanded the boundaries of his contract to design and build what was, in effect, an entirely new house showcasing his approach to the Prairie Style aesthetic.
"Koparion douglassi, a new dinosaur from the Morrison Formation (Upper Jurassic) of Dinosaur National Monument; the oldest troodontid (Theropoda: Maniraptora)." Brigham Young University Geology Studies, 40: 11-15. Within this context, Koparion could be used to refute the temporal paradox argument, that such a close relationship were unlikely because the then oldest known bird, Archaeopteryx, lived much earlier than the Deinonychosauria, i.e. the Troodontidae and the Dromaeosauridae;Brochu, C.A., and Norell, M.A., 2000, "Temporal congruence and the origin of birds", Journal of Vertebrate Paleontology, 20: 197-200 later also non-fragmentary Jurassic troodontid material was reported, from China.
Here the closed geodesics on play the role of prime numbers. At the same time, interest in the traces of Hecke operators was linked to the Eichler–Selberg trace formula, of Selberg and Martin Eichler, for a Hecke operator acting on a vector space of cusp forms of a given weight, for a given congruence subgroup of the modular group. Here the trace of the identity operator is the dimension of the vector space, i.e. the dimension of the space of modular forms of a given type: a quantity traditionally calculated by means of the Riemann–Roch theorem.
The characteristics of a Gothic-style church are largely in congruence with the ideology that the more breathtaking a church is, the better it reflects the majesty of God. This was accomplished through clever math and engineering in a time period where complex shapes, especially in huge cathedrals, were not typically found in structures. Through this newly implemented skill of being able to design complex shapes churches consisted of namely pointed arches, curved lights and windows, and rib vaults. Since these newly popular designs were implemented with respect to the width of the church rather than height, width was much more desired rather than height.
The reader should now take a moment to consider the case of a leading observer estimating distance to a trailing observer. There are other notions of distance, but the main point is clear: while the values of these various notions will in general disagree for a given pair of Rindler observers, they all agree that every pair of Rindler observers maintains constant distance. The fact that very nearby Rindler observers are mutually stationary follows from the fact, noted above, that the expansion tensor of the Rindler congruence vanishes identically. However, we have shown here that in various senses, this rigidity property holds at larger scales.
To ensure endorsement is successful the celebrity should match the brand and the consumer. The effect of using a celebrity endorser that consumers look up to and want to emulate can lead to increased congruence between the values of the consumers and the brand, and improve the relationship between the two. Industrial markets In industrial markets, organizations regard the 'heavy users' as 'major accounts' to be handled by senior sales personnel and even managers; whereas the 'light users' may be handled by the general sales force or by a dealer. Portfolios of brands Andrew Ehrenberg, then of the London Business School said that consumers buy 'portfolios of brands'.
He went on to complete a doctorate in functional analysis, advised by Ramaswamy S. Vaidyanathaswamy. He worked at Presidency College, Madras, Sri Venkateswara University, and the University of Missouri, before moving in 1963 to the University of Alberta, where he spent the rest of his professional career. In the 1960s Subbarao began to study the congruence properties of the partition function, p(n), which became one of his favourite problems. For example, he conjectured that if A and B are integers with 0 ≤ B < A, there are infinitely many n for which p(An+B) is even and infinitely many n for which p(An+B) is odd.
He made original contributions to Max Dehn's theory of the equivalence of polyhedra under polyhedral dissection and reassembly (scissors-congruence), extending and generalizing the theory with an entire class of new relations. Nicoletti collaborated in the writing of Enciclopedia Hoepli delle Matematiche elementari e complementi (published from 1930 to 1951) with the contribution of two monographic articles: Forme razionali di una o più variabili (Rational forms of one or more variables) and Proprietà generali delle funzioni algebriche (General properties of algebraic functions). A leading expert in mathematics education, he edited with Roberto Marcolongo a series of successful editions for secondary schools. Nicoletti was an Invited Speaker of the ICM in Rome.
Blues Funeral was released to positive critical acclaim. At Metacritic, which assigns a normalised rating out of 100 to reviews from mainstream critics, the album received an average score of 75, based on 32 reviews, indicating "generally favorable reviews." Mojo reviewer Keith Cameron said that "no other singer of his generation plumbs the depths so credibly, or does mournful with such grace," awarded the album a full five stars and referred to it as an "instant MOJO classic." Andy Gill of The Independent called Blues Funeral "the most accomplished of Lanegan's albums," adding that the album is "boasting a rare congruence between lyrical themes and musical evocations".
It would also strengthen the important work of translation and help different linguistic groups in the country to communicate meaningfully with one another." Arun Maheshwari, the Chairman of Vani Foundation, that has co-founded the Award, said on the occasion: "Our country's rich cultural diversity and its expression into arts and literature have been largely unexplored. Vani Foundation was established with the mission of not only re-discovering these idioms, but also connecting Indian languages with one another and with the world. We found congruence of energy and vision with the new team at ILF Samanvay and therefore feel proud to announce Vani- Samanvay Distinguished Translator Award.
It turns out that the most general pp-wave spacetime has only one Killing vector field, the null geodesic congruence k=\partial_v. However, for various special forms of H, there are additional Killing vector fields. The most important class of particularly symmetric pp- waves are the plane wave spacetimes, which were first studied by Baldwin and Jeffery. A plane wave is a pp-wave in which H is quadratic, and can hence be transformed to the simple form :H(u,x,y)=a(u) \, (x^2-y^2) + 2 \, b(u) \, xy + c(u) \, (x^2+y^2) Here, a,b,c are arbitrary smooth functions of u.
Findings of significant congruence between phylogenies of hantaviruses and phylogenies of their rodent reservoirs have led to the theory that rodents, although infected by the virus, are not harmed by it because of long-standing hantavirus–rodent host coevolution, although findings in 2008 led to new hypotheses regarding hantavirus evolution. Various hantaviruses have been found to infect multiple rodent species, and cases of cross-species transmission (host switching) have been recorded. Additionally, rates of substitution based on nucleotide sequence data reveal that hantavirus clades and rodent subfamilies may not have diverged at the same time. Furthermore, as of 2007 hantaviruses have been found in multiple species of shrews and moles.
In mathematics, a dilation is a function f from a metric space into itself that satisfies the identity :d(f(x),f(y))=rd(x,y) for all points (x, y), where d(x, y) is the distance from x to y and r is some positive real number.. In Euclidean space, such a dilation is a similarity of the space.. See in particular p. 110. Dilations change the size but not the shape of an object or figure. Every dilation of a Euclidean space that is not a congruence has a unique fixed point. that is called the center of dilation.. Some congruences have fixed points and others do not..
One cannot help noticing a certain congruence of this universalistic conception of teaching with the method Study Tech applied in scientology It is specified that "the Belarusian "Free theatre" is only interested in education of personnel who will work exclusively inside its own collective".Nikolai Khalezin, «Belarusian "Free theatre" is looking for talents», Charter’97, December 1, 2009 . In December 2009 the managers of the theatre announced a new recruitment in the studio, having declared, that out of 30 students admitted from the beginning of the project "Fortinbras" almost all of them were "eliminated".Nikolai Khalezin, "Results. Common and particular", Charter’97, January 1, 2010 .
The class of models is named after Georg Rasch, a Danish mathematician and statistician who advanced the epistemological case for the models based on their congruence with a core requirement of measurement in physics; namely the requirement of invariant comparison. This is the defining feature of the class of models, as is elaborated upon in the following section. The Rasch model for dichotomous data has a close conceptual relationship to the law of comparative judgment (LCJ), a model formulated and used extensively by L. L. Thurstone,Thurstone, L. L. (1927). A law of comparative judgment. Psychological Review, 34(4), 273.Thurstone and sensory scaling: Then and now. (1994).
In geometry, the Segment Addition Postulate states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC. This is related to the triangle inequality, which states that AB + BC \geq AC with equality if and only if A, B, and C are collinear (on the same line). This in turn is equivalent to the proposition that the shortest distance between two points lies on a straight line. The segment addition postulate is often useful in proving results on the congruence of segments.
The origins of Tambú can be traced back to the early 17th century, where a large number of African slaves arrived in Curaçao from Angola. The ritual was first associated with the Curaçao style of stick fighting called kokomakaku, where the Tambú referred to the rhythms played by the drummer (called a tamburero) on a single drum (also referred to as tambú). Since then, the performance has changed in congruence with the historical circumstances of the Curaçao island. Tambu can refer to the small drum on which the music is played, the dance that accompanies the music, or the event where the music and dance take place.
23 The Tuam provincial hierarchy's accommodation of the League up to 1900 reflected predominantly the genuine congruence of their social ideals with the stated aims of the movement.Miller, David: p.18 The League was equally and explicitly designed to reconcile the various parliamentary fragments by bringing them together in a new grass roots organisation around a programme of agrarian agitation, political reform, settlement of the Irish land question and pursuit of Irish Home Rule. William O'Brien was the prime mover, and the difficulty of the project can be gauged from the fact that the parliamentary leaders had very different opinions on the land question.
Like other modern axiomatizations of Euclidean geometry, Tarski's employs a formal system consisting of symbol strings, called sentences, whose construction respects formal syntactical rules, and rules of proof that determine the allowed manipulations of the sentences. Unlike some other modern axiomatizations, such as Birkhoff's and Hilbert's, Tarski's axiomatization has no primitive objects other than points, so a variable or constant cannot refer to a line or an angle. Because points are the only primitive objects, and because Tarski's system is a first-order theory, it is not even possible to define lines as sets of points. The only primitive relations (predicates) are "betweenness" and "congruence" among points.
Those cases concerned legislation which Congress had enacted in order to combat what it considered discrimination on the basis of age and disability. The Court stated that because such discrimination is not subjected to heightened scrutiny under the Constitution, and because the laws invalidated in Kimel and Garrett prohibited almost all such discrimination, the previous cases struck down laws which bore little "congruence and proportionality" to the wrongs they sought to remedy. Gender- based discrimination, by contrast, is subjected to intermediate scrutiny under the Constitution, and so in enacting the FMLA "it was easier for Congress to show a pattern of state constitutional violations."538 U.S. at 736.
De Cremer and colleagues (2013) suggest that individuals with a high need to belong care more about procedural fairness information and therefore pay closer attention to incoming information. Furthermore, Cornelis, Van Hiel, De Cremer and Mayer (2013) propose that leaders of a group are likely to be more fair when they are aware that the followers of the group have a high need to belong versus a low need to belong. This means that a leader who is aware that people in their group are motivated to adhere to group values is more fair. Leaders are also more fair in congruence with the amount of empathy they feel for followers.
Rig Veda: Mandala 5, Hymn LXXXII, line 3 Savitar is also unambiguously called Pusan and Mitra.Rig Veda: Mandala 5, Hymn LXXXI, last lines While Savitar certainly has directly been charged with using Surya's rays, Savitar has a much more direct congruence with other deities. The Vedic poet observes: > "[G]od Savitr has raised aloft his brilliance, making light for the whole > world; Surya shining brightly has filled heaven and earth and air with his > rays." In another hymn Surya is spoken of in terms Prasavitṛ (Vivifier), an adjective usually applied to Savitr, and in the third verse Savitr is apparently mentioned as the same god as Surya.
"Dynamic Capabilities thus reflect an organizations ability to achieve new and innovative forms of competitive advantage given path dependencies and market positions." "Path dependencies" refers to the history of development of organizational knowledge embedded in its capabilities, routines and technological assets – echoing the concept from Leonard, but on a macro-scale and explaining why competitive advantage takes time and persistence to build. The incorporation of "Routines" and path- dependent development of firms in the theory establishes the link to evolutionary theories of management and (business) strategy. The Dynamic Capabilities Theory also refers to notions of coherence, congruence and complementary assets across the firms portfolio of assets, routines, competencies and capabilities.
For example, the result of 5 × 7 = 35 mod 13 = 9\. Such finite fields can be defined for any prime p; using more sophisticated definitions, they can also be defined for any power m of a prime p m. Finite fields are often called Galois fields, and are abbreviated as GF(p) or GF(p m). In such a field with m numbers, every nonzero element a has a unique modular multiplicative inverse, a−1 such that This inverse can be found by solving the congruence equation ax ≡ 1 mod m, or the equivalent linear Diophantine equation : This equation can be solved by the Euclidean algorithm, as described above.
This is algebraic over and is the correct global Frobenius image in terms of the embedding of into ; moreover, the coefficients are algebraic and the result can be expressed algebraically. However, they are of degree 120, the order of the Galois group, illustrating the fact that explicit computations are much more easily accomplished if -adic results will suffice. If is an abelian extension of global fields, we get a much stronger congruence since it depends only on the prime in the base field . For an example, consider the extension of obtained by adjoining a root satisfying :\beta^5+\beta^4-4\beta^3-3\beta^2+3\beta+1=0 to .
In mathematics, the Alperin–Brauer–Gorenstein theorem characterizes the finite simple groups with quasidihedral or wreathedA 2-group is wreathed if it is a nonabelian semidirect product of a maximal subgroup that is a direct product of two cyclic groups of the same order, that is, if it is the wreath product of a cyclic 2-group with the symmetric group on 2 points. Sylow 2-subgroups. These are isomorphic either to three-dimensional projective special linear groups or projective special unitary groups over a finite field of odd order, depending on a certain congruence, or to the Mathieu group M_{11}. proved this in the course of 261 pages.
As a result of this joint effort, Cyrillic and Latin alphabets for Serbo-Croatian have a complete one-to-one congruence, with the Latin digraphs Lj, Nj, and Dž counting as single letters. Vuk's Cyrillic alphabet was officially adopted in Serbia in 1868, and was in exclusive use in the country up to the inter-war period. Both alphabets were co-official in the Kingdom of Yugoslavia and later in the Socialist Federal Republic of Yugoslavia. Due to the shared cultural area, Gaj's Latin alphabet saw a gradual adoption in Serbia since, and both scripts are used to write modern standard Serbian, Montenegrin and Bosnian; Croatian only uses the Latin alphabet.
Heyting algebras and interior algebras are the Lindenbaum–Tarski algebras for intuitionistic logic and the modal logic S4, respectively. A logic for which Tarski's method is applicable, is called algebraizable. There are however a number of logics where this is not the case, for instance the modal logics S1, S2, or S3, which lack the rule of necessitation (⊢φ implying ⊢□φ), so ~ (defined above) is not a congruence (because ⊢φ→ψ does not imply ⊢□φ→□ψ). Another type of logics where Tarski's method is inapplicable are relevance logics, because given two theorems an implication from one to the other may not itself be a theorem in a relevance logic.
Under Merovingian rule, a number of "Frankish synods" were held, marking a particularly Germanic development in the Western Church: to the usual regional or provincial councils, Germanic peoples added a traditional element from their systems of government, the idea of a national council, which was influenced by the Christian East. They also indicate a growing congruence between church and state. While Arian rulers kept their distance from the general councils, Visigoth rulers began influencing the councils only after the conversion of Reccared I. As soon as they had established themselves, Merovingian kings (and the Carolingians after them) exerted their influence on the councils.Rahner, Karl (1975). Encyclopedia of theology: a concise Sacramentum mundi, 301f.
He suffered a serious wound and was awarded the Iron Cross 1st and 2nd class. From 1920 to 1925 he studied mathematics and physics at the Technische Hochschule Berlin (TH Berlin) and then worked there successively as an assistant to the mathematician Georg Hamel, then to , and finally to . In 1926 Haenzel received his engineering doctorate with dissertation Zur synthetischen Theorie der Mechanik starrer Körper (On synthetic theory of the mechanics of rigid bodies) under the supervision of Stanislaus Jolles at TH Berlin. There Haenzel completed in 1929 his habilitation (Theory and classification of the collineations by involution on the linear congruence of rays; habilitation thesis) under the supervision of Erich Salkowski.
The current administration could also seek to integrate migrants and their families through education and training, making them more competitive in the job market. To tackle critical labour shortages, France also decided to participate in the EU Blue Card. Therefore, the outlook towards immigrants in France is shifting as unemployment continues to dominate the political agenda, along with political incentives to strengthen French national identity. Recent incidents, such as the 2005 civil unrest and Romani repatriation have shed light on France's immigration policies and how these are viewed globally, especially in congruence or discontinuity with the EU. A longitudinal study has been conducted since March 2010 to provide qualitative research regarding the integration of new immigrants.
The notion of ideal generalises to any Mal'cev algebra (as linear subspace in the case of vector spaces, normal subgroup in the case of groups, two-sided ideals in the case of rings, and submodule in the case of modules). It turns out that ker f is not a subalgebra of A, but it is an ideal. Then it makes sense to speak of the quotient algebra G/(ker f). The first isomorphism theorem for Mal'cev algebras states that this quotient algebra is naturally isomorphic to the image of f (which is a subalgebra of B). The connection between this and the congruence relation for more general types of algebras is as follows.
Psychosocial adaptation is a process a person experiences in order to achieve good fitness in person-environment congruence known as adjustment, a state of wisdom oriented activities and psychosocial equilibrium. Psychosocial support is the provision of psychological and social resources to a person by a supporter intended for the benefit of the receiver's ability to cope with problems faced. The allocentric principle within social relationships that promote health and well-being moves individuals to aid victims of terminal illness, disaster, war, catastrophe or violence to foster resilience of communities and individuals. It aims at easing resumption of normal life, facilitating affected people's participation to their convalescence and preventing pathological consequences of potentially traumatic situations.
In 1958, Shimura generalized the initial work of Martin Eichler on the Eichler–Shimura congruence relation between the local L-function of a modular curve and the eigenvalues of Hecke operators. In 1959, Shimura extended the work of Eichler on the Eichler–Shimura isomorphism between Eichler cohomology groups and spaces of cusp forms which would be used in Pierre Deligne's proof of the Weil conjectures. In 1971, Shimura's work on explicit class field theory in the spirit of Kronecker's Jugendtraum resulted in his proof of Shimura's reciprocity law. In 1973, Shimura established the Shimura correspondence between modular forms of half integral weight k+1/2, and modular forms of even weight 2k.
The first two previously mentioned radiographs are used to obtain precise measurements on laxity and joint congruence ,while the extended view is needed to collect further information on osteoarthritis if present. The purpose of these RXs is to obtain a technological calculated value that in the end an index of the joint laxity is given with less vulnerability to errors in comparison to the qualitative methods. The quantitative measure is called the distraction index (DI) which is the measurement of the maximal femoral head displacement from the acetabulum. It is calculated by dividing the distance between the geometric centre of the femoral head and the geometric centre of the acetabulum by the radius of the femoral head.
The example they give is of minority groups whose fictional television character is stereotypically more frequently victimized on television, creating an exaggerated perception of violence for individuals who watch more television Griffin sums it up nicely, when he states, "Gerbner claimed that other heavy viewers grow more apprehensive through the process of resonance." Furthermore, Gerbner said, "The congruence of the television world and real-life circumstances may 'resonate' and lead to markedly amplified cultivation patterns." This cultivation could have a large effect on our society if these viewers insist on receiving more security from the government, their work place, family, friends, etc. Resonance seeks to explain why heavy TV viewers often have an amplified vigilance about the world.
Delhi’s heritage has 2,000 years of history and includes more than 1,000 tombs, forts, havelis, baolis, and darwazas. The city received the title of a 'World heritage city'. To achieve that status, Indian National Trust for Art and Cultural Heritage (INTACH), a nationwide non-profit organization founded (by former Prime Minister Rajiv Gandhi) in 1984 to protect the common national heritage, Delhi Chapter, signed a MoU with the Delhi government with the objective of ensuring urban development in congruence with the architectural monuments of the city. In this context, William Dalrymple, an Indophile, states that "only Rome, Istanbul and Cairo can even begin to rival Delhi for the sheer volume and density of historic remains".
In 1993, the decree was reformed to open expectations regarding job training, inter-sectoral linkage, community support, and technological advice and assistance to companies. In 1994, according to the needs of the country, the school adopted the Competency Standards Based Education (EBNC) scheme, initiating the reform of its educational model in congruence with said approach. In 1998, as a result of his experience in the development of training programs under the EBNC scheme, he undertook a project for the accreditation of schools as Centers for the Evaluation of Labor Competences with the purpose of promoting the evaluation of competences acquired throughout the year. life, with the reference in Technical Standards of Labor Competence (NTCL).
Mathematics in China emerged independently by the 11th century BC.Chinese overview The Chinese independently developed a real number system that includes significantly large and negative numbers, more than one numeral system (base 2 and base 10), algebra, geometry, number theory and trigonometry. In the Han Dynasty, the Chinese made substantial progress on finding the nth root of positive numbers and solving linear congruence equations. The major texts from the period, The Nine Chapters on the Mathematical Art and the Book on Numbers and Computation gave detailed processes to solving various mathematical problems in daily life. All procedures were computed using a counting board in both texts, and they included inverse elements as well as Euclidean divisions.
However, it has been shown through simulation studies, testing with known in vitro viral phylogenies, and congruence with other methods, that the accuracy of parsimony is in most cases not compromised by this. Parsimony analysis uses the number of character changes on trees to choose the best tree, but it does not require that exactly that many changes, and no more, produced the tree. As long as the changes that have not been accounted for are randomly distributed over the tree (a reasonable null expectation), the result should not be biased. In practice, the technique is robust: maximum parsimony exhibits minimal bias as a result of choosing the tree with the fewest changes.
In classification problems, one might seek to find a complete set of invariants, such that if two objects have the same values for this set of invariants, then they are congruent. For example, triangles such that all three sides are equal are congruent under rigid motions, via SSS congruence, and thus the lengths of all three sides form a complete set of invariants for triangles. The three angle measures of a triangle are also invariant under rigid motions, but do not form a complete set as incongruent triangles can share the same angle measures. However, if one allows scaling in addition to rigid motions, then the AAA similarity criterion shows that this is a complete set of invariants.
In topology, a quotient space is a topological space formed on the set of equivalence classes of an equivalence relation on a topological space, using the original space's topology to create the topology on the set of equivalence classes. In abstract algebra, congruence relations on the underlying set of an algebra allow the algebra to induce an algebra on the equivalence classes of the relation, called a quotient algebra. In linear algebra, a quotient space is a vector space formed by taking a quotient group, where the quotient homomorphism is a linear map. By extension, in abstract algebra, the term quotient space may be used for quotient modules, quotient rings, quotient groups, or any quotient algebra.
In these systems, myco-heterotrophs play the role of "mycorrhizal cheaters", taking carbon from the common network, with no known reward. A special form of mycoheterotrophic association, which appears to be a chimera between the haustorial parasitism of a parasitic plant and mycohetertrophy, is observed in Parasitaxus usta, the only mycoheterotrophic gymnosperm. In congruence with older reports, it has been recently shown that some myco-heterotrophic orchids can be supported by saprotrophic fungi, exploiting litter- or wood-decaying fungi. In addition, several green plants (evolutionarily close to myco-heterotrophic species) have been shown to engage in partial myco-heterotrophy, that is, they are able to take carbon from mycorrhizal fungi, in addition to their photosynthetic intake.
Many of the artefacts from this expedition can be found in the British Museum's collection. After this Lubaantun was neglected by archeologists (although it suffered some looting by treasure hunters) until 1970, when a joint British Museum, Harvard, and Cambridge University project was begun led by archaeologist Norman Hammond. Norman Hammond, Kate Pretty, and Frank P. Saul excavated the site in the 1970s. Their research team, in congruence with Sharer and Traxler, believed that the site was founded in the Late Classic period as opposed to the Early Classic, suggested by Joyce. In addition, they postulated that the site saw no Postclassic reoccupation and considered it to be abandoned until the site’s later discovery.
A necessary and sufficient condition for a Heyting algebra to be subdirectly irreducible is for there to be a greatest element strictly below 1. The witnessing pair is that element and 1, and identifying any other pair a, b of elements identifies both a→b and b→a with 1 thereby collapsing everything above those two implications to 1. Hence every finite chain of two or more elements as a Heyting algebra is subdirectly irreducible. By Jónsson's Lemma, subdirectly irreducible algebras of a congruence-distributive variety generated by a finite set of finite algebras are no larger than the generating algebras, since the quotients and subalgebras of an algebra A are never larger than A itself.
Criteria for Authenticity in Historical-Jesus Research by Stanley E. Porter, Bloomsbury 2004 pp. 100–120 Primary among these areWho Is Jesus? by Thomas P. Rausch (Jul 1, 2003) pages 35–40John P. Meier "Criteria: How do we decide what comes from Jesus?" in The Historical Jesus in Recent Research by James D. G. Dunn and Scot McKnight, Eisenbrauns 2006 pages 126–142 the criterion of historical plausibility, the criterion of rejection and execution, and the criterion of congruence (also called cumulative circumstantial evidence), a special case of the older criterion of coherence.Petr Pokorny "Jesus Research as Feedback" Handbook for the Study of the Historical Jesus by Tom Holmen and Stanley E. Porter, Brill 2010 pp.
It is believed that the most important factor in successful therapy is the relational climate created by the therapist's attitude to their client. The therapist's attitude is defined by the three conditions focused on the therapist, which are often called the core conditions (3,4, and 5 of the six conditions): # Congruence: the willingness to transparently relate to clients without hiding behind a professional or personal facade. # Unconditional positive regard: the therapist offers an acceptance and prizing for their client for who he or she is without conveying disapproving feelings, actions or characteristics and demonstrating a willingness to attentively listen without interruption, judgement or giving advice. # Empathy: the therapist communicates their desire to understand and appreciate their client's perspective.
Staudt went beyond real projective geometry and into complex projective space in his three volumes of Beiträge zur Geometrie der Lage published from 1856 to 1860. In 1922 H. F. Baker wrote of von Staudt's work: :It was von Staudt to whom the elimination of the ideas of distance and congruence was a conscious aim, if, also, the recognition of the importance of this might have been much delayed save for the work of Cayley and Klein upon the projective theory of distance. Generalised, and combined with the subsequent Dissertation of Riemann, v. Staudt's volumes must be held to be the foundation of what, on its geometrical side, the Theory of Relativity, in Physics, may yet become.
Only in expression of joy is there congruence with what is visible in the face and what is internally experienced. Not so with the negative emotions: they are shown more often than experienced. Krause states that this will not allow information-sharing about the relationship between the two persons. He refers to old and often confirmed findings of Bühler (1934), according to which in a communication between a "sender" and his "receiver" signs of expression should be interpreted differently: as an "expression for the internal status of the sender", or in his "appeal function" that "should bring the receiver to a specific action", or as a kind of "mental comment" about something "the sender is talking or thinking about".
As a consequence, we define the congruence \sim as the least equivalence relation on the directed paths which is compatible with concatenation and relates γ to δ as soon as there is a directed homotopy from γ to δ. Going back to the computer science motivation where directed paths represent execution traces, directed homotopies provide a way to identify execution traces. Hence, given a directed space X which models some concurrent program P, the topology of X can be seen as the 'local commutations' of actions in the program P. In classical models of concurrency like 'asynchronous graphs' of 'Mazurkiewicz traces', the local commutations are provided by a relation over the arrows or the actions.
Humanistic psychology was developed in the 1950s in reaction to both behaviorism and psychoanalysis, largely due to the person-centered therapy of Carl Rogers (often referred to as Rogerian Therapy) and existential psychology developed by Viktor Frankl and Rollo May. Rogers believed that a client needed only three things from a clinician to experience therapeutic improvement—congruence, unconditional positive regard, and empathetic understanding. By using phenomenology, intersubjectivity and first-person categories, the humanistic approach seeks to get a glimpse of the whole person and not just the fragmented parts of the personality. This aspect of holism links up with another common aim of humanistic practice in clinical psychology, which is to seek an integration of the whole person, also called self-actualization.
The Jastorf culture extended south to the northern fringes of the Hallstatt culture, while towards the north a general congruence with the late phases of the Northern Bronze Age can be noted. Gravefields in today's Schleswig-Holstein, Mecklenburg, western Pomerania, in Brandenburg and in Lower Saxony show continuity of occupation from the Bronze Age far into the Jastorf period and beyond. The specific contributions from the various quarters witnessing the meeting of Celtic and indigenous cultures during the early periods can not be assessed by the present state of knowledge, although a shift to a northern focus has been noted to accompany the dwindling vitality of continental Celtic cultures later on.Herbert Schutz, (1983) The Prehistory of Germanic Europe, Ch. 6 "The Northern Genesis", 309–311.
While Arian rulers kept their distance from the general councils, Visigoth rulers began influencing the councils only after the conversion of Reccared I. As soon as they had established themselves, Merovingian kings (and the Carolingians after them) exerted their influence on the councils. According to Gregory Halfond, such congruence was a particular quality of the Gallo-Roman church, in which the Roman aristocracy made up an important part of the leadership of the Gallo-Roman (and later the Frankish) church; continuity in this power nexus is indicated also by the continued use of Roman procedures in the councils.Halfond 4-6. An early important churchman is Caesarius of Arles, who presided over the Visigoth synod held at Agde in 506,Halfond 6.
As an example, in his 1998 case study of Ms. Flood, Jeffrey R. Prince reported in the Career Development Quarterly, 46, "Environments that are purely Artistic usually reflect values of independence and self-expression through loosely structured activities, whereas Enterprising environments frequently include organizational structures that value status." Ms. Flood's RIASEC results reflected that her main GOT occupational theme code was AE, with S as a possible third theme code, but at a lower intensity. In this case, and according to Holland's RIASEC Hexagon, these theme codes may not be entirely congruent, correlated, or undifferentiated with Ms. Flood's interests. Theme codes that fall closer in proximity to each other on Holland's RIASEC hexagon are those that generally reflect greater congruence, correlation, and undifferentiation.
Published during the "first golden age of children's fiction", The Coral Island began a trend in boys' fiction by using boys as the main characters, a device now commonplace in the genre. It preserves, according to literary critic Minnie Singh, the moralizing aspects of didactic texts, but does so (and in this regard it is a "founding text") by the "congruence of subject and implied reader": the story is about boys and written retrospectively as though by a boy, for an audience of boys. According to literary critic Frank Kermode, The Coral Island "could be used as a document in the history of ideas". A scientific and social background for the novel is found in Darwinism, of the natural and the social kind.
From an early point in the development of attachment theory, there was criticism of the theory's lack of congruence with the various branches of psychoanalysis. Like other members of the British object-relations group, Bowlby rejected Melanie Klein's views that considered the infant to have certain mental capacities at birth and to continue to develop emotionally on the basis of fantasy rather than of real experiences. But Bowlby also withdrew from the object-relations approach (exemplified, for example, by Anna Freud), as he abandoned the "drive theory" assumptions in favor of a set of automatic, instinctual behaviour systems that included attachment. Bowlby's decisions left him open to criticism from well-established thinkers working on problems similar to those he addressed.
In mathematics, Hilbert's fourth problem in the 1900 Hilbert problems is a foundational question in geometry. In one statement derived from the original, it was to find — up to an isomorphism — all geometries that have an axiomatic system of the classical geometry (Euclidean, hyperbolic and elliptic), with those axioms of congruence that involve the concept of the angle dropped, and `triangle inequality', regarded as an axiom, added. If one assumes the continuity axiom in addition, then, in the case of the Euclidean plane, we come to the problem posed by Darboux: "To determine all the calculus of variation problems in the plane whose solutions are all the plane straight lines."G. Darboux, Lecons sur la theorie generale des surfaces, V.III, Paris, 1894.
Since they constitute a very simple and natural class of Lorentzian manifolds, defined in terms of a null congruence, it is not very surprising that they are also important in other relativistic classical field theories of gravitation. In particular, pp-waves are exact solutions in the Brans–Dicke theory, various higher curvature theories and Kaluza–Klein theories, and certain gravitation theories of J. W. Moffat. Indeed, B. O. J. Tupper has shown that the common vacuum solutions in general relativity and in the Brans/Dicke theory are precisely the vacuum pp- waves (but the Brans/Dicke theory admits further wavelike solutions). Hans- Jürgen Schmidt has reformulated the theory of (four-dimensional) pp-waves in terms of a two-dimensional metric-dilaton theory of gravity.
The Court, in an opinion by Justice Anthony Kennedy, struck down RFRA as it applies to the states as an unconstitutional use of Congress's enforcement powers. The Court held that it holds the sole power to define the substantive rights guaranteed by the Fourteenth Amendment--a definition to which Congress may not add and from which it may not subtract. Congress could not constitutionally enact RFRA because the law was not designed to have "congruence and proportionality" with the substantive rights that the Court had defined. Although Congress could enact "remedial" or "preventative" legislation to guarantee rights not exactly congruent with those defined by the Court, it could only do so to more effectively prevent, deter, or correct violations of those rights actually guaranteed by the Court.
Chris Willman of Variety opined that Swift has "a grand old time" identifying herself with women who lived decades before her. In congruence, Rob Sheffield of Rolling Stone wrote that the song satirizes the upper-class environment of "Starlight", the fifteenth track on Swift's 2012 album Red, and matched the similarities between the songs—the usage of the word "marvelous" and the muses being people who lived decades before Swift's birth. Uproxx writer Philip Cosores regarded "The Last Great American Dynasty" as entrenched in Swift's trademark "melodic warmth" and "vivid details", and complimented Dessner's slow-burning production. Olivia Ovenden of Esquire picked the song as the album's highlight, and commended it for "seamlessly" blending indie sounds with Swift's pop prowess.
Welsh code-switchers fall typically into one of three categories: the first category is people whose first language is Welsh and are not the most comfortable with English, the second is the inverse, English as a first language and a lack of confidence with Welsh, and the third consists of people whose first language could be either and display competence in both languages. Welsh and English share congruence, meaning that there is enough overlap in their structure to make them compatible for code-switching. In studies of Welsh English code-switching, Welsh frequently acts as the matrix language with English words or phrases mixed in. A typical example of this usage would look like dw i’n love-io soaps, which translates to "I love soaps".
In abstract algebraic logic, a branch of mathematical logic, the Leibniz operator is a tool used to classify deductive systems, which have a precise technical definition, and capture a large number of logics. The Leibniz operator was introduced by Wim Blok and Don Pigozzi, two of the founders of the field, as a means to abstract the well-known Lindenbaum–Tarski process, that leads to the association of Boolean algebras to classical propositional calculus, and make it applicable to as wide a variety of sentential logics as possible. It is an operator that assigns to a given theory of a given sentential logic, perceived as a free algebra with a consequence operation on its universe, the largest congruence on the algebra that is compatible with the theory.
A Wieferich number is an odd natural number n satisfying the congruence 2(n) ≡ 1 (mod n2), where denotes the Euler's totient function (according to Euler's theorem, 2(n) ≡ 1 (mod n) for every odd natural number n). If Wieferich number n is prime, then it is a Wieferich prime. The first few Wieferich numbers are: :1, 1093, 3279, 3511, 7651, 10533, 14209, 17555, 22953, 31599, 42627, 45643, 52665, 68859, 94797, 99463, ... It can be shown that if there are only finitely many Wieferich primes, then there are only finitely many Wieferich numbers. In particular, if the only Wieferich primes are 1093 and 3511, then there exist exactly 104 Wieferich numbers, which matches the number of Wieferich numbers currently known.
Shakespeare's views on Islam have been described by The Economist as "complex" and "multifaceted", and he "was ahead of his time in his sensitivity to the Islamic world and its inhabitants." According to the conclusion of Prof Matthew Dimmock, Shakespeare's depiction of Islam and Muslims "denied either scriptural congruence or religious coherence, embodied in the martially aggressive male." Shakespeare's works included several Muslim characters, including Aaron the Moor in Titus Andronicus (although the play is set in ancient Rome centuries before Islam existed), the Prince of Morocco in The Merchant of Venice and Othello in the eponymous play. These works are said to have been inspired by several Moorish delegations from Morocco to Elizabethan England around 1600, such as that of Abd el-Ouahed ben Messaoud.
Historians propose several explanations for this action: the common ones are that he missed his native land, that he was a British agent and the congruence of the goals of both wars. The first explanation suggests that when the wars of independence began San Martín thought that his duty was to return to his country and serve in the military conflict. The second explanation suggests that Britain, which would benefit from the independence of the South American countries, sent San Martín to achieve it. The third suggests that both wars were caused by the conflicts between Enlightenment ideas and absolutism, so San Martín still waged the same war; the wars in the Americas only developed separatist goals after the Spanish Absolutist Restoration.
Most implementations of RSA use the Chinese remainder theorem during signing of HTTPS certificates and during decryption. The Chinese remainder theorem can also be used in secret sharing, which consists of distributing a set of shares among a group of people who, all together (but no one alone), can recover a certain secret from the given set of shares. Each of the shares is represented in a congruence, and the solution of the system of congruences using the Chinese remainder theorem is the secret to be recovered. Secret sharing using the Chinese remainder theorem uses, along with the Chinese remainder theorem, special sequences of integers that guarantee the impossibility of recovering the secret from a set of shares with less than a certain cardinality.
The Siegel modular variety Ag, which parametrize principally polarized abelian varieties of dimension g, can be constructed as the complex analytic spaces constructed as the quotient of the Siegel upper half-space of degree g by the action of a symplectic group. Complex analytic spaces have naturally associated algebraic varieties by Serre's GAGA. The Siegel modular variety Ag(n), which parametrize principally polarized abelian varieties of dimension g with a level n-structure, arises as the quotient of the Siegel upper half-space by the action of the principal congruence subgroup of level n of a symplectic group. A Siegel modular variety may also be constructed as a Shimura variety defined by the Shimura datum associated to a symplectic vector space.
" Bobby Peacock from Roughstock gave the song four stars out of five and praised Swift's vocal, saying that "it's her best vocal since "Tim McGraw"". He concluded that "[the song] feels a little more focused, a little more mature and a little better- sung than her previous material." The Oxonian Review considers it the centerpiece of the melancholic album, noting how "equating regret with December is a mainstream American musical tradition" and this song is "the congruence of her singing and songwriting at its finest." Ryan Brockington from New York Post lauded the song, writing "it’s a very surprising, and somewhat brilliant, apology track where Taylor sings about wishing to fix a relationship she wished she wouldn't have ruined in the first place.
The Dedekind eta-function is an automorphic form in the complex plane. In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group G to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup \Gamma \subset G of the topological group. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups. Modular forms are automorphic forms defined over the groups SL(2, R) or PSL(2, R) with the discrete subgroup being the modular group, or one of its congruence subgroups; in this sense the theory of automorphic forms is an extension of the theory of modular forms.
The sense of agency and its disturbances in schizophrenia: a reappraisal. Experimental Brain Research These situations reveal that there are two levels of self-recognition, an automatic level for action identification, and a conscious level for the sense of agency, which both rely on the same principle of congruence of the action-related signals. Investigation of the sense of agency is important to explain positive symptoms of schizophrenia, like thought insertion and delusions of control. The core of the problem met by these patients is a disturbance of their sense of agency: the first rank symptoms, which represent one of the major features of the disease, are nothing but a loss of the ability to attribute their own thoughts, internal speech, covert or overt actions to themselves.
James Randi (2001) That Dratted Triangle, proof by Martin Gardner Congruence of edge lengths allows rotation of the selected triangles to form three equal-area parallelograms, which bisect into six triangles of equal size to the original interior triangle. An early exhibit of this geometrical construction and area computation was given by Robert Potts in 1859 in his Euclidean geometry textbook.Robert Potts (1859) Euclid's Elements of Geometry, Fifth school edition, problems 59 and 100, pages 78 & 80 via Internet Archive According to Cook and Wood (2004), this triangle puzzled Richard Feynman in a dinner conversation; they go on to give four different proofsR.J. Cook & G.V. Wood (2004) "Feynman's Triangle", Mathematical Gazette 88:299–302 A more general result is known as Routh's theorem.
For the special purpose of searching for a counterexample to the Collatz conjecture, this precomputation leads to an even more important acceleration, used by Tomás Oliveira e Silva in his computational confirmations of the Collatz conjecture up to large values of . If, for some given and , the inequality : holds for all , then the first counterexample, if it exists, cannot be modulo . For instance, the first counterexample must be odd because , smaller than ; and it must be 3 mod 4 because , smaller than . For each starting value which is not a counterexample to the Collatz conjecture, there is a for which such an inequality holds, so checking the Collatz conjecture for one starting value is as good as checking an entire congruence class.
To the south by the River Stour, dating from the 15th century, is a single surviving tower of Caldwall (or Caldwell) Castle, a fortified manor house. Caldwall Castle Kidderminster owes its growth to the early development of the cloth industry, which was aided by its position upon the River Stour, and its location at the congruence of four main roads to Birmingham, Dudley, Worcester and Bewdley and Bridgnorth. In a visit to the town sometime around 1540, King's Antiquary John Leland noted that Kidderminster "standeth most by clothing". Over the following centuries the town specialised in textile trades such as weaving, fulling, cloth working and milling, and was also home to numerous other trades including shoemaking, haberdashery, saddle making, dyers, tailors, tanners and glovers.
This model does not account for the fluidity of gender asserted by persons like American Psychologist Lisa M. Diamond who explains is not a stable, fixed trait – rather, it is socially constructed and may vary over time for an individual. This model directly contravenes both the notion of gender identity being individual and internal, by explaining its source as social behavior and its manifestation as a desire for congruence with a received notion of gender. It is unclear whether this contradiction occurs as an inconsistency in terminology or as a contradiction of two claims. Other proposed models include that of the Gender Schema Theory, which conjectures that the development of gender identity, is a process of self identification which must precede the ability for "children to label themselves and others as males or females".
Self-compassion is an emotionally positive self-attitude that is assumed to protect against the negative consequences of self-judgment, isolation, and rumination (such as depression). With a basic understanding of these two concepts, self-esteem and self- compassion, it becomes evident that adolescent egocentrism and personal fable have important consequences and affect many aspects of adolescent development. Neff argues that although there are similarities in self-esteem and self- compassion, the latter contains fewer pitfalls than the former. She asserts that self-compassion is "not based on the performance evaluations of self and others or the congruence with ideal standard... it takes the entire self- evaluation process out of the picture, focusing on feelings of compassion toward oneself and the recognition of one's common humanity rather than making self-judgments".
A quotient group or factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure (the rest of the structure is "factored" out). For example, the cyclic group of addition modulo n can be obtained from the group of integers under addition by identifying elements that differ by a multiple of n and defining a group structure that operates on each such class (known as a congruence class) as a single entity. It is part of the mathematical field known as group theory. In a quotient of a group, the equivalence class of the identity element is always a normal subgroup of the original group, and the other equivalence classes are precisely the cosets of that normal subgroup.
The monster group was investigated in the 1970s by mathematicians Jean-Pierre Serre, Andrew Ogg and John G. Thompson; they studied the quotient of the hyperbolic plane by subgroups of SL2(R), particularly, the normalizer Γ0(p)+ of the Hecke congruence subgroup Γ0(p) in SL(2,R). They found that the Riemann surface resulting from taking the quotient of the hyperbolic plane by Γ0(p)+ has genus zero if and only if p is 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59 or 71. When Ogg heard about the monster group later on, and noticed that these were precisely the prime factors of the size of M, he published a paper offering a bottle of Jack Daniel's whiskey to anyone who could explain this fact ().
If there is a unique probability measure that must be used to price assets in a market, then the market is called a complete market.Irreversible decisions under uncertainty by Svetlana I. Boyarchenko, Serge Levendorskiĭ 2007 page 11 Not all measures that intuitively represent chance or likelihood are probability measures. For instance, although the fundamental concept of a system in statistical mechanics is a measure space, such measures are not always probability measures. In general, in statistical physics, if we consider sentences of the form "the probability of a system S assuming state A is p" the geometry of the system does not always lead to the definition of a probability measure under congruence, although it may do so in the case of systems with just one degree of freedom.
In February 2013, Denmark and the European Union reached an agreement on a seven-year budget, to approve the Danish demand. On 25 May 2014, the Danish Unified Patent Court membership referendum was approved with 62.5% of the vote, enabling the government to proceed with the ratification of the Agreement on a Unified Patent Court, which constitutes the legal basis for the Unified Patent Court. In 2009 the Danish government sought to adjust its opt-outs in several policy areas by referendum, with the aim of deepening the congruence of Danish policies with those of the EU. This eventually resulted in the referendum on the home and justice affairs opt-out that took place on 3 December 2015, with the electorate turning down the proposed change to the full opt-out.
The ADEA, the Court concluded, "prohibits substantially more state employment decisions and practices than would likely be held unconstitutional under the applicable equal protection, rational basis standard." Therefore, the ADEA's remedy failed the "congruence and proportionality" test required by Boerne and so was not "a valid exercise of constitutional authority" under Section 5 of the Fourteenth Amendment. In explaining the application of rational basis review to classifications based on age, the majority stated: Justice Stevens's dissenting opinion said, "There is not a word in the text of the Constitution supporting the Court's conclusion that the judge-made doctrine of sovereign immunity limits Congress' power to authorize private parties, as well as federal agencies, to enforce federal law against the States." Justice Stevens referred to the doctrine of sovereign immunity as expanded by Seminole Tribe v.
Halsted introduced conics after the manner of a Steiner conic, here shown from a projectivity composed of two perspectivities \pi_A, \pi_B In 1896 Halsted published a chapter on synthetic geometry pertaining to three-dimensional projective geometry in Higher Mathematics distributed by Mansfield Merriman and Robert S. Woodward.Alexander Ziwet (1897) Review:Higher Mathematics Science 5 via Google Books In 1906 Synthetic Projective Geometry was published separately in 241 articles and 61 problems. A bibliography referring to Chasles, Steiner, and Clebsch appears on page 24. There are four pages of index, 58 of text, and a lyrical preface: “Man imprisioned in a little body, with short-arm hands instead of wings, created for his guidance a mole geometry, tactile space, codified by Euclid in his immortal Elements, whose basal principle is congruence, measurement.
For odd prime p, the p-adic Hamilton quaternions are isomorphic to the 2×2 matrices over the p-adics. To see the p-adic Hamilton quaternions are not a division algebra for odd prime p, observe that the congruence x2 \+ y2 = −1 mod p is solvable and therefore by Hensel's lemma — here is where p being odd is needed — the equation :x2 \+ y2 = −1 is solvable in the p-adic numbers. Therefore the quaternion :xi + yj + k has norm 0 and hence doesn't have a multiplicative inverse. One way to classify the F-algebra isomorphism classes of all quaternion algebras for a given field, F is to use the one-to-one correspondence between isomorphism classes of quaternion algebras over F and isomorphism classes of their norm forms.
Move UP is a nonfiction book written by Dr. Clotaire Rapaille and Dr. Andrés Roemer in 2013 that explains upward social mobility from a biological and cultural perspective, and how societies and nations create adequate environments for maintaining the bio-logical (a term they use referring to being logical about our biology) requirements of the human species. The book is based on the latest research in biology, evolutionary psychology, behavioral economics, neuroscience and anthropology. The authors question what factors allow us to move up taking into account the culture codes proposed by Dr. Rapaille, and their congruence with human biology, and Roemer's economic and biological precepts. Furthermore, the authors propose a new paradigm for understanding human needs and wants, contrasting Maslow's Pyramid of Needs with the Four S's: Survival, Sex, Security, and Success.
Herbert Eugene Bolton, founding director The university named history chairperson Herbert E. Bolton its founding director, a position he held for the library's first 22 years. In his dual capacity, he made Bancroft Library a great research center for American history in congruence with the department's rise to prominence. Until the decade of the 1960s, The Bancroft Library continued to focus exclusively on the history of the American West, particularly the borderlands of northern Mexico and the southern United States, from Florida to California, an area associated with the research interests of long-time directors Bolton (1918–1940) and George P. Hammond (1946–1966). In the 1950s and 1960s Bancroft added the University of California archives and the Regional Oral History Office, both significant to the history of California.
In a critical study of his prose and poems, the subjects depicted his nostalgia for the past, church rituals, legends, the mysterious, the different shades of evil, the power of the basic emotions over culture, the freedom of the will against fate, the mutability of the human body compared to the spirit, and the like. They are often set in old Manila, the walled city of Intramuros, and sometimes Paco – as a symbol of congruence, the glory and culture of the past, rather than a geographical concept. His characters are mostly cultured intellectuals of past generations, while the opposing characters are usually from the materialistic modern age. Unless they are portrayed to adjust better than old men, women seldom have significant roles in this cultured world of the past.
Koreatowns as an East Asian ethnic enclave have only been in existence since the mid 1860s as Korea had been a territorially stable polity for centuries; as Jaeeun Kim describe it, "The congruence of territory, polity, and population was taken for granted". Large-scale emigration from Korea was only mainly into the Russian Far East and Northeast China; these emigrants became the ancestors of the 2 million Koreans in China and several hundred thousand ethnic Koreans in Central Asia. Koreatowns in the western countries such as the United States, Canada have only been in place much later with the Los Angeles Koreatown receiving official recognition in 2008. Also many Koreatowns are not officially sanctioned where the only evidence of such enclaves exist as clusters of Korean stores with Korean signage existing only on the storefronts.
Carl Rogers's idea of "unconditional positive regard" and his stress on the importance of empathy has been compared to Buddhist conceptions of compassion (Karuṇā).Levine, Marvin; The Positive Psychology of Buddhism and Yoga: Paths to A Mature Happiness, 54 Mindfulness meditation has been seen as a way to aid the practice of person centered psychotherapy. Person centered therapist Manu Buzzano has written that "It seemed clear that regular meditation practice did help me in offering congruence, empathy and unconditional positive regard."Buzzano, Manu; The Buddha as a fully functioning person: toward a person-centered perspective on mindfulness, New School of Psychotherapy and Counselling, London He subsequently interviewed other person centered therapists who practiced meditation and found that it enhanced their empathy, nonjudgmental openness and quality of the relationship with their clients.
It has also been demonstrated that after emigrating from one continent to another, a human host's region of origin is predictive of which TB lineage they carry, which could reflect either a stable association between host populations and specific M. tuberculosis lineages and/or social interactions that are shaped by shared cultural and geographic histories. Regarding the congruence between human and M. tuberculosis phylogenies, a study relying on M. tuberculosis and human Y chromosome DNA sequences to formally assess the correlation between them, concluded that they are not congruent. Also, a more recent study which included genome sequences from M. tuberculosis complex members extracted from three 1,000-year-old Peruvian mummies, estimated that the most recent common ancestor of the M. tuberculosis complex lived only 4,000 – 6,000 years ago.
The 3-adic integers, with selected corresponding characters on their Pontryagin dual group In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems. The extension is achieved by an alternative interpretation of the concept of "closeness" or absolute value. In particular, two -adic numbers are considered to be close when their difference is divisible by a high power of : the higher the power, the closer they are. This property enables -adic numbers to encode congruence information in a way that turns out to have powerful applications in number theory – including, for example, in the famous proof of Fermat's Last Theorem by Andrew Wiles.
The constructive existence proof shows that, in the case of two moduli, the solution may be obtained by the computation of the Bézout coefficients of the moduli, followed by a few multiplications, additions and reductions modulo n_1n_2 (for getting a result in the interval (0, n_1n_2-1)). As the Bézout's coefficients may be computed with the extended Euclidean algorithm, the whole computation, at most, has a quadratic time complexity of O((s_1+s_2)^2), where s_i denotes the number of digits of n_i. For more than two moduli, the method for two moduli allows the replacement of any two congruences by a single congruence modulo the product of the moduli. Iterating this process provides eventually the solution with a complexity, which is quadratic in the number of digits of the product of all moduli.
To promote this concept of a "new man", the government also created a series of party-dominated institutions and mechanisms on all levels of society, which included organizations such as labor groups, youth leagues, women's groups, community centers, and houses of culture to promote state-sponsored art, music, and literature. In congruence with this, all educational, mass media, and artistic community based facilities were nationalized and utilized to instill the government's official socialist ideology. In describing this new method of "development", Guevara stated: A further integral part of fostering a sense of "unity between the individual and the mass", Guevara believed, was volunteer work and will. To display this, Guevara "led by example", working "endlessly at his ministry job, in construction, and even cutting sugar cane" on his day off.
A Microsatellite diversity was analysed in Gondi language speaking Madia Gonds of Maharashtra and three other Marathi speaking Proto – Australoid tribal groups, to understand their genetic structure and to identify the congruence between language and gene pool. Allele frequency data at 15 Short tandem repeat (STR) loci in studied tribes was compared with data of 22 Indo-European- and Dravidian-speaking caste and tribal populations using heterozygosity, allele size variance, analysis of molecular variance (AMOVA), GST (Glutathione S-transferase) estimate, PC plot, and Mantel correlation test. Results demonstrate that Gondi tribes comprising the Madia-Gond, a hunter-gatherer population, harbour lower diversity than Marathi tribal groups, which are culturally and genetically distinct. The Proto-Australoid tribal populations were genetically differentiated from castes of similar morphology, suggesting different evolutionary mechanisms operating upon the populations.
Now the midpoints of the sides of any triangle are the images of its vertices by a homothety with factor −½, centered at the barycenter of the triangle. Applied to the anticomplementary triangle, which is itself obtained from the Johnson triangle by a homothety with factor 2, it follows from composition of homotheties that the reference triangle is homothetic to the Johnson triangle by a factor −1. Since such a homothety is a congruence, this gives property 5, and also the Johnson circles theorem since congruent triangles have circumscribed circles of equal radius. For property 6, it was already established that the perpendicular bisectors of the sides of the anticomplementary triangle all pass through the point H; since that side is parallel to a side of the reference triangle, these perpendicular bisectors are also the altitudes of the reference triangle.
The book is divided into two parts, the first on the existence of paradoxical decompositions and the second on conditions that prevent their existence. After two chapters of background material, the first part proves the Banach–Tarski paradox itself, considers higher-dimensional spaces and non-Euclidean geometry, studies the number of pieces necessary for a paradoxical decomposition, and finds analogous results to the Banach–Tarski paradox for one- and two-dimensional sets. The second part includes a related theorem of Tarski that congruence-invariant finitely-additive measures prevent the existence of paradoxical decompositions, a theorem that Lebesgue measure is the only such measure on the Lebesgue measurable sets, material on amenable groups, connections to the axiom of choice and the Hahn–Banach theorem. Three appendices describe Euclidean groups, Jordan measure, and a collection of open problems.
For every algebraic number A, it is possible to find a unit distance graph G in which some pair of vertices are at distance A in all unit distance representations of G.. This result implies a finite version of the Beckman–Quarles theorem: for any two points p and q at distance A, there exists a finite rigid unit distance graph containing p and q such that any transformation of the plane that preserves the unit distances in this graph preserves the distance between p and q. The full Beckman–Quarles theorem states that any transformation of the Euclidean plane (or a higher-dimensional space) that preserves unit distances must be a congruence; that is, for the infinite unit distance graph whose vertices are all the points in the plane, any graph automorphism must be an isometry.
The family of congruence subgroups in a given arithmetic group \Gamma always has property (τ) of Lubotzky-Zimmer. This can be taken to mean that the Cheeger constant of the family of their Schreier coset graphs (with respect to a fixed generating set for \Gamma) is uniformly bounded away from zero, in other words they are a family of expander graphs. There is also a representation-theoretical interpretation: if \Gamma is a lattice in a Lie group G then property (τ) is equivalent to the non-trivial unitary representations of G occurring in the spaces L^2(G/\Gamma) being bounded away from the trivial representation (in the Fell topology on the unitary dual of G). Property (τ) is a weakening of Kazhdan's property (T) which implies that the family of all finite-index subgroups has property (τ).
He further suggested that these proposed bills, if enacted, could face difficult legal challenges. He further stated that despite their language stating that they are not promoting religious views, and wording to promote "scientific" rather than religious critiques, courts are likely to question the motives behind these bills, and their specific focus on evolution, and draw a conclusion as to "what's going on here." Michael Simpson, a lawyer for the National Education Association stated that courts have generally refused to afford significant free-speech protections to teachers for in-class remarks. He further offered the opinion that the legality of these measures would depend on a number of unknowns, such as how the critical views of evolution-critical views were presented, and possibly the degree of congruence between them and other state policies, such as state science curriculum.
Eliana Rubashkyn (born 25 June 1988) is a Colombian–born formerly stateless New Zealander, known internationally for being the first intersex person assigned male at birth legally recognised as a woman with a U.N. resolution under the international refugee statute. Rubashkyn is a pharmacist, chemist and polyglot; Eliana currently works as a nicotine harm reduction scientist and develops campaigns of support addressed to LGBTI asylum seekers, refugees and intersex persons in New Zealand. Rubashkyn's gender was recognised under the United Nations' 1951 Convention relating to the Status of Refugees. Rubashkyn's case attracted international media and legal attention after her mistreatment following her detention at Hong Kong International Airport because of the lack of congruence between her gender identity and her passport photo, resulting in several years of statelessness in Hong Kong, and inhumane reclusion into several refuge centers across Yuen Long.
Archbishop Roche explained that "The object of the changes is to define better the roles of the Apostolic See and the Conferences of Bishops in respect to their proper competencies which are different yet remain complementary." Magnum principium modified two clauses in canon 838 of the Code of Canon Law. Before its modifications the passage at issue read: The revised text read (highlighting in original): The role of the CDW is to review translations rather than authorize them. A note accompanying the release of Magnum principium authored by Archbishop Roche, explained that the CDW was tasked with confirming a translation, that the process "leaves responsibility for the translation, presumed to be faithful, to [...] the bishops' conference", and "presupposes a positive evaluation of the faithfulness and congruence of the produced texts with respect to the Latin text".
Euclid believed that his axioms were self-evident statements about physical reality. Euclid's proofs depend upon assumptions perhaps not obvious in Euclid's fundamental axioms, in particular that certain movements of figures do not change their geometrical properties such as the lengths of sides and interior angles, the so-called Euclidean motions, which include translations, reflections and rotations of figures. See, for example: and The group of motions underlie the metric notions of geometry. See Taken as a physical description of space, postulate 2 (extending a line) asserts that space does not have holes or boundaries (in other words, space is homogeneous and unbounded); postulate 4 (equality of right angles) says that space is isotropic and figures may be moved to any location while maintaining congruence; and postulate 5 (the parallel postulate) that space is flat (has no intrinsic curvature).
The subsequent notion of an "automorphic representation" has proved of great technical value when dealing with G an algebraic group, treated as an adelic algebraic group. It does not completely include the automorphic form idea introduced above, in that the adelic approach is a way of dealing with the whole family of congruence subgroups at once. Inside an L2 space for a quotient of the adelic form of G, an automorphic representation is a representation that is an infinite tensor product of representations of p-adic groups, with specific enveloping algebra representations for the infinite prime(s). One way to express the shift in emphasis is that the Hecke operators are here in effect put on the same level as the Casimir operators; which is natural from the point of view of functional analysis, though not so obviously for the number theory.
Ishii was especially focused on creating a truly cooperative multiplayer game, which he had wanted to create since Secret of Mana (1993), the second game in the series. Despite this, he chose not to utilize the DS's Nintendo Wi-Fi functionality in order to effect an experience in which players would interact with people in the near vicinity rather than remotely, in congruence with the local multiplayer found in Secret of Mana. He also designed the multiplayer to create a sense of chaotic excitement, such that players could interact without focusing on the difficulty or competing against each other. Several of the game's design choices were meant to focus more on the action components, such as attacks sending enemies flying across the screen and the use of both the buttons and stylus to keep the controls simple and directly connected to the action.
In mathematics, a bracket algebra is an algebraic system that connects the notion of a supersymmetry algebra with a symbolic representation of projective invariants. Given that L is a proper signed alphabet and Super[L] is the supersymmetric algebra, the bracket algebra Bracket[L] of dimension n over the field K is the quotient of the algebra Brace{L} obtained by imposing the congruence relations below, where w, w', ..., w" are any monomials in Super[L]: # {w} = 0 if length(w) ≠ n # {w}{w'}...{w"} = 0 whenever any positive letter a of L occurs more than n times in the monomial {w}{w'}...{w"}. # Let {w}{w'}...{w"} be a monomial in Brace{L} in which some positive letter a occurs more than n times, and let b, c, d, e, ..., f, g be any letters in L.
As with plane triangles, on a sphere two triangles sharing the same sequence of angle-side- angle (ASA) are necessarily congruent (that is, they have three identical sides and three identical angles). This can be seen as follows: One can situate one of the vertices with a given angle at the south pole and run the side with given length up the prime meridian. Knowing both angles at either end of the segment of fixed length ensures that the other two sides emanate with a uniquely determined trajectory, and thus will meet each other at a uniquely determined point; thus ASA is valid. The congruence theorems side- angle-side (SAS) and side-side-side (SSS) also hold on a sphere; in addition, if two spherical triangles have an identical angle-angle-angle (AAA) sequence, they are congruent (unlike for plane triangles).
D'Souza responds to Dawkins that an individual need not explicitly invoke atheism in committing atrocities if it is already implied in his worldview as is the case in Marxism. In a 1993 address to American bishops, Pope John Paul II spoke of a spreading "practical atheism" in modern societies which was clouding the moral sense of humans and fragmenting society: Journalist Robert Wright has argued that some New Atheists discourage looking for deeper root causes of conflicts when they assume that religion is the sole root of the problem. Wright argues that this can discourage people from working to change the circumstances that actually give rise to those conflicts. Mark Chaves has said that the New Atheists, amongst others who comment on religions, have committed the religious congruence fallacy in their writings by assuming that beliefs and practices remain static and coherent through time.
We know what “coprime” relation means (in a lucky way, its negation can be formulated in a concise form); thus, let us substitute in the appropriate way: :\exists i Using a “more” prenex normal form (but note allowing a constraint-like notation in quantifiers): :\exists i Because of a theorem on divisibility, p \mid m_i \land p \mid m_j allows us to also say :p \mid m_i - m_j. Substituting the definitions of m_k-sequence notation, we get m_i - m_j = (i-j) \cdot m, thus (as equality axioms postulate identity to be a congruence relation see also related notions, e.g. “equals for equals” (referential transparency), and another related notion Leibniz's law / identity of indiscernibles) we get : p \mid (i-j) \cdot m. Since p is a prime element (note that the irreducible element property is used), we get :p \mid i-j \lor p \mid m.
Book VI features a return to the basic definitions at the front of the book. “Equality” is determined by an application of areas. If one figure; that is, a section or a segment, is “applied” to another (Halley's si applicari possit altera super alteram), they are “equal” (Halley's aequales) if they coincide and no line of one crosses any line of the other. This is obviously a standard of congruence following Euclid, Book I, Common Notions, 4: “and things coinciding (epharmazanta) with one another are equal (isa).” Coincidence and equality overlap, but they are not the same: the application of areas used to define the sections depends on quantitative equality of areas but they can belong to different figures. Between instances that are the same (homos), being equal to each other, and those that are different, or unequal, are figures that are “same-ish” (hom- oios), or similar.
The Purnell Model facilitates the potential to acquire information directly relevant to various cultures due to consideration given to each patient's circumstances. Flexibility has been recognised as a critical quality of the model, as it is able to improve the prospective pertinence, of the model, to a range of settings like nursing. The importance of the model is also acknowledged due to its ability to represent multiple outlooks on the world; that assist when providing individuals with culturally competent care. The model has additionally been recognised to incorporate suppositions that are coherent in relation to the model's foundations, as well as containing well- defined explanations of the domains. Angela Cooper Brathwaite, who has conducted assessments on a variety of cultural competence models, has stated that the model is “comprehensive in content, very abstract, has logical congruence, conceptual clarity, demonstrates clinical utility and espouses the experiential-phenomenological perspective”.
Some of Roth's earliest works included a 1949 paper on sums of powers, showing that almost all positive integers could be represented as a sum of a square, a cube, and a fourth power, and a 1951 paper on the gaps between squarefree numbers, describes as "quite sensational" and "of considerable importance" respectively by Chen and Vaughan. His inaugural lecture at Imperial College concerned the large sieve: bounding the size of sets of integers from which many congruence classes of numbers modulo prime numbers have been forbidden. Roth had previously published a paper on this problem in 1965. The optimal square packing in a square can sometimes involve tilted squares; Roth and Bob Vaughan showed that non-constant area must be left uncovered Another of Roth's interests was the Heilbronn triangle problem, of placing points in a square to avoid triangles of small area.
His study of discrete geometric analysis includes a graph-theoretic interpretation of Ihara zeta functions, a discrete analogue of periodic magnetic Schrödinger operators as well as the large time asymptotic behaviors of random walk on crystal lattices. The study of random walk led him to the discovery of a "mathematical twin" of the diamond crystal out of an infinite universe of hypothetical crystals (2005). He named it the K4 crystal due to its mathematical relevance (see the linked article). What was noticed by him is that the K4 crystal has the "strong isotropy property", meaning that for any two vertices x and y of the crystal net, and for any ordering of the edges adjacent to x and any ordering of the edges adjacent to y, there is a net-preserving congruence taking x to y and each x-edge to the similarly ordered y-edge.
More importantly, one may define a function on a set, such as "radius of a circle in the plane", and then ask if this function is invariant under a group action, such as rigid motions. Dual to the notion of invariants are coinvariants, also known as orbits, which formalizes the notion of congruence: objects which can be taken to each other by a group action. For example, under the group of rigid motions of the plane, the perimeter of a triangle is an invariant, while the set of triangles congruent to a given triangle is a coinvariant. These are connected as follows: invariants are constant on coinvariants (for example, congruent triangles have the same perimeter), while two objects which agree in the value of one invariant may or may not be congruent (for example, two triangles with the same perimeter need not be congruent).
James G. Lochtefeld, Guna, in The Illustrated Encyclopedia of Hinduism: A-M, Vol. 1, Rosen Publishing, , page 265 These three Guṇas are ' (goodness, constructive, harmonious, virtuous), ' (passion, aimless action, dynamic, egoistic), and ' (darkness, destructive, chaotic, viciousness). All of these three gunas (good, evil, active) are present in everyone and everything, it is the proportion that is different, according to the Hindu worldview.M Innes-Brown and S Chatterjee (1999), The Relevance of the Guna Theory in the Congruence of Eastern Values and Western Management Practice, Journal of Human Values, 5(2), pages 93-102N Pani (2009), Hinduism, in Handbook of Economics and Ethics (Editors: Jan Peil and Irene Staveren), Edward Elgar, , 216-221 The interplay of these gunas defines the character of someone or something, and the costumes and face colouring in Kathakali often combines the various colour codes to give complexity and depth to the actor-dancers.
In universal algebra, an abstract algebra A is called simple if and only if it has no nontrivial congruence relations, or equivalently, if every homomorphism with domain A is either injective or constant. As congruences on rings are characterized by their ideals, this notion is a straightforward generalization of the notion from ring theory: a ring is simple in the sense that it has no nontrivial ideals if and only if it is simple in the sense of universal algebra. The same remark applies with respect to groups and normal subgroups; hence the universal notion is also a generalization of a simple group (it is a matter of convention whether a one-element algebra should be or should not be considered simple, hence only in this special case the notions might not match). A theorem by Roberto Magari in 1969 asserts that every variety contains a simple algebra.
In its genealogy of Abram (7:19), it makes no mention of the Cainan between Arpachsad and Shelah, in congruence with the Masoretic Text and Samaritan Pentateuch, but in conflict with the Septuagint (LXX) and Luke's genealogy in chapter 3 of his Gospel. In its highly interpolated account of God's testing of Abraham concerning Isaac, it says in 23:50-51: "And when they were going along Isaac said to his father: Behold, I see here the fire and wood, and where then is the lamb that is to be the burnt offering before the Lord? And Abraham answered his son Isaac, saying: The Lord has made choice of thee my son, to be a perfect burnt offering instead of the lamb." This conflicts with the biblical account, in which Abraham's response was only: "My son, God will provide himself a lamb for a burnt offering".
The proof of the negative solution for CLP shows that the problem of representing distributive semilattices by compact congruences of lattices already appears for congruence lattices of semilattices. The question whether the structure of partially ordered set would cause similar problems is answered by the following result. Theorem (Wehrung 2008). For any distributive (∨,0)-semilattice S, there are a (∧,0)-semilattice P and a map μ : P × P → S such that the following conditions hold: (1) x ≤ y implies that μ(x,y)=0, for all x, y in P. (2) μ(x,z) ≤ μ(x,y) ∨ μ(y,z), for all x, y, z in P. (3) For all x ≥ y in P and all α, β in S such that μ(x,y) ≤ α ∨ β, there are a positive integer n and elements x=z0 ≥ z1 ≥ ... ≥ z2n=y such that μ(zi,zi+1) ≤ α (resp.
The usage primarily comes from translations of Euclid's Elements, in which two line segments a and b are called commensurable precisely if there is some third segment c that can be laid end-to-end a whole number of times to produce a segment congruent to a, and also, with a different whole number, a segment congruent to b. Euclid did not use any concept of real number, but he used a notion of congruence of line segments, and of one such segment being longer or shorter than another. That ' is rational is a necessary and sufficient condition for the existence of some real number c, and integers m and n, such that :a = mc and b = nc. Assuming for simplicity that a and b are positive, one can say that a ruler, marked off in units of length c, could be used to measure out both a line segment of length a, and one of length b.
Cultural differences exist in the ventral visual cortex and many studies have shown this. In a study conducted in 2005 they found that East Asians were more likely to keep their eyes focused on background scenes than westerners who would instead focus more on the central object such as a giraffe in a savanna. In a similar 2006 study it showed that in congruence to the difference in society structure westerners showed more activation in object processing regions, including the bilateral middle temporal gyrus, left superior parietal gyrus, and right superior temporal gyrus, although no activation differences were observed in context-processing regions such as the hippocampus. However, there has been some research contradicting cultural bias in the oculomotor control such as one conducted in 2007 by Rayner, Li, Williams, Cave, and well who failed to find evidence that East Asians focus more on context although they did find evidence that they are more likely to focus less on central objects.
Grinevald also realised the congruence of Georgescu-Roegen's viewpoint and the French debates occurring at the time; this resemblance was captured in the title of the French edition. Taken together, the translation of Georgescu-Roegen's work into French both fed on and gave further impetus to the concept of décroissance in France—and everywhere else in the francophone world—thereby creating something of an intellectual feedback loop. By the 2000s, when décroissance was to be translated from French back into English as the catchy banner for the new social movement, the original term "decline" was deemed inappropriate and misdirected for the purpose: "Decline" usually refers to an unexpected, unwelcome, and temporary economic recession, something to be avoided or quickly overcome. Instead, the neologism "degrowth" was coined to signify a deliberate political action to downscale the economy on a permanent, conscious basis—as in the prevailing French usage of the term—something good to be welcomed and maintained, or so followers believe.
Even without knowledge that we are working in the multiplicative group of integers modulo n, we can show that a actually has an order by noting that the powers of a can only take a finite number of different values modulo n, so according to the pigeonhole principle there must be two powers, say s and t and without loss of generality s > t, such that as ≡ at (mod n). Since a and n are coprime, this implies that a has an inverse element a−1 and we can multiply both sides of the congruence with a−t, yielding as−t ≡ 1 (mod n). The concept of multiplicative order is a special case of the order of group elements. The multiplicative order of a number a modulo n is the order of a in the multiplicative group whose elements are the residues modulo n of the numbers coprime to n, and whose group operation is multiplication modulo n.
After receiving his BA in psychology in 1985, Sang Min Whang continued his studies at East Graduate School under professor Bong Yeon Suh's guidance. And in September 1986, he received a scholarship from The Korea Foundation for Advanced Studies to study Social Cognitive Development under Sheldon White's guidance in Harvard University's psychology doctorate program. The question that continues to be repeated in Sang Min Whang's work since his graduate school days can be summarized as follows: "How are peoples' minds living in a particular society or culture expressed in different ways for each individual?" His doctoral dissertation "The Organization of Everyday Places and their Dimensional Features: The Priming Effect of Dimensions on the Congruence of Place and Behavior" explored what kind of conceptions people had of everyday places, how the psychological meaning people attribute to places can be measured, and whether the measured results came from absolute characteristics of places or were results of peoples’ responses to places.
In March 1850, the meeting was organized and attended by the self-taught Serbian linguist and folklorist Vuk Stefanović Karadžić, his close follower Đuro Daničić; the most eminent Slavist of the period, Slovene philologist Franz Miklosich, and Croatian scholars and writers Ivan Kukuljević Sakcinski, Dimitrije Demeter, Ivan Mažuranić, Vinko Pacel, and Stjepan Pejaković. General guidelines for the conceived development of the common literary language for Croats and Serbs were agreed on; these were in accordance with Karadžić's basic linguistic and orthographic premises, and they partly corresponded with the fundamental Croatian Neo-Shtokavian pre-Illyrian literary language which the concept of Illyrian suppressed at the expense of South-Slavic commonality. The Ljudevit Gaj's Latin script and Karadžić's Cyrillic script were aligned to one-to-one congruence and both declared equal in a state of synchronic digraphia. The signatories agreed on five points: # They decided not to merge existing dialects, instead creating a new one, and that they should, following German and Italian models, pick one of the peoples' dialects and choose this as the literary basis according to which all text would be written.
In number theory and algebraic geometry, a modular curve Y(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of the complex upper half-plane H by the action of a congruence subgroup Γ of the modular group of integral 2×2 matrices SL(2, Z). The term modular curve can also be used to refer to the compactified modular curves X(Γ) which are compactifications obtained by adding finitely many points (called the cusps of Γ) to this quotient (via an action on the extended complex upper-half plane). The points of a modular curve parametrize isomorphism classes of elliptic curves, together with some additional structure depending on the group Γ. This interpretation allows one to give a purely algebraic definition of modular curves, without reference to complex numbers, and, moreover, prove that modular curves are defined either over the field Q of rational numbers, or a cyclotomic field. The latter fact and its generalizations are of fundamental importance in number theory.
After having successfully passed the school leaving exam in 1921, he entered the Friedrich- Wilhelm University in Berlin, where he studied mathematics, physics, and philosophy for two years. In 1923, as a head of the Berlin student organization Mathematisch-Physikalische Arbeitsgemeinschaft (Mathematics and Physics Working Group), he went with his father to the United States. The visit, which Rohrbach called his propaganda visit, was a tour of American universities to raise money for impoverished Berlin students. Germany's economy, which was undergoing a period of hyperinflation, was making life extremely difficult for students, who had to take employment to supplement their income. In the autumn of 1924 Rohrbach resumed his studies at the University of Berlin and studied there until 1929. In the late 1920s he started work on his PhD thesis, titled Die Charaktere der binären Kongruenzgruppen mod p2 (The characters of the binary congruence groups mod p2), advised by Issai Schur. He submitted it and was awarded his doctorate on 25 July 1932. While studying at Berlin University, Rohrbach met fellow student Rose Gadebusch (born 1905), who studied mathematics starting in 1925.
Where the angle is a right angle, also known as the Hypotenuse-Leg (HL) postulate or the Right-angle-Hypotenuse-Side (RHS) condition, the third side can be calculated using the Pythagorean Theorem thus allowing the SSS postulate to be applied. If two triangles satisfy the SSA condition and the corresponding angles are acute and the length of the side opposite the angle is equal to the length of the adjacent side multiplied by the sine of the angle, then the two triangles are congruent. If two triangles satisfy the SSA condition and the corresponding angles are acute and the length of the side opposite the angle is greater than the length of the adjacent side multiplied by the sine of the angle (but less than the length of the adjacent side), then the two triangles cannot be shown to be congruent. This is the ambiguous case and two different triangles can be formed from the given information, but further information distinguishing them can lead to a proof of congruence.
These four-dimensional coordinates may be transformed into three-dimensional coordinates by the formula :(a, b, c, d) → (a + b − c − d, a − b + c − d, −a + b + c − d).. Because the diamond structure forms a distance-preserving subset of the four-dimensional integer lattice, it is a partial cube. Yet another coordinatization of the diamond cubic involves the removal of some of the edges from a three-dimensional grid graph. In this coordinatization, which has a distorted geometry from the standard diamond cubic structure but has the same topological structure, the vertices of the diamond cubic are represented by all possible 3d grid points and the edges of the diamond cubic are represented by a subset of the 3d grid edges.. The diamond cubic is sometimes called the "diamond lattice" but it is not, mathematically, a lattice: there is no translational symmetry that takes the point (0,0,0) into the point (3,3,3), for instance. However, it is still a highly symmetric structure: any incident pair of a vertex and edge can be transformed into any other incident pair by a congruence of Euclidean space.
To make this showing, the committee needed to assemble evidence to demonstrate that the special provisions were generally successful in combating racial discrimination in voting, but not so successful as to no longer be necessary. Given the uncertainty surrounding the congruence and proportionality standard, political constraints, and the Supreme Court previously having upheld the special provisions as constitutional, the committee decided to reauthorize the special provisions without amending the coverage formula. The committee ultimately included in the record four types of evidence to support this reauthorization: statistics showing rates of minority voter registration, turnout, and elective officeholding in covered versus non-covered jurisdictions; statistics showing the behavior of covered jurisdictions and the Department of Justice in the preclearance process; instances of voting discrimination in covered jurisdictions; and data comparing successful Section 2 litigation in covered versus non-covered jurisdictions. On May 2, 2006, Representative Sensenbrenner introduced the Fannie Lou Hamer, Rosa Parks, and Coretta Scott King Voting Rights Act Reauthorization and Amendments Act of 2006.Pub. L. No. 109-246, 2006 U.S.C.C.A.N. (120 Stat.) 577 (codified at ) The bill proposed to extend the special provisions by 25 years and keep the coverage formula unchanged.
Automorphic forms are a generalization of modular forms to more general analytic functions, perhaps of several complex variables, with similar transformation properties.. The generalization involves replacing the modular group PSL2 (R) and a chosen congruence subgroup by a semisimple Lie group G and a discrete subgroup Γ. Just as modular forms can be viewed as differential forms on a quotient of the upper half space H = PSL2 (R)/SO(2), automorphic forms can be viewed as differential forms (or similar objects) on Γ\G/K, where K is (typically) a maximal compact subgroup of G. Some care is required, however, as the quotient typically has singularities. The quotient of a semisimple Lie group by a compact subgroup is a symmetric space and so the theory of automorphic forms is intimately related to harmonic analysis on symmetric spaces. Before the development of the general theory, many important special cases were worked out in detail, including the Hilbert modular forms and Siegel modular forms. Important results in the theory include the Selberg trace formula and the realization by Robert Langlands that the Riemann-Roch theorem could be applied to calculate the dimension of the space of automorphic forms.
See Arthur Donovan, Philosophical Chemistry in the Scottish Enlightenment, Edinburgh, 1975 Whether Cullen coined the phrase is not clear, but his usage seems to predate most others, although it rapidly became widespread across Europe, and was used in particular by the Swedish chemist Torbern Olof Bergman throughout his book (1775). Affinity theories were used in one way or another by most chemists from around the middle of the 18th century into the 19th century to explain and organise the different combinations into which substances could enter and from which they could be retrieved.On the variety of affinity theories, see Georgette Taylor, Variations on a Theme; Patterns of Congruence and Divergence among 18th Century Affinity Theories, VDM Verlag Dr Muller Aktiengesellschaft, 2008 Antoine Lavoisier, in his famed 1789 Traité Élémentaire de Chimie (Elements of Chemistry), refers to Bergman's work and discusses the concept of elective affinities or attractions. According to chemistry historian Henry Leicester, the influential 1923 textbook Thermodynamics and the Free Energy of Chemical Reactions by Gilbert N. Lewis and Merle Randall led to the replacement of the term "affinity" by the term "free energy" in much of the English-speaking world.
On pg. 529, Hendel writes "The doctrine of uniform inerrancy in the literal sense across all details is an innovation of the Catholic-Protestant polemics after Trent." Origen of Alexandria thought there were minor discrepancies between the accounts of the Gospels but dismissed them due to their lack of theological importance, writing "let these four [Gospels] agree with each other concerning certain things revealed to them by the Spirit and let them disagree a little concerning other things" (Commentary on John 10.4). Later, John Chrysostom was also unconcerned with the notion that the scriptures were in congruence with all matters of history unimportant to matters of faith. > But if there be anything touching time or places, which they have related > differently, this nothing injures the truth of what they have said … [but > those things] which constitute our life and furnish out our doctrine nowhere > is any of them found to have disagreed, no not ever so little (Homily on > Matthew 1.6) In his Commentary on Galatians, Jerome also argued that Paul's rebuke of Peter in Galatians 2:11-14 for acting like a Jew around the Jewish faction of the early Church was an insincere "white lie" as Paul himself had done the same thing.

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