Specifically, let χ be a character modulo k. Then we can write its Dirichlet L-function as

Specifically, let G be a group and let X and Y be two associated G-sets.

Specifically, let X be a separable normed space and B the closed unit ball in X < sup >∗</ sup >.

Specifically, the programs Front Row and Cover Flow, utilized in conjunction with the Apple Remote, let users easily browse through and view any multimedia content stored on their Macs.

The Dedekind zeta function satisfies a functional equation relating its values at s and 1 − s. Specifically, let Δ < sub > K </ sub > denote discriminant of K, let r < sub > 1 </ sub > ( resp.

Specifically, let X and Y be a topological spaces with A a subspace of Y.

Specifically, let L be a tame oriented knot or link in Euclidean 3-space ( or in the 3-sphere ).

Specifically, let LGdenote the space of continuous maps

Specifically, let X

The first isomorphism theorem states that the image of any group G under a homomorphism is always isomorphic to a quotient of G. Specifically, the image of G under a homomorphism is isomorphic to where ker ( φ ) denotes the kernel of φ.

Specifically, if L / K is a Galois extension, we consider the group G = Gal ( L / K ) consisting of all field automorphisms of L which keep all elements of K fixed.

This can be shown using the concept of left cosets of H in G. The left cosets are the equivalence classes of a certain equivalence relation on G and therefore form a partition of G. Specifically, x and y in G are related if and only if there exists h in H such that x

Specifically, if 〈 F, G, ε, η 〉 is an adjunction between C and D and 〈 F ′, G ′, ε ′, η ′〉 is an adjunction between D and E then the functor

Specifically, the adjacency matrix of a finite graph G on n vertices is the n × n matrix where the non-diagonal entry a < sub > ij </ sub > is the number of edges from vertex i to vertex j, and the diagonal entry a < sub > ii </ sub >, depending on the convention, is either once or twice the number of edges ( loops ) from vertex i to itself.

Specifically, if is an n-dimensional representation of G, then u < sub > ij </ sub > ∈ C ( G ) for all i, j, and for all i, j.

Specifically, given g ∈ G, ρ ( g ) is the linear map on V determined by its action on the basis by right translation by g < sup >− 1 </ sup >, i. e.

In general, a different choice of origin o will lead to a quotient of G by a different subgroup H < sub > o ′</ sub > which is related to H < sub > o </ sub > by an inner automorphism of G. Specifically,

Specifically, it is a single-subunit small GTPase, which is related in structure to the G < sub > α </ sub > subunit of heterotrimeric G proteins ( large GTPases ).

Specifically, if X and Y are the representation spaces of two linear representations of G then a linear map f: X → Y is called an intertwiner of the representations if it commutes with the action of G. Thus an intertwiner is an equivariant map in the special case of two linear representations / actions.

Specifically, GSM uses a regular pulse excited-long term prediction ( RPE-LTP ) coder for voice data between the mobile device and the BSS, but pulse code modulation ( A-law or μ-law standardized in ITU G. 711 ) upstream of the BSS.

Specifically, the G. R. E. A. T.

If H is a Lie subgroup of G, then there is a natural one-to-one correspondence between reductions of a G-bundle B to H and global sections of the fiber bundle B / H obtained by quotienting B by the right action of H. Specifically, the fibration B → B / H is a principal H-bundle over B / H.

Specifically, it will be asked whether the `` real '' questions people ask are not the `` ultimate '' questions that social science finds itself impotent in the face of.

Specifically, it can be used to test the equivalence principle, to probe dark matter, and test neutrino physics.

Specifically for fluids, the Knudsen number is used to assess to what extent the approximation of continuity can be made.

Specifically, the first four feet can either be dactyls or spondees more or less freely.

Specifically, the associativity and commutativity determine when repeated calculation can or cannot be avoided.

Specifically, if hair texture were simply the result of adaptively arbitrary human aesthetic preferences, one would expect that the global distribution of the various hair textures would be fairly random.

") appears to be much easier than the problem of actually finding the factors of N. Specifically, the former can be solved in polynomial time ( in the number n of digits of N ) with the AKS primality test.

Specifically, people allergic to latex, bananas, papayas or pineapples are likely to also be allergic to kiwifruit.

Specifically the final point stated: " A general association of nations must be formed under specific covenants for the purpose of affording mutual guarantees of political independence and territorial integrity to great and small states alike.

Specifically, it can be shown that for prime p > 2, M < sub > p </ sub >

Specifically, in diabetic mice the κ-opioid receptor appears to be involved in the antinociceptive effects of oxycodone, while in non-diabetic mice the μ < sub > 1 </ sub >- opioid receptor seems to be primarily responsible for these effects.

Specifically, in 1895 Pierre-Hector Coullié, archbishop of Lyon, voiced his official decision on the reinstatement of sports to Pierre de Coubertin, the founder of the Modern Olympic Games, by stating " Nous acceptons tout, sauf pankration " meaning " We accept all to be reinstated, except pankration ".

Specifically, he demonstrated an upper limit, known as Bell's inequality, regarding the strength of correlations that can be produced in any theory obeying local realism, and he showed that quantum theory predicts violations of this limit for certain entangled systems.

Specifically, results showed that those who believed that racial profiling was widespread and that racial tension would never be fixed were more likely to be opposed to racial profiling than those who did not believe racial profiling was as widespread or that racial tensions would be fixed eventually.

Specifically, for sailing boats, red and green sidelights and a white sternlight are required, although for vessels under 7 metres ( 23. 0 ft ) in length, these may be substituted by a torch or white all-round lantern.

Specifically, since electrons decay slowly from them, they can be piled up in this state without too much loss and then stimulated emission can be used to boost an optical signal.

Specifically, a construct in a language is called syntactic sugar if it can be removed from the language without any effect on what the language can do: functionality and expressive power will remain the same.

Specifically, the patch revision I. 5a was known to be one of the most stable.

Specifically, the weather must be better than basic VFR weather minima, i. e. in visual meteorological conditions ( VMC ), as specified in the rules of the relevant aviation authority.