Specifically, let G be a simply-connected Lie group with Lie algebra.

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 LGdenote the space of continuous maps

Specifically, let X

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.

Specifically, it is defined as the largest cardinality of an algebraically independent subset of L over K.

Specifically, the isoperimetric inequality states, for the length L of a closed curve and the area A of the planar region that it encloses, that

Specifically, LapTrap is described as being a Turbo T. U. R. T. L. E.

Specifically, if F is a diagram in Top and ( L, φ ) is a limit of UF in Set, the corresponding limit of F in Top is obtained by placing the initial topology on ( L, φ ).

Specifically, it implies that as a Galois extension of K, L is uniquely determined by the set of primes of K that split completely in it.

In the report by Major General Antonio M. Taguba regarding the alleged acts of brutality, abuse, and torture at the Enemy Prisoner of War facility at Abu Ghraib and other Enemy Prisoner of War Camps in Iraq and Afghanistan, Taguba said, "' Specifically I suspect that Col. Thomas M. Pappas, Lt. Col. Steve L. Jordan, Mr. Steven Stephanowicz and Mr. John Israel were either directly or indirectly responsible for the abuses at Abu Ghraib and strongly recommend immediate disciplinary actions ..."

Specifically, a small-world network is defined to be a network where the typical distance L between two randomly chosen nodes ( the number of steps required ) grows proportionally to the logarithm of the number of nodes N in the network, that is:

Specifically, the House managers said Ritter engaged in champerty (" a proceeding whereby a person having no legitimate interest in a lawsuit abets it with money or services in the hope of profit ") by " corruptly and unlawfully " receiving $ 4, 500 from a former law partner, Albert L. Rankin.

Specifically, L is the gas-liquid partition constant on hexadecane at 298 K ; E the excess molar refraction ; S the ability of a solute to stabilize a neighboring dipole by virtue of its capacity for orientation and induction interactions ; A the solute ’ s effective hydrogen bond acidity ; and B the solute ’ s effective hydrogen-bond basicity.

Specifically, the pumping lemma says that for any regular language L there exists a constant p such that any word w in L with length at least p can be split into three substrings, w = xyz, where the middle portion y must not be empty, such that the words xz, xyz, xyyz, xyyyz, … constructed by repeating y an arbitrary number of times ( including zero times ) are still in L. This process of repetition is known as " pumping ".

Specifically, the model must assign to each constant symbol of L an element of M, and to each n-ary function symbol f of L and each n-tuple < a < sub > 0 </ sub >,..., a < sub > n-1 </ sub >> of elements of M, the model must assign an element of M to the term f ( a < sub > 0 </ sub >,..., a < sub > n-1 </ sub >).

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.

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, 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.