We prove that a two-variable p-adic lq-function has the series expansion lp,q s, t, χ 2 q/ 2 F ∑F a 1, p,a 1 −1 a χ a qa/〈a pt〉 ∑∞ m 0 −s m F/〈a pt〉 mE∗ m,qF which interpolates the values lp,q −n, t, χ E∗ n,χn,q pt − pχn p 2 q/ 2 qp E∗ n,χn,q t , whenever n is a nonpositive integer. The proof of this original construction is due to Kubota and Leopoldt in 1964, although the method given in this ...

In this article we write algorithms and MATLAB programs to find the total energy of Cycle some related graphs. The concept matrix a graph G is introduced by K.Palani&M.Lalithakumari in [9]. Let G=(V, E) be (p, q) simple graph. V (G) = {νi/i 1,2, ... p} E {ei/i q}. T T(G) square order p + q whose (i, j)-entry defined as:

The cross section for the He(e, ed)p reaction has been measured as a function of the missing momentum pm in (q, ω)-constant kinematics at beam energies of 370 and 576 MeV for values of the three-momentum transfer q of 412, 504 and 604 MeV/c. The L(+TT), T and LT structure functions have been separated for q = 412 and 504 MeV/c. The data are compared to three-body Faddeev calculations, including...

The redox midpoint potential (E(m)) of Q(A), the primary quinone of bacterial reaction centers, is substantially modulated by the protein environment. Quite subtle mutations in the Q(A) binding site, e.g., at residues M218, M252 and M265, cause significant increases in the equilibrium constant for electron transfer to Q(B), which indicate relative lowering of the E(m) of Q(A). However, reports ...

Let p be an odd prime, and let m divide p−1. Let ζ = e and let ω = e. The field extension Q(ω) ⊂ Q(ω, ζ) is Galois with cyclic Galois group isomorphic to (Z/pZ)×. The unique field between Q(ω) and Q(ω, ζ) having degree m over Q(ω) takes the form Q(ω, τ) where τ is a Gauss sum, to be described below. Furthermore, under some conditions we can compute τ as an element α of Q(ω), thus expressing the...

Let p > q and let G be the group U(p, q) or Spin0(p, q). Let P = LN be the maximal parabolic subgroup of G with Levi subgroup L ∼=M × U where (M,U) = { (GLq(C),U(p− q)) if G = U(p, q) (GLq (R),Spin(p− q)) if G = Spin0(p, q). Let χ be a 1 dimensional character of M and τ an irreducible representation of U with highest weight μ. Let πχ,μ be the representation of P which is trivial on N and πχ,μ|L...

The first part of this paper deals with the topic of finding equivalent norms and characterizations for vector-valued Besov and Triebel-Lizorkin spaces Bs p,q(E) and F s p,q(E). We will deduce general criteria by transferring and extending a theorem of Bui, Paluszyński and Taibleson from the scalar to the vector-valued case. By using special norms and characterizations we will derive necessary ...

The group D(P ) of all endo-permutation modules for a finite p-group P is a finitely generated abelian group. We prove that its torsion-free rank is equal to the number of conjugacy classes of non-cyclic subgroups of P . We also obtain partial results on its torsion subgroup. We determine next the structure of Q⊗D(−) viewed as a functor, which turns out to be a simple functor SE,Q , indexed by ...

Let m × m complex matrix P and n × n complex matrix Q be k-involutions, i.e., Pk−1 = P, Qk−1 = Q for some integer k ≥ 2. An m × n complex matrix A is (P, Q, β)symmetric if PAQ = λβA, or (P, Q, α, β)-symmetric if PAQ−α = λβA, where λ = e2πi/k and α, β ∈ {1, 2, . . . , k}. In this paper, for given matrices X, Y, E, F with appropriate sizes, the solvability of matrix equations AX = E and Y A = F u...

The rst part of this diploma thesis deals with the topic of nding equivalent norms and characterizations for vector-valued Besov and Triebel-Lizorkin spaces Bs p,q(E) and F s p,q(E). We will deduce general criteria by transferring and extending a theorem of Bui, Paluszy«ski and Taibleson from the scalar to the vector-valued case. By using special norms and characterizations we will derive neces...