For a compact simply connected simple Lie group G with an involution α, we compute theGoZ/2-equivariant K-theory of G where G acts by conjugation and Z/2 acts either by α or by g 7→ α(g)−1. We also give a representation-theoretic interpretation of those groups, as well as of KG(G).

Let G be a finite group and α be an automorphism of G of order p n for an odd prime p. Suppose that α acts fixed point freely on every α-invariant p-section of G, and acts trivially or exceptionally on every elementary abelian α-invariant p-section of G. It is proved that G is a solvable p-nilpotent group of nilpotent length at most n + 1, and this bound is best possible.

Let G be a finite abelian group, let 0 < α < 1, and let A ⊆ G be a random set of size |G|. We let μ(A) = max B,C:|B|=|C|=|A| |{(a, b, c) ∈ A×B × C : a = b+ c}|. The issue is to determine upper bounds on μ(A) that hold with high probability over the random choice of A. Mennink and Preneel [4] conjecture that μ(A) should be close to |A| (up to possible logarithmic factors in |G|) for α ≤ 1/2 and ...

The stability number α(G) of a graph G is the size of a maximum stable set of G, core(G) = ∩{S : S is a maximum stable in G}, and ξ(G) = |core(G)|. In this paper we prove that for a graph G without isolated vertices, the following assertions are true: (i) if ξ(G) ≤ 1, then G is quasi-regularizable; (ii) if G is of order n and α(G) > (n + k − 1)/2, for some k ≥ 1, then ξ(G) ≥ k + 1, and ξ(G) ≥ k...

and Applied Analysis 3 Proof. Let p(z) be given by (11), which clearly belongs to the class A(n). Now differentiating (11), we have p 󸀠 (z) = ( f (z) ∗ g (z) z ) 1/(p+b−1) × 1 p + b − 1 { z(f (z) ∗ g (z)) 󸀠 f (z) ∗ g (z) + b − 1} (20) which gives 󵄨󵄨󵄨󵄨 arg p (z)󵄨󵄨󵄨󵄨 = 󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨 arg( f (z) ∗ g (z) z ) 1/(p+b−1) + arg{ 1 p+b−1 ( z(f (z) ∗ g (z)) 󸀠 f (z) ∗ g (z) +b−1)} 󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨 . (21) Thus using (...

An independent set in a graph is a set of pairwise non-adjacent vertices, and α(G) is the size of a maximum independent set in the graph G. If sk is the number of independent sets of cardinality k in G, then I(G;x) = s0 + s1x+ s2x 2 + ...+ sαx , α = α (G) , is called the independence polynomial of G (I. Gutman and F. Harary, 1983). If sα−i = f (i) · sα−j holds for every i ∈ {0, 1, ..., bα/2c}, ...

α-NiS/g-C3N4 nanocomposites were synthesized and used for photocatalytic hydrogen (H2) evolution tetracycline hydrochloride (TC) degradation. The fabricated characterized by XRD, XPS, SEM, TEM, UV-vis DRS, TRPL, PEC measurements. Photocatalytic studies show that the generation rate of 15%-α-NiS/g-C3N4 nanocomposite reaches 4025 μmol·g−1·h−1 TC degradation 64.6% within 120 min, both which are hi...

References 28 of 29 max_connected(G) The set of maximal connected subgraphs of the SDF graph G. The number of invocations of the source actor of SDF arc α that precede the ith invocation of sink(α) in schedule S. p(α) The number of samples produced onto SDF arc α by one invocation of source(α). periodic schedule A schedule that invokes each actor at least once and produces no net change in the ...