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1.
Let ind(G) be the number of independent sets in a graph G. We show that if G has maximum degree at most 5 then
ind(G) £ 2iso(G) ?uv ? E(G) ind(Kd(u),d(v))\frac1d(u)d(v){\rm ind}(G) \leq 2^{{\rm iso}(G)} \prod_{uv \in E(G)} {\rm ind}(K_{d(u),d(v)})^{\frac{1}{d(u)d(v)}} 相似文献
2.
Let ${\Gamma < {\rm SL}(2, {\mathbb Z})}
3.
Bart De Bruyn 《Annals of Combinatorics》2010,14(3):307-318
Let f be an isometric embedding of the dual polar space ${\Delta = DQ(2n, {\mathbb K})}
4.
Let G be a finite group. The prime graph Γ(G) of G is defined as follows. The vertices of Γ(G) are the primes dividing the order of G and two distinct vertices p and p′ are joined by an edge if there is an element in G of order pp′. We denote by k(Γ(G)) the number of isomorphism classes of finite groups H satisfying Γ(G) = Γ(H). Given a natural number r, a finite group G is called r-recognizable by prime graph if k(Γ(G)) = r. In Shen et al. (Sib. Math. J. 51(2):244–254, 2010), it is proved that if p is an odd prime, then B
p
(3) is recognizable by element orders. In this paper as the main result, we show that if G is a finite group such that Γ(G) = Γ(B
p
(3)), where p > 3 is an odd prime, then G @ Bp(3){G\cong B_p(3)} or C
p
(3). Also if Γ(G) = Γ(B
3(3)), then G @ B3(3), C3(3), D4(3){G\cong B_3(3), C_3(3), D_4(3)}, or G/O2(G) @ Aut(2B2(8)){G/O_2(G)\cong {\rm Aut}(^2B_2(8))}. As a corollary, the main result of the above paper is obtained. 相似文献
5.
For an Azumaya algebra A with center C of rank n
2 and a unitary involution τ, we study the stability of the unitary SK1 under reduction. We show that if R = C
τ is a Henselian ring with maximal ideal
\mathfrakm{\mathfrak{m}} and 2 and n are invertible in R then
SK1(A, t) @ SK1(A/ \mathfrakm A, overline t){{{\rm SK}_1}(A, \tau) \cong {{\rm SK}_1}(A/ \mathfrak{m} A, overline \tau)}. 相似文献
6.
7.
Let G be a finite non-Abelian group. We define a graph Γ
G
; called the noncommuting graph of G; with a vertex set G − Z(G) such that two vertices x and y are adjacent if and only if xy ≠ yx: Abdollahi, Akbari, and Maimani put forward the following conjecture (the AAM conjecture): If S is a finite non-Abelian simple group and G is a group such that Γ
S
≅ Γ
G
; then S ≅ G: It is still unknown if this conjecture holds for all simple finite groups with connected prime graph except
\mathbbA10 {\mathbb{A}_{10}} , L
4(8), L
4(4), and U
4(4). In this paper, we prove that if
\mathbbA16 {\mathbb{A}_{16}} denotes the alternating group of degree 16; then, for any finite group G; the graph isomorphism
G\mathbbA16 @ GG {\Gamma_{{\mathbb{A}_{16}}}} \cong {\Gamma_G} implies that
\mathbbA16 @ G {\mathbb{A}_{16}} \cong G . 相似文献
8.
It is proved that if Ω ⊂ Rn {R^n} is a bounded Lipschitz domain, then the inequality
|| u ||1 \leqslant c(n)\textdiam( W)òW | eD(u) | {\left\| u \right\|_1} \leqslant c(n){\text{diam}}\left( \Omega \right)\int\limits_\Omega {\left| {{\varepsilon^D}(u)} \right|} is valid for functions of bounded deformation vanishing on ∂Ω. Here eD(u) {\varepsilon^D}(u) denotes the deviatoric part of the symmetric gradient and òW | eD(u) | \int\limits_\Omega {\left| {{\varepsilon^D}(u)} \right|} stands for the total variation of the tensor-valued measure eD(u) {\varepsilon^D}(u) . Further results concern possible extensions of this Poincaré-type inequality. Bibliography: 27 titles. 相似文献
9.
For a continuous function s\sigma defined on [0,1]×\mathbbT[0,1]\times\mathbb{T}, let \ops\op\sigma stand for the (n+1)×(n+1)(n+1)\times(n+1) matrix whose (j,k)(j,k)-entries are equal to \frac1 2pò02p s( \fracjn,eiq) e-i(j-k)q dq, j,k = 0,1,...,n . \displaystyle \frac{1} {2\pi}\int_0^{2\pi} \sigma \left( \frac{j}{n},e^{i\theta}\right) e^{-i(j-k)\theta} \,d\theta, \qquad j,k =0,1,\dots,n~. These matrices can be thought of as variable-coefficient Toeplitz matrices or as the discrete analogue of pseudodifferential operators. Under the assumption that the function s\sigma possesses a logarithm which is sufficiently smooth on [0,1]×\mathbbT[0,1]\times\mathbb{T}, we prove that the asymptotics of the determinants of \ops\op\sigma are given by det[\ops] ~ G[s](n+1)E[s] \text as n?¥ , \det \left[\op\sigma\right] \sim G[\sigma]^{(n+1)}E[\sigma] \quad \text{ as \ } n\to\infty~, where G[s]G[\sigma] and E[s]E[\sigma] are explicitly determined constants. This formula is a generalization of the Szegö Limit Theorem. In comparison with the classical theory of Toeplitz determinants some new features appear. 相似文献
10.
In this paper we introduce and study a family An(q)\mathcal{A}_{n}(q) of abelian subgroups of GLn(q){\rm GL}_{n}(q) covering every element of GLn(q){\rm GL}_{n}(q). We show that An(q)\mathcal{A}_{n}(q) contains all the centralizers of cyclic matrices and equality holds if q>n. For q>2, we obtain an infinite product expression for a probabilistic generating function for |An(q)||\mathcal{A}_{n}(q)|. This leads to upper and lower bounds which show in particular that
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