Surfaces with pg?=?q?=?1, K2?=?8 and nonbirational bicanonical map

We prove that if the bicanonical map of a minimal surface of general type S with p _g  = q = 1 and K_S²=8{K_{S}^2=8} is nonbirational, then it is a double cover onto a rational surface. An application of this theorem is the complete classification of minimal surfaces of general type with p_g=q=1, K_S²=8{p_{g}=q=1, K_{S}^2=8} and nonbirational bicanonical map.     

Hypersurfaces in the Lorentz-Minkowski space satisfying Lkψ?=?Aψ?+?b

We study hypersurfaces in the Lorentz-Minkowski space \mathbbLⁿ⁺¹{\mathbb{L}^{n+1}} whose position vector ψ satisfies the condition L _k ψ = Aψ + b, where L _k is the linearized operator of the (k + 1)th mean curvature of the hypersurface for a fixed k = 0, . . . , n − 1, A ? \mathbbR^(n+1)×(n+1){A\in\mathbb{R}^{(n+1)\times(n+1)}} is a constant matrix and b ? \mathbbLⁿ⁺¹{b\in\mathbb{L}^{n+1}} is a constant vector. For every k, we prove that the only hypersurfaces satisfying that condition are hypersurfaces with zero (k + 1)th mean curvature, open pieces of totally umbilical hypersurfaces \mathbbSⁿ₁(r){\mathbb{S}^n_1(r)} or \mathbbHⁿ(-r){\mathbb{H}^n(-r)}, and open pieces of generalized cylinders \mathbbS^m₁(r)×\mathbbR^n-m{\mathbb{S}^m_1(r)\times\mathbb{R}^{n-m}}, \mathbbH^m(-r)×\mathbbR^n-m{\mathbb{H}^m(-r)\times\mathbb{R}^{n-m}}, with k + 1 ≤ m ≤ n − 1, or \mathbbL^m×\mathbbS^n-m(r){\mathbb{L}^m\times\mathbb{S}^{n-m}(r)}, with k + 1 ≤ n − m ≤ n − 1. This completely extends to the Lorentz-Minkowski space a previous classification for hypersurfaces in \mathbbRⁿ⁺¹{\mathbb{R}^{n+1}} given by Alías and Gürbüz (Geom. Dedicata 121:113–127, 2006).     

Quasirecognition by prime graph of F4(q) where q?=?2n?>?2

The prime graph of a finite group G is denoted by Γ(G). In this paper as the main result, we show that if G is a finite group such that Γ(G) = Γ(F ₄(q)), where q = 2 ⁿ  > 2, then G has a unique nonabelian composition factor isomorphic to F ₄(q). We also show that if G is a finite group satisfying |G| = |F ₄(q)| and Γ(G) = Γ(F ₄(q)), where q = 2 ⁿ  > 2, then G @ F₄(q){G \cong F_4(q)}. As a consequence of our result we give a new proof for a conjecture of Shi and Bi for F ₄(q) where q = 2 ⁿ  > 2.     

Cuspidal representations of rational Cherednik algebras at t?=?0

We study those finite dimensional quotients of the rational Cherednik algebra at t?=?0 that are supported at a point of the centre. It is shown that each such quotient is Morita equivalent to a certain ??cuspidal?? quotient of a rational Cherednik algebra associated to a parabolic subgroup of W.     

Factorable surfaces in the three-dimensional Euclidean and Lorentzian spaces satisfying Δr i ?=?λ i r i

In this paper we classify the factorable surfaces in the three-dimensional Euclidean space ${\mathbb{E}^{3}}$ and Lorentzian ${\mathbb{E}_{1}^{3}}$ under the condition ??r _i ?=??? _i r _i , where ${\lambda_{i}\in\mathbb{R}}$ and ?? denotes the Laplace operator and we obtain the complete classification for those ones.     

On the asymptotic boundedness of the energy of solutions of the wave equation u tt ? a(t)Δu?=?0

Applying a class of quadratic forms introduced by Manfrin (Port. Math. 65(4):447?C484, 2008), we study the asymptotic behavior, as t ?? +??, of the energy of the solutions to the Cauchy problem for wave equations with time dependent propagation speed.     

关于环Fpm+uFpm+u2Fpm上循环码的注记

本文研究了环F_p^m+uF_p^m+u²F_p^m上长度为p^s的循环码分类.通过建立环F_p^m+uF_p^m+u²F_p^m到环F_p^m+uF_p^m的同态,给出了环F_p^m+uF_p^m+u²F_p^m上长度为p^s的循环码的新分类方法.应用这种方法,得到了环F_p^m+uF_p^m+u²F_p^m长度为p^s的循环码的码词数.     

Embedding of Hpω in the class eL

We obtain the necessary conditions for the embedding H _p ^ω ⊂ e ^L (1≤p∞) with convex modulus of continuity ω in terms of this modulus. In the case p=1 these conditions are also sufficient.     

On the nonlinear wave equation Utt−B(t,‖Ux‖)Uxx=f(x,t,U,Ux,Ut) associated with the mixed homogeneous conditions

In this paper we consider the following nonlinear wave equation

(1)     

环Fpm[u]/<ua>上一类常循环码

本文研究有限链环上一类λ-常循环码.利用x~n-1在R_a[x]上可唯一分解为两两互素的首一基本不可约多项式乘积,刻画了R_a中长为p~sn的所有λ-常循环码,推广了开晓山等人在文献[4]中的结果.     

关于矩阵方程X+A*X-αA+B*X-βB=I的正定解

本文研究了矩阵方程X+A*X-αA+B*X-βB=I在α,β∈(0,1]时的正定解.利用单调有界极限存在准则,构造三种迭代算法,获得了方程的正定解,拓宽了此类方程的求解方法.数值算例说明算法的可行性.     

On irreducible characters of the group Sn that are semiproportional on An or Sn?An. II

In the author’s previous paper, the hypothesis that the alternating groups A _n have no pairs of semiproportional irreducible characters is reduced to a hypothesis concerning the problem of describing the pairs of irreducible characters of the symmetric group S _n that are semiproportional on one of the sets A _n or S _n ∖A _n . In this hypothesis, properties of such a pair of characters are expressed in terms of Young’s diagrams corresponding to these characters. The theorem proved in this paper allows one to exclude from consideration some stages of the verification of this hypothesis.     

LPE GaxIn1-xAs1-ySby/InP和GaxIn1-xAs1-ySby/InAs的生长及其估价

将电负性差法估算的Ga_xIn_1-xAs_1-ySb_y/InP和Ga_xIn_1-xAs_1-ySb_y/InAs的固相和液相组份数据应用于液相外延生长,均获得了晶格匹配的材料,并首次获得了波长λ>3.5μm的Ga_xIn_1-xAs_1-ySb_y/InAs异质外延材料。Ga_xIn_1-xAs_1-ySb_y/InP的固体组份为...     

KO?i groups of G3(?n), n odd

We use the work of Karoubi and Mudrinski on the real Grothendieck's groups of certain complex projective bundles to show that the torsion of the KO ^–i groups of G ₃( ⁿ ), n odd, are related to the known torsion of the KO ^–i groups of G₂( ⁿ ).     

Balanced colombeau products of the distributions x±-p and x-p

Results on singular products of the distributions x _± ^-p and x ^-p for natural p are derived, when the products are balanced so that their sum exists in the distribution space. These results follow the pattern of a known distributional product published by Jan Mikusiski in 1966. The results are obtained in the Colombeau algebra of generalized functions, which is the most relevant algebraic construction for tackling nonlinear problems of Schwartz distributions.     

环Fp+vFp上互补对偶常循环码

本文研究了环F_p+vF_p上互补对偶（1-2v）-常循环码.利用环F_p+vF_p上（1-2v）-常循环码的分解式C=vC_1-v ⊕（1-v）C_v,得到了环F_p+vF_p上互补对偶（1-2v）-常循环码的生成多项式.然后借助从F_p+vF_p到F_p²的Gray映射,证明了环F_p+vF_p上互补对偶（1-2v）-常循环码的Gray像是F_p的互补对偶循环码.     

完全二部图Km,n的Kp,q-因子分解

如果完全二部图K_m,n的边集可以划分为K_m,n的K_p,q-因子, 则称K_m,n存在K_p,q-因子分解. 给出K_m,n存在K_p,q-因子分解的一个充分条件. 同时证明: 对于任意正整数k, 当p:q = k:(k + 1)时, K_m,n存在K_p,q-因子分解, 即Martin的BAC猜想成立.     

��ǿռ��������ȨM/M/n/m�Ŷ�ϵͳ

Concerning the problem that network congestion risk of computer network service system for some data frames having a full priority of transmission, a method about nonpreemptive limited-priority M/M/n/m queuing system model was proposed. Firstly, as the parameter r of limited-priority was introduced into the model, the data frame with full priority was converted to the one with limited priority. Secondly, in order to lower the risk of computer network service system and stabilize the network system further, the fairness among different priorities was studied in the model. Moreover, by making use of Total Probability Theorem, three results of the models, the average waiting time, the average dwelling time and the average queue length were obtained.     

Small solutions of the congruencea1x12 +a2x22 +a3x32 +a4x42 ≡c(modp)

For any integersa ₁,a ₂,a ₃,a ₄ andc witha ₁ a ₂ a ₃ a ₄≢0(modp), this paper shows that there exists a solutionX=(x ₁,x ₂,x ₃,x ₄) ∈Z ⁴ of the congruencea ₁ x ₁ ² +a ₂ x ₂ ² +a ₃ x ₃ ² +a ₄ x ₄ ² ≡c(modp) such that