Derivative formulas and Poincaré inequality for Kohn-Laplacian type semigroups

As a generalization to the heat semigroup on the Heisenberg group, the diffusion semigroup generated by the subelliptic operator L :=1/2 sum from i=1 to m X_i~2 on R~(m+d):= R~m× R~d is investigated, where X_i(x, y) = sum (σki?xk) from k=1 to m+sum (((A_lx)_i?_(yl)) from t=1 to d,(x, y) ∈ R~(m+d), 1 ≤ i ≤ m for σ an invertible m × m-matrix and {A_l}_1 ≤ l ≤d some m × m-matrices such that the Hrmander condition holds.We first establish Bismut-type and Driver-type derivative formulas with applications on gradient estimates and the coupling/Liouville properties, which are new even for the heat semigroup on the Heisenberg group; then extend some recent results derived for the heat semigroup on the Heisenberg group.     

Domination numbers of undirected toroidal mesh

The (d, m)-domination number γd,m is a new measure to characterize the reliability of resources-sharing in fault tolerant networks, in some sense, which can more accurately characterize the reliability of networks than the m-diameter does. In this paper, we study the (d, 4)-domination numbers of undirected toroidal mesh Cd1 × Cd2 for some special values of d, obtain that γd,4 (Cd1 × C3) = 2 if and only if d4(G) e1 ≤ d d4(G) for d1 ≥ 5, γd,4 (Cd1 × C4) = 2 if d4(G) (2e1-[d1+e1]/2) ≤ d d4(G) for d1 ≥ 24, and γd,4 (Cd1 × Cd2 ) = 2 if d4(G) ( e1-2) ≤ d d4(G) for d1 = d2 ≥ 14.     

On The Limit Cycles Of A Kind Of Lienard System With A Nilpotent Center Under Perturbations

In this paper, we study the limit cycles of a kind of Li é nar d systemwith a nilpotent center under perturbations. Let L(m; n) denote the numberof limit cycles of this Li é nard system ẋ = y- ɛ F(x) ; ẏ =-g (x) near theorigin, where m = deg g; n = deg F. We o btain some results of L(m; n) for m = 4; 2 n ≤ 20, m = 5, 2 ≤ 10, m = 6, 2 ≤ n ≤ 5, m = 7, 2 ≤ n ≤ 4, where some results are new.     

Gaussian fluctuations of eigenvalues in log-gas ensemble: Bulk case I

We study the central limit theorem of the k-th eigenvalue of a random matrix in the log-gas ensemble with an external potential V = q2mx2 m. More precisely, let Pn(d H) = Cne-nTrV(H)dH be the distribution of n × n Hermitian random matrices, ρV(x)dx the equilibrium measure, where Cnis a normalization constant, V(x) = q2mx2m with q2m=Γ(m)Γ(12)/Γ(2m+1/2), and m ≥ 1. Let x1 ≤···≤ xnbe the eigenvalues of H. Let k := k(n) be such that k(n)/n∈ [a, 1- a] for n large enough, where a ∈(0,12).Define G(s) :=∫s-1ρV(x)dx,- 1 ≤ s ≤ 1,and set t := G-1(k/n). We prove that, as n →∞,xk- t log n1/2 2π21/2nρV(t)→ N(0, 1)in distribution. Multi-dimensional central limit theorem is also proved. Our results can be viewed as natural extensions of the bulk central limit theorems for GUE ensemble established by J. Gustavsson in 2005.     

RESEARCH ANNOUNCEMENTS ON“MINIMAL TIME CONTROL OF EXACT SYNCHRONIZATION FOR PARABOLIC SYSTEMS”

正1 Introduction and Main Results LetΩ■R~d (with d≥1) be a bounded domain with a C~2 boundary Ω.Letω■Ωbe an open and nonempty subset with its characteristic function χ_ω.Let A■(a_(ij))_(1≤i,j≤n)∈R~(n×n)and B■(b_(ij))_(1≤i≤n,1≤j≤m)∈R~(n×m) be two constant matrices,where n≥2 and m≥1.Let y_0∈L~2(Ω)~n.Consider the controlled linear parabolic system     

凸体间的逼近

For the affine distance d(C, D) between two convex bodies C, D C R^n, which reduces to the Banach-Mazur distance for symmetric convex bodies, the bounds of d(C, D) have been studied for many years. Some well known estimates for the upper-bounds are as follows: F. John proved d(C, D) ≤ n^1/2 if one is an ellipsoid and another is symmetric, d(C, D) ≤ n if both are symmetric, and from F. John's result and d(C1, C2) ≤ d(C1, C3)d(C2, C3) one has d(C, D) ≤ n^2 for general convex bodies; M. Lassak proved d(C, D) ≤ (2n - 1) if one of them is symmetric. In this paper we get an estimate which includes all the results above as special cases and refines some of them in terms of measures of asvmmetrv for convex bodies.     

On the maximal eccentric connectivity indices of graphs

For a connected simple graph G, the eccentricity ec(v) of a vertex v in G is the distance from v to a vertex farthest from v, and d(v) denotes the degree of a vertex v. The eccentric connectivity index of G, denoted by ξc(G), is defined as v∈V(G)d(v)ec(v). In this paper, we will determine the graphs with maximal eccentric connectivity index among the connected graphs with n vertices and m edges(n ≤ m ≤ n + 4), and propose a conjecture on the graphs with maximal eccentric connectivity index among the connected graphs with n vertices and m edges(m ≥ n + 5).     

ON THE CROSSING NUMBER OF THE COMPLETE TRIPARTITE GRAPH K_(1,8,n)

The well known Zarankiewicz' conjecture is said that the crossing number of the complete bipartite graph Km,n (m≤n) is Z(m,n). where Z(m,n) = [m/2] [(m-1)/2] [n/2] [(n-1)/2](for and real number x, [x] denotes the maximal integer no more than x). Presently, Zarankiewicz' conjecture is proved true only for the case m≤G. In this article, the authors prove that if Zarankiewicz' conjecture holds for m≤9, then the crossing number of the complete tripartite graph K1,8,n is Z(9, n) 12[n/2].     

本刊英文版Vol.27(2011),No.11论文摘要

<正>For a bipartite graph G on m and n vertices,respectively,in its vertices classes, and for integers s and t such that 2≤s≤t,0≤m-s≤n-t,and m+n≤2s+t-1,we prove that if G has at least mn -(2(m - s) + n - t) edges then it contains a subdivision of the complete bipartite K_((s,t)) with s vertices in the m-class and t vertices in the n-class.Furthermore, we characterize the corresponding extremal bipartite graphs with mn -(2(m - s) + n - t + 1) edges for this topological Turan type problem.     

Real submanifolds in complex spaces

Let(z_(11),..., z_(1N),..., z_(m1),..., z_(mN), w_(11),..., w_(mm)) be the coordinates in C~(mN) +m~2. In this note we prove the analogue of the Theorem of Moser in the case of the real-analytic submanifold M defined as follows W = ZZ~t+ O(3),where W = {w_(ij)}_(1≤i,j≤m)and Z = {z_(ij) }_(1≤i≤m, 1≤j≤N). We prove that M is biholomorphically equivalent to the model W = ZZ~t if and only if is formally equivalent to it.     

部分临界点轨道收敛于无穷大时的多项式动力系统

设Ｐ（ｚ）是ｄ（≥２）次多项式，Ｊ是Ｐ（ｚ）的Ｊｕｌｉａ集，σ：∑ｎ→∑ｎ是ｎ个符号的单边符号空间∑ｎ上的转移自映射．本文证明了当ｐ（ｚ）的某ｍ（１≤ｍ≤ｄ－１）个有穷临界点的轨道收敛于∞时，ｐ｜Ｊ拓扑半共轭于σ：∑（ｍ＋１）→∑（ｍ＋１），而当ｍ＝ｄ－１时，ｐ｜Ｊ拓扑共轭于σ：∑ｄ→∑ｄ。     

經驗分佈之比的極限分佈

<正> §1.引言 令x為一隨機變數,其分佈函數為F(x).對於x作n次相互獨立的试驗,便得n個結果x_1,x_2,…,x_n.我們也可以把x_1,x_2,…,x_n看作是遵循同一個分佈函數F(x)的相互獨立隨機變數.現在把x_1,x_2,…,x_n依其值由小到大的次序排列,我們得到     

一种场站设置问题中的几个结论

本文研究如下一种场站设置问题:设S是欧空间E~m中由有限个点A_1,A_2,…,A_n组成的集合.d(A_i,A_j)表示点A_i和A_j之间的距离.令σ(S)=Σ_(1≤i相似文献   

关于用多维样条逼近的饱和度

<正> 作者在工作[1]中,研究了一维样条逼近的饱和度问题,得到了下述定理: 定理A 设{△_k}是区间[a,b]的一分划序列,‖△_k‖→0(k→∞),R_(△k)≤β<∞(k=1,2,…),若f(x)∈c~n[a,b],S_(△_k)(x)是(n-1)次多项式样条,如果 对任一p成立,(p=0,1,…,n)则 D~nf(x)≡0. 本文是[1]的续篇,对多维样条进行研究,可得一些类似的结果,为明确起见,我们仅对二维情形进行讨论.     

2-(v,6,1)设计的可解区传递自同构群

设G是一个2-（v,6,1）设计的可解区传递自同构群,且G非旗传递,则：（1）v＝91,G=Z91×Zd,这里3|d|12;（2）v=pm,G≤AL（1,pm）,之一成立．其中p≠2．当p＝3时,4|m见且m＞4;当p＞5时,pm≡1（mod30）。     

一個關於行列式的不等式

<正> 在研究多複變數函數論的時候,我們發現了以下的不等式:本文的目的在於給這不等式以一個代數證明,並且把它更精密化些.關於(1)式中所涉及的符號,作以下的說明:在本文中一切拉丁大寫字母都代表n行列的     

布尔矩阵行空间基数的存在点

设 Ｂｎ 表示所有的ｎ 阶布尔矩阵的集合, Ｒ（ Ａ）表示 Ａ∈ Ｂｎ 的行空间,｜ Ｒ（ Ａ）｜表示 Ｒ（ Ａ）的基数．设ｍ ,ｎ,ｋ 为正整数,本文证明了当ｎ≥９, ｎ＋ ５２ ≤ｋ≤ｎ－ ３ 时,对任意的 ｍ ,２ｋ≤ｍ ≤２ｋ＋ ２ｎ－ ｋ＋ ２＋ ２ｎ－ ｋ＋ １ ＋ …＋ ２３,存在 Ａ∈ Ｂｎ,使得｜ Ｒ（ Ａ）｜＝ ｍ ．     

一类特殊的有限循环环

证明了一类n阶(n=P_1P_2…p_m,p_i(i=1,2,…,m)互异为素数)环是有限循环环,并讨论了他们的结构及相关性质,最后给出了这类n阶环有零因子或有子域的充要条件.主要结果:P_1P_2…P_m阶环共有2^m个,它们是(p_(1m个,它们是(p_(1^k_1) p_(2k_1) p_(2^k_2)…p_(mk_2)…p_(m^k_m)Z)/(p_(1k_m)Z)/(p_(1^k_1+1)p_(2k_1+1)p_(2^k_2+1)…p_(mk_2+1)…p_(m^k_m+1)Z),其中k_i=0或1,1≤i≤m;阶是n=P_1P_2…p_m的环R可唯一分解为m个素数阶理想的直和,即R=〈α〉=(?);含pi(1≤i≤m)阶子域的P_1P_2…P_m阶环共有2k_m+1)Z),其中k_i=0或1,1≤i≤m;阶是n=P_1P_2…p_m的环R可唯一分解为m个素数阶理想的直和,即R=〈α〉=(?);含pi(1≤i≤m)阶子域的P_1P_2…P_m阶环共有2^(m-1)个,它们是p_(1(m-1)个,它们是p_(1^k_1) p_(2k_1) p_(2^k_2)…p_(mk_2)…p_(m^k_m)Z)/(p_(1k_m)Z)/(p_(1^k_1+1)p_(2k_1+1)p_(2^k_2+1)…p_(mk_2+1)…p_(m^k_m+1)Z),其.中k_i=0,k_j=0或1,1≤j≤m,j≠i.     

关于非负随机变量的几个矩不等式

设X是非负随机变量且0相似文献   

套链分解

Let X1,X2,...,Xk be k disjoint subsets of S with the same cardinality m.Define H(m,k) = {X (C) S: X (C) Xi for 1 ≤I ≤k} and P(m,k) = {X (C) S : X ∩ Xi ≠φ for at least two Xi's}.Suppose S = Uki=1 Xi,and let Q(m,k,2) be the collection of all subsets K of S satisfying|K ∩ Xi|≥ 2 for some 1 ≤ I ≤ k.For any two disjoint subsets Y1 and Y2 of S,we define F1,j = {X (C) S : either |X ∩ Y1|≥ 1 or |X ∩ Y2|≥ j}.It is obvious that the four posers are graded posets ordered by inclusion.In this paper we will prove that the four posets are nested chain orders.