Calculation method of electronic structure and its application to (I h andI) fullerenes

A new calculation method was discussed to treat the Hückel Hamiltonian of any fullerene with a certain point group symmetry. This method was applied to calculating the electronic energy levels of icosahedral fullerenes C\-n(I\-h: n=60h 2, 0相似文献   

形成原子核群子结构的四项原理及其等腰三角形核素周期律

根据第四统计力学——JRG群子统计理论,首次提出了形成原子核结构的四项原理及相应的原子核周期律。这四项原理为:一是原子核有群子结构单元;二是形成原子核时群子通过热核聚合反应过程使核素结构有严格的排列顺序;三是原子核内群子结构间有动态共振作用;四是偶数群子稳定,而非偶数群子是引起总角动量和β⁺,β^-衰变的根源。基于上述四项原理,提出了核群子结构基本单元有(PB),(PB₂),(P₂B₃),并随着质子数Z的增加,核群子结构由(PB)_k过渡到(PB)_k(P₂B₃)_l;由(PB)_n(PB₂)_m过渡到(P₂B₃)_s(PB₂)_t。从而导出了k(-t)=2n(s)-Z,k(-t)=Z-2l(m)的关系式。基于此,可以画出等腰三角形原子核群子周期律。还发现,不管A,N,Z如何变化,有下列严格关系式:Z/N=(n+m)/(n+2m)或Z/N=(k+l)/(k+3l)并且Z=n+l。此公式高度地反映了所有原子核内质子和中子分布的整数规律。还可以通过等腰三角形周期律得知:k,l,m,n,s,t均与核素群子(PB),(PB₂), (P₂B₃),(P₃B₄)的2,3,5,7整数倍有关。     

一些拉普拉斯谱确定的图

如果与图G同拉普拉斯谱的图都与图G同构,则称图G由它的拉普拉斯谱确定.给出了三类基图为B(P_3,P_3,P_3)(即连接2点的3条长为2的内不交的路)的连通二部双圈图类H(n;n_1),H(n;n_1,n_2)和B(n;n_1,n_2).证明了H(n;n1),H(n;n_1,n_2)和B(n;n_1,n_2)是拉普拉斯谱确定的,且与完全图经并接运算后所得图也是拉普拉斯谱确定的.     

最小Q-特征值第二小的给定悬挂点数的非二部单圈图

图的最小Q-特征值常被用来衡量一个图的非二部程度,受到研究者的广泛关注。在路Pn-k-2的一端接出一个圈C3,另一端接出k个悬挂边,所得的n阶图记为Ukn(3)。范益政等人最近证明Ukn(3)是最小Q-特征值达到最小的图。在他们的基础上,证明C13(n-k-1)是最小Q-特征值达到第二小的图,其中C13(n-k-1)是将Ukn(3)的一条悬挂边移至与悬挂邻点相邻的非悬挂点上所得的图。     

Almost sure convergence of weighted sums of NA sequences

For double arrays of constants {a _ni, 1≤i≤k _n, n≥1} and NA r.v. 's {X _n, n≥1}, conditions for almost sure convergence of are given. Both casesk _n ↑ ∞ andk _n=∞ are treated. A Marcinkiewicz-type theorem for i. d. NA sequences is obtained as a special case. Supported by the National Natural Science Foundation of China Cheng Riyan: born in 1968, MS student     

完全图Kn的{P5,C5}分解

图分解问题已在很多邻域中得到了广泛的应用。用P₅表示5个顶点的路，C₅表示5个顶点的圈，本研究讨论了完全图K_n分解成5个顶点的路P₅和圈C₅的存在性，给出完全图K_n存在{P₅,C₅}-强制分解的充分必要条件是n≥7(n≠8)，以及完全图K_n存在{P₅,C₅}-分解的充分必要条件是n≥5(n≠6)。     

Superconvergence for L2-projection in finite elements

Two classes of superconvergence points for L 2 projection u\-n in n degree finite elements on uniform grids are shown by element analysis method. Superconvergence points of u n are n+1 order Gauss point G n+1 for odd d≥1 (so the endpoint of each element is of superconvergent), and n+1 order pointset Z n+1 for even n ≥2 (which includes the endpoints and midpoint), respectively. Symmetry point is only an important part of them.     

Vertex disjoint cycles in intersection graphs of bases of matroids

The intersection graph of bases of a matroid M=(E, B) is a graph G=G~I(M) with vertex set V(G) and edge set E(G) such that V(G)=B(M) and E(G)={BB′:|B∩B′|≠0, B, B′∈B(M), where the same notation is used for the vertices of G and the bases of M. Suppose that|V(G~I(M))| =n and k_1+k_2+…+k_p=n, where k_i is an integer, i=1, 2,…, p. In this paper, we prove that there is a partition of V(G~I(M)) into p parts V_1 , V_2,…, V_p such that |V_i| =k_i and the subgraph H_i induced by V_i contains a k_i-cycle when k_i ≥3, H_i is isomorphic to K_2 when k_i =2 and H_i is a single point when k_i =1.     

Walsh spectrum properties of rotation symmetric boolean function

Rotation symmetric function was presented by Pieprzyk. The algebraic configuration of rotation symmetric（RotS） function is special. For a Rots n variables function f（x1, x2, …, xn） we have f（ρn^k （x1, x2, …xn））=f（x1, x2, …, xn） for k=0, 1, …, n-1. In this paper, useing probability method we find that when the parameters of RotS function is under circular translation of indices, its walsh spectrum is invariant. And we prove the result is both sufficient and necessary.     

几类图的符号星控制数

给出Km×Cn,Cm×Cn,Km×Kn这三类图的符号星控制数.     

两类非连通图(P2∨Kn)（0，0,r1,0,…,0,rn)∪St(m)及(P2∨Kn)（r1+a,r2,0,…,0)∪Gr的优美性

 对自然数n, m, i∈N,设K_i表示i个顶点的完全图,K_n表示K_n的补图,St(m) 表示m+1个顶点的星形树,G_r为有r条边的优美图,P_n为n个节点的路,P₂∨K_n是P₂与K_n联图。 给出了非连通图(P₂∨K_n)（0,0,r₁,0,…,0,r_n)∪St(m)和(P₂∨K_n)（r₁+a,r₂,0,…,0)∪G_r的定义,并论证了当n≥2时,这两类图都是优美图。     

Morita equivalent blocks in subgroups of finite groups

0 IntroductionLeRte(f K.[,1]O), ,ki) .e b.e, aOips- am ocdoumlaplre tseys dtiesmcre(tese eva lCuhatpito .nII Iri nignwith unique maxi mal idealJ(O) suchthatJ(O) =(π)forπ∈O,Kis the quotient field ofOcharacteristic 0 ,andkis theresidue fieldO/(π)of characteristicp, wherepis a fixedpri me number .Inthis paper , we fix a finite groupG,andletKcontains all the |G|-throots of unity,where |G|is the or-der of finite groupG.In particular bothKandkare splittingfields of every subgroup ofG.D…     

Lüroth Expansion Digits and Maclaurin's Inequality

It is well known that for almost all real number x, the geometric mean of the first n digits d_i(x) in the Lüroth expansion of x converges to a number K_0 as n→∞. On the other hand, for almost all x, the arithmetric mean of the first n Lüroth expansion digits d_i(x) approaches infinity as n→∞. There is a sequence of refinements of the AM-GM inequality, Maclaurin's inequalities, relating the 1/k-th powers of the k-th elementary symmetric means of n numbers for 1≤k≤n. In this paper, we investigate what happens to the means of Lüroth expansion digits in the limit as one moves f(n) steps away from either extreme. We prove sufficient conditions on f(n) to ensure divergence when one moves away from the arithmetic mean and convergence when one moves f(n) steps away from geometric mean.     

Almost sure convergence of weighted sums of NA sequences

For double arrays of constants {a _ni, 1≤i≤k _n, n≥1} and NA r.v. 's {X _n, n≥1}, conditions for almost sure convergence of are given. Both casesk _n ↑ ∞ andk _n=∞ are treated. A Marcinkiewicz-type theorem for i. d. NA sequences is obtained as a special case. Supported by the National Natural Science Foundation of China Cheng Riyan: born in 1968, MS student     

A matrix version of the Wielandt inequality and its application to statistics

Suppose that A is an n × n positive definite Hemitain matrix. Let X and Y be n × p and n × q matrices (p+ q≤n), such that X* Y = 0. The following inequality is proved X*AY( Y* AY)-Y Y*AX≤( (λ1-λn)/(λ1+λn))2 X*AX, where λ1 and λn are respectively the largest and smallest eigenvalues of A, and M- stands for a generalized inverse of M. This inequality is an extension of the well-known Wielandt inequality in which both X and Y are vectors. The inequality is utilized to obtain some interesting inequalities about covari-ance matrix and various correlation coefficients including the canonical correlation, multiple and simple correlation.     

Parallel (M−N)SVD algorithms on the SIMD computers

LetA bem byn matrix,M andN be positive definite matrices of orderm andn respectively. This paper presents an efficient method for computing (M?N) singular value decomposition ((M?N) SVD) ofA on a cube connected single instruction stream-multiple data stream (SIMD) parallel computer. This method is based on a one-sided orthogonalization algorithm due to Hestenes. On the cube connected SIMD parallel computer witho(n) processors, the (M?N)SVD of a matrixA requires a computation time ofo(m ³logm/n).     

A newC *-algebra and its essential commutant

A newC ^*-algebraE + E _* is established. It contains the large Hankel algebra N^G produced by all Toeplitz operators and Hankel operators. It is the proper algebra ofB(H ²) and its essential commutant is obtained, which is generated by those Toeplitz operators that have symmetric continuous function symbols and compact operators.     

乘积构形的超可解性

本文给出了乘积构形格的几个运算性质。证明了乘积构形格L中元素是模元的充要条件，并利用该结论证明了乘积构形(a₁×…×a_k，V₁+…+V_k)是超可解构形的充要条件是每个因子构形(a₁，V_i)，1≤i≤k都是超可解构形。最后证明了若因子构形(a_k,V_i)，1≤i≤k均是良分划构形，则乘积构形(a₁×…×a_k，V1+…+V_k)也是良分划构形。     

A note on characteristic generators of a free cyclic code and its dual

Let C be a free cyclic code over Z _n ^α and dim _p C = k. In the paper, we prove that if the k characteristic generators of C are p-linearly independent then the corresponding nα − k characteristic generators of C ^⊥ are p-linearly independent. We then show that to any trellis that can be constructed from k p-linearly independent characteristic generators of C, there exists a trellis for C ^⊥ with the same state-complexity profile, which generalizes the conjecture of Koetter and Vardy to a free cyclic code over Z _n ^α. Foundation item: Supported by the National Natural Science Foundation of China(60673071)