完全图与完全n部图的完全多部图分解

§ 1　IntroductionLet V(G) and E(G) be the vertex setand the edge setof a graph G,respectively.Fori=1 ,...,p,if V(Gi) V(G) ,E(Gi)∩ E(Gj) = for i≠ j,and∪pi=1 E(Gi) =E(G) ,then wecall{ G1 ,...,GP} a decomposition of G.Let[i,j] be the integer interval including i and j.Let Knbe a complete graph with the vertex set[1 ,n] .For m disjointsubsets A1 ,...Amof[1 ,n] ,let K(A1 ,...,Am) be a complete m-partite graph having partite-sets A1 ,...,Am.If| Ai| =1 ,Ai is called a S-set;otherwi…     

车多项式对Ferrers矩阵的刻画

In this paper,we show that there exist precisely W(A) Ferrers matrices F(C1,C2,…,cm)such that the rook polynomials is equal to the rook polynomial of Ferrers matrix F(b1,b2,…,bm), where A={b1,b2-1,…,bm-m 1} is a repeated set,W(A) is weight of A.     

The Interior Layer Problem for the Strongly Nonlinear Singularly Perturbed System

The nonlinear strongly singularly perturbed systemεyi" = fi(t, y,y'), a < t < b, i = 1, 2, …, n, yi(a,ε)-pily'i(a,ε) = Ai, yi(b,ε) pi2y'i(b,ε) = Biare considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of interior solution for the problems are studied.     

High-dimensional D. H. Lehmer problem over short intervals

Letk be a positive integer and n a nonnegative integer,0 λ1,...,λk+1 ≤ 1 be real numbers and w =(λ1,λ2,...,λk+1).Let q ≥ max{[1/λi ]:1 ≤ i ≤ k + 1} be a positive integer,and a an integer coprime to q.Denote by N(a,k,w,q,n) the 2n-th moment of(b1··· bk c) with b1··· bk c ≡ a(mod q),1 ≤ bi≤λiq(i = 1,...,k),1 ≤ c ≤λk+1 q and 2(b1+ ··· + bk + c).We first use the properties of trigonometric sum and the estimates of n-dimensional Kloosterman sum to give an interesting asymptotic formula for N(a,k,w,q,n),which generalized the result of Zhang.Then we use the properties of character sum and the estimates of Dirichlet L-function to sharpen the result of N(a,k,w,q,n) in the case ofw =(1/2,1/2,...,1/2) and n = 0.In order to show our result is close to the best possible,the mean-square value of N(a,k,q) φk(q)/2k+2and the mean value weighted by the high-dimensional Cochrane sum are studied too.     

含k-Brocard距离的一类几何不等式

Let P be an inner point of a convex N-gonΓN:A1A2…ANA1(N≥3), and let di,k denote the distance from the point Ai k, to the line PAi(i=1,2,…,N,Ai=Aj(?)i=j(modN)), which is called the k-Brocard distance for P ofΓN. We have proved the following double-inequality: If P∈ΓN, and then .     

关于《关于一类单叶函数》一文的注记

Let T be the class of functions of the form f(z)=z sum from n=2 to∞a_nz~n which are analytic inthe unit disc U={z:|z|<1}.A function f(z)∈T is said to be a member of the classR(a,b)if and only if it satisfies     

关于圆外切闭折线周长的一个不等式

设△ ABC的三边长为 a,b,c,其内切圆半径为 r,则有下面熟知的不等式 :　　 a b c≥ 6 3r ( 1 )当且仅当△ ABC为正三角形时取等号 .本文将推广这个不等式 ,证明关于圆外切闭折线周长的一个不等式 .定理 1　设闭折线 A1A2 A3 … An A1有内切圆⊙ ( I,r) ,闭折线的环数为 t,各边长为| Ai Ai 1| =ai( i=1 ,2 ,… ,n,且 An 1为 A1) ,则有　 ∑ni=1ai ≥ 2 nrtan tnπ ( 2 )当且仅当闭折线为正星形时取等号 .图 1证明　如图 1 ,设边Ai Ai 1与圆 I相切于 Bi,连Ai I,Bi I,Ai 1I,则ai =| Ai Bi| | Bi Ai 1|=r( cot Ai2 co…     

ADMISSIBLE ESTIMATES IN THE IMPORTANT CLASS OF ESTIMATES OF THE COVARIANCE MATRIX

Let X1,…XN(where N&gt;m)be independent Nm(μ,∑）random vectors,and put X^-=1/N ∑i=1^N Xi and T‘T=A=∑i=1^N(Xi-X^-)(Xi-X^-)‘,where T is upper-triangular with positive diagonal elements.The author considers the problem of estimating ∑,and restricts his attention to the class of estimates D={T‘△^*T+Nb^*X^-X^‘&#183;△^* is any diagonal matrix and b^* is any nonnegative constant}because it has the following attractive features:(a)Its elements are all quadratic forms of the sufficient and complete statistics(X^-,T).(b)It contains all estimates of the form αA+NbX^-X^-‘(α≥0 and b≥0),which construct a complete subclass of the class of nonnegative quadratic estimates D^8={X‘BX:B≥0}(where X=(X1,…,XN)‘)for any strict convex loss function.(c)It contains all invariant estimates under the transformation group of upper-triangular matrices.The author obtains the characteristics for an estimate of the form.T‘△T+NbX^-X^-‘(△=diag{δ1,…，δm}≥0 and b≥0)of ∑ to be admissible in D when the loss function is chosen as tr(∑^-1∑-I)^2,and shows,by an example,that αA+NX^-X^-‘(α≥0 and b≥0)is admissible in D^* can not imply its admissibility in D.     

2004年高考数学模拟训练试题

选择题　本大题共 12小题 ,每小题 5分 ,共 6 0分 .在每小题给出的四个选项中 ,只有一项符合题目要求 .1.设集合M ={x|x =4k± 1,k∈Z} ,N ={x|x =2k +1,k∈Z} ,其中Z表示整数集 ,则下列各项错误的是 (　　 )(A)M∪ (CZN) =Z .　 (B) (CZM )∩N = .(C)M =N . (D)M∪N =Z .2 .已知a ,b是两个单位向量 ,下列命题中错误的是 (　　 )(A) |a|=|b|.(B)a·b =1.(C)a与b方向相反时 ,a +b =0 .(D)a与b方向相同时 ,a =b .3.设命题 p :3≤ 4 ,q :5 6∈ [6 5 ,+∞ ) ,则三个复合命题 :“p且q” ,“p或q” ,“非 p”中 ,真命题的个数为 (　　 …     

Continuity of functors with respect to generalized inductive limits

Let(Ai,φi,i+1) be a generalized indue Live system of a sequeiiee (Ai) of unital separable C^*-algebras,with A =limi→∞(Ai,φi,i+1). Set φj,i=φi-1,i^0…0φj+1,j+2^0 φj,j+1 for all i>j. We prove that if φj,i are order zero completely positive contractions for all j and i>j, And L:=inf{λ|λ∈σ(φj,i(1Aj)) for all j uud i>j}>0, where σ(φj,i(1Aj)) is the speetrum of φj,i(1Aj),than limi→∞(Cu(Ai),Cu((φi,i+1))=Cu(A), where Cu(A) is a stable version of the Cuntz semigroup of C^*-algebra A. Let (An,φm,n) be a generalized inductive syfitem of C^*-algahrafl, with the ipmkn order zero completely positive contractions. We also prove that if the decomposition rank (nuclear dimension) of ,4n is no more t han some integer k for each n, then the decompostition rank (nuclear dimension) of A is also no more than k.     

Estimation of the number of components of finite mixtures of multivariate distributions

An estimator of the number of components of a finite mixture ofk-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of ak-dimensional independent random sample. A consistency of the estimator is shown. Some simulation results are given in a case of finite mixtures of two-dimensional normal distributions.     

Extreme values of the sum of squares of degrees of bipartite graphs

In this paper we determine the minimum and maximum values of the sum of squares of degrees of bipartite graphs with a given number of vertices and edges.     

Eigenvector p-Bases of Rings of Constants of Derivations

Let A be a UFD of characteristic p > 0, let 𝒵 be a set of some eigenvectors of a derivation of A. We prove, under some additional assumptions, a necessary and sufficient condition for 𝒵 to be a p-basis of the minimal ring of constants containing 𝒵. The main preparatory result is the unique decomposition theorem with respect to a factor from a given subalgebra containing A^p.     

Galois Structure of K-Groups of Rings of Integers

N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.     

有资格限制的指派问题的求解方法

在实际的指派工作中，常会遇到某个人有没有资格去承担某项工作的问题，因此，本建立了有资格限制的指派问题的数学模型。在此数学模型中，将效益矩阵转化为判定矩阵，由此给出了判定此种指派问题是否有解的方法；在有解的情况下，进一步将效益矩阵转化为求解矩阵，从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。     

Number of connected components of groups of real points of adjoint groups

We present a unified approach to compute the number of connected components in the group of real points of adjoint almost simple real algebraic groups.     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

Radius of convexity of certain classes of analytic functions

We consider the classes of analytic functions introduced recently by K.I. Noor which are defined by conditions joining ideas of close-to-convex and of bounded boundary rotation functions. We investigate coefficients estimates and radii of convexity.     

Convergence of sequences of sets of associated primes

It is a well-known result of M. Brodmann that if is an ideal of a commutative Noetherian ring , then the set of associated primes of the -th power of is constant for all large . This paper is concerned with the following question: given a prime ideal of which is known to be in for all large integers , can one identify a term of the sequence beyond which will subsequently be an ever-present? This paper presents some results about convergence of sequences of sets of associated primes of graded components of finitely generated graded modules over a standard positively graded commutative Noetherian ring; those results are then applied to the above question.