LARGEST EIGENVALUE OF A UNICYCLIC MIXED GRAPH

The graphs which maximize and minimize respectively the largest eigenvalue over all unicyclic mixed graphs U on n vertices are determined. The unicyclic mixed graphs U with the largest eigenvalue λ1 (U)=n or λ1 (U)∈ (n ,n 1] are characterized.     

EIGENVALUES ON THE BOUNDARY OF CERTAIN INCLUSION FOR THE SPECTRUM OF A MATRIX

We introduce four types of special eigenvalues which lie on the boundary of certain inclusion regions for the spectrum of a complex square matrix, i.e. , R_r(G_c)-,O(a)-,B_r(B_c)-. and OB(a)- eigenvalues. Then we characterize these eigenvalues and their corresponding eigenvectors for irreducible matrices, Finally we give some new sufficient conditions for an irreducible complex matrix to be nonsingular.     

A STABILITY ANALYSIS OF THE （k） JACOBI MATRIX INVERSE EIGENVALUE PROBLEM

In this paper we will analyze the perturbation quality for a new algorithm of the (k) Jacobi matrix inverse eigenvalue problem.     

GENERAL MINIMAX ESTIMATORS ON THE LOCATION MATRIX OF A MIXTURE OF NORMALS

This paper considers the estimate problem on the mean matrix of mixtureof normals. In order to evaluate estimators of the mean matrix, a fundamental frameof Ф-(general) decision problem is established. Under the frame, a class of Ф-minimax estimators are constructed.     

ON THE TOTAL COLORING OF GRAPH G ∨H

ＯＮＴＨＥＴＯＴＡＬＣＯＬＯＲＩＮＧＯＦＧＲＡＰＨＧ∨Ｈ￥ＸｕＢａｏｇａｎｇ（许宝刚）（Ｍａｔｈ．ｏｆＤｅｐｔ．，ＳｈａｎｄｏｎｇＵｎｉｖｅｒｓｉｔｙ，Ｊｉｎａｎ２５０１００，Ｃｈｉｎａ．）Ａｂｓｔｒａｃｔ：Ｔｈｅｔｏｔａｌｃｈｒｏｍａｔｉｃｎｕｍｂ...     

SPECTRUM OF THE LAPLACIAN OF COMPACT MANIFOLDS

ＳＰＥＣＴＲＵＭＯＦＴＨＥＬＡＰＬＡＣＩＡＮＯＦＣＯＭＰＡＣＴ　ＭＡＮＩＦＯＬＤＳ￥ＸｕＳｅｎｌｉｎ（徐森林）ＣｈｅｎＣｈｕｎｓｈｅｎｇ（陈春生）ＺｈａｎｇＨｅａｄｉｎｇ（张华明）ＣｈｅｎＧｕａｎｇｈｕａ（陈广华）（Ｄｅｐｔ．ｏｆＸａｔｈ．,Ｕｎｉｖ...     

THE BINDING NUMBER OF A GRAPH AND ITS TRIANGLE

In this paper we prove the following conjecture of Woodall:if bind(G)≥3/2,then Gcontains a triangle.Moreover,we also prove that if bind(G)≥3/2,then each vertex is contained ina 4-cycle,each edge is contained in a 5-cycle when V(G)≥11,and there exists a 6-cycle in G.     

A NEW LAPLACIAN COMPRISON THEOREM AND THE ESTIMATE OF EIGENVALUES

Ａ ＮＥＷ ＬＡＰＬＡＣＩＡＮ ＣＯＭＰＲＩＳＯＮ ＴＨＥＯＲＥＭ ＡＮＤ ＴＨＥ ＥＳＴＩＭＡＴＥ ＯＦ ＥＩＧＥＮＶＡＬＵＥＳ ￥ＤＩＮＧＱＩＮＧＡｂｓｔｒａｃｔ：ＴｈｉｓｐａｐｅｒｅｓｔａｂｌｉｓｈｅｓａｎｅｗＬａｐｌａｃｉａｎｃｏｍｐａｒｉｓ...     

ON THE DERIVATIVE OF A POLYNOMIAL

For an entire function f(z), let M(f,r) = max is a polynomial of degree n, then, ingeneral, it is difficult to obtain a lower bound far M (p',1). But if the zeros of the polynomial are close to the origin, then various lower bounds for M(p' ,1) have been obtained in the past. In this paper, we have considered polynomials having all their zeros in , with a possible zero of order m(m>0) at the origin and have obtained a lower bound for M(p', 1), which is better than most of the known lower bounds. Our bound is sharp for m=0.     

GENERAL VARYING LAW OF THE LARGEST VELOCITY OF STEP-ROCKETS

In this paper, we shall propose a method to solve the problem for the varying law of the largest velocity of step-roekets.     

THE OSCILLATION OF A CLASS NONLINEAR MATRIX DIFFERENTIAL EQUATION

1DefinitionandPropertyInthematrixdifferentialequation,weconsider(p(t)y,(t)), Q(t)y(t) F(t,y(t),y'(t))=0(1)P,Q,y,Farearealcontinuousnxn-th--ordermatrixintheinterval[a, co),andP,Q,Fareasymmetricmatrix,andPisapositivedefinitematrix.F(t,:!/(t),y'(t))gfij(t,yl…     

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].     

ON LOWNER-ORDERING ANTITONICITY OF MATRIX INVERSION

ＯＮＬＯＷＮＥＲ－ＯＲＤＥＲＩＮＧＡＮＴＩＴＯＮＩＣＩＴＹＯＦＭＡＴＲＩＸＩＮＶＥＲＳＩＯＮ￥ＥＲＫＫＩＰ．ＬＩＳＫＩ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｔａｌＳｃｉｅｎｃｅｓ，ＵｎｉｖｅｒｓｉｔｖｏｆＴａｍｐｅｒｅ，Ｆｉｎｌａｎｄ）Ａｂｓｔ...     

ON THE BEST APPROXIMATION MATRIX PROBLEM AND MATRIX FOURIER SERIES

In this paper the concept of positive definite bilinear matrix moment functional. acting on the space of all the matrix valued continuous functions defined on a bounded interval [a,b], is introduced. The best approximation matrix problem with respect to such a functional is solved in terms of matrix Fourier series. Basic properties of matrix Fourier series such as the Kiemann -Lebesgue matrix property and the bessel-parseval matrix inequality are proved. The concept of total set vjith respect to a positive definite matrix functional is introduced , and the totallity of an orthonormal sequence of matrix polynomials with respect to the functional, is established.     

THE EIGENVALUE PROBLEM OF QUASILINEAR ELLIPTIC EQUATION

In this paper, we are concerned with the following eigenvalue problems Find a function u and a real number λ such that When p=2, above problems are of semilinear eigenvalue problems on R~N     

EQUISTABILITY OF THE MATRIX DIFFERENTIAL EQUATIONS

１ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ［１］，ｔｈｅｉｄｅａｓｏｆａｇｅｎｅｒａｌｉｚｅｄｍａｔｒｉｘｖａｌｕｅｄｎｏｒｍａｎｄｍａｔｒｉｘＬｙａｐｕｎｏｖｆｕｎｃｔｉｏｎｓｈａｖｅｂｅｎｐｒｏｐｏｓｅｄａｎｄｔｈｅｍａｉｎｃｏｍｐａｉｒｓｏｎｔｈｅｏｒｅ...     

ON THE MINIMUM FEASIBLE GRAPH FOR FOUR SETS

ＯＮＴＨＥＭＩＮＩＭＵＭＦＥＡＳＩＢＬＥＧＲＡＰＨＦＯＲＦＯＵＲＳＥＴＳＸＵＹＩＮＦＥＮＧＡＮＤＦＵＸＩＡＯＢＩＮＧＡｂｓｔｒａｃｔ：ＧｉｖｅｎａｃｏｍｐｌｅｔｅｇｒａｐｈｗｉｔｈｖｅｒｔｅｘｓｅｔＸａｎｄｓｕｂｓｅｔｓＸ＿１，Ｘ＿２，．．．，Ｘ＿ｎ...     

THE EIGENVALUE PROBLEMS OF ELLIPTIC EQUATIONS OF HIGHER ORDER

§ 1. Introduction Let Ω be a smooth bounded domain in R~n with n≥2. We are concerned with the eigenvalue problem where v is the unit outward normal to Ω. According to the theory of eigenvalue, problem (1.1) has discrete real eigenvalue. They can be lined into     

THE STRUCTURE OF EIGENVALUE REGIONS FOR A TWO-DELAY DIFFERENTIAL SYSTEM WITH A TWIN-PARAMETER

This paper is concerned with positive solutions and the structure of eigenva- lue regions for a two-delay singular differential system with a twin-parameter.     

A VARIATION ON THE BLOCK ARNOLDIMETHOD FOR LARGE UNSYMMETRIC MATRIX EIGENPROBLEMS

1.IntroductionLarge-scalematrixeigenproblemsariseinappliedsciencesandmanyengineeringapplications.Arnoldi'smethod[1'2]anditsblockversion[3--6]areverypopularforsolvingthem.Thesemethodshavebeenintensivelyinvestigatedsincethe1980s,bothintheoryandinalgorithms;wereferto[7--17]fordetails.WhenmstepsoftheblockArnoldiprocessareperformed,anorthonormalbasis{K}7=1oftheblockKrylovsubspaceK.(VI,A)spannedbyVI5AVI,'IAm--1VIisgenerated,whereVIisaninitialNxporthogonalmatrix,andtherestrictionofAtoKm(V…