Second Equivalence Theorem of Multivariate Polynomial System and Eigenproblem

In[1,2] we have constructed the Joint eigenproblem equivalent to multivariatepolynomial system and presented an algorithm to solve latter.In this paper we willstudy another equivalence theorem for the same problem.The computation of thecorresponding eigenvalues is numerically stable. Consider multivarite polynomial system     

RESEARCH ANNOUNCEMENTS：Morrey Regularity of the Solution to the Diri

To study the local regularity of solutions to second orderelliptic partial differential equations, Morrey in ［1］ introduced somefunction spaces, which are called the Morrey spaces today. Since then, manymathematicians have studied regularities of solutions to some kinds of secondorder elliptic equations in Morrey spaces.     

The Structure of Solutions to Algebraic System and Matrices in Eigenvalue Method

ＴｈｅＳｔｒｕｃｔｕｒｅｏｆＳｏｌｕｔｉｏｎｓｔｏＡｌｇｅｂｒａｉｃＳｙｓｔｅｍ　ａｎｄＭａｔｒｉｃｅｓｉｎ　Ｅｉｇｅｎｖａｌｕｅ　ＭｅｔｈｏｄＦｅｎｇＧｕｏｃｈｅｎ（冯果忱）ＺｈａｎｇＳｈｕｇｏｎｇ（张树功）ａｎｄＬｉｕＹｉｎｇ（刘颖）（Ｉｎｓｔｉ...     

On the Number and Locations of the Eigenvalues of Generalized Eigenvalue Problem

The gerleralized eigenvalue problem Aχ=λBχ (1) where A and B are teal symmetric n×n matrices,is one 0f the basie Problems in matrix theory,which apPears in many fields,Such as physics,mechanics and engineering.When B is a positiVe definite matrix(1)can be solved by reducing it to the form     

RESEARCH ANNOUNCEMENTS—On a Generalization of the c—numerical Range

Let Cn×n be the set of n × n complex matrices and An the set of orthonormal n-tuples of vectors in Cn. For a vector c in Cn and a matrix A in Cn×n, the c-numerical range of A is the set Wc(A)={n∑i=1 Ci(Axi,xi):(x1,…xn)∈∧n} When c = (1,0,…,0), Wc(A) is reduced to the classical numerical range W(A) (see [1]). For the classical numerical range and its generalizations, one may see the survey article[2].     

RESEARCH ANNOUNCEMENTS The Lower Bound of the Number of Input Bits to Strong n×n S-boxes

ThesecurityoftheDES-likecrytosystemsdependsheavilyonthestrengthofthesub-stitutionboxes(S-boxes)used.ThedesignofnewS-boxesisthereforeanimportantconcerninthecreationofnewandmoresecurecryptosystems.ThefullsetofdesigucriteriafortheS-boxesoftheDEShasnever...     

RESEARCH ANNOUNCEMENTS The New Necessary and Sufficient Conditions for the Uniformly Continuous and Continuous of Duality Mappings

In[1],Ma shaoqin gave the necessary and sufficient condition for the uniformlycontinuous and continuous of duality mappings.In the note,We give very simplecriteria for the uniformly continuous and continuous of duality mappings.And by[1],the necessary and sufficient conditions for the norm of a real Banach Space to beuniformly Frechet differentiable and Frechet differentiable are described.     

RESEARCH ANNOUNCEMENTS On the Uniqueness of Limit Cycle for a Generalized Liénard System

ＲＥＳＥＡＲＣＨＡＮＮＯＵＮＣＥＭＥＮＴＳＯｎｔｈｅＵｎｉｑｕｅｎｅｓｏｆＬｉｍｉｔＣｙｃｌｅｆｏｒａＧｅｎｅｒａｌｉｚｅｄＬｉéｎａｒｄＳｙｓｔｅｍＨｅＱｉｍｉｎ（何启敏）（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＳｕｚｈｏｕＵｎｉｖｅｒｓｉｔｙ，Ｓｕｚｈｏｕ，...     

RESEARCH ANNOUNCEMENTS The C~1-Admissible Approximation for Lipschitz Fun-ctions and the Hamiltonian Inclusions

In this paper,C~(1-0)(D,R)denotes the set of the locally Lipschitz continuousfunctions from D to R,For f∈C~(1-0)(D,R)and x∈D,f(x)denotes the Clarke’sgeneralized gradient of f at x. Definition 1 Let D be an open subset of R~n and f∈C~(1-0)(D,R).Suppose thatε:D→R is a positive function.If a function g∈C~1(D,R)and satisfies     

RESEARCH ANNOUNCEMENTS The Comparison Theorem for the Bergman and Kobayashi Metrics on a Class of Pseudoconvex Domains

ＲＥＳＥＡＲＣＨＡＮＮＯＵＮＣＥＭＥＮＴＳＴｈｅＣｏｍｐａｒｉｓｏｎＴｈｅｏｒｅｍｆｏｒｔｈｅＢｅｒｇｍａｎａｎｄＫｏｂａｙａｓｈｉＭｅｔｒｉｃｓｏｎａＣｌａｓｓｏｆＰｓｅｕｄｏｃｏｎｖｅｘＤｏｍａｉｎｓ￥ＹｉｎＷｅｉｐｉｎｇ（Ｍａｔｈｅｍａｔｉｃａ...     

RESEARCH ANNOUNCEMENTS The Uniqueness of Topology and Continuity of Systems of Derivations on Locally Convex F-Algebras(*)

The uniqueness of topology is an important problem in the theory of auto-matic continuity.In 1967,Johnson proved the famous uniqueness theorem of normwhich asserts that any Jacobson semisimple Bauach algebra has the unique com-plete norm topology.Carpenter proved this for commutative Frechet algebras.In1976,Esterle proved that a Jacobson semisimple Banach algebra has the unique-topology as an F-algebra.A main result we obtained here was that a Jacobsonsemisimple locally convex F—algebra whose maximal regular right ideals are clo-sed has the unique topology as an F—algebra.     

RESEARCH ANNOUNCEMENTS——Einstein—Kahler Metric on Cartan—Hartogs Domain of the First Type

S. Y. Cheng and S. T. Yau showed in [CY] that any C2 bounded pseudoconvex domain in Cnhas a complete Einstein-Kahler metric with constant negative Ricci curvature. N. Mok and S. T.Yau[MY] have extended this result to arbitrary bounded pseudoconvex domain in Cn. CompleteEinstein-Kahler metric with Explicit form, however, is only known in the case of homogeneousdomain.     

RESEARCH ANNOUNCEMENTS——On Multiplication Tables of Normal Bases and Their Dual-bases Over Finite Fields

Let q be a power of a prime p and n be a positive integer,let K=Fq be the finite fiele with q elements and F=Fqn be the nte extension of K.N=｛αi|i=0,1,…,n-1｝is a normal basis of F over Fq,where αi=α^qi,i=0,1…,n-1.     

The Monge Problem of “Piles and Holes” on the Torus and the Problem of Small Denominators

We discuss the problem of existence of a smooth endomorphism of a closed n-dimensional manifold carrying a differential n-form into a prescribed volume form. Of course, we assume that the integrals of these forms over the whole manifold are equal. The solution of this problem for the n-dimensional torus reduces to the problem of small denominators well known in analysis.     

The Problem of Finding the Kernels in the System of Integro-Differential Maxwell’s Equations

Journal of Applied and Industrial Mathematics - We pose the direct and inverse problems of finding the electromagnetic field and the diagonal memory matrix for the reduced canonical system of...     

The Perturbed Problem on the Boussinesq System of Rayleigh-Bénard Convection

In this paper,the infinite Prandtl number limit of Rayleigh-B′enard convection is studied.For well prepared initial data,the convergence of solutions in L∞(0,t;H2(G)) is rigorously justified by analysis of asymptotic expansions.     

The Dual Functionals for the Generalized Ball Basis of Wang-Said Type and Basis Transformation Formulas

The generalized Ball curves of Wang-Said type with a position parameter L not only unify the Wang-Ball curves and the Said-Ball curves, but also include several useful intermediate curves. This paper presents the dual functionals for the generalized Ball basis of Wang-Said type. The relevant basis transformation formulae are also worked out.