多元函数有无穷多个驻点时的极值问题

讨论了二元函数和三元函数在有无穷多个驻点时的极值的判定方法,并进一步介绍了该判定方法在证明不等式方面的应用.     

黄铜合金气瓶阀体多向模锻工艺初探

介绍黄铜合金锻造中的一些基本要求，并具体介绍了气瓶阀阀体多向模段工艺及模具。     

多时滞非线性差分方程振动解的渐近性

给出了多时滞非线性差分方程Δxn anxn f(n,∑-s=-kqsxn s)=0,(n≥0）所有振动解xn趋于0的一族充分条件。推广和改进了已有结果。     

Complex versus real orthogonal polynomials of two variables

Orthogonal polynomials of two real variables can often be represented in complex variables. We explore the connection between the two types of representations and study the structural relations of complex orthogonal polynomials. The complex Hermite orthogonal polynomials and the disk polynomials are used as illustrating examples.     

Clifford analysis in two and several vector variables

In this paper we present some basic function theoretic results and ideas concerning nullsolutions of several Dirac type operators. In particular we consider plane wave solutions, axial symmetry, zonal functions and irreducible representations of the group SO (m).     

Relaxation results for functions depending on polynomials changing sign on rank-one matrices

In this paper, we are interested in computing the different convex envelopes of functions depending on polynomials, especially those having it is main part change sign on rank-one matrices. Our main result applies to functions of the type W(F)=φ(P(F)), W(F)=φ(P(F))+f(detF) or W(F)=φ(P(F))+g(adjnF) defined on the space of matrices, where φ, f:R→R and g:R³→R are three continuous functions, and P=P₀+P₁+?+Pd is a polynomial such that Pd has the property of changing sign on rank-one matrices. Then the polyconvex, quasi-convex and rank-one convex envelopes of W are equal.     

关于多滞量差分不等式的讨论

在此讨论以下形式的差分不等式的最终正m解的不存在性yn 1-yn ∑i=1pi(n)yn-ki≤0(*),其中m≥1,pi(n)≥0。证明了m≥2,且li mn→∞inf{∑mi=1pi(n)[(ki 1)ki 1/kiki] δ0rn}>1时,(*)无最终正解。     

Maps of several variables of finite total variation. II. E. Helly-type pointwise selection principles

Given a=(a₁,…,an), b=(b₁,…,bn)∈Rn with a<b componentwise and a map f from the rectangle into a metric semigroup M=(M,d,+), denote by the Hildebrandt-Leonov total variation of f on , which has been recently studied in [V.V. Chistyakov, Yu.V. Tretyachenko, Maps of several variables of finite total variation. I, J. Math. Anal. Appl. (2010), submitted for publication]. The following Helly-type pointwise selection principle is proved: If a sequence{fj}_j∈Nof maps frominto M is such that the closure in M of the set{fj(x)}_j∈Nis compact for eachandis finite, then there exists a subsequence of{fj}_j∈N, which converges pointwise onto a map f such that. A variant of this result is established concerning the weak pointwise convergence when values of maps lie in a reflexive Banach space (M,‖⋅‖) with separable dual M^∗.     

Canonical partial least squares—a unified PLS approach to classification and regression problems

We propose a new data compression method for estimating optimal latent variables in multi‐variate classification and regression problems where more than one response variable is available. The latent variables are found according to a common innovative principle combining PLS methodology and canonical correlation analysis (CCA). The suggested method is able to extract predictive information for the latent variables more effectively than ordinary PLS approaches. Only simple modifications of existing PLS and PPLS algorithms are required to adopt the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.