新超复结构和Clifford分析

本文在Ｈ．Ｍａｌｏｎｅｋ［１］新的超复结构的意义下，研究Ｃｌｉｆｆｏｒｄ分析中Ａ值函数超复可微性及其一种新的锁链规则和微分法则．     

Fredholmness and invertibility of Toeplitz operators with matrix almost periodic symbols

We consider Toeplitz operators with symbols that are almost periodic matrix functions of several variables. It is shown that under certain conditions on the group generated by the Fourier support of the symbol, a Toeplitz operator is Fredholm if and only if it is invertible.

     

Critical Points and Error Rank in Best H 2 Matrix Rational Approximation of Fixed McMillan Degree

This paper deals with best rational approximation of prescribed McMillan degree to matrix-valued functions in the real Hardy space of the complement of the unit disk endowed with the Frobenius L ₂ -norm. We describe the topological structure of the set of approximants in terms of inner-unstable factorizations. This allows us to establish a two-sided tangential interpolation equation for the critical points of the criterion, and to prove that the rank of the error F-H is at most k-n when F is rational of degree k , and H is critical of degree n . In the particular case where k=n , it follows that H=F is the unique critical point, and this entails a local uniqueness result when approximating near-rational functions. January 23, 1996. Date revised: September 16, 1996.     

Fuzzy logic in measurements

Our main interest in this paper is to translate from “natural language” into “system theoretical language”. This is of course important since a statement in system theory can be analyzed mathematically or computationally. We assume that, in order to obtain a good translation, “system theoretical language” should have great power of expression. Thus we first propose a new frame of system theory, which includes the concepts of “measurement” as well as “state equation”. And we show that a certain statement in usual conversation, i.e., fuzzy modus ponens with the word “very”, can be translated into a statement in the new frame of system theory. Though our result is merely one example of the translation from “natural language” into “system theoretical language”, we believe that our method is fairly general.     

Evaluating the Complexity of Index Sets for Families of General Recursive Functions in the Arithmetic Hierarchy

The complexity of index sets of families of general recursive functions is evaluated in the Kleene–Mostowski arithmetic hierarchy.     

Pseudonormality and a Lagrange Multiplier Theory for Constrained Optimization

We consider optimization problems with equality, inequality, and abstract set constraints, and we explore various characteristics of the constraint set that imply the existence of Lagrange multipliers. We prove a generalized version of the Fritz–John theorem, and we introduce new and general conditions that extend and unify the major constraint qualifications. Among these conditions, two new properties, pseudonormality and quasinormality, emerge as central within the taxonomy of interesting constraint characteristics. In the case where there is no abstract set constraint, these properties provide the connecting link between the classical constraint qualifications and two distinct pathways to the existence of Lagrange multipliers: one involving the notion of quasiregularity and the Farkas lemma, and the other involving the use of exact penalty functions. The second pathway also applies in the general case where there is an abstract set constraint.     

Ti：LiNbO3光波导导模的场分布

给出了Ti扩散LiNbO_3条波导任意阶导模场分布的试探解.通过变分法分析,不但可以合理地确定其中的待定参数,而且也得到了相应导模传播常数的近似值.与扩展的有效折射率方法比较:这种解不但在函数形式上简单,待定常数确定方便,而且具有精度高的优点.还可以得到等效一维波导折射率分布的解析表达式.     

On interpolation with products of positive definite functions

In this paper we consider the problem of scattered data interpolation for multivariate functions. In order to solve this problem, linear combinations of products of positive definite kernel functions are used. The theory of reproducing kernels is applied. In particular, it follows from this theory that the interpolating functions are solutions of some varational problems.     

Approximation to the Sobolev classesW q r of functions of several variables by bilinear forms inL p for 2≤q≤p≤∞

We study the approximation of functions of several variables by bilinear forms that are the pairwise products of functions of fewer variables. The order of approximation of Sobolev classesW _q ^r by bilinear forms inL _p for 2≤q≤p≤∞ is found. Translated by N. K. Kulman Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 18–34, July, 1997.     

On the zeros of certain polynomials

We prove that certain naturally arising polynomials have all of their roots on a vertical line.