二次微分系统的中心条件和通积分

本文给出在中国分类之下二次微分系统有中心时两种情况的通积分.     

A generalization of the inertia theorem for quadratic matrix polynomials

We show that the inertia of a quadratic matrix polynomial is determined in terms of the inertia of its coefficient matrices if the leading coefficient is Hermitian and nonsingular, the constant term is Hermitian, and the real part of the coefficient matrix of the first degree term is definite. In particular, we prove that the number of zero eigenvalues of such a matrix polynomial is the same as the number of zero eigenvalues of its constant term. We also give some new results for the case where the real part of the coefficient matrix of the first degree term is semidefinite.     

一类具有二阶细焦点的二次系统

本文证明了一类具有二阶细焦点的二次系统（在其二阶细焦点外围）至多存在一个极限环．     

On the weak uniform convexity of

We will discuss the geometry of the unit sphere in the Banach space of integrable holomorphic quadratic differentials on a Riemann surface and answer some questions posed by L.R. Goldberg (Proc. Amer. Math. Soc. 118 (1993), 1179--1185).

     

Exact arithmetic on the Stern–Brocot tree

In this paper we present the Stern–Brocot tree as a basis for performing exact arithmetic on rational numbers. There exists an elegant binary representation for positive rational numbers based on this tree [Graham et al., Concrete Mathematics, 1994]. We will study this representation by investigating various algorithms to perform exact rational arithmetic using an adaptation of the homographic and the quadratic algorithms that were first proposed by Gosper for computing with continued fractions. We will show generalisations of homographic and quadratic algorithms to multilinear forms in n variables. Finally, we show an application of the algorithms for evaluating polynomials.     

关于Siegel-Tatuzawa定理

设0<ε<1/（6log10）,x为模k的实原特征且k大于e1/ε.则除去至多一个可能的例外特征外,均有这改进了Hoffstein等人的结果.     

Parameter identification problem for the equation of motion of membrane with strong viscosity

The parameter identification problem of constant parameters in the equation of membrane with strong viscosity is studied. The problem is formulated by a minimization of quadratic cost functionals by distributive measurements. The existence of optimal parameters and necessary optimality conditions for the parameters are proved.     

Optimal objective function approximation for separable convex quadratic programming

We present an optimal piecewise-linear approximation method for the objective function of separable convex quadratic programs. The method provides guidelines on how many grid points to use and how to position them for a piecewise-linear approximation if the error induced by the approximation is to be bounded a priori.Corresponding author.     

A polynomially bounded algorithm for a singly constrained quadratic program

This paper presents a characterization of the solutions of a singly constrained quadratic program. This characterization is then used in the development of a polynomially bounded algorithm for this class of problems.     

Quadratic geometric programming with application to machining economics

Geometric Programming is extended to include convex quadratic functions. Generalized Geometric Programming is applied to this class of programs to obtain a convex dual program. Machining economics problems fall into this class. Such problems are studied by applying this duality to a nested set of three problems. One problem is zero degree of difficulty and the solution is obtained by solving a simple system of equations. The inclusion of a constraint restricting the force on the tool to be less than or equal to the breaking force provides a more realistic solution. This model is solved as a program with one degree of difficulty. Finally the behavior of the machining cost per part is studied parametrically as a function of axial depth. This research was supported by the Air Force Office of Scientific Research Grant AFOSR-83-0234