One way to solve the parametric quadratic programming problem

A method is presented for the solution of the parametric quadratic programming problem by the use of conjugate directions. It is based on the method for quadratic programming proposed by the author in [1].While engaged in this research the author had a part-time post with the Manpower Services Commission.     

Improved algorithm for mixed-integer quadratic programs and a computational study

In a recent paper [6] we suggested an algorithm for solving complicated mixed-integer quadratic programs, based on an equivalent formulation that employs a nonsingular transformation of variables. The objectives of the present paper are two. First, to present an improved version of this algorithm, which reduces substantially its computational requirements; second, to report on the results of a computational study with the revised algorithm.     

Comments on ‘the group velocity of some numerical schemes’

The proper phase and group speeds when quadratic finite elements are applied to the one-dimensional pure advection equation are presented and the myth of a spurious computational mode is dispelled.     

Stability of the Quadratic Equation of Pexider Type

We will investigate the stability problem of the quadratic equation (1) and extend the results of Borelli and Forti, Czerwik, and Rassias. By applying this result and an improved theorem of the author, we will also prove the stability of the quadratic functional equation of Pexider type,f ₁ (x +y) + f₂(x -y) =f ₃(x) +f ₄(y), for a large class of functions.     

Complex Structures in Real Algebras. I. Two-Dimensional Commutative Case

Abstract

We study complex structures in real two-dimensional commutative algebras and show their connection with homotopy properties of the multiplications. An application to the Riccati equation in rank three algebras is also discussed.     

Central difference limit for derivatives of ill-posed functions: Best approach in supercomputing era

A polynomial-time algorithm based on a revised method of iterative central difference limit is presented for computing the numerical value of the derivative of a given analytic function. Through numerical experiments, we establish that this algorithm is a best one. This can be used to obtain the derivative to a desired accuracy subject to the precision of the computer for violently fluctuating or rapidly oscillatory functions. The concerned time/computational complexity is so small in practice that in the non-main-frame supercomputing era when over estimated 95% of computing resources is unutilized and hence a waste, the complexity here is not an issue. We have, for the purpose of a comparison, also included Matlab symbolic-cum-numerical computation to obtain the derivative of the foregoing functions numerically. Matlab programs in both Matlab standard precision as well as Matlab variable precision are also included for the central difference limit along with the symbolic-cum-numerical computation. The reader concerned with computing the derivative of an ill-conditioned function - large or small - can use these programs by copying, pasting, and executing and can readily check the quality of the derivative.     

Low-temperature phase transitions in the quadratic family

We give the first example of a quadratic map having a phase transition after the first zero of the geometric pressure function. This implies that several dimension spectra and large deviation rate functions associated to this map are not (expected to be) real analytic, in contrast to the uniformly hyperbolic case. The quadratic map we study has a non-recurrent critical point, so it is non-uniformly hyperbolic in a strong sense.     

具有二个焦点的二次系统极限环的分布与个数

本文证明了具有二个焦点的二次系统必在其中一个焦点外围至多有一个极限环这一猜想．从而得到具有二个焦点的二次系统之极限环必是（Ｏ,ｉ）或（１,ｉ）分布（ｉ＝ ０, １, ２,）．     

关于虚二次域Tame核计算的一个注记

本文给出了一种计算数域Tame核的方法.应用到虚二次域上,证明了当 Nv>8δD6时,(？)t／:K2S'F／K2SF→k*是双射。