Regular points for Lagrange interpolation on the unit disk

A set of points on the unit disk of the Euclidean plane is given, which admits unique Lagrange interpolation. The points have rotational symmetry and they form an example of natural lattices of Chung and Yao [2]. Properties of Lagrange interpolation with respect to these points are studied.Work done when visiting the University of Oregon at Eugene, Oregon.Supported by National Science Foundation under Grant No. 9302721.     

图T1,1,m与Q(3,n)中有路因子的充分必要条件及T1,1,m的匹配等价类

如果一个图的匹配多项式可以被一个路的匹配多项式整除,我们就称此路是该图的一个路因子,路因子在刻画图的匹配等价类,研究匹配唯一性方面有很重要的作用.本文得到了图T1,1.m与图Q(3,n)中有路因子的充分必要条件.     

Unit Commitment by Augmented Lagrangian Relaxation: Testing Two Decomposition Approaches

One of the main drawbacks of the augmented Lagrangian relaxation method is that the quadratic term introduced by the augmented Lagrangian is not separable. We compare empirically and theoretically two methods designed to cope with the nonseparability of the Lagrangian function: the auxiliary problem principle method and the block coordinated descent method. Also, we use the so-called unit commitment problem to test both methods. The objective of the unit commitment problem is to optimize the electricity production and distribution, considering a short-term planning horizon.     

Portfolio optimization under D.C. transaction costs and minimal transaction unit constraints

This paper addresses itself to a portfolio optimization problem under nonconvex transaction costs and minimal transaction unit constraints. Associated with portfolio construction is a fee for purchasing assets. Unit transaction fee is larger when the amount of transaction is smaller. Hence the transaction cost is usually a concave function up to certain point. When the amount of transaction increases, the unit price of assets increases due to illiquidity/market impact effects. Hence the transaction cost becomes convex beyond certain bound. Therefore, the net expected return becomes a general d.c. function (difference of two convex functions). We will propose a branch-and-bound algorithm for the resulting d.c. maximization problem subject to a constraint on the level of risk measured in terms of the absolute deviation of the rate of return of a portfolio. Also, we will show that the minimal transaction unit constraints can be incorporated without excessively increasing the amount of computation.     

Synthesis and properties of new soluble triphenylamine‐based aromatic poly(amine amide)s derived from N,N′‐bis(4‐carboxyphenyl)‐N,N′‐diphenyl‐1,4‐phenylenediamine

A new triphenylamine‐containing aromatic dicarboxylic acid, N,N′‐bis(4‐carboxyphenyl)‐N,N′‐diphenyl‐1,4‐phenylenediamine, was synthesized by the condensation of N,N′‐diphenyl‐1,4‐phenylenediamine with 4‐fluorobenzonitrile, followed by the alkaline hydrolysis of the intermediate dinitrile compound. A series of novel triphenylamine‐based aromatic poly(amine amide)s with inherent viscosities of 0.50–1.02 dL/g were prepared from the diacid and various aromatic diamines by direct phosphorylation polycondensation. All the poly(amine amide)s were amorphous in nature, as evidenced by X‐ray diffractograms. Most of the poly(amine amide)s were quite soluble in a variety of organic solvents and could be solution‐cast into transparent, tough, and flexible films with good mechanical properties. They had useful levels of thermal stability associated with glass‐transition temperatures up to 280 °C, 10% weight‐loss temperatures in excess of 575 °C, and char yields at 800 °C in nitrogen higher than 60%. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 94–105, 2003     

关于单位圆内涉及导数与重值的全纯函数的奇异点的存在性

本文证明了单位圆内涉及导数与重值的全纯函数的奇异点存在性。     

Social norms and choice: a weak folk theorem for repeated matching games

A folk theorem which holds for all repeated matching games is established. The folk theorem holds any time the stage game payoffs of any two players are not affinely equivalent. The result is independent of population size and matching rule—including rules that depend on players choices or the history of play.      

Stable subsets of modules and the existence of a unit in associative rings

We obtain criteria for the existence of a (left) unit in rings (arbitrary, Artinian, Noetherian, prime, and so on) that are based on the systematic study of properties of stable subsets of modules and their stabilizers that generalize the technique of idempotents. We study a class of quasiunitary rings that is a natural extension of classes of rings with unit and of von Neumann (weakly) regular rings, which inherits may properties of these classes. Some quasiunitary radicals of arbitrary rings are constructed, and the size of these radicals “measures the probability” of the existence of a unit. Translated fromMatematicheskie Zametki, Vol. 61, No. 4, pp. 596–611, April, 1997. Translated by A. I. Shtern