Basicness of Semialgebraic Sets

This paper is concerned with the problem of deciding whether a semialgebraic set S of an algebraic variety X over R is basic. Furthermore, in such a case, we decide what is the sharp number of inequalities defining S. For that, it suffices to desingularize X, as well as the boundary of S, and then ask the same question for the trace of S on its boundary. In this way, after a finite number of blowing-ups, we lower the dimension of the data and by induction we get a finite decision procedure to solve this problem. Decidability of other known criteria is also analyzed.     

经典分形集测度上估的计算机搜索Ⅰ──对典型例子Sierpinski垫片编码技术的剖析

分形集的Hausdorff测度是一个非线性科学的理论课题,至今结果甚少,即使对于一些生成很有规则的经典分形集亦是如此间．SISrpinski垫片就是这样一个经典分形集,但因其预分形的图形尚未被研究者解析地认识,所以对其Hausdorff测度的研究进展很慢．文献问猜测1十年之后,这个猜测才被文献问以估值否定．接着,文献同又得到更好的估值出由于采取了对Sierpinski垫片发生规则的编码技术,从而方便地得到H”（S）的一个上方估值函数o（x）．上面提到的一系列猜测值或上方估值,依次由0（1／2）,o（l／4）,以司对给出,而则给出TH”（S）…     

The difference between common knowledge of formulas and sets

Common knowledge can be defined in at least two ways: syntactically as the common knowledge of a set of formulas or semantically, as the meet of the knowledge partitions of the agents. In the multi-agent S5 logic with either finitely or countably many agents and primitive propositions, the semantic definition is the finer one. For every subset of formulas that can be held in common knowledge, there is either only one member or uncountably many members of the meet partition with this subset of formulas held in common knowledge. If there are at least two agents, there are uncountably many members of the meet partition where only the tautologies of the multi-agent S5 logic are held in common knowledge. Whether or not a member of the meet partition is the only one corresponding to a set of formulas held in common knowledge has radical implications for its topological and combinatorial structure.     

Homicidal Chauffeur Game with Target Set in the Shape of a Circular Angular Sector: Conditions for Existence of a Closed Barrier

A planar constant-speed pursuit-evasion problem with dynamic model similar to the one of the homicidal chauffeur game and with prescribed angular constraints in the capture criterion is analyzed as a differential game of kind. Because of the angular constraints, the target set of the game has the shape of a circular angular sector. Conditions for the existence of the game barrier (closed) are obtained. Using these conditions, a necessary and sufficient condition for capture of a slower evader from any initial state of the game is established. This condition is represented by an expression for the minimal nondimensional capture radius, normalized by the pursuer minimal turning radius, which guarantees capture of all slower evaders. This minimal capture radius depends on the angular constraints. Capture from any initial state implies that the barrier of the game does not exist and vice versa. In this game, two types of barrier are derived, with termination at either points of smoothness or points of nonsmoothness (corner points) of the boundary of the target set. The results are illustrated by numerical examples.     

Second-Order Optimality Conditions in Multiobjective Optimization Problems

In this paper, we develop second-order necessary and sufficient optimality conditions for multiobjective optimization problems with both equality and inequality constraints. First, we generalize the Lin fundamental theorem (Ref. 1) to second-order tangent sets; then, based on the above generalized theorem, we derive second-order necessary and sufficient conditions for efficiency.     

Contracted Gaussian-type basis functions revisited. III. Atoms K through Kr

Six minimal basis sets of contracted Gaussian-type functions (GTFs) are developed for the third-row atoms K through Kr. The smallest and largest sets for transition metal atoms are (3333/33/3) and (8433/84/8), respectively, where a slash distinguishes the s, p, and d symmetries and single-digit figures in the parentheses denote the numbers of primitive GTFs. The two largest sets, (7433/74/7) and (8433/84/8), surpass the (62111111/33111/311) set of Schaefer et al. in the associated total energies. Our (8433/84/8) set is also superior to their (842111/631/411) set. The quality of the present basis sets is tested by self-consistent field (SCF) and configuration interaction (CI) calculations on the Cu₂ molecule. As the accuracy of the basis set increases, SCF calculations show a decrease in the dissociation energy and an increase in the equilibrium internuclear distance. The same tendencies are found in the results of CI calculations with and without a Davidson correction. All the present basis sets are freely available at the internet address: http://202.35.198.41/∼htatewak/. Received: 17 June 1998 / Accepted: 4 August 1998 / Published online: 23 November 1998     

Multidimensional van der Corput and sublevel set estimates

Van der Corput's lemma gives an upper bound for one-dimensional oscillatory integrals that depends only on a lower bound for some derivative of the phase, not on any upper bound of any sort. We establish generalizations to higher dimensions, in which the only hypothesis is that a partial derivative of the phase is assumed bounded below by a positive constant. Analogous upper bounds for measures of sublevel sets are also obtained. The analysis, particularly for the sublevel set estimates, has a more combinatorial flavour than in the one-dimensional case.

     

赋范线性空间中的最佳共逼近的一点注记

本文用例子表明最佳共逼近与最佳逼近间有着区别．指出强共逼近的元未必是唯一的;凸集未必是共太阳集和强共Ｋｏｌｍｏｇｏｒｏｖ集;而在最佳逼近论中它们的相应回答均是肯定的．     

Regularities of the photoluminescence of porous silicon after chemical etching in HF

The effect of chemical treatment of porous silicon samples by HF on its photoluminescence and its evolution with time in sample aging in air is investigated. It is shown that the effect of HF on the luminescence parameters depends on the duration of the treatment and the initial photoluminescence intensity of the sample. It is found that chemical etching in HF accelerates the growth of the total luminescence intensity in aging of the sample in air. The evolution of the photoluminescence spectrum in aging of the sample in air after chemical etching can be explained within the framework of the quantum-size model of the luminescence of porous silicon. Presented at the Fall Meeting of the Material Research Society, December 1–5, 1997, Boston, USA Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 3, pp. 423–427, May–June, 1999.     

多孔涂层横向抽吸效应强化膜状凝结换热的研究

研究多孔涂层界面抽吸效应对强化膜状凝结换热的影响。考察了多孔涂层的特性参数对凝液膜厚度和换热系数的影响。与Nusselt理论预示值对照表明,多孔涂层界面抽吸效应是强化膜状凝结换热的重要因素。