论多目标分式规划

论多目标分式规划徐增堃（浙江师范大学数学系，金华３２１００４）基金项目：浙江省教委自然科学基金资助课题．１９９０年１０月２９日收到，１９９１年１０月５日收到第一次修改稿．１９９２年９月７日收到第二次修改稿，１９９３年２月１３日收到第三次修改、压缩稿．...     

非线性波的指数衰减(I)

非线性波的指数衰减（Ｉ）盛其荣（新疆大学，乌鲁木齐市８３００４６）国家自然科学基金资助项目．１９９１年５月２２日收到，１９９１年１１月１１日收到修改稿．一、引言考虑下面问题：其中中的有界开集，边界且存在常数ｃ＞０使中的有界函数且在。内，（５）这里中非...     

求解粘性系数的迭代方法及其收敛性

求解粘性系数的迭代方法及其收敛性丛文相（黑龙江大学，哈尔滨１５００８０）１９９１年８月３０日收到．１９９２年８月２５日收到第一次修改稿．１９９２年１２月４日收到第二次修改稿．一、引言研究地震正、反问题时，一般把地球假设为完全弹性体，而实际地球介质并非...     

实轴上Freud-Fourier级数的平均收敛性

实轴上Ｆｒｅｕｄ－Ｆｏｕｒｉｅｒ级数的平均收敛性闵国华，肖资阳（南京理工大学应用数学系，南京２１００１４）１９９１年２月４日收到１９９２年２月１０日收到修改压缩稿．一、引言记Ｈｅｒｍｉｔｅ权函数，Ｓｎ（ｘ）为ｆ（ｘ）的Ｈｅｒｍｉｔｅ级数的前１项和．关...     

平面上全局半稳定系统

平面上全局半稳定系统郑作环（海南师范学院数学系，海口５７１１００）１９９０年６月２日收到，１９９１年８月２８日收到修改稿．一、前言设函数Ｘ（ｘ，ｙ）与Ｙ（ｘ，ｙ）在平面Ｒ２上连续，又设微分方程组满足解对初始值的连续依赖性条件，记ｆ（ｐ，ｔ）为（１）式...     

关于代数体函数的展布关系及其应用

关于代数体函数的展布关系及其应用杨连中（山东大学数学系，济南２５０１００）国家青年自然科学基金资助课题．１９９１年５月１５日收到，１９９２年２月２１日收到修改稿．一、引言设ｆ（ｚ）于开平面亚纯，下级为有穷正数．若复数ａ是ｆ（ｚ）的一个亏值，则下述展布...     

回归曲线的加权正交级数估计

回归曲线的加权正交级数估计杨瑛（北京大学概率统计系，北京１００８７１）国家自然科学基金资助项目．１９８９年１２月３日收到．１９９０年１１月２２日收到第一次修改稿．１９９２年８月７日收到第二次修改稿．一、引论自１９６２年Ｃｅｎｃｏｖ［１］提出了密度函数...     

油藏盆地发育数值模拟中的偏微分方程组的有限元方法和理论分析

油藏盆地发育数值模拟中的偏微分方程组的有限元方法和理论分析袁益让，王文洽，羊丹平（山东大学数学系，济南２５０１００）国家教委博士点基金资助项目．１９９０年４月２日收到，１９９０年８目２７日收到第一次修改压缩稿．１９９０年１２月１４日收到第二次修改稿．...     

一类三次系统的定性分析

一类三次系统的定性分析陈文灯（中央财政金融学院信息系，北京１０００８１）国家自然科学基金资助项目．１９９２年６月５日收到．１９９３年６月１６日收到修改稿．本文对一类三次系统进行了定性分析，得出系统（１）的极限环的存在性、唯一性及不存在性的条件．定理１...     

线性码译码的一种算法

线性码译码的一种算法杜宏（中国科学院系统科学研究所，北京１０００８０）１９９２年３月２５日收到．引言线性码的译码算法一直是一个公开问题．Ｊ．Ｊｕｓｔｅｓｅｎ等人在文［２］中给出了平面代数曲线上代数几何码译码的一种算法之后，Ａ．Ｎ．Ｓｋｏｒｏｂｏｇａｔ...     

Partial Geometric Difference Families

We introduce the notion of a partial geometric difference family as a variation on the classical difference family and a generalization of partial geometric difference sets. We study the relationship between partial geometric difference families and both partial geometric designs and difference families, and show that partial geometric difference families give rise to partial geometric designs. We construct several infinite families of partial geometric difference families using Galois rings and the cyclotomy of Galois fields. From these partial geometric difference families, we generate a list of infinite families of partial geometric designs and directed strongly regular graphs.     

Higher-Order Logic Formalization of Conformal Geometric Algebra and its Application in Verifying a Robotic Manipulation Algorithm

Conformal geometric algebra (CGA) is an advanced geometric language used in solving three-dimensional Euclidean geometric problems due to its simple, compact and coordinate-free formulations. It promises to stimulate new methods and algorithms in all areas of science dealing with geometric properties, especially for engineering applications. This paper presents a higher-order logic formalization of CGA theories in the HOL-Light theorem prover. First, we formally define the classical algebraic operations and representations of geometric entities in the new framework. Second, we use these results to reason about the correctness of operation properties and geometric features such as the distance between the geometric entities and their rigid transformations in higher-order logic. Finally, in order to demonstrate the practical effectiveness and utilization of this formalization, we use it to formally model the grasping algorithm of a robot based on the conformal geometric control technique and verify the property that whether the robot can grasp firmly or not.     

On geometric semilattices

We define geometric semilattices, a generalization of geometric lattices. The poset of independent sets of a matroid is another example. We prove several axiomatic and constructive characterizations, for example: geometric semilattices are those semilattices obtained by removing a principal filter from a geometric lattice. We also show that all geometric semilattices are shellable, unifying and extending several previous results.Partially supported by NSF grant MCS 81-03474.     

Partial geometric difference sets and partial geometric difference families

The concept of a partial geometric difference set (or $1\frac{1}{2}$-difference set) was introduced by Olmez in 2014. Recently, Nowak, Olmez and Song introduced the notion of a partial geometric difference family, which generalizes both the classical difference family and the partial geometric difference set. It was shown that partial geometric difference sets and partial difference families give rise to partial geometric designs. In this paper, a number of new infinite families of partial geometric difference sets and partial geometric difference families are constructed. From these partial geometric difference sets and difference families, we generate a list of infinite families of partial geometric designs.     

Automorphisms and Distinguishing Numbers of Geometric Cliques

A geometric automorphism is an automorphism of a geometric graph that preserves crossings and noncrossings of edges. We prove two theorems constraining the action of a geometric automorphism on the boundary of the convex hull of a geometric clique. First, any geometric automorphism that fixes the boundary of the convex hull fixes the entire clique. Second, if the boundary of the convex hull contains at least four vertices, then it is invariant under every geometric automorphism. We use these results, and the theory of determining sets, to prove that every geometric n-clique in which n≥7 and the boundary of the convex hull contains at least four vertices is 2-distinguishable.     

New partial geometric difference sets and partial geometric difference families

Using Galois rings and Galois fields, we construct several infinite classes of partial geometric difference sets, and partial geometric difference families, with new parameters. Furthermore, these partial geometric difference sets (and partial geometric difference families) correspond to new infinite families of directed strongly regular graphs. We also discuss some of the links between partially balanced designs, 2-adesigns (which were recently coined by Cunsheng Ding in “Codes from Difference Sets” (2015)), and partial geometric designs, and make an investigation into when a 2-adesign is a partial geometric design.     

A story-based dynamic geometry approach to improve attitudes toward geometry and geometric proof

This work is a part of a larger study, which presents geometry through a daily life story using dynamic geometry software. It aimed in particular to enable students to feel the importance of geometry in daily life, to share in the process of formulating geometric statements and conjectures, to experience the geometric proof more than validating the correctness of geometric statements and to start with a real-life situation and go through seven steps to geometric proof. The content of the suggested approach was organized so that every activity was a prerequisite for entering the next one, either in the structure of geometric concepts or in the geometric story context. Some indications will be presented according to three Likert-type questionnaires, which were prepared by the researcher with the purpose of assessing students?? attitudes toward geometry and geometric proof, using computers in mathematics learning and the suggested approach. The analysis of single responses to questionnaire items showed significant changes in students?? beliefs about geometry, importance and functions of geometric proof and toward using the suggested approach.     

The triples of geometric permutations for families of disjoint translates

A line meeting a family of pairwise disjoint convex sets induces two permutations of the sets. This pair of permutations is called a geometric permutation. We characterize the possible triples of geometric permutations for a family of disjoint translates in the plane. Together with earlier studies of geometric permutations this provides a complete characterization of realizable geometric permutations for disjoint translates.     

Operator geometric stable laws

Operator geometric stable laws are the weak limits of operator normed and centered geometric random sums of independent, identically distributed random vectors. They generalize operator stable laws and geometric stable laws. In this work we characterize operator geometric stable distributions, their divisibility and domains of attraction, and present their application to finance. Operator geometric stable laws are useful for modeling financial portfolios where the cumulative price change vectors are sums of a random number of small random shocks with heavy tails, and each component has a different tail index.     

Rough posynomial geometric programming

A rough posynomial geometric programming is put forward by the author. This model is advantageous for us to consider questions not only from the quantity of aspect, but from the quality because it contains more information than a traditional geometric programming one. Here, a rough convex function concept is advanced in rough value sets on foundation of rough sets and rough convex sets. Besides, a knowledge expression model in rough posynomial geometric programming is established and so is a mathematical one. Thirdly, solution properties are studied in mathematical model of rough posynomial geometric programming, and antinomy of the more-for-less paradox is solved with an arithmetic in rough posynomial geometric programming given, which can be changed into a rough linear programming after monomial rough posynomial geometric programming is solved. Finally, validity in model and algorithm is verified by examples.