柔性圆环壳在子午面内整体弯曲的复变量方程及细环壳的一般解

在З.Л.Аксельрад(E.L.Axelrad)非轴对称载荷下柔性旋转壳线性方程的基础上,导出了圆环壳在子午面内整体弯曲的复变量方程和相应的细环壳方程.该方程可与钱伟长给出了一般解的В.В.Новожилов(V.V.Novozhilov)轴对称环壳方程相类比.通过类比,给出了细环壳在子午面内整体弯曲的一般解.所给出的解可以用来计算波纹管整弯曲的应力和端面位移.     

平易近人的微积分

微积分学本属于高等数学,一直是大学理工科的必修课程.但在大学生中,没有真正学懂微积分的人为数不少.难怪许多大学教授不主张在中学开设微积分课程.然而,天不遂人愿,近几年来,微积分悄然进入了高中,在老师和学生中,不免引发了一些心理失衡.为了缓解人们的忧虑,作者撰写此文.     

互补约束问题的一种新松弛规划及其收敛性

在G.H.Lin与M.Fukushima思想的启发下,针对一般形式的互补约束问题,本文构造了一种新的松弛规划.通过修正和简化G.H.Lin与M.Fukushima的证明方法,在比其更弱的假设条件下获得了该松弛规划的收敛性质.     

人文素质教育在数学教学中的重要性及其渗透

人文素质教育最重要的功能是教人做人.数学教育必须以人性完善为终级目标,这是人文主义教育观坚持的核心观点.在数学教学中,应重视把人文知识或人文精神与数学内容融合在一起,浸润在数学知识中.渗透人文素质教育,关键在教师.     

追溯对策理论的深远渊源——传统对策(博弈)论的源头

本文内容分三大部分:1.中华民族在对策论形成、发展中的卓越贡献,分六个方面加以分述;2.国外智者在对策论形成、发展中的促进作用;3.聪明、智术是生物在生存进化过程逐渐积累的智慧之光.     

非牛顿流体内流传热研究

在本文中,研究了注入轴对称模腔非牛顿流体非定常流动.本文的第二部份研究了上随体Maxwell流体管内热流动.对于注入模腔流动.其本构方程采用幂律流体模型方程.为了避免在表现粘度中温度关系引起的非线性.引进了一特征粘度的概念.描述本力学过程的基本方程是,本构方程、定常状态的运动方程、非定常能量方程及连续方程.该方程组在空间是二维问题,在数学上是三维问题.采用分裂差分格式求得本方程组的数值解答.分裂法曾成功应用于求解牛顿流体问题.在本文中,首次将分裂法成功地应用解决非牛顿流体流动问题.对于圆管内热流,给出了差分格式,使基本方程组化为一个三对角方程组.其结果,给出了不同时刻的模腔内二维温度分布.     

三线八角

教材:北师大版七年级(下) 课型:新授课 教学目标 1.理解各类角的概念;2.能在图中正确地识别各类角;3.理解掌握对顶角、邻补角的性质. 教学重点、难点:在较复杂的图形中寻找一个角的同位角、内错角、同旁内角. 教学关键:掌握构成各类角的基本图形.     

古代筮法产生的随机数研究

随机数在现代科学中有着重要应用,随机数隶属可测函数范畴,因此随机数历.史是数学史的重要组成部分.追朔随机数的历史,可以在《易经》中的《系辞传》中发现筮法.筮法是古代中国产生随机数的方法.筮法过程可以看作为带外来输入的随机过程,也就是说筮法是数学史中的随机过程的古代中国实例.在严格的概率论模型的基础上,给出了筮法所产生的随机数概率,并给出了其信息熵.结果修改了向传三的结果.     

维纳和布朗运动

布朗运动,作为一种特殊的随机过程,在随机过程理论处于一个中心地位.布朗运动理论在其他许多领域也有重要应用.在布朗运动理论的发展和完善过程中,布朗,爱因斯坦和维纳等人都作出了重要贡献.通过解读原始文献,考察了维纳建立布朗运动数学理论的过程.揭示了维纳在布朗运动的数学理论严格化进程中的重要作用.     

任何非递归r.e.度之下存在孤立d-r.e.度

证明了在任何非递归r.e.度之下都存在孤立d-r.s.度。     

Optimal control of nonlinear evolution inclusions

In this paper, we study the optimal control of nonlinear evolution inclusions. First, we prove the existence of admissible trajectories and then we show that the set that they form is relatively sequentially compact and in certain cases sequentially compact in an appropriate function space. Then, with the help of a convexity hypothesis and using Cesari's approach, we solve a general Lagrange optimal control problem. After that, we drop the convexity hypothesis and pass to the relaxed system, for which we prove the existence of optimal controls, we show that it has a value equal to that of the original one, and also we prove that the original trajectories are dense in an appropriate topology to the relaxed ones. Finally, we present an example of a nonlinear parabolic optimal control that illustrates the applicability of our results.This research was supported by NSF Grant No. DMS-88-02688.     

On intermediate inquisitive and dependence logics: An algebraic study

This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete for all intermediate inquisitive and dependence logics. To this end, we define inquisitive and dependence algebras and we investigate their model-theoretic properties. We then focus on finite, core-generated, well-connected inquisitive and dependence algebras: we show they witness the validity of formulas true in inquisitive algebras, and of formulas true in well-connected dependence algebras. Finally, we obtain representation theorems for finite, core-generated, well-connected, inquisitive and dependence algebras and we prove some results connecting team and algebraic semantics.     

Asymptotic behaviour of a closed‐loop thermosyphon with linear friction and viscoelastic binary fluid

Viscoelastic fluids represent a major challenge both from an engineering and from a mathematical point of view. Recently, we have shown that viscoelasticity induces chaos in closed‐loop thermosyphons even when we consider binary fluids, this is, when we consider a solute in the fluid, as water and antifreezes, for example. In this work, we consider a linear friction law, and we show that in this case with the addition of a solute to the fluid we can prove, under some conditions, chaotic asymptotic behavior for suitable geometry of the circuit and heat flux or ambient temperature functions.     

Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems

Although planar quadratic differential systems and their applications have been studied in more than one thousand papers, we still have no complete understanding of these systems. In this paper we have two objectives.First we provide a brief bibliographical survey on the main results about quadratic systems. Here we do not consider the applications of these systems to many areas as in Physics, Chemist, Economics, Biology, …Second we characterize the new class of planar separable quadratic polynomial differential systems. For such class of systems we provide the normal forms which contain one parameter, and using the Poincaré compactification and the blow up technique, we prove that there exist 10 non-equivalent topological phase portraits in the Poincaré disc for the separable quadratic polynomial differential systems.     

关于均值KIRCHHOFF板非线性边界镇定问题的几点注记

对于均值K IRCHHOFF板非线性边界镇定问题给出几点注记.首先应用G reen公式对具有非线性边界反馈控制的均值K IRCHHOFF板所决定的非线性系统的能量衰减速度进行了重新推导,从而修正了前人的结果.然后应用极大单调函数的定义和分部积分技巧,对均值K IRCHHOFF板非线性边界镇定问题所决定的非线性算子A的极大单调性给出了重新证明,进而更正了已有文献中相应证明的欠妥之处.     

Nonlinear elliptic differential equations with multivalued nonlinearities

In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all ℝ. Assuming the existence of an upper and of a lower solution, we prove the existence of a solution between them. Also for a special version of the problem, we prove the existence of extremal solutions in the order interval formed by the upper and lower solutions. Then we drop the requirement that the monotone nonlinearity is defined on all of ℝ. This case is important because it covers variational inequalities. Using the theory of operators of monotone type we show that the problem has a solution. Finally in the last part we consider an eigenvalue problem with a nonmonotone multivalued nonlinearity. Using the critical point theory for nonsmooth locally Lipschitz functionals we prove the existence of at least two nontrivial solutions (multiplicity theorem).     

Hereditary atomicity in integral domains

If every subring of an integral domain is atomic, we say that the latter is hereditarily atomic. In this paper, we study hereditarily atomic domains. First, we characterize when certain direct limits of Dedekind domains are Dedekind domains in terms of atomic overrings. Then we use this characterization to determine the fields that are hereditarily atomic. On the other hand, we investigate hereditary atomicity in the context of rings of polynomials and rings of Laurent polynomials, characterizing the fields and rings whose rings of polynomials and rings of Laurent polynomials, respectively, are hereditarily atomic. As a result, we obtain two classes of hereditarily atomic domains that cannot be embedded into any hereditarily atomic field. By contrast, we show that rings of power series are never hereditarily atomic. Finally, we make some progress on the still open question of whether every subring of a hereditarily atomic domain satisfies ACCP.     

Parallel local search

We present a survey of parallel local search algorithms in which we review the concepts that can be used to incorporate parallelism into local search. For this purpose we distinguish between single-walk and multiple-walk parallel local search and between asynchronous and synchronous parallelism. Within the class of single-walk algorithms we differentiate between multiple-step and single-step parallelism. To describe parallel local search we introduce the concepts of hyper neighborhood structures and distributed neighborhood structures. Furthermore, we present templates that capture most of the parallel local search algorithms proposed in the literature. Finally, we discuss some complexity issues related to parallel local search.     

基于卫星观测数据的预测模型及其应用

在战争中为了避开敌方军事卫星的侦查,需要对其过顶时间进行预警.对于参数公开的卫星,可以通过根数来进行准确的预报.而对于参数未知的卫星,提出了一种根据过往观测数据来对卫星过顶时间进行预测的思路:将卫星与地球之间复杂的三维耦合运动进行降维,并且以地面为参考系,发现卫星星下点运动轨迹具有高度的周期性·根据这种思路,可以通过获取的过往观测数据来对卫星未来的过顶时间进行准确预测.而对于战时地面运动单位躲避卫星的问题,可以根据所面对的不同侦查卫星通过设置一个固定的路线,让地面单位在该路线中有计划的行驶,能够躲避多种卫星的侦查.     

修正的IPA算法的建立及在不等式约束凸优化问题中的应用

本文首先对IPA算法进行了修正，并证明了修正IPA算法的收敛性，然后将修正后的IPA应用到不等式约束凸优化问题中得到新的内点算法，并与传统的障碍函数法作了比较，从理论上体现了新算法的优势，并给出了其工程解求解法以及收敛性的证明．