证明积分不等式的几种方法

通过实例介绍证明积分不等式的几种常用方法     

几何定理机器证明的方法--吴方法思想的形成

计算机在自己发展的早期就与数学结下了不解之缘 .众所周知 ,数值计算无论是在数学发展之初 ,还是现在 ,甚至在未来的数学发展中都将占据着至关重要的地位 .因此 ,在解决越来越复杂的数值计算过程中 ,世界各民族都创造了各式各样的计算工具 :屈指计算 →卵石计算 (结绳计算、刻痕计算 ) →算筹 →算盘→计算尺 →…… ,而计算机成了数值计算工具中的佼佼者 ,从手摇 (机械 )计算机 →电动 (机械 )计算机 →直到现在发展的高速电子计算机 (电脑 ) .计算机作为数值计算工具的发明要归功于 1 5世纪法国著名的数学家、物理学家和思想家帕斯卡 (B…     

可由用户持续发展的几何自动推理平台

提出并实现了可由用户持续发展的几何自动推理平台(SGARP).它由知识库、知识编辑器、信息库、推理引擎、信息查询窗口和动态几何作图系统等六部分组成.在这个平台上,用户可以添加几何对象、谓词和规则,也可以综合使用多种推理方法进行推理.     

微积分中几种问题的处理方法

在微积分的教学中 ,有些计算题或证明题经常会有学生反映不知如何下手 ,为此给出这几种问题的处理方法 .1　一类数列的极限问题极限的运算中 ,有一类数列的极限我们常遇到 .例如 :( i) limn→∞a· ( a+ 1 ) ( a+ 2 )… ( a+ n)b· ( b+ 1 ) ( b+ 2 )… ( b+ n) ( 0 相似文献   

一类初等微分几何定理机器证明的算法与实现

空间曲面上的曲线论是初等微分几何的重要部分．作者提出了一种以外微分运算和向量计算为主要工具,可以进行有关曲面上曲线局部性质的定理机器证明的算法．该算法结合了曲面上的活动标架,曲面上曲线的测地标架和曲线自身的Frenet标架,在Maple 9下得到实现．对20个例子进行的测试表明,由该算法生成的自动证明简短可读．     

直线与平面垂直判定定理的另一种证明方法

直线与平面垂直判定定理的证明,是课本中的一个难点．通过对课本中的证明方法的分析思考,我利用三角形的中线公式得出了这个定理的另一种证明方法．     

只有一种"足球"的证明

在高二学习多面体欧拉定理时,我遇到了这样一道题目:题:欲制作一个由正六边形和正五边形皮子组成的足球,现有5块六边形皮子,请问需要几块正五边形皮子解:设正五边形皮子的个数为,由多面体欧拉定理F V-E=2知:(5 x) 13(6×5 5x)-21(6×5 5x)=2,解得:x=12,即需要12块正五边形皮子.     

一种新的对偶空间描述

本文描述了一种保持张量积的对偶空间．对有限维线性空间，它与经典对偶空间一致．在代数状态，它与Ｓｗｅｅｄｌｅｒ的代数对偶一致     

一种几何定理机器证明的零维化方法

本文对一类初等几何定理的证明给出了一种机械化方法，利用这种方法，可计算出一个由有限个素理想组成的集合，所有属于假设部分对应的某一扩域上的理想的素理想都在这个集合中出现并且可以挑选出来．因而一个几何定理一般真确，当且仅当终结多项式属于全部的这种素理想，即对其不可约特征列的余式为零．     

Bernoulli序列的无规则性定理的一种分析证法

本文的目的是要利用纯分析的方法，证明Bernoulli序列的无规则性定理．     

A new parallel chasing algorithm for transforming arrowhead matrices to tridiagonal form

Rutishauser, Gragg and Harrod and finally H.Y. Zha used the same class of chasing algorithms for transforming arrowhead matrices to tridiagonal form. Using a graphical theoretical approach, we propose a new chasing algorithm. Although this algorithm has the same sequential computational complexity and backward error properties as the old algorithms, it is better suited for a pipelined approach. The parallel algorithm for this new chasing method is described, with performance results on the Paragon and nCUBE. Comparison results between the old and the new algorithms are also presented.

     

代数不等式的分拆降维方法与机器证明

利用双变元对称型所构成实线性空间的特点,设计了一种特殊形式的基,基中元素是非负的.如果一个元在此基下的坐标非负,则该元自身也是非负的.于是要证明某个元非负将被归结为证明其在指定基下的坐标非负.通常坐标中的变元数,少于原对称型的变元数,从而起到了降低维数的作用.对非对称型,可通过对称化转换为对称型来处理.根据该方法编制了Maple通用程序Bidecomp.虽此方法并非完备的,但大量的应用实例表明了此种方法证明多项式型不等式的有效性.     

基于吴方法的几何定理证明的恒等式方法

多年来通常认为以吴方法为代表的几何定理机器证明的坐标法给出的证明不可读,或不是图灵意义下的类人解答.其实,只要对吴氏的算法做不多的改进,即将命题的结论多项式表示为其条件多项式的线性组合,就能获得不依赖于理论、算法和大量计算过程的恒等式明证.这样的恒等式可以转化为其他更简明且更有直观几何意义的点几何形式或向量及其他形式,从而获得多种证明方法.这也证明了点几何恒等式明证方法对等式型几何命题的普遍有效性.     

Stable marker-particle method for the Voronoi diagram in a flow field

The Voronoi diagram in a flow field is a tessellation of water surface into regions according to the nearest island in the sense of a “boat-sail distance”, which is a mathematical model of the shortest time for a boat to move from one point to another against the flow of water. The computation of the diagram is not easy, because the equi-distance curves have singularities. To overcome the difficulty, this paper derives a new system of equations that describes the motion of a particle along the shortest path starting at a given point on the boundary of an island, and thus gives a new variant of the marker-particle method. In the proposed method, each particle can be traced independently, and hence the computation can be done stably even though the equi-distance curves have singular points.     

A basis for the right quantum algebra and the “1=q” principle

We construct a basis for the right quantum algebra introduced by Garoufalidis, Lê and Zeilberger and give a method making it possible to go from an algebra subject to commutation relations (without the variable q) to the right quantum algebra by means of an appropriate weight-function. As a consequence, a strong quantum MacMahon Master Theorem is derived. Besides, the algebra of biwords is systematically in use.      

A note on the fundamental theorem of algebra for the octonions

This paper is a revision of a portion of the author's doctoral dissertation submitted to the University of Oregon. Using elementary concepts of K$K$-theory, the Brouwer degree of the power map in the octonions is computed. Later, a proof of a weaker version of the fundamental theorem of algebra for polynomials with coefficients in the octonions is given. As a partial complement, a lower bound to the number of solutions of a homogeneous monomial equation over the octonions is obtained.     

A q-Analog of the Hook Walk Algorithm for Random Young Tableaux

A probabilistic algorithm, called the q-hook walk, is defined. For a given Young diagram, it produces a new one by adding a random box with probabilities, depending on a positive parameter q. The corresponding Markov chain in the space of infinite Young tableaux is closely related to the knot invariant of Jones, constructed via traces of Hecke algebras. For q = 1, the algorithm is essentially the hook walk of Greene, Nijenhuis, and Wilf. The q-hook formula and a q-deformation of Young graph are also considered.S. Kerov: Supported by a grant from CRM (Université de Montréal), during its Operator Algebras year     

A noncommutative Szegö theorem for subdiagonal subalgebras of von Neumann algebras

For almost forty years now the most frustrating open problem regarding the theory of finite maximal subdiagonal algebras has been the question regarding the universal validity of a non-commutative Szegö theorem and Jensen inequality (Arveson, 1967). These two properties are known to be equivalent. Despite extensive efforts by many authors, their validity has to date only been established in some very special cases. In the present note we solve the general problem in the affirmative by proving the universal validity of Szegö's theorem for finite maximal subdiagonal algebras.

     

A proximal point method for the sum of maximal monotone operators

In this paper, we concentrate on the maximal inclusion problem of locating the zeros of the sum of maximal monotone operators in the framework of proximal point method. Such problems arise widely in several applied mathematical fields such as signal and image processing. We define two new maximal monotone operators and characterize the solutions of the considered problem via the zeros of the new operators. The maximal monotonicity and resolvent of both of the defined operators are proved and calculated, respectively. The traditional proximal point algorithm can be therefore applied to the considered maximal inclusion problem, and the convergence is ensured. Furthermore, by exploring the relationship between the proposed method and the generalized forward‐backward splitting algorithm, we point out that this algorithm is essentially the proximal point algorithm when the operator corresponding to the forward step is the zero operator. Copyright © 2013 John Wiley & Sons, Ltd.