常见的代数不等式的证明

给出了利用导数证明常见的几种代数不等式的基本方法,并对J.B.W ilke不等式给出了一个简单的证明     

2011年中考考点复习策略(12)——“图形与证明”

义务教育新课标要求学生掌握基本的图形基础知识与基本技能;了解证明的含义,掌握证明的方法,体会证明的过程;能把所学的公理、定理和基本事实正确运用到证明的过程中,在合情推理的基础上发展初步的演绎推理能力;初步通过观察、实验、归纳、类比、推测获得     

证明不等式的常用技巧

文[1]介绍了证明不等式的四种基本方法，下面将介绍证明不等式的三种常用技巧．     

一个统计基本定理的三种证明方法

本文依托多元正态分布的性质,给出了数理统计中一个基本定理的三种证明方法.     

Gromov引理在高等数学中的应用

将从基于一元函数的一个基本事实的Gromov引理出发,探讨Gromov引理产生的基本想法,并将其应用到高等数学的几个常见不等式的证明上,给出常见不等式的新的证明方法.     

拉普拉斯级数收敛性的一种简单证明

拉普拉斯级数的收敛性有多种证明方法[1 - 3 ] .本文给出了一种非常简单的证明 ,其中主要只用到了正项级数的一个基本定理 .相比之下 ,本文的方法是很容易理解的 ,在工科的教学中采纳比较合适     

Ramanujan循环和的一个注记

推广了Ramanujan循环和,给出了一个基本的证明方法,还给出了一些应用并得到一些新的theta函数恒等式.     

向量积性质的另一种证明

对于向量积的性质以及公式的证明,在高等数学教材中基本上均是利用行列式的性质给出的.本文利用向量之间的基本运算,给出了有关向量积性质的另一种证明方法.     

2013年中考专题复习(15)——“图形与证明”

【考点聚焦】图形与证明是空间与图形的核心内容之一,课标要求学生掌握基本的图形基础知识与基本技能;了解证明的含义,掌握证明的方法,体会证明的过程;能把所学的公理、定理和基本事实正确运用到证明的过程中,在合情推理的基础上发展初步的演绎推理能力;初步通过观察、实验、归纳、类比、推测获得数学猜想,体验数学活动充满着探索性和创造性,感受证明的必要性、证明过程的严谨性及结论的稳定性,它贯穿在整个     

对数不等式的源与流

含对数的不等式常用构造函数求导数的方法证明,但这种方法并不是放之四海而皆准的,有时会遇到导数越求越麻烦的情况,使思路陷入僵局.下面介绍一个基本对数不等式,用它可以证明一些含有对数的不等式问题,以此说明它在解决含对数不等式问题中的优越之处.一、基本对数不等式     

An easy proof of the Rogers-Ramanujan identities

A proof of the Rogers-Ramanujan identities is presented which is brief, elementary, and well motivated; the “easy” proof of whose existence Hardy and Wright had despaired. A multisum generalization of the Rogers-Ramanujan identities is shown to be a simple consequence of this proof.     

Pool resolution is NP-hard to recognize

A pool resolution proof is a dag-like resolution proof which admits a depth-first traversal tree in which no variable is used as a resolution variable twice on any branch. The problem of determining whether a given dag-like resolution proof is a valid pool resolution proof is shown to be NP-complete.     

A constructive proof of the Peter‐Weyl theorem

We present a new and constructive proof of the Peter‐Weyl theorem on the representations of compact groups. We use the Gelfand representation theorem for commutative C*‐algebras to give a proof which may be seen as a direct generalization of Burnside's algorithm [3]. This algorithm computes the characters of a finite group. We use this proof as a basis for a constructive proof in the style of Bishop. In fact, the present theory of compact groups may be seen as a natural continuation in the line of Bishop's work on locally compact, but Abelian, groups [2]. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Probabilistic verification of proofs in calculuses

We define a special kind of a probabilistically checkable proof system, namely, probabilistically checkable proof calculuses (PCP calculuses). A proof in such a calculus can be verified with sufficient confidence by examining only one random path in the proof tree, without reading the whole proof. The verification procedure just checks all applications of inference rules along the path; its running time is assumed to be polynomial in the theorem length. It is shown that the deductive power of PCP calculuses is characterized as follows: (i) the decision problem for theorems is in PSPACE for all PCP calculuses; and (ii) the mentioned problem is PSPACE-hard for some of the calculuses. Bibliography: 14 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 241, 1997, pp. 97–116 This research was supported in part by the Russian Foundation for Basic Research. Translated by E. Ya. Dintsin.     

Proving programs correct: Some techniques and examples

Proving the correctness of computer programs is justified as both advantageous and feasible. The discipline of proof provides a systematic search for errors, and a completed proof gives sufficient reasons why the program must be correct. Feasibility is demonstrated by exhibiting proofs of five pieces of code. Each proof uses one or more of the illustrated proof techniques of case analysis, assertions, mathematical induction, standard prose proof, sectioning and a table of variable value changes. Proofs of other programs, some quite lengthy, are cited to support the claim that the techniques work on programs much larger than the examples of the paper. Hopefully, more programmers will be encouraged to prove programs correct.     

An alternative proof for the derivation of the joint distribution of a set of linear functions of correlated normal random variables

A single proof is given for the joint distribution of a set of linear functions of correlated normal random variables. The proof avoids using the characteristic function and does not require the transformation matrix to be non-singular.     

Rotational symmetry and properties of the ancient solutions of Ricci flow on surfaces

We give a simple proof for the rotational symmetry of ancient solutions of Ricci flow on surfaces. As a consequence we obtain a simple proof of some results of Daskalopoulos, Hamilton and Sesum on the a priori estimates for the ancient solutions of Ricci flow on surfaces. We also give a simple proof for the solution to be a Rosenau solution under some mild conditions on the solutions of Ricci flow on surfaces.     

The standard proof,the elegant proof,and the proof without words of tasks in geometry,and their dynamic investigation

Solution of problems in mathematics, and in particular in the field of Euclidean geometry is in many senses a form of artisanship that can be developed so that in certain cases brief and unexpected solutions may be obtained, which would bring out aesthetically pleasing mathematical traits. We present four geometric tasks for which different proofs are given under the headings: standard proof, elegant proof, and the proof without words. The solutions were obtained through a combination of mathematical tools and by dynamic investigation of the geometrical properties.     

Class numbers of cyclic 2-extensions and Gross conjecture over Q

The Gross conjecture over Q was first claimed by Aoki in 1991.However,the original proof contains too many mistakes and false claims to be considered as a serious proof.This paper is an attempt to find a sound proof of the Gross conjecture under the outline of Aoki.We reduce the conjecture to an elementary conjecture concerning the class numbers of cyclic 2-extensions of Q.