On the real parts of eigenvalues of a matrix

We apply a theorem of K_y Fan on eigenvalue location to give a new proof of a result of K. J. Palmer concerning the real parts of the eigenvalues of a matrix.     

A new proof of the equivalence of injectivity and hyperfiniteness for factors on a separable Hilbert space

In 1975 A. Connes proved the fundamental result that injective factors on a separable Hilbert space are hyperfinite. In this paper a new proof of this result is presented in which the most technical parts of Connes proof are avoided. Particularly the proof does not rely on automorphism group theory. The starting point in this approach is Wassermann's simple proof of injective ? semidiscrete together with Choi and Effros' characterization of semidiscrete von Neumann algebras as those von Neumann algebras N for which the identity map on N has an approximate completely positive factorization through n × n-matrices.     

一个高等数学命题的证法探析

从探究解题方法方面讨论如何学习高等数学,以求培养学生分析问题的能力.对一条关于周期函数积分的命题给出新的证法,揭示出插入点的含义和周期函数积分的本质,弥补通常证法只侧重凑积分限技巧的不足.     

On a class of discontinuous vector-valued functions and the associated quasi-variational inequalities

We study in detail a class of discontinuous vector-valued functions defined on a closed convex subset of Rn, which was introduced by B. Ricceri [7] and which is very useful in the theory of variational inequalities. The results are used to give a new proof for the existence theorem due to P. Cubiotti [3]. The proof allows us to have a better understanding of quasi-variational inequalities associated with the abovementioned class of functions.     

New proof of a characterization of geodetic graphs

In [3], the present author used a binary operation as a tool for characterizing geodetic graphs. In this paper a new proof of the main result of the paper cited above is presented. The new proof is shorter and simpler.     

关于一维Moran集Hausdorff维数的一个新证明和 一个新结果

利用分形儿何中的技巧给出了关于一维Moran集Hausdorff维数的一个新证明和一个新结果,这可看做是对原有结果的一个有益补充.     

On a local uniqueness result for the inverse Sturm-Liouville problem

A new and fairly elementary proof is given of the result by B. Simon [S], that the potential in a Sturm-Liouville operator is determined by the asymptotics of the associatedm-function near −∞. The proof given is based on relations between the classical transformation operators and them-function.     

关于一类HJ方程的Godunov通量的一点注记

本文对[1]中关于一类HJ方程的Godunov通量的命题作出改进,并给出新的证明.     

An identity of Andrews and a new method for the Riordan array proof of combinatorial identities

We consider an identity relating Fibonacci numbers to Pascal's triangle discovered by G.E. Andrews. Several authors provided proofs of this identity, most of them rather involved or else relying on sophisticated number theoretical arguments. We present a new proof, quite simple and based on a Riordan array argument. The main point of the proof is the construction of a new Riordan array from a given Riordan array, by the elimination of elements. We extend the method and as an application we obtain other identities, some of which are new. An important feature of our construction is that it establishes a nice connection between the generating function of the A-sequence of a certain class of Riordan arrays and hypergeometric functions.     

On Optimal Smoothness of the Green Function for the Complement of a Cantor-Type Set

We give a new streamlined proof of a recent result by Totik concerning the local Holder 1/2 property of the Green function for the complement of a Cantor-type set taken with respect to the extended complex plane. To simplify the proof we find certain families of curves and estimate their moduli. In addition, we extend Totik's theorem to more general Cantor-type sets.     

Homoclinic orbits for a class of second-order Hamiltonian systems without a coercive potential

In this paper we establish some new sufficient conditions on the existence of homoclinic solutions for a class of second-order Hamiltonian systems without a coercive potential. The proof is based on a new critical point theorem in combination with periodic approximation.     

A finite algorithm for the Drazin inverse of a polynomial matrix

Based on Greville's finite algorithm for Drazin inverse of a constant matrix we propose a finite numerical algorithm for the Drazin inverse of polynomial matrices. We also present a new proof for Decell's finite algorithm through Greville's finite algorithm.     

A note on the stability criterion for a class of nonlinear fractional differential systems

This paper is devoted to dealing with a flaw that existed in a recent paper (Zhou et al. 2014). We give a new proof of Th. 3.1 in Zhou et al. (2014), which is a correction of the original proof.     

A sample-path approach to the optimality of echelon order-up-to policies in serial inventory systems

We present a new proof of the optimality of echelon order-up-to policies in serial inventory systems, first proved by Clark and Scarf. Our proof is based on a sample-path analysis as opposed to the original proof based on dynamic programming induction.     

Orbit equivalence of Cantor minimal systems: A survey and a new proof

We give a new proof of the classification, up to topological orbit equivalence, of minimal AF-equivalence relations and minimal actions of the group of integers on the Cantor set. This proof relies heavily on the structure of AF-equivalence relations and the theory of dimension groups; we give a short survey of these topics.     

Newton's solution to the equiangular spiral problem and a new solution using only the equiangular property

This paper is a study of Proposition IX of Book I of Newton's Principia, the problem of determining the centripetal force for an equiangular spiral. In Newton's main proof of this proposition there is an error concerning his reason for the figure SPRQT being “given in kind,” and a very interesting technique of varying things in the neighborhood of a limit. This main proof utilized Newton's formula for the limit of SP²QT²/QR given in Corollary I to Proposition VI of the Principia. Newton also gave an alternate proof which utilized his formula for SY²PV given in Corollary III to Proposition VI. The “given” of Proposition IX was “a spiral PQS, cutting all the radii SP, SQ, &c., in a given angle.” Both the main proof and the alternate proof implicitly depend on the property of the equiangular spiral that the radius of curvature at any point is proportional to the pole distance SP. We here offer a new proof of Newton's proposition which does not depend on this implicit assumption.     

On the correspondence between arithmetic theories and propositional proof systems – a survey

The purpose of this paper is to survey the correspondence between bounded arithmetic and propositional proof systems. In addition, it also contains some new results which have appeared as an extended abstract in the proceedings of the conference TAMC 2008 [11]. Bounded arithmetic is closely related to propositional proof systems; this relation has found many fruitful applications. The aim of this paper is to explain and develop the general correspondence between propositional proof systems and arithmetic theories, as introduced by Krají?ek and Pudlák [46]. Instead of focusing on the relation between particular proof systems and theories, we favour a general axiomatic approach to this correspondence. In the course of the development we particularly highlight the role played by logical closure properties of propositional proof systems, thereby obtaining a characterization of extensions of EF in terms of a simple combination of these closure properties (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

对一道数学分析题证明方法的改进

某文献在处理一道关于高阶导数的应用问题时,反复利用Rolle定理来证明高阶导数为零．考虑到这种做法过于繁琐,遂通过对其证明方法的改进,综合使用Lagrange中值定理和Taylor公式,使该问题的解决获得简化．     

Equality of multiplicities of a Sturm-Liouville eigenvalue

We give a new and unified proof of the fact that for any eigenvalue of a self-adjoint Sturm-Liouville problem with limit-circle end points, its analytic and geometric multiplicities are equal. This proof is geometric in nature and can be generalized to the case of high-order differential equations.     

Stability relative to a set and to the whole space revisited

In [1] P. Seibert suggested without proof some theorems on stability. These theorems involved two new concepts: The first is a local stability of a subset Y of a metric space X on a subset Z of Y. The second is a notion of conditionally attracting set Y ⊆ X on Z ⊆ Y. Using the first of Seibert's concepts, we suggest new theorems and provide the corresponding proofs. However, our theorems are logically independent of those of Seibert. In addition, a proof of a criterion on local stability suggested by Seibert is given.