Turán type inequalities for hypergeometric functions

In this note our aim is to establish a Turán type inequality for Gaussian hypergeometric functions. This result completes the earlier result that G. Gasper proved for Jacobi polynomials. Moreover, at the end of this note we present some open problems.

     

An oscillation criterion for forced half-linear differential equations with mixed nonlinearities

In this note, a new oscillation criterion for forced half-linear second order differential equations with mixed nonlinearities is obtained by using a generalized Riccati transformation. The result of this note generalizes and improves some previous results in the literature.     

Improved Optimum Radius for Robust Stability of Schur Polynomials

An approach based on the Rouché theorem was introduced in the literature to compute the optimum radius for robust stability of Schur polynomials. Later an attempt was made to improve the result, but it was shown to be incorrect. The purpose of this note is to show that an improved optimum radius still can be obtained by modifying the proposed method. The result of this note can be easily extended to the multidimensional cases.     

Anwendungen der De Rhamschen Zerlegung auf Probleme der lokalen Flächentheorie

Various questions of classical differential geometry lead to the problem of determining all those hypersurfaces of euclidean space for which the covariant derivative of the second fundamental form vanishes identically. In the first part of this note, we investigate these hypersurfaces; the result is summarized in the theorem of the opening paragraph, whose proof is based in the decomposition theorem of De Rham (see e.g. [6], pp. 180–186). Applying this result in the second part of the note, we give local characterizations of the Euclidean sphere.     

一类非散度型椭圆方程解的局部W~(2,p)正则性

本文得到了一类具有小BMO系数的非散度型椭圆方程解的局部W2,p(p≥2) 正则性结果,并给出了这个结果的一个应用．     

A continuous version of a result of Du and Hwang

In the proof of Gilbert-Pollak conjecture on the Steiner ratio, a result of Du and Hwang on a minimax problem played an important role. In this note, we prove a continuous version of this result.Support in part by the NSF under grant CCR-9208913     

The nonexistence of colorings

The purpose of this note is to prove the following result about the nonexistence of colorings.     

关于小Bloch函数

给出了一个小Bloch函数的几个等价条件。     

重积分的对称性质

在重积分的计算中,经常要用到对称性质.而限于时间和篇幅,现行大多数教科书上都不加讨论的引用对称性质.这就使初学者感到重积分的对称性质不好掌握.本文通过重积分的变量替换公式,给出重积分对称性质的一个一般定理和两个推论,最后给出一个具体实例.     

First order pseudodifferential operators on the torus: Normal forms,diophantine phenomena and global hypoellipticity

In this note we give an existence result for a boundary value problem for integro-differential equations.     

Addendum to “On Attractors of Multivalued Semiflows and Differential Inclusions” [Set-Valued Anal., 6 (1998), 83–111]

In this note we extend a previous result concerning the existence of global compact attractors for multivalued semiflows in metric spaces.      

Effective stability for slow time-dependent near-integrable Hamiltonians and application

The aim of this note is to prove a result of effective stability for a non-autonomous perturbation of an integrable Hamiltonian system, provided that the perturbation depends slowly on time. Then we use this result to clarify and extend a stability result of Giorgilli and Zehnder for a mechanical system with an arbitrary time-dependent potential.     

A note on: “Relaxation oscillators with exact limit cycles”

In this note we give a family of planar polynomial differential systems with a prescribed hyperbolic limit cycle. This family constitutes a corrected and wider version of an example given in the work [M.A. Abdelkader, Relaxation oscillators with exact limit cycles, J. Math. Anal. Appl. 218 (1998) 308-312]. The result given in this note may be used to construct models of Liénard differential equations exhibiting a desired limit cycle.     

关于Ekeland—Caristi定理的一点注记

1.引言 为适应讨论映象满射性等问题的需要,W.O.Ray和A.M.Walker在[1]中对Ekeland—Caristi定理作了新的推广,获得如下的结果: 定理1.1 设(M,d)为完备距离空间,:M→[0,∞)下半连续,C:[0,∞)→[0,∞)连续,不增,且integral from 0 to ∞(C(s)ds=∞)。x_0∈M为某一固定点。若映象g:M→M满足     

Simple proof of a large deviation result

In this note we prove the large deviation principle for the following process in R:dxt = b(xt, t)dt edwt, t E [0, 1], (1)where the initial point xo is fixed, wt is a Wiener process5 E > 0 is a small parameter whichtends to 0, b(x, t) is a bounded piecewise Lipschitz function of the form(b (x, t), x > 0t,b(xlt)={b--(::t)i x<0jf (2)where e is a smooth curve, bf are two bounded Lipschitz functions on (--oo, co) x [0, oo)satisfyingb--(0t, t) 2 b (0t, t). (3)If (3) is replaced with an opposite …     

On lower bounds for singular values of matrix sums

It is pointed out by a counterexample that the result on lower bounds for the absolute singular values of sum of matrices given in [1] is not valid. Moreover, in this note a new result is established on such lower bounds.     

A note on the method of multipliers

Implementation of the penalty function method for constrained optimization poses numerical difficulties as the penalty parameter increases. To offset this problem, one often resorts to Newton's method. In this note, working in the context of the penalty function method, we establish an intimate connection between the second-order updating formulas which result from Newton's method on the primal problem and Newton's method on the dual problem.The author wishes to thank Professor R. A. Tapia for his careful review of this note. He has contributed significantly to its content through several crucial observations.     

A note on multi-point boundary value problems

Multi-point boundary value problems for a second-order ordinary differential equation are considered in this note. An existence result is obtained with the help of coincidence degree theory.     

On an inequality for spectral radius

In this note, we first extend and then give a related result to an inequality involing the spectral radius of nonnegative matrices that recently appcared in the literature.     

An improvement of the Kolmogorov–Riesz compactness theorem

The purpose of this short note is to provide a new and very short proof of a result by Sudakov (1957), offering an important improvement of the classical result by Kolmogorov–Riesz on compact subsets of Lebesgue spaces.