Boundedness of Solutions in Asymmetric Oscillations via the Twist Theorem

In this paper we consider the boundedness of all the solutions for the equation x″ + ax ⁺−bx ⁻ = f(t) is a smooth 2π-periodic function, a and b are positive constants (a≠b). Received November 27, 1998, Accepted October 15, 1999     

A Quasi Fixed-Point Theorem for a Product of u.s.c. or o.l.s. Correspondences with an Economic Application

In the first place, we present a quasi fixed-point theorem for a correspondence defined on some infinite-dimensional locally convex topological vector space such that some variables have open lower sections and the other ones are upper semicontinuous.In the second place, we propose a direct application of the quasi fixed-point result in an economic model. More precisely, we prove a nonemptiness result of the core of an exchange economy with asymmetric information, a continuum of states and a finite number of commodities.     

Barth type vanishing theorem

In this paper we give a vanishing result for cohomology groups of symmetric powers of the co-normal bundle of a non-degenerate smooth subvariety X of projective space, then we use this theorem to give a Barth type vanishing theorem.      

Anisotropic norms of dirichlet kernels and some other trigonometric polynomials

In the paper new estimates of anisotropic norms for trigonometric polynomials are obtained. Translated fromMatematischeskie Zametki, Vol. 67, No. 5, pp. 686–701, May, 2000.     

Non-collision periodic solutions of second order singular dynamical systems

We study the existence of non-collision periodic solutions for second order singular dynamical systems. The repulsive case and the attractive case are dealt with using a unified topological approach. The proof is based on a well-known fixed point theorem for completely continuous operators, involving a new type of cone. We do not need to consider so-called strong force conditions. Moreover, for the repulsive case, the critical case can be covered. Recent results in the literature, even in the scalar case, are complemented, generalized and improved.     

A limit theorem for products of free unitary operators

This paper establishes necessary and sufficient conditions for the sequence of products of freely independent unitary operators to converge in distribution to the uniform law on the unit circle. The author would like to express his gratitude to Diana Bloom for her help with editing, and to Professor Raghu Varadhan for useful discussions.     

A handy proof of Gay's theorem

In 1979, Gay proved that Broyden's methods, when used for n‐square linear systems, terminate in at most 2n iterations (SIAM J. Numer. Anal. 1979; 16 :623–630). Also, the ABS methods were introduced in 1984 (Numer. Math. 1984; 45 :1361–1376). In this paper we show another (handy) proof of Gay's theorem by these algorithms. Copyright © 2008 John Wiley & Sons, Ltd.     

Kolmogorov’s 1954 paper on nearly-integrable Hamiltonian systems

Following closely Kolmogorov’s original paper [1], we give a complete proof of his celebrated Theorem on perturbations of integrable Hamiltonian systems by including few “straightforward” estimates.      

积分学第一中值定理“中间点”的渐近性研究新进展

对积分学第一中值定理的中间点当区间长度趋于零时的渐近性研究.新得到的结果不仅包含了过去若干已有结果,而且对涉及函数f(x),g(x)要求的条件几乎就是中值定理的,一个为连续,一个为可积不变号.     

Banach空间中N阶脉冲积分-微分方程边值问题的解

运用Monch不动点定理，获得了Banach空间中一类N阶非线性混合型脉冲积分-微分方程边值问题解的存在性．最后给出一个三阶无穷脉冲积分-微分方程边值问题的例子来说明文中所给的条件是合理的．