A new summation identity for the Srivastava-Singhal polynomials

In his recent investigations involving differential operators for some generalizations of the classical Laguerre polynomials, H. Bavinck [J. Phys. A Math. Gen. 29 (1996) L277-L279] encountered and proved a certain summation identity for the classical Laguerre polynomials. The main object of this sequel to Bavinck's work is to prove a generalization of this summation identity for the Srivastava-Singhal polynomials. The demonstration, which is presented here in the general case, differs markedly from the earlier proof given for the known special case. It is also indicated how the general summation identity can be applied to derive the corresponding result for one class of the Konhauser biorthogonal polynomials.     

Qualitative Theory and Identification of Dynamic System with One Degree of Freedom

Dynamic systems described by nonlinear differential equations of the second order are studied. It is assumed that certain preliminary information on the dissipative or elastic characteristics of systems is known. A new approach is demonstrated to obtaining full information on unknown or partially known characteristics of a system from measurements of not only displacements but also velocities and accelerations __________ Published in Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 139–143, June 2005.     

A general Hsu-Robbins-Erdős Type estimate of tail probabilities of sums of independent identically distributed random variables

Periodica Mathematica Hungarica - Let X 1,X 2,... be a sequence of independent and identically distributed random variables, and put % MATHTYPE!MTEF!2!1!+-%...     

Maximal σ‐polynomials of connected 3‐chromatic graphs

In the set of graphs of order n and chromatic number k the following partial order relation is defined. One says that a graph G is less than a graph H if c_i(G) ≤ c_i(H) holds for every i, k ≤ i ≤ n and at least one inequality is strict, where c_i(G) denotes the number of i‐color partitions of G. In this paper the first ? n/2 ? levels of the diagram of the partially ordered set of connected 3‐chromatic graphs of order n are described. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 210–222, 2003     

PERIODIC SOLUTIONS OF PLANAR SYSTEM WITH SIX DELAYS

In this paper we obtain some sufficient conditions for the existence of non-constant periodic solutions of the following planar system with six delaysOur approach is based on the continuation theorem of the coincidence degree.     

关于"太阳在银河系中所受引力与到银心距离r的关系"的讨论

讨论了银道面内的引力场强分布和太阳在银河系中所受引力与到银心距离r的关系，指出引力场强g并不是与r的平方成反比，这是由于银河系的大小和形状不能忽略造成的．强调了万有引力定律的适用条件．     

NOTE ON THE OSCILLATION OF THE SOLUTION FOR GENERALIZED LIENARD EQUATIONS

Ｃｏｎｓｉｄｅｒｉｎｇｓｙｓｔｅｍ：ｘ＝φ（ｙ）－Ｆ（ｘ），ｙ＝－ｇ（ｘ）｛（Ｅ）ｉｎｗｈｉｃｈＦ（ｘ）＝∫ｘ０ｆ（ｔ）ｄｔ，ｆ（ｘ），ｇ（ｘ），φ（ｙ）ａｒｅｃｏｎｔｉｎｕｏｕｓ，ａｎｄｓａｔｉｓｆｙｔｈｅｃｏｎｄｉｔｉｏｎｓｗｈｉｃｈｅｎｓｕｒ...     

具有两台专用机,两台通用机的Q4／／Cmax问题的近似算法

本文讨论具有两台专用机、两台通用机的两组工件的同种类平行机的Q4／／Cmax问题，对这类特殊的排序问题，提出一种启发式算法，得到了最差情况下性能指标的严格的界．     

灰色模型的最优化及其参数的直接求法

基于灰色模型的内涵表达式和白化方程响应式均为等比级数的观点,提出了一种不用求ago值、均值,不涉及灰色微分方程,白化微分方程概念,直接求灰色模型参数a,c的方法,通过此方法建立的新模型不仅从理论上可保证是在满足给定评价标准为模拟绝对误差平方和最小(或模拟相对误差平方和最小)、给定精度条件下的最优化模型,从而结束了灰色模型只有更优,没有最优的历史.并从理论上证明了新模型具有白化指数律重合性、白化系数律重合性,伸缩变换一致性.最后通过实例编程验证该方法具有可操作性,且预测精度高,效果好.     

Almost-sure path properties of fractional Brownian sheet

The almost sure sample function behavior of the vector-valued fractional Brownian sheet is investigated. In particular, the global and the local moduli of continuity of the sample functions are studied. These results give precise information about the continuity and the oscillation behavior of the sample functions.