Extension of Hilbert's inequality

In this paper we make some further extensions of discrete Hilbert's inequality by using Euler-Maclaurin summation formula. We give the improvements of some previously obtained results and also compare our results with some previously known from the literature.     

Stirling公式的一个推广

关于n!的S tirling渐近式,无论在理论上或者实际上,都有重要应用.应用Eu ler-M aclau lrin求和公式及Γ函数的性质,推导出一般等差级数连乘积并有余项估计式的类似表达式.     

A note on the gradient of heat semigroup

A new representation for the gradient of heat semigroup on Riemannian manifold is given by using the integration by parts formula on Wiener space, which reflects in some sense the asymptotic property of Brownian motion.     

Reliability formula &; limit law of the failure time of “<Emphasis Type="Italic">m</Emphasis>-consecutive-<Emphasis Type="Italic">k</Emphasis>-out-of-<Emphasis Type="Italic">n</Emphasis>:<Emphasis Type="Italic">F</Emphasis> system”

An “m-consecutive-k-out-of-n:F system” consists of n components ordered on a line; the system fails if and only if there are at least m nonoverlapping runs of k consecutive failed components. In this paper, we give a recursive formula to compute the reliability of such a system. Thereafter, we state two asymptotic results concerning the failure time Z _n of the system. The first result concerns a limit theorem for Z _n when the failure times of components are not necessarily with identical failure distributions. In the second one, we prove that, for an arbitrary common failure distribution of components, the limit system failure distribution is always of the Poisson class.      

利用Lebesgue-Stieljes积分证明Jordan公式

利用Lebesgue-Stieljes积分,结合示性函数的有关性质证明了著名的Jordan公式和测度上下极限不等式.     

Note on the Norm Convergence of the Unitary Trotter Product Formula

We discuss when the unitary Trotter product formula converges in operator norm and apply the results obtained to the unitary group generated by the Dirac operator and the relativistic Schrödinger operator with suitable potentials.     

Exact waiting time and queue size distributions for equilibrium <Emphasis Type="Italic">M</Emphasis>/<Emphasis Type="Italic">G</Emphasis>/1 queues with Pareto service

This paper solves the problem of finding exact formulas for the waiting time cdf and queue length distribution of first-in-first-out M/G/1 queues in equilibrium with Pareto service. The formulas derived are new and are obtained by directly inverting the relevant Pollaczek-Khinchin formula and involve single integrals of non-oscillating real valued functions along the positive real line. Tables of waiting time and queue length probabilities are provided for certain parameter values under heavy traffic conditions.      

On the Schrödinger Equation with Potentials which are Laplace Transforms of Measures

We construct a pointwise solution for the time dependent Schrödinger equation on R^d with potentials and initial conditions which can grow exponentially at infinity and belong to the class of smooth Laplace transforms of complex measures on R^d. The methods used are both analytic and probabilistic and the result can be looked upon as an extension of rigorously defined Feynman path integrals to the case of potentials which can strongly grow at infinity. An appendix with the calculation of some Wiener integrals is also presented.     

X射线荧光光谱分析检出限计算公式

本文根据测量的统计误差理论,对XRFS分析中不同背景和基体校正方式下的检出限述一进行讨论并导出了相应的计算公式,所得结论可作为选择微量元素XRFS分析的背景和基体校正方法以及拟定最佳实验条件以获得最低检出限的理论依据。