广义中心阶乘数与高阶Nrlund Euler-Bernoulli多项式

本文讨论了广义中心阶乘数的性质,刻画了广义中心阶乘数与高阶Ｅｕｌｅｒ－Ｂｅｒｎｏｕｌｌｉ数和多项式的关系,建立了一些包含 Ｎｏｒｌｕｎｄ Ｅｕｌｅｒ－Ｂｅｒｎｏｕｌｌｉ多项式恒等式,推广了 Ｄｉｌｃｈｅｒ Ｋ．［１］,Ｚｈａｎｇ Ｗｅｎｐｅｎｇ［２］和 Ｚｅｉｔｌｉｎ　Ｄａｖｉｄ［３］的结果．     

Localization of the first zero of the Dedekind zeta function

Using Weil's explicit formula, we propose a method to compute low zeros of the Dedekind zeta function. As an application of this method, we compute the first zero of the Dedekind zeta function associated to totally complex fields of degree less than or equal to 30 having the smallest known discriminant.

     

MOMENT GENERATING FUNCTIONS OF RANDOM VARIABLES AND ASYMPTOTIC BEHAVIOUR FOR GENERALIZED FELLER OPERATORS

1. Introduction and NotationsThe generalized Feller operators which include many famous operators, such ajsBernstein, Szasz-Mirakjan, BaskakoV, Meyer--K5nig and Zeller operators, can be constructed by making use of the probabilistic method. In the paper [1][2], Xu JihuaPr(--lvjdetl a general scheme f(,r its construction, and Zhao Jillghui showed that theFeller type operators are of good approximations f'or unbounded functions.Our purpose is to present representation of moment generating …     

Solutions with time-dependent singular sets for the heat equation with absorption

We consider the heat equation with a superlinear absorption term ${?}_{t}u?\mathrm{\Delta }u=?u^p$ in ${\mathbb{R}}^n$ and study the existence of nonnegative solutions with an m-dimensional time-dependent singular set, where $n?m\ge 3$. We prove that if $1<p<(n?m)/(n?m?2)$, then there are two types of singular solutions. Moreover, we show the uniqueness of the solutions and specify the exact behavior of the solutions near the singular set.     

L^2[a,\infty)上高阶 Sturm-Liouville 算子下半有界性与谱

采用泛函分析与不等式渐近估计的方法,根据微分算子系数的特点,研究了高阶Sturm-Liouville微分算子下半有界性并得到其为下半有界的一些判定准则,同时给出了其下界的估计.这些结果对研究微分算子的谱是有益的.     

高阶亚线性Duffing方程的周期解

在本文中，二阶亚线性Ｄｕｆｆｉｎｇ方程周期解存在的结果被推广到高阶Ｄｕｆｆｉｎｇ方：ｘ＾（２ｎ）＋ｇ（ｘ）＝ｐ（ｔ）＝ｐ（ｔ＋２π）（ｎ≥１）和ｘ＾（２ｎ＋１）＋ｇ（ｘ）－ｐ（ｔ）＝ｐ（ｔ＋２π）。     

Higher harmonic thermal wave detection in thermoreflectance microscopy with combined electrical and optical heating

Insulating lines and channels prepared by focused ion beam implantation on SIMOX wafers have been investigated by thermally modulated optical reflectance microscopy using optical and electrical excitation. Continuous hot lines and hot spots can be visualized by modulated electrical heating, whereas insulating lines forming channels can be imaged only with simultaneous optical and electrical excitation. Three different schemes have been investigated for the combined excitation: (i) optical modulation with additional DC voltage, (ii) optical and electrical pumps modulated at the same frequency with the detection effected at higher harmonics and (iii) two different modulation frequencies used for optical and electrical excitation with the detection effected at sum and difference frequencies. When detecting at higher frequencies, best contrast for the observation of the insulating lines adjacent to a channel is achieved by recording the modulated reflectance signal at the fourth harmonic 4f where f is the modulation frequency of the optical and electrical pump. The observed contrast enhancement of the double excited thermoreflectance signal is found to be mainly of a thermal origin.     

Uniqueness properties of higher order dispersive equations

In this paper we study unique continuation properties of solutions to higher (fifth) order nonlinear dispersive models. The aim is to show that if the difference of two solutions of the equations, u₁−u₂, decays sufficiently fast at infinity at two different times, then u₁≡u₂.     

Positive solutions to a multi-point higher order boundary value problem

The authors consider a higher order multi-point boundary value problem. Some existence and nonexistence results for positive solutions of the problem are obtained by using Krasnosel'skii's fixed point theorem. Examples are included to illustrate the results.