一类脉冲微分方程零解的稳定性

本文研究了一类在非固定时刻的脉冲微分方程。利用Lyapunov第二方法,建立了零解为稳定,渐近稳定及不稳定的判别准则。结果表明脉冲可能影响甚至改变相应的无脉冲时的微分方程的稳定性。文中还给出一例说明所得主要结果的应用。     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A CLASS OF SECOND ORDER QUASILINEAR DIFFERENTIAL EQUATIONS WITH DELAY DEPENDING ON THE UNKNOWN FUNCTION

The asymptotic behavior of the solutions to a class of second order quasilinear differential equations is considered. The main results improve and generalize those in Elbert and Kusano [3].     

B值渐近鞅的强弱大数定律

本文用Ｂ值渐近鞅的Ｄｏｏｂ分解，研究了取值于具有ＲＮＰ且对偶可分的Ｂａｎａｃｈ空间Ｂ值渐近鞅的强弱大数定律．给出了一系列结果及其证明     

氢原子第二激发态的多极动态极化率和两体色散系数

基于径向库仑格林函数的积分性质,严格导出了处于第二激发态的氢原子的2l极动态极化率的解析表达式,绘出了处于第二激发态的氢原子的电偶极、电四极和电八极动态极化率随光场频率变化的曲线图.在此基础上,用两种不同的方法计算了H(3s)-H(3s)体系的两体色散系数,两种方法的计算结果相当一致.     

Effect of different solvents on the habit of meta‐nitroaniline single crystals

The habit of the organic non‐linear optical material meta‐nitroaniline (mNA) crystallized from different organic solvents such as acetone, benzene, ethyl acetate, n‐hexane, methanol and toluene were studied. Solubility of mNA in these solvents at various temperatures in the range between 288 and 323 K was determined by gravimetric method. Crystals were grown by restricted evaporation of solvents method. Solutions with different solvents having different chemical nature and polarity yielded crystals with different habits: one‐dimensional needles, two‐dimensional rhombic platelets and three‐dimensional octahedral. In addition, the mNA crystals show unidirectional growth behaviour along its polar [001] direction irrespective of the solvents used. All the grown crystals were found to be orthorhombic system with point group mm2 and space group Pbc2₁ which was confirmed by powder X‐ray diffraction study. Optical transmittance study showed that the grown mNA single crystals have optical transparency in the wavelength range between 430 and 1550 nm. SHG efficiency of the grown mNA crystal was 3 times grater than KDP. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Heuristic Spectral Techniques for the Reduction of Bandwidth and Work-Bound of Sparse Matrices

In this paper, we present heuristic techniques for the reduction of the bandwidth of a sparse matrix as well as for the reduction of the cost of the associated Cholesky factorization. Our algorithms are inspired by the spectral method of Barnard, Pothen and Simon (1995), which derives a permutation for reducing the envelope-size of a sparse matrix by computing the second eigenvector of the associated Laplacian matrix. Two main modifications of that method are proposed and tested. The first is based on the experimental observation that it is often preferable to perform only few iterations of an iterative method converging to the second eigenvector; the second is the introduction of a weighted Laplacian. These simple ideas allow us to obtain a family of spectral methods that have been carefully tested on a set of matrices whose size ranges from few hundred to one million.     

Limit theorems for sums of random exponentials

We study limiting distributions of exponential sums as t→∞, N→∞, where (X_i) are i.i.d. random variables. Two cases are considered: (A) ess sup X_i = 0 and (B) ess sup X_i = ∞. We assume that the function h(x)= -log P{X_i>x} (case B) or h(x) = -log P {X_i>-1/x} (case A) is regularly varying at ∞ with index 1 < ϱ <∞ (case B) or 0 < ϱ < ∞ (case A). The appropriate growth scale of N relative to t is of the form , where the rate function H₀(t) is a certain asymptotic version of the function (case B) or (case A). We have found two critical points, λ₁<λ₂, below which the Law of Large Numbers and the Central Limit Theorem, respectively, break down. For 0 < λ < λ₂, under the slightly stronger condition of normalized regular variation of h we prove that the limit laws are stable, with characteristic exponent α = α (ϱ, λ) ∈ (0,2) and skewness parameter β ≡ 1.Research supported in part by the DFG grants 436 RUS 113/534 and 436 RUS 113/722.Mathematics Subject Classification (2000): 60G50, 60F05, 60E07     

三点边值问题正解的存在性

给出了以下边值问题正解存在的充分条件,(p(t)u′(t)′ α(t)f(t,u(t))=r(t) t∈(0,1) u(0)=0,au(η)=u(l)其中0＜η＜1，α＞0，应用锥上的不动点定理证明在不同的假设条件下，以上边值问题仅有唯一正解，或有两个正解，或无数个正解．     

de Sitter空间中具平行平均曲率向量的完备类空子流形

本文证明了ｄｅＳｉｔｔｅｒ空间中具平行平均曲率向量的完备类空子流形在Ｈ２〉Ｃ时其第二基本形式模长平方是上有界的，从而推广了Ｕ－ＨａｎｇＫＩ＾（４）及Ｑ．Ｍ．Ｃｈｅｎｇ＾（３）中的结果。