正相协列乘积和的重对数律与强大数律

证明了强平稳正相协列乘积和的重对数律与不同分布正相协列乘积和的强大数律,指出了部分和服从强大数律但乘积和未必服从强大数律这一事实,并讨论了定理2中一个条件的必要性．     

Synthesis, crystal structure and nonlinear optical property of Rb3V5O14

The new nonlinear optical crystal Rb₃V₅O₁₄ has been synthesized by solid state reaction and characterized by single-crystal X-ray diffraction, IR and thermogravimetric analysis. The crystal Rb₃V₅O₁₄ crystallizes in the trigonal system with space P31m (No. 157), a=b=8.7134(12) Å, c=5.2807(11) Å and α=90°, β=90°, γ=120°, Z=1, ρ=3.516 g/cm³. It is a layered structure that is very flat and strongly parallel to c. The V₅O₁₄ layer structure consists of corner-linked square and triangular pyramids. The layers are separated by Rb⁺ ions, which fit equally well on the V₅O₁₄ layer. The Kurtz powder SHG measurement, using 1064 nm radiation, showed that the second-harmonic generation efficiency of Rb₃V₅O₁₄ is about two times that of KDP.     

带不同分布增量的随机和的局部渐近性

在Asmussen,Foss and Korshunov(J.Theoretical Probab.,2003,16(2):489-518)的基础上,讨论了支撑在(-∞,∞)上的不同分布的卷积的封闭性及带上述不同分布增量的局部渐近性.上述分布包括了常见的轻尾分布和重尾分布.     

Asymptotics of convolution with the semi-regular-variation tail and its application to risk

In this paper, according to a certain criterion, we divide the exponential distribution class into some subclasses. One of them is closely related to the regular-variation-tailed distribution class, and is called the semi-regular-variation-tailed distribution class. The new class possesses several nice properties, although distributions in it are not convolution equivalent. We give the precise tail asymptotic expression of convolutions of these distributions, and prove that the class is closed under convolution. In addition, we do not need to require the corresponding random variables to be identically distributed. Finally, we apply these results to a discrete time risk model with stochastic returns, and obtain the precise asymptotic estimation of the finite time ruin probability.     

Tail behavior of the product of two dependent random variables with applications to risk theory

Let the random vector (X,Y) follow a bivariate Sarmanov distribution, where X is real-valued and Y is nonnegative. In this paper we investigate the impact of such a dependence structure between X and Y on the tail behavior of their product Z?=?XY. When X has a regularly varying tail, we establish an asymptotic formula, which extends Breiman’s theorem. Based on the obtained result, we consider a discrete-time insurance risk model with dependent insurance and financial risks, and derive the asymptotic and uniformly asymptotic behavior for the (in)finite-time ruin probabilities.     

Tail behavior of supremum of a random walk when Cramér’s condition fails

We investigate tail behavior of the supremum of a random walk in the case that Cramer＇s condition fails, namely, the intermediate case and the heavy-tailed ease. When the integrated distribution of the increment of the random walk belongs to the intersection of exponential distribution class and O-subexponential distribution class, under some other suitable conditions, we obtain some asymptotic estimates for the tail probability of the supremum and prove that the distribution of the supremum also belongs to the same distribution class. The obtained results generalize some corresponding results of N. Veraverbeke. Finally, these results are applied to renewal risk model, and asymptotic estimates for the ruin probability are presented.     

Total Synthesis of Bryostatin 8 Using an Organosilane‐Based Strategy

Convergent total synthesis of bryostatin 8 has been accomplished by an organosilane‐based strategy. The C ring is constructed stereoselectively through a geminal bis(silane)‐based [1,5]‐Brook rearrangement, and the B ring through geminal bis(silane)‐based Prins cyclization, thus efficiently joining the northern and southern parts of the molecule.     

(D)族负象限相依随机变量和的精致大偏差

在负象限相依结构下,得到了支撵在(-∞,∞)上的(D)族随机变量非中心化以及中心化部分和的精致大偏差.同时,还在较弱的条件下,得到了相应的中心化随机和的精致大偏差.     

Characteristics of Wave Propagation in The Saturated Thermoelastic Porous Medium

Took into consideration the coupling effect of thermo, hydraulics and mechanics, a set of thermo–hydro-mechanical coupled wave equations for fluid–saturated soil are developed. In these wave equations, the $P_{3}$ -wave in solid phase and $P_{4}$ -wave in fluid phase are coupled into $T$ -wave in fluid–saturated soil by the assumption that the temperature of the solid phase is equal to the temperature of liquid phase at the same position. The dispersion equations for the thermo-elastic wave, which can be degraded to the equations for elastic wave in fluid–saturated soil, are derived from the above equations by introducing four potential functions. Then, these equations are solved numerically. The characteristics of wave phase velocity, attenuation and the effect of thermal expansion, initial temperature and porosity, etc., on phase velocities of $P_{1}$ -, $P_{2}$ -, and $T$ -wave are discussed. As a reference, the characteristics of the propagation of elastic waves in fluid–saturated soil are also studied. The computation results show that (1) the phase velocity of $P_{1}$ -wave obtained by the theory of thermoporoelascity (THM) is faster than that by the theory of poroelasticity (HM); (2) the attenuation of $P_{1}$ -wave obtained by either the theory of THM or HM are consistent; (3) the dissemination characteristics of $P_{2}$ -wave are almost consistent; (4) the phase velocity of $T$ -wave is the slowest among the three compressional waves; and (5) The attenuation versus frequency characteristic of $T$ -wave is similar to that of $P_{2}$ -wave.