随机环境中的生死链的灭绝概率及平均吸收时间的计算

本文将［２］中所讨论的ＢＤＩＲＥＺ＿ｎｎ≥Ｏ的状态空间｛０，１，２，…，Ｎ｝推广到Ｚ～＋＝｛０，１，２，…｝上，利用马氏链的理论，得出了关于灭绝概率及平均吸收时间的向量差分方程     

复等位基因遗传疾病的数学模型

运用马尔可夫链的理论，建立复等位基因遗传疾病的数学模型，其结果与一般临床观察经验相符合，利用这一模型可以予测任何一种此类疾病的发病规律。     

基于超材料的雷达吸波材料研究进展

雷达吸波材料能够有效地抑制透射波和反射波,因而被广泛应用于隐身、电磁屏蔽和兼容以及无线通信等领域。受制于材料的电磁频散特性,传统吸波材料的宽带低频吸波性能难以进一步提高。近年来,随着超材料结构设计的不断发展,基于超材料构架设计实现的宽带电磁吸波,由于具有更加灵活的电磁调控能力,因而在其电磁性能提升方面具有更大拓展空间。围绕雷达吸波超材料的最新研究进展,结合电磁吸波超材料的发展背景、设计原理和性能表征方面的内容,着重介绍了基于多谐振叠加吸波结构、超材料与传统材料复合吸波结构、三维阵列吸波结构以及人工表面等离激元吸波结构设计的宽带雷达吸波超材料,并对于未来雷达吸波超材料的发展趋势做进一步展望。     

Algebraic methods applied to the study of energy transfer in anharmonic systems

We make use of two different methodologies to study the transition probabilities in a molecular anharmonic system in the presence of an external perturbation. For the first method, we use a series expansion of the displacement coordinate keeping up to fourth order terms; for the second method we use a deformed algebra to approximate the anharmonic Hamiltonian via a harmonic oscillator's Hamiltonian written in terms of deformed operators. We evaluate vibrational transition probabilities as a function of the collision energy and compare the results obtained with the two approaches.     

Discrete binning: correspondence limit consistent analysis of classical probabilities using faux angular momenta and multi-polar harmonic moments to give ‘quantum-like’ probabilities

This paper develops discrete binning (DB) for N_i slices for classical probability functions for an arbitrary number of classical continuous variables, x_i , where 0 ≤?x_i ≤?1 or ?1 ≤?x_i ≤?1. Faux angular momenta, j_i , are introduced where 2j_i +?1 =?N_i , and the discrete probabilities for the various |j_im_i ? are calculated with a generalisation of the theory of Anderson and Aquilanti. Discrete probabilities are calculated from Legendre moments of the classical intensities with Clebsch–Gordan moments. The m_i may represent vibrational quanta, rotational angular momenta, or discrete values of the impact parameter, scattering angles and other variables. DB directly yields probabilities for different m_i , but in the correspondence limit (large j_i ) the discrete probabilities correspond to classical probabilities, I({x _{m i} }), at known discrete values {x _{m i} }. DB probabilities sum to unity, but some may be negative. Since the Clebsch–Gordan coefficients appropriate for this work are actually Gram (discrete Chebyshev) polynomials, DB is equivalent to compression and/or smoothing of data using Gram polynomials. For large N_i , DB and histogram binning (HB) provide equivalent probabilities and statistical errors. However, smoothing can often reduce the statistical errors for DB probabilities. DB is related to Legendre moment binning (LMB), but DB guides the most consistent implementation of LMB. The rule of three is introduced to provide finer resolution for DB, HB, and LMB analysis. This also leads to fractional slice binning (FSB), which is equivalent to Gaussian binning. The paper presents one-, two-, and three-dimensional examples, and spectroscopic plots are very useful for summarising the results.     

Approximate tolerance limits for Zipf–Mandelbrot distributions

Zipf–Mandelbrot distributions are commonly used to model natural phenomena where the frequency of an event’s occurrence is inversely proportional to its rank based on that frequency of occurrence. This discrete distribution typically exhibits a large number of rare events; however, it may be of interest to obtain reasonable limits that bound the majority of the number of different events. We propose the use of statistical tolerance limits as a way to quantify such a bound. The tolerance limits are constructed using Wald confidence limits for the Zipf–Mandelbrot parameters and are shown through a simulation study to have coverage probabilities near the nominal levels. We also calculate Zipf–Mandelbrot tolerance limits for two real datasets and discuss the associated computer code developed for the R programming language.     

ON THE SPH-DISTRIBUTION CLASS

Following up Neuts‘ idea, the SPH-distribution class associated with bounded Q matrices for infinite Markov chains is defined. The main result in this paper is to characterize the SPH class through the derivatives of the distribution functions. Based on the characterization theorem, closure properties, the expansion, uniform approximation,and the matrix representations of the SPH class are also discussed by the derivatives of the distribution functions at origin.Key words Phase type distribution, absorbing Markov chain, operator theory, SPH- distribution, properties     

A heavy traffic limit theorem for a class of open queueing networks with finite buffers

We consider a queueing network of d single server stations. Each station has a finite capacity waiting buffer, and all customers served at a station are homogeneous in terms of service requirements and routing. The routing is assumed to be deterministic and hence feedforward. A server stops working when the downstream buffer is full. We show that a properly normalized d-dimensional queue length process converges in distribution to a fd-dimensional semimartingale reflecting Brownian motion (RBM) in a d-dimensional box under a heavy traffic condition. The conventional continuous mapping approach does not apply here because the solution to our Skorohod problem may not be unique. Our proof relies heavily on a uniform oscillation result for solutions to a family of Skorohod problems. The oscillation result is proved in a general form that may be of independent interest. It has the potential to be used as an important ingredient in establishing heavy traffic limit theorems for general finite buffer networks. This revised version was published online in June 2006 with corrections to the Cover Date.     

汽车减振器连杆镀铬层的吸氢与耐腐蚀性能

针对汽车减振器连杆高效镀铬工艺在高电流密度条件下因镀层吸氢量大而引起的耐腐蚀性能差的问题，研究了电流密度与镀层组织及耐腐蚀性能的关系．动用扩散理论得到了电流密度与镀层氢含量的关系曲线．试验证明，在J＝58A／dm^2的工艺条件下镀层含氢量小，吸氢速度平缓，此时的镀层耐腐蚀性最好．研究结果对汽车减振器连杆电镀生产工艺的改进提供了理论依据，具有较高的工程实用价值．