A note on the gambling team method

Gerber and Li (1981) formulated, using a Markov chain embedding, a system of equations that describes relations between generating functions of waiting time distributions for occurrences of patterns in a sequence of independent repeated experiments when the initial outcomes of the process are known. We show how this system of equations can be obtained by using the classical gambling team technique. We also present a form of solution of the system and give an example showing how first results of trials influence the probabilities that a chosen pattern precedes the remaining ones in a realization of the process.     

A regularity criterion for 2D MHD flows with horizontal dissipation and horizontal magnetic diffusion

This paper concerns the conditional global regularity of incompressible MHD equations with horizontal dissipation and horizontal magnetic diffusion in two dimension. When only horizontal dissipation and horizontal magnetic diffusion are present, there is no control on the vertical derivatives of velocity field and magnetic field, which is the main difficulty to establish the global regularity. In this paper, we establish a global regularity criterion in terms of one entry of the velocity gradient tensor or one entry of the magnetic field gradient tensor, which extends the recent work (Fan and Ozawa, 2014).     

半马氏环境连续时间马氏决策过程：平均准则

本文讨论半马氏环境连续时间马氏决策过程中的平均准则．首先讨论了半马氏报酬过程中的逼近问题，进而讨论平均目标函数逼近问题。     

Statistical testing of optimality conditions in multiresponse simulation-based optimization

This article studies simulation-based optimization with multiple outputs. It assumes that the simulation model has one random objective function and must satisfy given constraints on the other random outputs. It presents a statistical procedure for testing whether a specific input combination (proposed by some optimization heuristic) satisfies the Karush–Kuhn–Tucker (KKT) first-order optimality conditions. The article focuses on “expensive” simulations, which have small sample sizes. The article applies the classic t test to check whether the specific input combination is feasible, and whether any constraints are binding; next, it applies bootstrapping (resampling) to test the estimated gradients in the KKT conditions. The new methodology is applied to three examples, which gives encouraging empirical results.     

整机电子产品企业标准制定刍议

整机电子产品企业标准是企业产品的法律依据。从技术、工艺、安全、检验等参数进行规定,能反映产品性能、技术水平,较全面分析引用标准;采用强制标准、强调采用国际标准等方面来制定企业标准。     

Local Thermodynamic Equilibrium in Laser-Induced Breakdown Spectroscopy: Beyond the McWhirter criterion

In the Laser-Induced Breakdown Spectroscopy (LIBS) technique, the existence of Local Thermodynamic Equilibrium (LTE) is the essential requisite for meaningful application of theoretical Boltzmann–Maxwell and Saha–Eggert expressions that relate fundamental plasma parameters and concentration of analyte species. The most popular criterion reported in the literature dealing with plasma diagnostics, and usually invoked as a proof of the existence of LTE in the plasma, is the McWhirter criterion [R.W.P. McWhirter, in: Eds. R.H. Huddlestone, S.L. Leonard, Plasma Diagnostic Techniques, Academic Press, New York, 1965, pp. 201–264]. However, as pointed out in several papers, this criterion is known to be a necessary but not a sufficient condition to insure LTE. The considerations reported here are meant to briefly review the theoretical analysis underlying the concept of thermodynamic equilibrium and the derivation of the McWhirter criterion, and to critically discuss its application to a transient and non-homogeneous plasma, like that created by a laser pulse on solid targets. Specific examples are given of theoretical expressions involving relaxation times and diffusion coefficients, as well as a discussion of different experimental approaches involving space and time-resolved measurements that could be used to complement a positive result of the calculation of the minimum electron number density required for LTE using the McWhirter formula. It is argued that these approaches will allow a more complete assessment of the existence of LTE and therefore permit a better quantitative result. It is suggested that the mere use of the McWhirter criterion to assess the existence of LTE in laser-induced plasmas should be discontinued.     

A Regularity Criterion for Semigroup Rings

An analogue of the Kunz–Frobenius criterion for the regularity of a local ring in a positive characteristic is established for general commutative semigroup rings.     

Absorbing boundary conditions for electromagnetic wave propagation

In this paper, the theoretical perfectly absorbing boundary condition on the boundary of a half-space domain is developed for the Maxwell system by considering the system as a whole instead of considering each component of the electromagnetic fields individually. This boundary condition allows any wave motion generated within the domain to pass through the boundary of the domain without generating any reflections back into the interior. By approximating this theoretical boundary condition a class of local absorbing boundary conditions for the Maxwell system can be constructed. Well-posedness in the sense of Kreiss of the Maxwell system with each of these local absorbing boundary conditions is established, and the reflection coefficients are computed as a plane wave strikes the artificial boundary. Numerical experiments are also provided to show the performance of these local absorbing boundary conditions

     

沿两条内部平行裂纹受压时材料的断裂问题

顺着平面内的平行裂纹受压材料的断裂问题并不能在线性断裂力学的框架内进行描述，Grif-fith－Irvin型或COC型的断裂判据，虽然可以用来处理经典的线性断裂力学，但对本题则完全不适用，这是因为这些压力对应力强度系数没有影响，与裂缝孔隙值也没有关系[1，2]，这一类问题只能采用新的方法，本文的第一作者曾建议过一种新方法，在这一方法中仍然使用了线性关系，但这种线性关系是从变形固体力学中的非线性方程导出的[3，4，5]．这里必须指出，这种方法曾在变形体稳定性问题中广泛地采用过。作为断裂开始的判据，我们采用了裂缝缺陷附近的局部失稳的判据，在这类情况下，我们认为是从失稳过程引发断裂过程的。     

MARS: selecting basis functions and knots with an empirical Bayes method

An empirical Bayes method to select basis functions and knots in multivariate adaptive regression spline (MARS) is proposed, which takes both advantages of frequentist model selection approaches and Bayesian approaches. A penalized likelihood is maximized to estimate regression coefficients for selected basis functions, and an approximated marginal likelihood is maximized to select knots and variables involved in basis functions. Moreover, the Akaike Bayes information criterion (ABIC) is used to determine the number of basis functions. It is shown that the proposed method gives estimation of regression structure that is relatively parsimonious and more stable for some example data sets.