On the explicit differential operator formulae for the Oldroyd rate type constitutive equation

We have established the conditions under which the implicit Oldroyd type constitutive equation is equivalant to a differential type constitutive equation. Physical interpretations of these conditions are given. Finally some explicit forms for Maxwell type and Oldroyd type constitutive equations are given as illustrations.     

Asymptotically minimum variance unbiased estimation for a class of power series distributions

Summary The problem of finding an asymptotically minimum variance unbiased estimator (A.M.V.U.E.) for the parameter of certain truncated power series distributions, is discussed, when the generating function of their coefficients are i) polynomials of binomial type ii) generalized ascending factorials iii) polynomials with coefficients the well known Eulerian numbers.     

方波信号的傅里叶分解实验

选择通用设备，建立了一个简易的周期信号傅里叶分析系统，通过其测试了方波信号各谐波成份的频率和幅度值，验证了方波信号的傅氏展开关系．     

A map describing EEG activity of human brain

A model of electrical activity of human brain considered as a complex dynamical system is given based on the EEG time series. The model fits the data remarkably well. The predictive ability of the model is limited to a few time steps as expected for a chaotic time series.     

A Hypergeometric Hierarchy for the Andrews Evaluations

Several 6F5(1) evaluations are given which generalize Andrews' 5F4(1) evaluations. All such evaluations are shown to be equivalent to transformations for a 4F3(z). The methodology allows for higher evaluations, for example an 8F7(1) is given which specializes to over one hundred 5F4(1) results, including all of Andrews'.     

A reinforcement-depletion urn model: A contiguity case

Summary An urn contains balls ofs different colors. The problem of the reinforcement of a specified color and random depletion of balls has been considered by Bernard (1977,Bull. Math. Biol.,39, 463–470) and Shenton (1981,Bull. Math. Biol.,43, 327–340), (1983,Bull. Math. Biol.,45, 1–9). Here we consider a special relation between a reinforcement and depletion, leading to a hypergeometric distribution. Research sponsored in part by the Applied Mathematical Sciences Research Program, Office of Energy Research, U.S. Department of Energy under contract DE-AC05-840R21400 with the Martin Marietta Energy Systems, Inc.     

Discrete distributions of orderk on a binary sequence

Summary This paper considers discrete distributions of orderk based on a binary sequence which is defined as an extension of independent trials with a constant success probability and is more practical than the independent trials. Some results on calculation of probabilities and characteristics of the distributions are obtained as well as their formal expressions. Examples and an application are also given. The Institute of Statistical Mathematics     

Sequence transformations as statistical tools

A number of sequence transformations are actually used in statistics to solve different kinds of problems. In the two first parts of this paper we set the statistical problem of estimating the unknown orders of an ARMA process and we give its equivalent formulation in terms of invariance properties of sequence transformations: the most used among them are reviewed in the third part. The study of this estimation problem occuring in the Box-Jenkins method has led to new properties of Hankel determinants which are given in the part four.     

High Temperature Expansion for a Driven Bilayer System

Based directly on the microscopic lattice dynamics, a simple high temperature expansion can be devised for non-equilibrium steady states. We apply this technique to investigate the disordered phase and the phase diagram for a driven bilayer lattice gas at half filling. Our approximation captures the phases first observed in simulations, provides estimates for the transition lines, and allows us to compute signature observables of non-equilibrium dynamics, namely, particle and energy currents. Its focus on non-universal quantities offers a useful analytic complement to field-theoretic approaches.