D.C.隶属函数模糊集及其应用(I)--D.C.隶属函数模糊集基本概念与性质

本文是D.C.隶属函数模糊集及其应用系列研究的第一部分.建立了D.C.隶属函数模糊集的基本概念.探讨了D.C.隶属函数模糊集的基本性质和D.C.隶属函数模糊集对一些常见的重要t模、余模和伪补的封闭性.并以此建立了丰富的模糊数学应用模型.     

名人名著谈统计学

W.E.Denting(1940),Discussion of Professor Hottelling's Paper "The Teaching of Statistics"(Ann.Math.Stat.Vol.11,457-470): Above all,a statistician must be a scientist. 最重要的是,统计学家应该是科学家.     

仿酉对称矩阵的构造及对称正交多小波滤波带的参数化

仿酉矩阵在小波、多小波、框架的构造中发挥了重要的作用.本文给出仿酉对称矩阵(简记为p.s.m.)的显式构造算法,其中仿酉对称矩阵是元素为对称或反对称多项式的仿酉矩阵.基于已构造的p.s.m.和已知的正交对称多小波(简记为o.s.m.),给出o.s.m.的参数化.恰当地选择一些参数,可得到具有一些优良性质的o.s.m.,例如Armlet.最后作这一个算例,构造出一类对称的Chui-Lian Armlet滤波带.     

(伪)单调集值映射拟均衡问题

主要讨论G-凸上的广义向量拟均衡问题,推广W.O ettli,D.Sch l ger,Q.H.A nsari,I.V.K onnov,和J.C.Y ao的一些主要结果.     

柔性圆环壳在子午面内整体弯曲的复变量方程及细环壳的一般解

在З.Л.Аксельрад(E.L.Axelrad)非轴对称载荷下柔性旋转壳线性方程的基础上,导出了圆环壳在子午面内整体弯曲的复变量方程和相应的细环壳方程.该方程可与钱伟长给出了一般解的В.В.Новожилов(V.V.Novozhilov)轴对称环壳方程相类比.通过类比,给出了细环壳在子午面内整体弯曲的一般解.所给出的解可以用来计算波纹管整弯曲的应力和端面位移.     

股价最简微分方程,其解及与Black-Scholes模型的假设的相互关系

在系数的某种等价关系条件下,股价的两类数学表达式,一类是基于明确型描述的由类似固体力学方法导出的最简微分方程(S.D.E.)的解,另一类是基于不确定型描述(即统计理论)的Black-Scholes模型的假设(A.B-S.M.),即股价密度函数服从对数正态分布,可以是完全相同的.S.D.E.的解仅适用于股市的常规情形(无利好或利空消息,等),因此,A.B-S.M.的适用范围也相同.     

中学生中存在的24种不良学习习惯

良好的学习习惯是有效提高学业成绩的保障,不良的学习习惯影响、制约着广大学生的学习效率.现列举24种当代中学生不良学习习惯,愿广大学生、家长对照参考,矫正不足,养成良好习惯,提高学习水平.1.学习、生活、作息不规律,无计划.2.学习用品乱堆乱放,用时又找不到.3.审题不清,随意下笔.4.课堂上不主动回答老师提出的问题.     

Improvement of convergence to steady state solutions of Euler equations with weighted compact nonlinear schemes

The convergence to steady state solutions of the Euler equations for weighted compact nonlinear schemes (WCNS) [Deng X. and Zhang H. (2000), J. Comput. Phys. 165, 22-44 and Zhang S., Jiang S. and Shu C.-W. (2008), J. Comput. Phys. 227, 7294-7321] is studied through numerical tests. Like most other shock capturing schemes, WCNS also suffers from the problem that the residue can not settle down to machine zero for the computation of the steady state solution which contains shock waves but hangs at the truncation error level. In this paper, the techniques studied in [Zhang S. and Shu. C.-W. (2007), J. Sci. Comput. 31, 273-305 and Zhang S., Jiang S and Shu. C.-W. (2011), J. Sci. Comput. 47, 216-238], to improve the convergence to steady state solutions for WENO schemes, are generalized to the WCNS. Detailed numerical studies in one and two dimensional cases are performed. Numerical tests demonstrate the effectiveness of these techniques when applied to WCNS. The residue of various order WCNS can settle down to machine zero for typical cases while the small post-shock oscillations can be removed.     

对Aubin与Frankowska关于闭凸集值映射最小选择的一个结果的讨论

本文对J.-P.Aubin与H.Frankowska最近关于自反严格凸Banach空间中闭凸集值映射最小选择连续的一个结果加以讨论,首先在比自反性较强的一类空间中讨论了在弱于J.-P.Aubin与H.Frankowska的条件下闭凸集值映射最小选择的连续性,其次对J.-P.Aubin与H.Frankowska的结果给出一个新的简单证明,最后用反例说明本文给出的条件与J.-P.Aubin与H.Frankowska条件都是充分而不必要的.     

Uniqueness of entire functions sharing one value

We deal with the problem of entire functions sharing one value weakly. Moreover, we improve and generalize some former results obtained by J.-F.Chen, et al. [6], Y.Xu and H.L.Qiu [4], M.L. Fang [5], C.C. Yang, and X.H. Hua [3].     

Dynamic deformation of a stationary rubber flow

The effect of dynamic deformation on the stationary flow of a rubber composition has been experimentally investigated for comparable values of the stationary and dynamic strain rates. The dependence of the effective viscosity on the stationary shear rate is not equivalent to its dependence on the periodic shear rate amplitude. An expression is given for calculating the effective viscosity in the case of combined stationary and dynamic shear deformation. The effectiveness of the dynamic deformation, estimated in terms of the effective viscosity, depends on whether it is superimposed on the stationary flow at constant stationary shear rate or at constant stress. It is proposed to estimate the effectiveness of dynamic deformation of a stationary non-Newtonian flow in terms of the change in the power of the stationary forces. When the effective viscosity is reduced by dynamic deformation of the stationary flow, the power of the stationary forces increases at constant shear stress and falls at constant stationary shear rate.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 489–496, May–June, 1971.     

Variation analysis of uncertain stationary independent increment processes

A stationary independent increment process is an uncertain process with stationary and independent increments. This paper aims to calculate the variance of stationary independent increment processes, and gains that, for each fixed time, the variance is a constant multiplying the square of time. Based on this result, it is proved that the total variation of stationary independent increment process with finite variance is bounded almost surely. Besides, the quadratic variation of stationary independent increment process with finite variance is 0 almost surely and in mean.     

The stationary solution of a one-dimensional bipolar quantum hydrodynamic model

In this paper, we consider the existence and uniqueness of stationary solution to the bipolar quantum hydrodynamic model in one dimensional space with general non-constant doping profile. The existence of the stationary solution is proved by Leray-Schauder fixed-point theorem and a crucial truncation technique is used to derive the positive upper and lower bounds of the stationary solution. The uniqueness of the stationary solution is shown by a delicate energy estimate.     

随机环境中马氏链的平稳分布(英文)

本文引入了随机环境中马氏链平稳分布的概念. 在合适的条件下, 给出了随机环境中马氏链的平稳分布存在的一些充分条件. 特别地, 讨论了Cogburn链的平稳分布存在性问题. 同时, 构造了一个随机环境中马氏链的例子, 它的平稳分布是存在的.     

中国A股股票相邻两期β系数稳定性的Chow检验

本文用Chow检验方法研究了中国A股股票相邻两期的β系数是否稳定的问题。主要的发现有:1.对于个股而言,80%以上股票的β系数在上半年和下半年是稳定的。在扩展检验时期至相邻两年后,股票相邻两期的β系数稳定的概率有所降低,但是仍然高于60%;2.股票组合β系数稳定性的概率超过70%;3.股票组合的β系数在相邻两期稳定的概率与个股并无显著差异,并且,组合中的股票数量与组合的β系数在相邻两期是否稳定的概率并无显著的相关关系。     

Stability of stationary solutions in models of the Calvin cycle

In this paper results are obtained concerning the number of positive stationary solutions in simple models of the Calvin cycle of photosynthesis and the stability of these solutions. It is proved that there are open sets of parameters in the model of Zhu et al. (2009) for which there exist two positive stationary solutions. There are never more than two isolated positive stationary solutions but under certain explicit special conditions on the parameters there is a whole continuum of positive stationary solutions. It is also shown that in the set of parameter values for which two isolated positive stationary solutions exist there is an open subset where one of the solutions is asymptotically stable and the other is unstable. In related models derived from the work of Grimbs et al. (2011), for which it was known that more than one positive stationary solution exists, it is proved that there are parameter values for which one of these solutions is asymptotically stable and the other unstable. A key technical aspect of the proofs is to exploit the fact that there is a bifurcation where the centre manifold is one-dimensional.     

Wavelet analysis and covariance structure of some classes of non-stationary processes

Processes with stationary n-increments are known to be characterized by the stationarity of their continuous wavelet coefficients. We extend this result to the case of processes with stationary fractional increments and locally stationary processes. Then we give two applications of these properties. First, we derive the explicit covariance structure of processes with stationary n-increments. Second, for fractional Brownian motion, the stationarity of the fractional increments of order greater than the Hurst exponent is recovered.     

Effect of cross-diffusion on the stationary problem of a diffusive competition model with a protection zone

This paper is concerned with the positive stationary problem of a Lotka–Volterra cross-diffusive competition model with a protection zone for the weak competitor. The detailed structure of positive stationary solutions for small birth rates and large cross-diffusion is shown. The structure is quite different from that without cross-diffusion, from which we can see that large cross-diffusion has a beneficial effect for the existence of positive stationary solutions. The effect of the spatial heterogeneity caused by protection zones is also examined and is shown to change the shape of the bifurcation curve. Thus the environmental heterogeneity, together with large cross-diffusion, can produce much more complicated stationary patterns. Finally, the asymptotic behavior of positive stationary solutions for any birth rate as the cross-diffusion coefficient tends to infinity is given, and moreover, the structure of positive solutions of the limiting system is analyzed. The result of asymptotic behavior also reveals different phenomena from that of the homogeneous case without protection zones.     

Computing the Stationary Distribution of an SRBM in an Orthant with Applications to Queueing Networks

In [15], a BNAfm (Brownian network analyzer with finite element method) algorithm was developed for computing the stationary distribution of a semimartingale reflecting Brownian motion (SRBM) in a hypercube. In this companion paper, that BNAfm algorithm is extended to computing the stationary distribution of an SRBM in an orthant, which is achieved by constructing a converging sequence of SRBMs in hypercubes. The SRBM in the orthant serves as an approximation model of queueing networks with infinite buffers. We show that the constructed sequence of SRBMs in the hypercubes converges weakly to the SRBM in the orthant as the hypercubes approach the orthant. Under the conjecture that the set of the stationary distributions of the SRBMs in the hypercubes is relatively compact, we prove that the sequence of the stationary distributions of the SRBMs in the hypercubes converges weakly to the stationary distribution of the SRBM in the orthant. A three-machine job shop example is presented to illustrate the effectiveness of the SRBM approximation model and our BNAfm algorithm. The BNAfm algorithm is shown to produce good estimates for stationary probabilities of queueing networks.     

Boson fock representations of stochastic processes

A classification theory of quantum stationary processes similar to the corresponding theory for classical stationary processes is presented. Our main result is the classification of those pairs of classical stationary processes that admit a joint boson Fock canonical representation. Translated fromMatematicheskie Zametki, Vol. 67, No. 1, pp. 3–14, January, 2000.