A note on the attainability of states by equalizing processes

In this paper, we consider regions of attainability in certain state spaces as a function of the initial state under a well-defined and physically relevant class of processes. These processes are the continuous and chaos-enhancing processes (in the sense of Ruch and Uhlmann). It turns out that these sets have complicated geometrical structures: They are polyhedra which are generally non-convex. The proof — a rather geometrical one — is given. A theorem of Hardy, Littlewood, and Polya and properties of bistochastic matrices are used crucially.     

Autoregressive approximation in nonstandard situations: the fractionally integrated and non-invertible cases

Autoregressive models are commonly employed to analyze empirical time series. In practice, however, any autoregressive model will only be an approximation to reality and in order to achieve a reasonable approximation and allow for full generality the order of the autoregression, h say, must be allowed to go to infinity with T, the sample size. Although results are available on the estimation of autoregressive models when h increases indefinitely with T such results are usually predicated on assumptions that exclude (1) non-invertible processes and (2) fractionally integrated processes. In this paper we will investigate the consequences of fitting long autoregressions under regularity conditions that allow for these two situations and where an infinite autoregressive representation of the process need not exist. Uniform convergence rates for the sample autocovariances are derived and corresponding convergence rates for the estimates of AR(h) approximations are established. A central limit theorem for the coefficient estimates is also obtained. An extension of a result on the predictive optimality of AIC to fractional and non-invertible processes is obtained.     

Orientational order parameters of nematogenic trans-4-propyl cyclohexyl-4 (trans-4-alkyl cyclohexyl) benzoates

The refractive indices and densities of three members of trans-4-propyl cyclohexyl-4 (trans-4-alkyl cyclohexyl) benzoates are reported as functions of temperature in the nematic and isotropic phases. The principal molecular polarizabilities and order parameters (S) have been evaluated using the anisotropic internal field model (Neugebauer’s approach). Also order parameters have been estimated by studying the dipole-dipole splittings in the wide line proton magnetic resonance (PMR) spectra. The results obtained are in close agreement with those obtained from refractive index measurements.     

CONVERGENCE RATE OFDISTRIBUTIONS OF TRIMMED SUMS

1.IntroductionLet{Xn,n2l}beasequenceofi.i.d.randomvariableswithnondegeneratedistributionF.Fornonnegativeintegersk.andrn,k. rn相似文献   

A Bound on the Approximation Order of Surface Splines

The functions φ _m :=|.| ^2m-d if d is odd, and φ _m :=|.| ^2m-d \log|.| if d is even, are known as surface splines, and are commonly used in the interpolation or approximation of smooth functions. We show that if one's domain is the unit ball in R ^d , then the approximation order of the translates of φ _m is at most m . This is in contrast to the case when the domain is all of R ^d where it is known that the approximation order is exactly 2m . April 23, 1996. Date revised: May 5, 1997.     

关于范畴中态射集偏序的刻划问题

本文讨论范畴中态射集偏序的刻划问题，给出了态射偏序的一致刻划。     

Stiffness in numerical initial-value problems

This paper reviews various aspects of stiffness in the numerical solution of initial-value problems for systems of ordinary differential equations.     

Pawlak代数及其性质

本文用公理化方法给出了Ｐａｗｌａｋ粗集代数的格形式,即Ｐａｗｌａｋ代数并研究了其构造,从而初步展示了这种代数结构与序结构、拓扑结构之间的关系     

Inequalities for ordered sums

Summary Letx _i =y _i +z _i ,i=1, ...n, and writex ₍₁₎≦...≦x _(n) , with corresponding notation for the orderedy _i andz _i . It is shown, for example, that ,r=1, ...n. Inequalities are also obtained for convex (or concave) functions of thex _(i) . The results lead immediately to bounds for the expected values of order statistics in nonstandard situations in terms of simpler expectations. A small numerical example illustrates the method. Research supported by U.S. Army Research Office.     

介绍一种剪力墙结构分析的高阶开孔单元

在香港大学Y.K.Cheung和Sisodiya提出用于剪力墙结构分析的带面内转角的平面应力单元的基础上,本文提出了一类具有32-56个自由度的高阶矩形单元,这类单元在铅垂方向采用3-6次多项式插值,具有8-14个结点,每个结点具有2个位移自由度和2个面内转角自由度,在上述单元的基础上,又提出了一类采用三角级数或梁的振型函数作泡状函数的自由度数目为58-74的高阶开孔矩形单元,对开孔剪力墙的计算表明,本文单元与8节点矩形单元和4节点双线性矩形单元相比,其位移精度分别提高2倍和4倍以上,应力精度提高的幅度则更大.而且该二类单元由于考虑了面内转角,可方便地与梁柱单元相连接.