Virial expansion for a polymer with a realistic pair-potential interaction

No modern theory of polymer excluded volume adequately describes the crossover from poor solvent to good solvent conditions; a fundamental difficulty is a singularity in the binary cluster integral. Mayer expansion techniques are applied to a model with a pair interaction between monomers to clarify the distinction between geometric and solvent contributions to excluded volume. Detailed calculations are undertaken for a hard-core potential and a mimic Lennard-Jones potential. The significance of the singularity in the binary cluster integral for calculations in the crossover regime is discussed.     

On three conjectures by K. E. Shuler

Some fifteen years ago, Shuler formulated three conjectures relating to the large-time asymptotic properties of a nearest-neighbor random walk on ² that is allowed to make horizontal steps everywhere but vertical steps only on a random fraction of the columns. We give a proof of his conjectures for the situation where the column distribution is stationary and satisfies a certain mixing codition. We also prove a strong form of scaling to anisotropic Brownian motion as well as a local limit theorem. The main ingredient of the proofs is a large-deviation estimate for the number of visits to a random set made by a simple random walk on . We briefly discuss extensions to higher dimension and to other types of random walk.Dedicated to Prof. K. E. Shuler on the occasion of his 70th birthday, celebrated at a Symposium in his honor on July 13, 1992, at the University of California at San Diego, La Jolla, California.     

Heterogeneities of grain boundary arrangement in polycrystals

Data on mutual arrangements of different types of grain boundaries in polycrystals are presented. The heterogeneity in grain boundary distribution, namely, the effect of gathering low-angle or special tilt grain boundaries is found in pure aluminum thin films, in sheets of Fe-3% Si alloy and in Al₂O₃ doped with MgO or MgO and Y ₂O₃. The local texture, i.e., formation of colonies or clusters of close-oriented grains is considered as a reason of this heterogeneity. The influences of grain boundary gathering on the transport properties of polycrystals and on the crack propagation are discussed. A new concept of effective grain size is suggested to analyze the relationship between material microstructures and material properties.     

Small ball probabilities for a Wiener process under weighted sup-norms,with an application to the supremum of bessel local times

LetR be the radial part of ad-dimensional Wiener process, starting from 0. In this paper, small ball probabilities are evaluated for sup_0<11(t ^–p R(t)) and sup _t 0(e ^–1 R(t)), withp[0, 1/2]. Chung's law of the iterated logarithm is established for the supremum of the local times of a two-dimensional Bessel process.     

Mosco approximation of integrands and integral functionals

It is shown that, given a lower semicontinuous convex integrandf satisfying a suitable integrability condition, there exists a sequence of Lipschitz simple integrands which Mosco converges tof and such that the sequence of conjugate integrands Mosco converges tof ^*. Moreover, this sequence can be chosen so that the sequence of associated integral functionals, respectively defined onL ¹(X) andL (X ^*), Mosco converges as well.We wish to thank Professor Erik J. Balder for interesting remarks on the first version of this work.     

Fubini theorem for anticipating stochastic integrals in Hilbert space

Let (X,l,) be a measure space, letW be a cylindrical Hilbert-Wiener process, and let be an anticipating integrable process-valued function onX. We prove, under natural assumptions on, that there exists a measurable version Y_x,x X, of the anticipating integral of(x) such that the integral _x Y_x(dx) is a version of the anticipating integral of _X (x)(dx). We apply this anticipating Fubini theorem to study solutions of a class of stochastic evolution equations in Hilbert space.     

Stochastic dominance with nonadditive probabilities

Choquet expected utility which uses capacities (i.e. nonadditive probability measures) in place of-additive probability measures has been introduced to decision making under uncertainty to cope with observed effects of ambiguity aversion like the Ellsberg paradox. In this paper we present necessary and sufficient conditions for stochastic dominance between capacities (i.e. the expected utility with respect to one capacity exceeds that with respect to the other one for a given class of utility functions). One wide class of conditions refers to probability inequalities on certain families of sets. To yield another general class of conditions we present sufficient conditions for the existence of a probability measureP with f dC= f dP for all increasing functionsf whenC is a given capacity. Examples includen-th degree stochastic dominance on the reals and many cases of so-called set dominance. Finally, applications to decision making are given including anticipated utility with unknown distortion function.     

An application of the generalized alternating polynomials to the numerical solution of Fredholm integral equations

Generalized alternating polynomials have been introduced by the author earlier. In the present paper their indirect analogue is constructed for numerical solution of the Fredholm linear integral equations. Although the proposed method is a particular case of the general projection scheme, its valuable feature is the presence of a sequence of parameters, which, for sufficiently smooth kernels and inhomogeneous terms, serves as an indicator of the quality of approximation.     

偶极积分与Boys法分子轨道定域化

定域分子轨道在分子体系的化学图象和物理图象之间充当重要的桥梁作用,它的产生依赖于定域化准则,其中最普遍使用的是Foster-Boys和Edmiston-Ruedenberg(E—R)提出的两种定域化准则。这两种定域化准则是等价的,因而结果也是一致的。但对于E—R定域化来说,由于涉及到大量的多中心积分的计算,计算极为费时,因而远不如Foster-Boys定     

A New Method to Investigate the Clustering Phenomena in Supercritical Fluids

EstimationoflocaldensityofsolventaboutthesoluteSolvatochromicbehaviorsofspectroscopicprobesarewidelyusedtoestimatethesol-ventstrengthofsupercriticalfluids(SCF,).i-3lnthiswork,thesolvatochrondcshiftofthen-n*transitionbandforacetone(O.o37mo1.L-')insupercrihcal(SC)CO2wasde-terminedbyUVspectroscopytostUdythesolvationeffect.TheMcRae-BaylissexpressionbasedonthedielectriccontinUUInmodelgivestherelahonshipbetWeenso1vatochromicshiftandpo1arizabilityofnonPolarsolvents4-5asfollows:wherevisthewave…