Statistical approach to light scattering from deformed textured heterogeneous polymer materials

A statistical theory of light scattering from deformed isotropic and textured heterogeneous polymer materials is formulated. Two types of textured structures are analyzed: assemblies of optically isotropic and anisotropic rods and a spatially anisotropic distribution of isotropic spherical inclusion centers. The small-angle H_v light-scattering patterns are calculated. The appearance of scattering from isotropic rods and spheres in deformed materials has been demonstrated. The changes of the H_v scattering patterns as a function of elongation and strucuture parameters are discussed. © 1993 John Wiley & Sons, Inc.     

Spectral shift function and trace formula

The complete proofs of Krein’s theorem on the spectral shift function and the trace formula are given for a pair of self-adjoint operators such that either (i) their difference is trace-class or (ii) the difference of their resolvents is trace-class. The proofs, essentially due to Krein, is based on Herglotz’s theorem on the boundary value of the analytic functions whose imaginary part is non-negative on the upper half plane, and an almost optimal class of functions are obtained for which the trace formula is valid. Also an alternative method based on Weyl-von Neumann’s theorem for self-adjoint operators, avoiding the complex function theory and inspired by Voiculescu’s work, is given for the first case. Furthermore, some applications of the spectral shift function have been discussed.     

On a problem of Zygmund

It is proved that there exists an integrable function on [0, 1]² whose integral is nondifferentiable in each direction belonging to a set everywhere dense in [0, 2π] but is strongly differentiable. Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 749–762, November, 1998.     

多元K-拟全纯函数及其正规定则

研究函数族的正规性定则是复变函数论中的一个重要且有意义的工作．引进多元K-拟全纯函数的定义，并给出了多元K-拟全纯函数族的一个正规定则．     

Decomposition of multiattribute expected-utility functions

This paper integrates and extends the theory of the decomposition of multiattribute expected-utility functions based on utility independence. In a preliminary section, the standard decision model of expected utility is briefly discussed, including the fact that the decision maker's preference forlotteries with two outcomes determines the utility function uniquely. The decomposition possibilities of a utility function are captured by the concept ofautonomous sets of attributes, an affine separability of some kind known as generalized utility independence.Overlapping autonomous sets lead to biaffine-associative, i.e.multiplicative oradditive decompositions. The multiplicative representation shows that autonomy has strongerclosure properties than utility independence, for instance with respect to set-theoretic difference. Autonomy is also a concept with a wider scope since it applies to the decomposition of Boolean functions, games and a number of other topics in combinatorial optimization. This relationship to the well-known theory ofsubstitution decomposition in discrete mathematics also reveals a kind of discrete core behind the decomposition of utility functions. The entirety of autonomous sets can be represented by a compact data structure, the so-calledcomposition tree, which frequently corresponds to a natural hierarchy of attributes. Multiplicative/additive ormulti-affine functions correspond to the hierarchy steps. The known representation of multi-affine functions is shown to be given by aMoebius inversion formula. The entire approach has the advantage that it allows the application of more sophisticated representation methods on a detailed level, whereas it employs onlyfinite set theory andarithmetic on the main levels in the hierarchy.     

新型重整催化剂的研究—Pt／BaKL型沸石中钡的作用

本文采用XRD,NH_3-TPD,IR以及TEM等方法考察了Pt/BaKL沸石中Ba~(2+)的作用。NH_3-TPD结果表明,交换Ba~(2+)后的L型沸石的酸性,由于阳离子的作用仅在弱酸范围内有些改变,但与载铂的沸石的催化活性无明显的对应关系。IR及XRD谱线表明,BaKL沸石中Ba~(2+)在最佳交换度(26.3%)时,随预培烧温度的提高,使Ba~(2+)处于沸石孔道中B、C、D位置,接近于最佳分布,此时IR谱线上1421cm~(-1)处有一新峰。当沸石负载铂后,因铂与Ba~(2+)的相互作用,新峰消失,导致铂粒在沸石上分布更加均匀;铂粒在1.5—3.0nm之间占有最大比例,使得Pt/BaKL沸石呈现芳构化活性及选择性高于Pt/KL沸石,分别为～98%和～95%。     

用θ-2θ型衍射仪测定溶液结构的新方法

叙述了用θ－２θ型Ｘ射线衍射仪精确测定电解质溶液结构的新实验技术。设计制作了具有恒温功能的超厚液体样品池，并建立了样品池窗口强度的校正方法。优化了液体Ｘ射线衍射数据和结构参数精细化的计算机程序，获得了非常令人满意的实验结果。由θ－２θ型Ｘ射线衍射仪精确测定的径向分布函数与θ－θ型衍射仪自由散射比较，表明ＤＲＦ分辨率有所提高。     

The Mathematical Theory of Ito Diffusions on Hypersurfaces, with Applications to NMR Relaxation Problems

A mathematical framework for translational Brownian motion on hypersurfaces is presented, using an imbedding of the surface and Ito diffusions in the ambient space. This includes a survey of Ito calculus and differential geometry. Computational methods for time correlation functions relevant to spin relaxation studies on curved interfaces are given, and explicit calculations of time correlation functions and order parameters for a Rippled surface are presented.