二阶非线性积-微分方程的初值问题的上下解方法

建立了无限区间上二阶积－微分方程的比较定理,用上下解方法证明了无限区间上的Ｂａ－ｎａｃｈ空间二阶非线性积－微分方程的初值问题的解的存在性．     

On Local Coefficients for Non-generic Representations of Some Classical Groups

This paper is concerned with representations of split orthogonal and quasi-split unitary groups over a nonarchimedean local field which are not generic, but which support a unique model of a different kind, the generalized Bessel model. The properties of the Bessel models under induction are studied, and an analogue of Rodier's theorem concerning the induction of Whittaker models is proved for Bessel models which are minimal in a suitable sense. The holomorphicity in the induction parameter of the Bessel functional is established. Local coefficients are defined for each irreducible supercuspidal representation which carries a Bessel functional and also for a certain component of each representation parabolically induced from such a supercuspidal. The local coefficients are related to the Plancherel measures, and their zeroes are shown to be among the poles of the standard intertwining operators.     

Minimality and unique ergodicity of homogeneous actions

Consider a connected Lie groupG, a lattice Γ inG, a connected subgroupH ofG, and the adjoint representation Ad ofG on its Lie algebra g. Suppose that Ad(H) splits into a semidirect product of a reductive subgroup and the unipotent radical. We prove that the minimality of the leftH-action onG/Γ then implies its unique ergodicity. Simultaneously, we suggest a reduction of the study of finite ergodic measures for an arbitrary action (G/Γ,H), where the subgroupH∈G is connected and Γ∈G is discrete, to the case of an Abelian subgroupH. Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 293–301, August, 1999.     

Completely J —positive linear systems of finite order

Completely J — positive linear systems of finite order are introduced as a generalization of completely symmetric linear systems. To any completely J — positive linear system of finite order there is associated a defining measure with respect to which the transfer function has a certain integral representation. It is proved that these systems are asymptotically stable. The observability and reachability operators obey a certain duality rule and the number of negative squares of the Hankel operator is estimated. The Hankel operator is bounded if and only if a certain measure associated with the defining measure is of Carleson type. We prove that a real symmetric operator valued function which is analytic outside the unit disk has a realization with a completely J — symmetric linear space which is reachable, observable and parbalanced. Uniqueness and spectral minimality of the completely J — symmetric realizations are discussed.     

On some properties of a linguistic classifier

A general structure of a linguistic classifier wherein sub-subclassifiers are the building blocks is suggested. Some properties of these sub-subclassifiers are proposed and proved. The physical significances of these properties are explored and it is shown that a condensed measure of belongingness of patterns to any class can be obtained which can conveniently be used for forming classification rules.     

An application of the Kriging method in global sensitivity analysis with parameter uncertainty

For structural systems with both epistemic and aleatory uncertainties, the effect of epistemic uncertainty on failure probability is measured by the variance based sensitivity analysis, which generally needs a “triple-loop” crude sampling procedure to solve and is time consuming. Thus, the Kriging method is employed to avoid the complex sampling procedure and improve the computational efficiency. By utilizing the Kriging predictor model, the conditional expectation of failure probability on the given epistemic uncertainty can be calculated efficiently. Compared with the Sobol’s method, the proposed one can ensure reasonable accuracy of results but with lower computational cost. Three examples are employed to demonstrate the reasonability and efficiency of the proposed method.     

FRACTAL PROPERTIES OF STATISTICALLY SELF-SIMILAR SETS I

In this paper,authors compute the Packing dimension of statistically selfsimilar sets and obtaine the dimension and dimension distribution of statistically selfsimilar measure.