Banach空间中二阶积分-微分方程的初值问题

使用锥理论及单调迭代技术，首先讨论了Banach空间中一阶积分-微分方程初值问题的最小最大解的存在性，并在此基础上讨论了带有一阶微分项的二阶积分-微分方程初值问题的最小最大解的存在性。     

All Subvarieties of ℒpq Have Finite Bases of Identities

We consider the varieties of lattice ordered groups with the identity of commutation of the nth powers of elements. We establish that every such l-variety with n=pq, where p and q are distinct prime numbers, has a finite basis of identities.     

Orientational Ordering of the Near-Surface Layers of Nitrobenzene

Two types of absorption centers, one being related to monomers and the other to dimers, have been revealed by the method of statistical analysis of the normalized absorption spectra of a superthin interlayer of nitrobenzene of variable thickness formed on activated surfaces of quartz and barium fluoride and measured for different thicknesses of the interlayer. On a decrease in the interlayer thickness the concentration of dimers increases.     

Orbital-selective Mott-insulator transition in Ca 2 - x Sr x RuO 4

The electronic structures of the metallic and insulating phases of the alloy series Ca_2-xSr_xRuO₄ ( 0 ? x ? 2) are calculated using LDA, LDA+U and Dynamical Mean-Field Approximation methods. In the end members the groundstate respectively is an orbitally non-degenerate antiferromagnetic insulator (x = 0) and a good metal (x = 2). For x > 0.5 the observed Curie-Weiss paramagnetic metallic state which possesses a local moment with the unexpected spin S = 1/2, is explained by the coexistence of localized and itinerant Ru-4d-orbitals. For 0.2 < x < 0.5 we propose a state with partial orbital and spin ordering. An effective model for the localized orbital and spin degrees of freedom is discussed. The metal-insulator transition at x = 0.2 is attributed to a switch in the orbital occupation associated with a structural change of the crystal. Received 27 July 2001     

Ergodic theory of amenable semigroup actions

In this paper, among other things, we state and prove the mean ergodic theorem for amenable semigroup algebras.     

Caristi 不动点定理的推广及应用

本文推广了古典的Garisti不动点定理,作为应用,古典的Ekeland变分原理得到了推广,并且证明了推广的Garisti不动点定理和推广的Ekeland变分原理是等价的．     

The Choquet-Deny convolution equation μ=μ*σ for probability measures on Abelian semigroups

In this note, we characterize the regular probability measures satisfying the Choquet-Deny convolution equation =* on Abelian topological semigroups for a given probability measure .     

Optimality for set functions with values in ordered vector spaces

Let (X, , ) be a finite atomless measure space,L a convex subfamily of , andY andZ locally convex Hausdorff topological vector spaces which are ordered by the conesC andD, respectively. LetF:LY beC-convex andG:LZ beD-convex set functions. Consider the following optimization problem (P): minimizeF(), subject to L andG() _D . The paper generalizes the Moreau-Rockafellar theorem with set functions. By applying this theorem, a Kuhn-Tucker type optimality condition and a Fritz John type optimality condition for problem (P) are established. The duality theorem for problem (P) is also studied.This work was partially supported by National Science Council, Taipei, Taiwan. This paper was written while the first author was visiting at the University of Iowa, 1987-88.The authors would like to express their gratitude to the two anonymous referees for their valuable comments. Also, they would like to thank Professor P. L. Yu for his encouragement and suggestions which improved the material presented here considerably.     

Stochastic flows on a countable set: Convergence in distribution

Consider a sequenceF ₁,F ₂,... of i.i.d. random transformations from a countable setV toV. Such a sequence describes a discrete-time stochastic flow onV, in which the position at timen of a particle that started at sitex isM _n(x), whereM _n =F _n F _n–1 F ₁. We give conditions on the law ofF ₁ for the sequence (M _n) to be tight, and describe the possible limiting law. an example called the block charge model is introduced. The results can be formulated as a statement about the convergence in distribution of products of infinite-dimensional random stochastic matrices. In practical terms, they describe the possible equilibria for random motions of systems of particles on a countable set, without births or deaths, where each site may be occupied by any number of particles, and all particles at a particular site move together.     

Automorphisms on a Lie group contracting modulo a compact subgroup and applications to semistable convolution semigroups

Let ( _t ) _t0 be a -semistable convolution semigroup of probability measures on a Lie groupG whose idempotent ₀ is the Haar measure on some compact subgroupK. Then all the measures ₁ are supported by theK-contraction groupC _K() of the topological automorphism ofG. We prove here the structure theoremC _K()=C()K, whereC() is the contraction group of . Then it turns out that it is sufficient to study semistable convolution semigroups on simply connected nilpotent Lie groups that have Lie algebras with a positive graduation.