一类退化型Schrodinger方程解的连续性

该文通过一种基本的分析方法,得到了一类退化型Schrodinger方程解的连续性结果,方程的类型为:Lu+vu=(f_i)_{x_i},其中L为一退化椭圆算子,v属于某一Kato类的类比,而f_i 属于某一加权L^p空间.     

完全二部图Ka,b的迭线图L^m（Ka，b）的谱特征

本证明了当(a，b)不属于{(1，8)，(2，4)，(3，6)，(4，4)，(2s^2-s，2s^2 s))时，L^m(Ka,b)以谱为特征，其中a≤b，s≥2．     

非Lipschitz系数的倒向半线性随机发展方程的适度解

文中将研究如下的无穷维空间的倒向半线性随机发 展方程x(t)+∫TteA(s-t)f(s,x(s),y(s))ds+∫Tte A(s-t )(g(s,x(s))+y(s))dw(s)=eA(T-t)X,在类似于Ymada条件下获得了该方程适度解的存在性和唯一性定理.     

Exact solutions and geometric phase factor of time-dependent three-generator quantum systems

There exist a number of typical and interesting systems and/or models, which possess three-generator Lie-algebraic structure, in atomic physics, quantum optics, nuclear physics and laser physics. The well-known fact that all simple 3-generator algebras are either isomorphic to the algebra sl (2, C) or to one of its real forms enables us to treat these time-dependent quantum systems in a unified way. By making use of both the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation, the present paper obtains exact solutions of the time-dependent Schr?dinger equations governing various three-generator Lie-algebraic quantum systems. For some quantum systems whose time-dependent Hamiltonians have no quasialgebraic structures, it is shown that the exact solutions can also be obtained by working in a sub-Hilbert-space corresponding to a particular eigenvalue of the conserved generator (i.e., the time-independent invariant that commutes with the time-dependent Hamiltonian). The topological property of geometric phase factors and its adiabatic limit in time-dependent systems is briefly discussed. Received 6 July 2002 / Received in final form 21 October 2002 Published online 11 February 2003     

Schiff碱水杨醛苯甲酰腙的特性

研究了 Schiff碱水杨醛苯甲酰腙 (简称 SBH)晶体在 DMSO及其 DMSO- H2 O的混合溶剂中的红外光谱 ,通过 SBH氘代前后的 IR对比发现 ,羟基氢质子与混合溶剂 DMSO- H2 O(3∶ 1 ,V/ V)产生较大的相互作用。向溶有 SBH的 75 % DMSO- 2 5 % H2 O的溶液滴加 KOH发现 ,SBH分子上的 C O羰基基团先与 KOH作用 ,其后与 O H 羟基基团作用     

复合广义齐次Poisson过程的多险种破产概率

本文推广了经典的复合泊松风险模型，建立了两类复合广义齐次poisson过程的多险种破产模型．对于新模型，我们得到了初始资本为u的破产概率φ(u)的精确表达式以及特殊情况下φ(0)的表达式，并且导出了调节系数方程和调节系数R的上下界．     

Interpretive approach to collective effects of electrons in multicenter problems

Interpretive theoretical tools prove valuable in guiding the analysis of experiments in the realm of atomic clusters. Here, we review basic elements of an analytic approach that makes it possible to find and visualize the effective electrostatic potential and Coulomb correlations in multicenter problems. To illustrate the utility of these concepts we apply them to exploring molecular-doped metallic clusters. This study is aiming at a systematic, visual assessment of changes induced in screening, Coulomb correlation and effective potential by varying the charge of the electronegative impurity and its position in the cluster cage.     

Artinian level modules and cancellable sequences

In order to use dualization to study Hilbert functions of artinian level algebras we extend the notion of level sequences and cancellable sequences, introduced by Geramita and Lorenzini, to include Hilbert functions of certain artinian modules. As in the case of algebras a level sequence is cancellable, but now by dualization its reverse is also cancellable which gives a new condition on level sequences. We also give a characterization of the cancellable sequences involving Macaulay representations.     

A Theta Lift for Spin7

We establish an example of a functorial lift from generic cuspidal representations of a similitude group of the type A ₁×C ₂ to generic representations of Spin₇. Our construction uses the theta correspondence associated to the dual pair of the type (A ₁×C ₂ B ₃) inside E ₇. We also consider another theta correspondence associated to the dual pair of type (A ₁×C ₂ A ₁×A ₁) in D ₆ and show that these two pairs fit into a tower and the standard properties of a tower of theta correspondences hold.