B（X）上保点谱的可加映射和初等算子

记Ｘ为复数域上无限维Ｂａｎａｃｈ空间，Ｈ为无限维复可分Ｈｉｌｅｒｔ空间。本文给出Ｂ（Ｘ）上保持点谱的满射可加射具有的形式，以及Ｂ（Ｈ）上某些初等算子保点谱的充要条件。     

Notes on the Elliptic Ruijsenaars Operators

We construct the spaces that the elliptic Ruijsenaars operators act on. It is shown that they are extensible to nonnegative selfadjoint operators on a space of square integrable functions, or preserve a finite dimensional vector space of entire functions. These facts are shown in terms of the R-operators which satisfy the Yang–lBaxter equation. The elliptic Ruijsenaars operators are considered as the elliptic analogues of the Macdonald operators or the difference analogues of the Lamé operators.     

The variational Lyapunov function and strict stability theory for differential systems

In this paper, we investigate strict stability of differential systems by variational Lyapunov function. We obtain some sufficient conditions and comparison theorems.     

飞秒激光脉冲在三能级有机分子介质中传播时的频谱分析

通过采用预估校正的时域有限差分法求解麦克斯韦-布洛赫方程,我们研究了飞秒激光脉冲在三能级有机分子(4,4-二甲氨基二苯乙烯分子)介质中传播时脉冲的频谱演化情况.在单光子共振情况下,即入射脉冲频率等于1、2能级之间的共振频率,对大面积入射脉冲,由于强的二次激发的作用,电场频谱中出现了在ω32附近振荡的频率成分,ω32是2、3能级之间的共振频率,说明对大面积入射脉冲二能级模型已经失效,需要采用多能级模型来描述分子介质.在双光子共振情况下,即入射脉冲频率等于1、3能级之间的共振频率的一半,由于介质中放大的自发辐射和四波混频的作用,部分入射脉冲能量转化为高频和低频电场成分的能量,分子介质表现出了很强的光功率限幅特性.     

Constant Q-curvature metrics in arbitrary dimension

Working in a given conformal class, we prove existence of constant Q-curvature metrics on compact manifolds of arbitrary dimension under generic assumptions. The problem is equivalent to solving a nth-order non-linear elliptic differential (or integral) equation with variational structure, where n is the dimension of the manifold. Since the corresponding Euler functional is in general unbounded from above and below, we use critical point theory, jointly with a compactness result for the above equation.     

Activity evaluation of carbon paste electrodes loaded with pt nanoparticles prepared in different radiolytic conditions

Three Pt-based catalysts prepared in different radiolytic conditions and supported on graphite powder were packed into a carbon paste electrode configuration. They were compared to each other, to the commercial (Pt) deposited on activated carbon powder (Johnson Matthey) and to pure Vulcan XC-72 for their respective abilities toward the hydrogen evolution reaction (HER). The Tafel parameters were determined for all these electrodes. From the I–V curves and their quantitative treatment, the following order of activity emerged unambiguously and reads: (PtCO)₂ (fcc structure) > (PtCO)₁ (Chini cluster) > (Pt)_neat > (Pt)_JM (Johnson Matthey) ≫ (Vulcan XC-72). As expected, all the Pt-loaded electrodes were more efficient than Vulcan XC-72. The classification appears to be linked with the mean nanoparticle size, and for comparable sizes, with the surface morphology of the materials. The results and the stability of the electrodes suggest that the small particle sizes and the good dispersity on the carbon support were maintained during the HER.     

Symmetric form of the Hudson-Parthasarathy stochastic equation

We prove that the Hudson-Parthasarathy equation corresponds, up to unitary equivalence, to the strong resolvent limit of Schrödinger Hamiltonians in Fock space and that the symmetric form of this equation corresponds to the weak limit of the Schrödinger Hamiltonians.Translated fromMatematicheskie Zametki, Vol. 60, No. 5, pp. 726–750, November, 1996.     

Multiple local solutions to nonlinear control processes

We use the topological tool of Nielsen fixed-point theory to study the controllability of perturbed linear control processes whose control space can be reduced to a finite-dimensional one. These methods produce a lower bound on the number of controls that achieve a given target. We concentrate particularly on the case where the perturbation has sublinear growth, and we exhibit examples of multiple controls of various types that are detected by the Nielsen theory method.This research was partly supported by the Research Grant Teoria del Controllo dei Sistemi Dinamici, Ministero della Pubblica Istruzione, Roma, Italy.     

A new quantum statistical evaluation method for time correlation functions

Considering a system ofN identical interacting particles, which obey Fermi-Dirac or Bose-Einstein statistics, we derive new formulas for correlation functions of the type (whereB _j is diagonal in the free-particle states) in the thermodynamic limit. Thereby we apply and extend a superoperator formalism, recently developed for the derivation of long-time tails in semiclassical systems. As an illustrative application, the Boltzmann equation value of the time-integrated correlation functionC(t) is derived in a straightforward manner. Due to exchange effects, the obtained t-matrix and the resulting scattering cross section, which occurs in the Boltzmann collision operator, are now functionals of the Fermi-Dirac or Bose-Einstein distribution.