Boundary Value Problems for Ordinary Differential Equations with Deviated Arguments

We discuss differential equations with nonlinear boundary conditions. We formulate sufficient conditions under which problems with deviating arguments have quasisolutions or solutions. To obtain the results, we apply the method of monotone iterations.     

The double exponential map and covariant derivation

We study the double exponential map which is a composition of a special form of two exponential maps on a manifold with connection. We relate this map and the composition of covariant derivations as well as the composition of pseudodifferential operators on these manifolds.     

Gauge-invariant treatment of the exponential decay of an unstable atomic state

Summary By using a self-consistent projection-operator method, developed recently by the present author, a gauge-invariant Markovian treatment of the spontaneous decay of an unstable atomic state is presented. Without ignoring retardation and electron-spin effects a gauge-invariant result for the probability amplitude of finding the atom in the unstable state is obtained.     

On the Solvability of the Multidimensional Version of the First Darboux Problem for a Model Second-Order Degenerating Hyperbolic Equation

A multidimensional version of the first Darboux problem is considered for a model second-order degenerating hyperbolic equation. Using the technique of functional spaces with a negative norm, the correct formulation of this problem in the Sobolev weighted space is proved.     

Classical limit of relativistic quantal system with attractive Coulomb interaction

Using the appropriate harmonic oscillator states and reasonable approximations, we construct coherent wavepackets corresponding to the solutions of the Klein-Gordon equation for the attractive potentialV(r)=−k/r, k>0, in two and three space dimensions. We deduce the corresponding classical limit in two dimension by requiring that the expectation value 〈r〉 of the radial variable is large. In the case of three dimensions, besides the condition of large 〈r〉, we make the uncertainty Δr=[〈r ²〉 − 〈r〉²]^1/2 a minimum with respect to certain parameter of the wavepacket. We then investigate the trajectory traversed by the wavepacket in the classical limit. We find that the classical limit of this relativistic quantal problem gives, in the leading order, the same expression for the rate of motion of the perihelion as that given by the solution of the corresponding special relativistic classical dynamical problem. We also briefly discuss some of the subtle aspects of the classical limit of the relativistic quantal system, in general.     

关于非齐次m阶马氏信源的渐近均分割性

本文研究非齐次m阶马氏信源的渐近均分割性，首先我们得到关于此种信源m 1元函数的一类强极限定理，作为推论，得到关于任意非齐次m阶马氏信源状态和熵密度的几个极限定理，最后得到一类非齐次m阶马氏信源的渐近均分割性。     

一维介观结链中电荷孤子的控制

研究了一维介观结链中的电势分布随各岛上门电压和电子数分布的变化关系,并发现在一个岛上加一个门电压会产生一个静电势孤子.通过调节门电压可以较好地控制静电势孤子的形状及其位置,从而达到对电荷孤子的有效控制. 关键词： 电荷孤子 介观结 单电荷隧穿     

玻色─爱因斯坦关联半径和源半径对实验窗口的依赖及它们的差异

研究了１６０ＡＧｅＶＰｂ＋Ｐｂ反应中π源的玻色─爱因斯坦关联半径和源半径（均方根半径）的关系，以及它们对实验窗口的依赖。模型冗源由ＵＲＡＳｉＭＡ生成器产生。研究表明关联半径和源半径不仅数值不等，而且变化行为也不同。     

Derived Brackets

We survey the many instances of derived bracket construction in differential geometry, Lie algebroid and Courant algebroid theories, and their properties. We recall and compare the constructions of Buttin and of Vinogradov, and we prove that the Vinogradov bracket is the skew-symmetrization of a derived bracket. Odd (resp., even) Poisson brackets on supermanifolds are derived brackets of canonical even (resp., odd) Poisson brackets on their cotangent bundle (resp., parity-reversed cotangent bundle). Lie algebras have analogous properties, and the theory of Lie algebroids unifies the results valid for manifolds on the one hand, and for Lie algebras on the other. We outline the role of derived brackets in the theory of Poisson structures with background'.