含时耦合谐振子体系的动力学演化

利用含时量子变换理论,给出含时双模耦合谐振子的严格解.并根据这一结果,对于给定的初态为Fock态和相干态情形,讨论了其动力学演化.     

含时谐振子的动力学演化

利用含时量子变换理论,由量子变换理论中的变换矩阵,方便地给出了含时谐振子的演化算符,从而求得了含时谐振子的精确解. 关键词： 含时谐振子 含时量子变换 动力学演化     

A constraint generation scheme to probabilistic linear problems with an application to power system expansion planning

In this paper, we first describe a constraint generation scheme for probabilistic mixed integer programming problems. Next, we present a decomposition approach to the peak capacity expansion planning of interconnected hydrothermal generating systems, with bounds on the transmission capacity between the regions. The objective is to minimize investments in generating units and interconnection links, subject to constraints on supply reliability. The problem is formulated as a stochastic integer program. The constraint generation scheme, which is similar to Benders decomposition, is applied in the solution of the peak capacity expansion problem. The master problem in this decomposition scheme is an integer program, solved by implicit enumeration. The operating subproblem corresponds to a stochastic network flow problem, and is solved by a maximum flow algorithm and Monte Carlo simulation. The approach is illustrated through a case study involving the expansion of the system of the Brazilian Southeastern region.     

Spectrum of the Operator Corresponding to the M/M/1 Queueing Model with Vacations and Multiple Phases of Operation and Application

We describe the point spectrum of the operator which corresponds to the M/M/1 queueing model with vacations and multiple phases of operation. Then by using this result we prove that the essential growth bound of the C₀-semigroup generated by the operator is 0, the C₀-semigroup is not compact, not eventually compact, even not quasi-compact. Moreover, we verify that it is impossible that the time-dependent solution of the M/M/1 queueing model with vacations and multiple phases of operation exponentially converges to its steady-state solution. In addition, we obtain the spectral radius and essential spectral radius of the C₀-semigroup. Lastly, we discuss other spectrum of the operator and obtain a set which belongs to the union of its continuous spectrum and residual spectrum.     

用激光测量高热可靠性电子器件的热变形

本文提出了一种测量大功率电子器件热变形的双曙光激光全息干涉法，针对一种可靠性要求很高的电子器件-火箭点火用固态继电器进行实际测试，试验结果表明，固态继电器在大负载功率工作状态时，芯片表面的干涉条纹较多，条纹弯曲程度较大，因此反映了芯片热变形和热应力增大趋势较为明显。     

一类二阶线性时变系统的稳定性

本文讨论了一类二阶线性时变系统在临界情况下的稳定性，给出了保证该系统零解稳定的充分条件，这一结果将拓宽控制论中二维线性时变控制系统的研究范围。     

Sharp maximal estimates for doubly oscillatory integrals

We study doubly oscillatory integrals

and prove a sharp maximal estimate which is an immediate consequence of a well-known conjecture in Fourier analysis on .

     

Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part II: Higher order FEM

Averaging techniques are popular tools in adaptive finite element methods since they provide efficient a posteriori error estimates by a simple postprocessing. In the second paper of our analysis of their reliability, we consider conforming -FEM of higher (i.e., not of lowest) order in two or three space dimensions. In this paper, reliablility is shown for conforming higher order finite element methods in a model situation, the Laplace equation with mixed boundary conditions. Emphasis is on possibly unstructured grids, nonsmoothness of exact solutions, and a wide class of local averaging techniques. Theoretical and numerical evidence supports that the reliability is up to the smoothness of given right-hand sides.

     

From the Von-Neumann Equation to the Quantum Boltzmann Equation in a Deterministic Framework

In this paper, we investigate the rigorous convergence of the Density Matrix Equation (or Quantum Liouville Equation) towards the Quantum Boltzmann Equation (or Pauli Master Equation). We start from the Density Matrix Equation posed on a cubic box of size L with periodic boundary conditions, describing the quantum motion of a particle in the box subject to an external potential V. The physics motivates the introduction of a damping term acting on the off-diagonal part of the density matrix, with a characteristic damping time ^–1. Then, the convergence can be proved by letting successively L tend to infinity and to zero. The proof relies heavily on a lemma which allows to control some oscillatory integrals posed in large dimensional spaces. The present paper improves a previous announcement [CD].