Some Properties of Solutions to the Novikov Equation with Weak Dissipation Terms

In this paper, we investigate the Novikov equation with weak dissipation terms. First, we give the local well-posedness and the blow-up scenario. Then, we discuss the global existence of the solutions under certain conditions. After that, on condition that the compactly supported initial data keeps its sign, we prove the infinite propagation speed of our solutions, and establish the large time behavior. Finally, we also elaborate the persistence property of our solutions in weighted Sobolev space.     

Single machine group scheduling with ordered criteria

The single machine group scheduling problem is considered. Jobs are classified into several groups on the basis of group technology, i.e. jobs of the same group have to be processed jointly. A machine set-up time independent of the group sequence is needed between each two consecutive groups. A schedule specifies the sequence of groups and the sequence of jobs in each group. The quality of a schedule is measured by the criteriaF ₁, ...,F _m ordered by their relative importance. The objective is to minimize the least important criterionF _m subject to the schedule being optimal with respect to the more important criterionF _m–1 which is minimized on the set of schedules minimizing criterionF _m–2 and so on. The most important criterion isF ₁, which is minimized on the set of all feasible schedules. An approach to solve this multicriterion problem in polynomial time is presented if functionsF ₁, ...,F _m have special properties. The total weighted completion time and the total weighted exponential time are the examples of functionsF ₁, ...,F _m–1 and the maximum cost is an example of functionF _m for which our approach can be applied.The research of the authors was partially supported by a KBN Grant No. 3 P 406 003 05, the Fundamental Research Fund of Belarus, Project N 60-242, and the Deutsche Forschungsgemeinschaft, Project Schema, respectively. The paper was completed while the first author was visiting the University of Melbourne.     

Lower semicontinuous solutions of the Bellman equation for the minimum time problem

The minimum time problem associated with a nonlinear control system is considered, and the unicity of the lower semicontinuous solution of the corresponding Bellman equation is investigated. A main tool in our approach is the Kruzkov transformation that enables us to work on ⁿ –{0}, where {0} is the target set, instead of the unknown reachable set.This research was carried out while the first author was visiting the Department of Mathematics, University of Genova, Genova, Italy.     

Large deviation analysis of the single server queue

We establish the large deviation principle (LDP) for the virtual waiting time and queue length processes in the GI/GI/1 queue. The rate functions are found explicitly. As an application, we obtain the logarithmic asymptotics of the probabilities that the virtual waiting time and queue length exceed high levels at large times. Additional new results deal with the LDP for renewal processes and with the derivation of unconditional LDPs for conditional ones. Our approach applies in large deviations ideas and methods of weak convergence theory.This work was supported in part by AT&T Bell Labs.     

Covering with blocks in the non-symmetric case

Considering an infinite string of i.i.d. random letters drawn from a finite alphabet we define the cover timeW _n as the number of random letters needed until each pattern of lenghtn appears at least once as a substring. Sharp weak and a.s. limit results onW _n are known in the symmetric case, i.e., when the random letters are uniformly distributed over the alphabet. In this paper we determine the limit distribution ofW _n in the nonsymmetric case asn. Generalizations in terms of point processes are also proved.Dedicated to Endre Csáki on his 60th birthday.     

Stochastic phase lockings in a relaxation oscillator forced by a periodic input with additive noise: A first-passage-time approach

Noise effects on phase lockings in a system consisting of a piecewise-linear van der Pol relaxation oscillator driven by a periodic input are studied. The problem of finding the period of the oscillator is reduced to the first-passage-time problem of the Ornstein-Uhlenbeck process with time-varying boundary. The probability density functions of the first-passage time are used to define the operator which governs a transition of an input phase density after one cycle of the oscillator. Phase lockings in a stochastic sense are investigated on the basis of the density evolution by the operator.     

Probabilistic approach to homoclinic chaos

Three-dimensional systems possessing a homoclinic orbit associated to a saddle focus with eigenvalues ±i, – and giving rise to homoclinic chaos when the Shil'nikov condition < is satisfied are studied. The 2D Poincaré map and its 1D contractions capturing the essential features of the flow are given. At homoclinicity, these 1D maps are found to be piecewise linear. This property allows one to reduce the Frobenius—Perron equation to a master equation whose solution is analytically known. The probabilistic properties such as the time autocorrelation function of the state variablex are explicitly derived.     

基于时间域读出的大动态范围CMOS图像传感器

设计了一款基于时间域读出的大动态范围CMOS图像传感器。传感器基于一种新型的结构,其可在时间域下探测高输入光强,在模拟域下探测低输入光强。该设计在传统电容反馈式跨阻放大器(CTIA)的基础上,新增了时间域测量电路,在不改变原有积分过程的同时可实现连续的大动态范围。基于0.35μm,5V-CMOS工艺进行了256×1线列CMOS图像传感器流片,光电二极管面积为22.5μm×22.5μm,并对器件的光电特性进行了后仿真验证。仿真测试结果表明,基于时间域读出的图像传感器可实现96dB的大动态范围,且时间域和模拟域的两路输出信号可同步输出,功耗为7.98mW。     

970 nm超辐射发光二极管弯曲脊形波导数值分析

本文基于光束传播法(beam propagation method, BPM)和时域有限差分法(finite difference time domain method, FDTD)建立了分析模型,模拟并分析了弯曲脊形波导超辐射发光二极管(superluminescent light emitting diode, SLD)不同结构参数(刻蚀深度、曲率半径、脊形宽度)对波导损耗的影响和倾斜脊形波导不同结构参数(刻蚀深度、脊形宽度、倾斜角度、发射波长)对模式反射率的影响。计算表明,弯曲脊形波导的刻蚀深度和曲率半径是影响波导损耗的重要因素。刻蚀深度较浅使波导对光场的限制作用较弱,过小的曲率半径会使模式传输泄露严重,损耗大大增加。脊形宽度越大,波导损耗越小,其对波导损耗影响较小。脊形波导的端面倾斜角度是抑制模式反射率的重要因素,脊形宽度增加,模式反射率逐渐减小,并在特定的几个角度形成的奇点达到最小值。刻蚀深度对于模式反射率的影响作用较小,但随着刻蚀深度的增加,奇点发生的角度产生了向小角度偏移。在特定的倾斜角度范围内,随着波长减小,奇点的数目会逐渐增加。研究结果可对设计具有优越性能的SLD器件...     

航空机载软件全数字仿真测试系统的设计与实现

针对航空机载软件测试环境与开发环境冲突、测试环境可控性和通用性差、非干预性测试困难的问题,分析了全物理实装测试环境、半实物仿真测试环境的优缺点,研究了全数字仿真测试技术,设计并实现了一种航空机载软件全数字仿真测试系统。该系统由仿真核心平台、仿真工具组件、协同仿真组件和人机交互组件构成,提供了航空机载处理器、内存、外设等多种可重用库。提出了基于底层虚拟机的动态二进制翻译技术、协同仿真时间同步和数据通信机制等关键技术,实现了航空机载软件全数字高速闭环仿真运行。工程实践证明,该系统能达到降低硬件设备的依耐性、简化测试环境搭建的复杂度、提高测试效率约42%的目的。