Modeling of thin isotropic elastic plates with small piezoelectric inclusions and distributed electric circuits

This paper is the second part of a work devoted to the modelling of thin elastic plates with small, periodically distributed piezoelectric inclusions. We consider the equations of linear elasticity coupled with the electrostatic equation, with various kinds of electric boundary conditions. We derive the corresponding effective models when the thickness a of the plate and the characteristic dimension ϵ of the inclusions tend together to zero, in the two following situations: first, when a ≃ ϵ, and second, when a ∕ ϵ tends to zero. Copyright © 2013 John Wiley & Sons, Ltd.     

Satisfiability of algebraic circuits over sets of natural numbers

We investigate the complexity of satisfiability problems for {∪,∩,⁻,+,×}-circuits computing sets of natural numbers. These problems are a natural generalization of membership problems for expressions and circuits studied by Stockmeyer and Meyer (1973) [10] and McKenzie and Wagner (2003) [8].Our work shows that satisfiability problems capture a wide range of complexity classes such as NL, P, NP, PSPACE, and beyond. We show that in several cases, satisfiability problems are harder than membership problems. In particular, we prove that testing satisfiability for {∩,+,×}-circuits is already undecidable. In contrast to this, the satisfiability for {∪,+,×}-circuits is decidable in PSPACE.     

Traveling Wave Solutions In Coupled Chua'S Circuits,Part I: Periodic Solutions

We study a singularly perturbed system of partial di erential equations that models a one-dimensional array of coupled Chua's circuits. The PDE system is a natural generalization to the FitzHugh-Nagumo equation. In part I of the paper, we show that similar to the FitzHugh-Nagumo equation, the system has periodic traveling wave solutions formed alternatively by fast and slow flows. First, asymptotic method is used on the singular limit of the fast/slow systems to construct a formal periodic solution. Then, dynamical systems method is used to obtain an exact solution near the formal periodic soluion. In part II, we show that the system can have more complicated periodic and chaotic traveling wave solutions that do not exist in the FitzHugh-Nagumos equation.     

Quantum-circuit guide to optical and atomic interferometry

Atomic (qubit) and optical or microwave (modal) phase-estimation protocols are placed on the same footing in terms of quantum-circuit diagrams. Circuit equivalences are used to demonstrate the equivalence of protocols that achieve the Heisenberg limit by employing entangled superpositions of Fock states, such as N00N states. The key equivalences are those that disentangle a circuit so that phase information is written exclusively on a mode or modes or on a qubit. The Fock-state-superposition phase-estimation circuits are converted to use entangled coherent-state superpositions; the resulting protocols are more amenable to realization in the lab, particularly in a qubit/cavity setting at microwave frequencies.     

Circuits through prescribed vertices in k‐connected k‐regular graphs

We show that every set of vertices in a k‐connected k‐regular graph belongs to some circuit. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 145–163, 2002     

基于开关序列的RTD多值反相器设计

共振隧穿二极管(Resonant Tunneling Diode-RTD)本身所具有的负阻抗(Negative Differential Resistance-NDR)特性使其成为天然的多值器件.本文描述了RTD以及三端共振隧穿(Resonant Tunneting-RT)器件的伏安特性,介绍了元件用PSPICE软件的模拟方法,并以开关序列原理为指导思想设计出更为简洁的三值、四值反相器电路.设计出的电路具有低功耗和高速的特点,适合作为超高速大规模数字集成电路中的单元电路.     

闭模糊拟阵模糊圈的算法研究

用闭模糊拟阵的基本序列来研究和描述它的模糊圈,找到了从闭模糊拟阵的模糊相关集或模糊独立集计算模糊圈的方法,并给出了相应的算法.     

关于扩展PLA逻辑综合能力的若干技术

本文提出了克服PLA固定容量的限制,扩展逻辑综合能力的两种技术:一是在改用带二位译码器PLA的情况下,减少函数乘积项的算法;二是将逻辑函数修改技术用于PLA的逻辑综合技术。     

基于并联开关技术的ECL电路设计

本文首先指出了采用电压信号的多值电路中,在多个开关串联时存在的问题,进而提出了适合于ECL电路设计的两种将串联开关转换成并联开关的方法,并具体设计了采用并联开关的三值ECL电路。设计实例表明这些方法具有简便、规范的特点。用PSPICE对设计的电路进行模拟得到的结果表明,采用并联开关技术设计的电路不仅具有正确的逻辑功能,而且比采用串联开关设计的电路具有更快的速度。