Stabilization of fixed modes in expansions of LTI systems

The objective of this note is to propose a method for stabilization of structurally fixed modes in expansions of LTI dynamic systems in the scope of overlapping decentralized control design based on the expansion/contraction framework, enabling successful design for a broader class of problems than considered so far. The method is based on a judicious choice of complementary matrices in the expanded space. Numerical examples are provided to illustrate simplicity and efficiency of the proposed approach.     

气浮设备的应用与比较

结合气浮设备的工作原理，从使用效果这一角度介绍了几种气浮设备的应用情况。对新型高效浅池气浮设备的“零速原理”及国内外同类设备对比、应用情况作了简单的介绍。     

Paul阱中共线两离子量子力学问题

运用熟知的级数截断方法,设计程序计算了线性Paul阱中两离子量子门系统Schr(o)dinger方程的精确解,分析了质心波函数几个较低能级的态,并作出对应的几率分布图;计算相对距离的方均差△r2＞(h)/2,相对运动的动量方均差△p2＜(h)/2,并满足量子力学的Heisenberg不确定度关系△r.△p＞(h)/2,它满足压缩态的条件,即质心处于基态时,两离子相对位置的量子态是一个压缩态,并得到了两离子纠缠态的表达式.纠缠的存在对量子计算和量子信息有影响,量子测量的不确定度和纠缠是在实验中应加以考虑的问题.     

M型四能级原子与三模场相互作用系统的动力学特性

采用全量子理论,研究了M型四能级原子与三模场相互作用系统的动力学特性,通过数值计算,分析了光场失谐量、初始光子数和原子初始状态对原子布居概率和光子统计演化规律的影响.     

Weak coin flipping with small bias

This paper presents a quantum protocol that demonstrates that weak coin flipping with bias ≈0.239, less than 1/4, is possible. A bias of 1/4 was the smallest known, and followed from the strong coin flipping protocol of Ambainis in [33rd STOC, 2001] (also proposed by Spekkens and Rudolph [Phys. Rev. A 65 (2002) 012310]). Protocols with yet smaller bias ≈0.207 have independently been discovered by Ambainis (2001) and Spekkens and Rudolph [Phys. Rev. Lett. 89 (2002) 227901]. We also present an alternative strong coin flipping protocol with bias 1/4 with analysis simpler than that of Ambainis [33rd STOC, 2001].     

Fast and accurate 4‐node quadrilateral

An accurate and variationally consistent 4‐node quadrilateral element is introduced where high coarse mesh accuracy and low mesh distortion sensitivity are characteristic qualities, even when incompressibility is approached for plane strain. One‐point quadrature integration procedure is adopted and a new improved stabilization technique is developed. Orthogonality conditions are utilized so that the patch test is satisfied for arbitrary quadrilaterals. Several numerical examples including a convergence rate study are presented which confirm the excellent performance of this element. Copyright © 2004 John Wiley & Sons, Ltd.     

Controllability of One Spin and Two Interacting Spins

Mathematics of Control, Signals, and Systems - ?We consider the problem of steering control for the systems of one spin ½ particle and two interacting spin ½ particles in an...     

Singular Trajectories in Multi-Input Time-Optimal Problems: Application to Controlled Mechanical Systems

This paper deals with the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with such mechanical systems have certain special properties. These properties are explored and used in conjunction with the Pontryagin maximum principle to determine the structure of singular extremals and, in particular, time-optimal trajectories. The theory is illustrated by an application to a time-optimal problem for a class of underwater vehicles.     

On the complexity of simulating space-bounded quantum computations

This paper studies the space-complexity of predicting the long-term behavior of a class of stochastic processes based on evolutions and measurements of quantum mechanical systems. These processes generalize a wide range of both quantum and classical space-bounded computations, including unbounded error computations given by machines having algebraic number transition amplitudes or probabilities. It is proved that any space s quantum stochastic process from this class can be simulated probabilistically with unbounded error in space O(s), and therefore deterministically in space O(s²).     

数学专业方向设置的问题初探——基于广东工业大学数学专业优化与调整的七年实践

通过在广东工业大学数学专业7年的专业调整实践，探索了广东工业大学应用数学学院以信息科学、统计科学为数学专业方向的社会时代背景，说明了各个专业方向培养的侧重点和就业前景，阐明了传统学科专业与新增专业方向的联系与区别。