Infinite horizon quadratic control of linear singularly perturbed systems with small state delays: an asymptotic solution of Riccati-type equations

Email: valery{at}techunix.technion.ac.il Received on January 31, 2006; Accepted on October 5, 2006 An infinite horizon linear-quadratic optimal control problemfor a singularly perturbed system with multiple point-wise anddistributed small delays in the state variable is considered.The set of Riccati-type equations, associated with this problemby the control optimality conditions, is studied. Since thesystem in the control problem is singularly perturbed, the equationsof this set are also perturbed by a small parameter of the singularperturbations. The zero-order asymptotic solution to this setof equations is constructed and justified. Based on this asymptoticsolution, parameter-free sufficient conditions for the existenceand uniqueness of solution to the original optimal control problemare established.     

非线性Schr■dinger方程的一种数值模拟方法

该文通过对非线性Schr■dinger方程增加耗散项,提出了一种新的三层线性差分格式.证明了该格式满足连续方程所具有的两个守恒量及收敛性和稳定性.通过数值例子与已知格式进行比较,结果表明该格式计算简单且具有较高精度.     

基于α-肉桂酰环乙烯酮二硫缩酮的一类新型D-A有机发光材料的理论

用密度泛函理论B3LYP方法对四种新型D-π-A分子(PKD,NKD,TKD和CKD)进行基态几何构型全优化,计算分子的电离势IP和电子亲和势EA等相关能量。用含时密度泛函(TDDFT)方法计算吸收光谱,用单组态相互作用方法(CIS)优化四种化合物分子的S₁激发态结构,分析其能量与发射光谱的关系。根据化合物组成的不同恰当地选择泛函计算分子的发射光谱,并与实验结果对照表明,计算结果比较可靠。     

CPA方程计算醇+卤代烃体系气液相平衡

醇+卤代烃混合体系,尤其是乙醇、三氟乙醇(TFE)等与卤代烃的混合工质在吸收式制冷、热泵、蒸气动力循环等领域中有着重要的应用.CPA方程可以描述缔合流体的性质,用于含醇类组元的混合体系气液相平衡性质描述.本文首先从纯物质饱和性质实验数据回归得到了CPA方程参数;将CPA方程应用于醇+卤代烃混合体系的气液相平衡计算,采用并比较了2种缔合方案;比较了CPA方程与G~E-EoS模型的相平衡计算效果.CPA状态方程在揭示分子间相互作用的基础上可准确描述醇+卤代烃混合体系的气液相平衡性质.     

New solitons and kink solutions for the Gardner equation

The Gardner equation, also called combined KdV–mKdV equation, is studied. New hyperbolic ansatze are proposed to derive solitons solutions. The tanh method is used as well to obtain kink solutions.     

Cauchy problem for a quasilinear parabolic equation with a source term and an inhomogeneous density

The following quasilinear parabolic equation with a source term and an inhomogeneous density is considered:

$\rho (x)\frac{{\partial u}}{{\partial t}} = div(u^{m - 1} \left| {Du} \right|^{\lambda - 1} Du) + u^p $

. The conditions on the parameters of the problem are found under which the solution to the Cauchy problem blows up in a finite time. A sharp universal (i.e., independent of the initial function) estimate of the solution near the blowup time is obtained.

     

GENERALIZED SOLUTION OF SINGULARLY PERTURBED PROBLEMS FOR REACTION DIFFUSION EQUATIONS

The singularly perturbed initial boundary value problem for reaction diffusion equation is considered. Under suitable conditions the existence, uniqueness and asymptotic behavior of the generalized solution for the problems are studied.     

The characteristics of O＋HD （v = 0, j = 0） reaction dynamics

The analytical potential energy function of HDO is constructed at first using the many-body expansion method.The reaction dynamics of O+HD(v = 0,j = 0) in five product channels are all studied by quasi-classical trajectory(QCT) method.The results show that the long-lived complex compound HDO is the dominant product at low collision energy.With increasing collision energy,O+HD → OH+D and O+HD → OD+H exchange reactions will occur with remarkable characteristics,such as near threshold energies,different reaction probabilities,and different reaction cross sections,implying the isotopic effect between H and D.With further increasing collision energy(e.g.,up to 502.08 kJ/mol),O+HD → O+H+D will occur and induce the complete dissociation into single O,H,and D atoms.     

一种实现光子晶体波导定向耦合型多路光均分的新方法

将多光子晶体单模波导平行、邻近放置构成定向耦合器. 依据自映像原理,数值分析了输入光场对称入射时,该系统中光的传播行为. 基于此结构,以三、四通道为例,设计了超微多路光分束器,并仅通过对称地改变耦合区中两个介质柱的有效折射率,使光场在横向发生重新分布,实现了输出能量的均分或自由分配. 和已报道结果相比,此调制方法更为简单易行而且效率更高,并可以推广到具有更多输出通道的光分束器中,在未来的集成光回路中具有广泛的应用价值. 关键词： 光子晶体波导 定向耦合器 分束器 能量均分     

YAB晶体中Yb3+到Er3+的能量传递

1.55 μm波段是光通讯的一个重要波段,而且对人眼安全,有高的大气透过率,因此可以广泛应用于通讯和遥感测距等领域。由于Er³⁺离子对商品化的InGaAs激光二极管的抽运波长不能有效吸收,因此一般通过在基质中共掺杂Yb³⁺和Er³⁺离子来获得1.55 μm波段激光输出。采用助熔剂法生长了不同Yb³⁺和Er³⁺掺杂浓度的YAl₃(BO₃)₄(YAB)晶体。运用速率方程模型研究了晶体中Yb³⁺到Er³⁺能量传递过程,得到了根据Yb³⁺离子的荧光寿命计算能量传递系数的简单计算公式。计算了不同掺杂离子浓度的YAB晶体中的能量传递系数等相关参数。结果表明,在YAB晶体中,Yb³⁺到Er³⁺能量传递非常有效,YAB晶体可以作为一种能获得1.55 μm激光输出的良好介质材料。