Exponential Decay Rates for Structural Acoustic Model with an Overdamping on the Interface and Boundary Layer Dissipation

We study uniform stability properties of a strongly coupled system of Partial Differential Equations of hyperbolic/parabolic type, which arises from the analysis and control of acoustic models with structural damping on an interface. A challenging feature of the present model is the presence of additional strong boundary damping which is responsible for lack of uniform stability of the free system ( overdamping phenomenon). It has been shown recently that by applying full viscous damping in the interior of the domain and suitable static damping on the interface, then the corresponding feedback system is uniformly stable. In this article we prove that uniform decay rates of solutions to the system can be achieved even if viscous damping is active just in an arbitrary thin layer near the interface.     

Existence and Comparison Results for First Order Periodic Implicit Difference Equations with Maxima

In this paper, we establish comparison results (maximum principles) which allow us to use the monotone method and the method of upper and lower solutions in order to build convergent sequences to the solutions of difference equations of the type j u k = f k , u k +1 , max l ] { k m h +1,…, k +1} u l , k ] I , u 0 = u T , with j u k = u k +1 m u k , I ={0,1,…, T m 1} and f ] C ( I 2 R 2 R , R ).     

Special Pair of Dual Parametric Nonlinear Optimization Problems with Common Set of Optimal Points

On the base of a given strictly convex function defined on the Euclidean space E n ( n S 2) we can-without the assumption that it is differentiable - introduce some manifolds in topologic sense. Such manifolds are sets of all optimal points of a certain parametric non-linear optimization problem. This paper presents above all certain generalization of some results of [F. No ? i ) ka and L. Grygarová (1991). Some topological questions connected with strictly convex functions. Optimization , 22 , 177-191. Akademie Verlag, Berlin] and [L. Grygarová (1988). Über Lösungsmengen spezieller konvexer parametrischer Optimierungsaufgaben . Optimization 19 , 215-228. Akademie Verlag Berlin], under less strict assumptions. The main results are presented in Sections 3 and 4, in Section 3 the geometrical characterization of the set of optimal points of a certain parametric minimization problem is presented; in Section 4 we study a maximization non-linear parametric problem assigned to it. It seems that it is a certain pair of parametric optimization problems with the same set of their optimal points, so that this pair of problems can be denoted as a pair of dual parametric non-linear optimization problems. This paper presents, most of all in Section 2, a number of interesting geometric facts about strictly convex functions. From the point of view of non-smooth analysis the present article is a certain complement to Chapter 4.3 of the book [B. Bank, J. Guddat, D. Klatte, B. Kummer and K. Tammer (1982). Nonlinear Parametric Optimization . Akademie Verlag, Berlin] where a convex parametric minimization problem is considered under more general and stronger conditions (but without any assumptions concerning strict convexity and without geometrical aspects).     

On rank variation of block matrices generated by Nevanlinna matrix functions

Within the framework of the multiple Nevanlinna–Pick matrix interpolation and its related matrix moment problem, we study the rank of block moment matrices of various kinds, generalized block Pick matrices and generalized block Loewner matrices, as well as their Potapov modifications, generated by Nevanlinna matrix functions, and derive statements either on rank (or inertia) invariance in different senses or on rank variation of such types of block matrices (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Guided-Wave Two-Dimensional Acousto-Optic Scanner Using Proton-Exchanged Lithium Niobate Waveguide

Two-dimensional scanning of a 0.6328 mum guided-light beam has been realized using noncolinear acousto-optic (AO) coplanar Bragg diffraction together with colinear AO guided-mode to substrate radiation-mode conversion in a Z-cut Xpropagation LiNbO3 proton-exchanged (PE) waveguide. The two surface acoustic (SAW) waves utilized are at the center frequencies of 500 and 200 MHz, propagating in the Y and X axes, respectively. Two-dimensional scanning of approximately 720 resolvable light beam spots, namely, 18 40 (horizontal vertical) scanning, has been demonstrated using a light beam of 1.0 mm aperture. The total number of resolvable beam spots can be greatly increased from 720 by simply utilizing SAW transducers of larger bandwidth and a light beam of greater aperture. It should also be possible to significantly increase the diffraction efficiency from 3 % by optimizing the parameters of the PE waveguide and the SAWs.     

Multifunction Optimization Problems Involving Parameters: Necessary Optimality Conditions

We prove the Fritz John and Kuhn-Tucker necessary optimality conditions for vector optimization problems involving multifunctions and parameters under relaxed assumptions.     

On pricing and reserving with-profits life insurance contracts

As a first approximation, asset and liability management issues faced by life insurance companies originate from the sale of with-profits contracts. These contracts are bond-type products with several rate guarantees and other interestsensitive embedded options. Benefits paid out to policyholders mostly depend on the investment performance of a given asset portfolio in which premiums are invested. Thus, guarantees and options granted to policyholders may become effective when the investment performance of the asset portfolio is poor. Issuing a with-profits contract is therefore not equivalent to issuing plain-vanilla debt. The purpose of this paper is to value with-profits liabilities in a consistent option-pricing framework and to develop efficient asset or liability strategies to manage profitability and variability of shareholder value.     

基于自组织可增长映射的移动机器人仿生定位算法研究

为提高移动机器人在同步定位和地图构建(SLAM)中的定位精度,该文提出一种基于自组织可增长映射 (GSOM)的仿生定位算法。该方法将位置细胞的激活特性和神经网络输出层神经元建立响应连接,通过GSOM神经网络构建空间的拓扑地图,利用感知距离信息实现位置细胞的激活响应从而估计机器人位置,以此还原机器人的运行路径。实验结果表...     

RADIUS OF STARLIKENESS FOR THE CLASS S(α,n)

In this paper we shall investigate the bound of starlikeness r for the classS(α, n) in [1]. We obtain the following sharp result:where α_0 is the unique solution of the equationα[1+(1-2α)r~(2n)]/1-r~(2n)={1-(1-2α)r~n/1+r~n}~2with respect to α in the open interval (0, 1). This result is also the extension of somewell-known ones in [2], [3, Theorem 1] and [4, Theorem 2]