Optimal transmission of “television type” gaussian signals through a noiseless feedback channel

Using the methods and results of the theory of conditionally Gaussian filtering of stochastic processes and fields, an optimal scheme of “television type” signal transmission through a noiseless feedback channel is constructed under the usual power conditions, the signals being evolutionary Gaussian fields θ={θ_t(x)),tε[0,T),xεDεRⁿ . Explicit representations for optimal coding and decoding functionals, which are optimal in the sense of a special square criterion, and the expression for the error of signal reproduction are given.     

一类艾滋病传播的数学模型的定态非负解

利用分歧理论讨论带扩散问题艾滋病传播数学模型定态非负解及全局性质．     

Exponential Stability in Mean Square for a General Class of Discrete-Time Linear Stochastic Systems

Abstract

The problem of the mean square exponential stability for a class of discrete-time linear stochastic systems subject to independent random perturbations and Markovian switching is investigated. The case of the linear systems whose coefficients depend both to present state and the previous state of the Markov chain is considered. Three different definitions of the concept of exponential stability in mean square are introduced and it is shown that they are not always equivalent. One definition of the concept of mean square exponential stability is done in terms of the exponential stability of the evolution defined by a sequence of linear positive operators on an ordered Hilbert space. The other two definitions are given in terms of different types of exponential behavior of the trajectories of the considered system. In our approach the Markov chain is not prefixed. The only available information about the Markov chain is the sequence of probability transition matrices and the set of its states. In this way one obtains that if the system is affected by Markovian jumping the property of exponential stability is independent of the initial distribution of the Markov chain.

The definition expressed in terms of exponential stability of the evolution generated by a sequence of linear positive operators, allows us to characterize the mean square exponential stability based on the existence of some quadratic Lyapunov functions.

The results developed in this article may be used to derive some procedures for designing stabilizing controllers for the considered class of discrete-time linear stochastic systems in the presence of a delay in the transmission of the data.     

Symmetric boundary integral formulations for Helmholtz transmission problems

In this work we propose and analyze numerical methods for the approximation of the solution of Helmholtz transmission problems in two or three dimensions. This kind of problems arises in many applications related to scattering of acoustic, thermal and electromagnetic waves. Formulations based on boundary integral methods are powerful tools to deal with transmission problems in unbounded media. Different formulations using boundary integral equations can be found in the literature. We propose here new symmetric formulations based on a paper by Martin Costabel and Ernst P. Stephan (1985), that uses the Calderón projector for the interior and exterior problems to develop closed expressions for the interior and exterior Dirichlet-to-Neumann operators. These operators are then matched to obtain an integral system that is equivalent to the Helmholtz transmission problem and uses Cauchy data on the transmission boundary as unknowns. We show how to simplify the aspect and analysis of the method by employing an additional mortar unknown with respect to the ones used in the original paper, writing it in an appropriate way to devise Krylov type iterations based on the separate Dirichlet-to-Neumann operators.     

Design and FPGA-realization of a self-synchronizing chaotic decoder in the presence of noise

This paper describes requirement for wireless transmission of Chaotic Code Division Multiplexed Access (Chaotic CDMA) and it focuses on real-time synchronization algorithm embedded into electronic programmable device. CDMA with quasi-orthogonal codes is used to allow multi-users to transmit simultaneously in the same channel. Since the channel is shared between all users, the receiver system has to cope with channel noise and overall with interference from other users. As a result, one of the main problems of communication with quasi-orthogonal chaotic codes is to implement a real time decoder in presence of noise. Even if set-membership algorithm are efficient in real time synchronization of chaotic discrete generators in the presence of noise, these algorithms require a large memory resource. In this paper, we propose an evolution of set-membership algorithm toward genetic algorithm to be implemented into electronic programmable device. The advantage of genetic algorithm compared with set-membership algorithm is that they require a fixed size of memory.     

具有垂直传染的SEIA传染病模型的稳定性

建立和研究一类具有垂直传染的SEIA传染病模型,得到模型基本再生数R₀的表达式,运用Lyapunov函数和第二加性复合矩阵理论证明了当R₀〈1时无病平衡点全局渐近稳定,当R₀〉1时地方病平衡点全局渐近稳定.     

一类具有隔离的脉冲免疫接种SIQR传染病模型的全局动力学行为

建立了一类具有隔离和垂直传染的SIQR传染病模型,在脉冲免疫接种条件下,分析了其全局动力学行为.利用频闪映射,获得了无病周期解,给出了此周期解的全局稳定性分析.并获得了系统一致持续生存的条件.     

Naive audience and communication bias

We introduce the possibility that the receiver naively believes the sender’s message in a game of information transmission with partially aligned objectives. We characterize an equilibrium in which the communication language is inflated, the action taken is biased, and the information transmitted is more precise than in the benchmark fully-strategic model. We provide comparative statics results with respect to the amount of asymmetric information, the proportion of naive receivers, and the size of the sender’s bias. As the state space grows unbounded, the equilibrium converges to the fully-revealing equilibrium that results in the limit case with unbounded state space.      

Some Spectral Properties of One Sturm-Liouville Type Problem with Discontinuous Weight

We consider a discontinuous weight Sturm-Liouville equation together with eigenparameter dependent boundary conditions and two supplementary transmission conditions at the point of discontinuity. We extend and generalize some approaches and results of the classic regular Sturm-Liouville problems to the similar problems with discontinuities. In particular, we introduce a special Hilbert space formulation in such a way that the problem under consideration can be interpreted as an eigenvalue problem for a suitable selfadjoint operator, construct the Green’s function and resolvent operator, and derive asymptotic formulas for eigenvalues and normalized eigenfunctions.Original Russian Text Copyright © 2005 Mukhtarov O. Sh. and Kadakal M.__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 860–875, July–August, 2005.     

摩托车正时链和传动链磨损特性的研究

研究油润滑条件下摩托车发动机正时链的磨损特性,发现疲劳磨损,裂纹的形成和扩展是影响疲劳寿命的主要因素;定期刷油或滴油润滑条件下,摩托车传动链的磨损机制是磨粒磨损,并伴有疲劳磨损,销轴和套筒零件的渗层及心部组织等是影响链条磨损特性的重要因素,因为中碳调质钢经碳氮共渗后可获得弥散分布的颗粒状碳化物的表层组织及回火屈氏体的心部组织,从而显示出表层耐磨、心部强韧性好及抗塑变能力高的综合机械性能。