Positive equilibria of weakly reversible power law kinetic systems with linear independent interactions

In this paper, we extend our study of power law kinetic systems whose kinetic order vectors (which we call interactions) are reactant-determined (i.e. reactions with the same reactant complex have identical vectors) and are linear independent per linkage class. In particular, we consider PL-TLK systems, i.e. such whose T-matrix (the matrix with the interactions as columns indexed by the reactant complexes), when augmented with the rows of characteristic vectors of the linkage classes, has maximal column rank. Our main result states that any weakly reversible PL-TLK system has a complex balanced equilibrium. On the one hand, we consider this result as a Higher Deficiency Theorem for such systems since in our previous work, we derived analogues of the Deficiency Zero and the Deficiency One Theorems for mass action kinetics (MAK) systems for them, thus covering the Low Deficiency case. On the other hand, our result can also be viewed as a Weak Reversibility Theorem (WRT) in the sense that the statement any weakly reversible system with a kinetics from the given set has a positive equilibrium holds. According to the work of Deng et al. and more recently of Boros, such a WRT holds for MAK systems. However, we show that a WRT does not hold for two proper MAK supersets: the set PL-NIK of non-inhibitory power law kinetics (i.e. all kinetic orders are non-negative) and the set PL-FSK of factor span surjective power law kinetics (i.e. different reactants imply different interactions)

Research and Design of a Routing Protocol in Large-Scale Wireless Sensor Networks

无线传感器网络，作为全球未来十大技术之一，集成了传感器技术、嵌入式计算技术、分布式信息处理和自组织网技术，可实时感知、采集、处理、传输网络分布区域内的各种信息数据，在军事国防、生物医疗、环境监测、抢险救灾、防恐反恐、危险区域远程控制等领域具有十分广阔的应用前景。 本文研究分析了无线传感器网络的已有路由协议，并针对大规模的无线传感器网络设计了一种树状路由协议，它根据节点地址信息来形成路由，从而简化了复杂繁冗的路由表查找和维护，节省了不必要的开销，提高了路由效率，实现了快速有效的数据传输。 为支持此路由协议本文提出了一种自适应动态地址分配算——ADAR（AdaptiveDynamicAddre...As one of the ten high technologies in the future, wireless sensor network, which is the integration of micro-sensors, embedded computing, modern network and Ad Hoc technologies, can apperceive, collect, process and transmit various information data within the region. It can be used in military defense, biomedical, environmental monitoring, disaster relief, counter-terrorism, remote control of haz...学位：工学硕士院系专业：信息科学与技术学院通信工程系_通信与信息系统学号：2332007115216

Asymptotic behavior of the approximate controls for parabolic equations with interfacial contact resistance

International audienceIn this paper, we study the approximate control for a class of parabolic equations with rapidly oscillating coefficients in an epsilon-periodic composite with an interfacial contact resistance as well as its asymptotic behavior, as epsilon -> 0. The condition on the interface depends on a parameter gamma is an element of (-1, 1]. The case gamma = 1 is the most interesting one, and the more delicate, since the homogenized problem is given by coupled system of a P.D.E. and an O.D.E., giving rise to a memory effect. The variational approach to approximate controllability introduced by Lions in [J.-L. Lions. In Proc. of Jornadas Hispano-Francesas sobre Control de Sistemas Distribuidos, octubre 1990. Grupo de Analisis Matematico Aplicado de la University of Malaga, Spain (1991) 77-87] lead us to the construction of the control as the solution of a related transposed problem. The final data of this problem is the unique minimum point of a suitable functional J(epsilon). The more interesting result of this study proves that the control and the corresponding solution of the epsilon-problem converge respectively to a control of the homogenized problem and to the corresponding solution. The main difficulties here are to find the appropriate limit functionals for the control of the homogenized system and to identify the limit of the controls

Approximate Controllability of a Parabolic System with Imperfect Interfaces

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Corrector results for a parabolic problem with a memory effect

The aim of this paper is to provide the correctors associated to the homogenization of a parabolic problem describing the heat transfer. The results here complete the earlier study in [Jose, Rev. Roumaine Math. Pures Appl. 54 (2009) 189–222] on the asymptotic behaviour of a problem in a domain with two components separated by an ε-periodic interface. The physical model established in [Carslaw and Jaeger, The Clarendon Press, Oxford (1947)] prescribes on the interface the condition that the flux of the temperature is proportional to the jump of the temperature field, by a factor of order εγ. We suppose that -1 < γ ≤ 1. As far as the energies of the homogenized problems are concerned, we consider the cases -1 < γ < 1 and γ = 1 separately. To obtain the convergence of the energies, it is necessary to impose stronger assumptions on the data. As seen in [Jose, Rev. Roumaine Math. Pures Appl. 54 (2009) 189–222] and [Faella and Monsurrò, Topics on Mathematics for Smart Systems, World Sci. Publ., Hackensack, USA (2007) 107–121] (also in [Donato et al., J. Math. Pures Appl. 87 (2007) 119–143]), the case γ = 1 is more interesting because of the presence of a memory effect in the homogenized problem

Asymptotic behavior of the approximate controls for parabolic equations with interfacial contact resistance

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On the Solvability of a Quasilinear Parabolic Problem with Neumann Boundary Condition

This paper establishes the existence and uniquenesss of a weak solution of a quasilinear parabolic problem in an open set whose boundary is the union of two disjoint closed surfaces. A Dirichlet condition is prescribed on the exterior boundary and a Neumann condition on the interior boundary. The existence of a solution of the parabolic problem is shown using the Faedo-Galerkin method and some a priori estimates are established to provide bounds for the solution

Asymptotic analysis of a parabolic problem with a rough interface

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Asymptotic analysis of a parabolic problem with a rough interface

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