On topological properties of the Hartman-Mycielski functor

We investigate some topological properties of a normal functorH introduced earlier by Radul which is some functorial compactification of the Hartman-Mycielski construction HM. We prove that the pair (H X, HMY) is homeomorphic to the pair (Q, σ) for each nondegenerated metrizable compactumX and each denseσ-compact subsetY.     

Collaborative distributed decision making for large scale disaster relief operations: Drawing analogies from robust natural systems

One of the most ignored, but urgent and vital challenges confronting society today is the vulnerability of urban areas to extreme events. Current organization of response systems, predominantly based on a command and control model, limits their effectiveness and efficiency. Particularly, in decision‐making processes where a large number of actors may be involved. In this article, a new distributed collaborative decision‐making model is proposed to overcome command and control limitations encountered in stressful, hostile, chaotic, and large‐scale settings. This model was derived by borrowing concepts from the collective decision making of honeybees foraging, a successful process in solving complex tasks within complex settings. The model introduced in this article was evaluated through differential equations, i.e., continuous analysis, and difference equations, i.e., discrete analysis. The most important result found is that the best available option in any large‐scale decision‐making problem can be configured as an attractor, in a distributed and timely manner. We suggest that the proposed model has the potential to facilitate decision‐making processes in large‐scale settings. © 2005 Wiley Periodicals, Inc. Complexity 11:28–38, 2005     

Lithium heptadecafluorooctanesulfonate catalyzed Mannich-type and aza-Diels-Alder reactions in supercritical carbon dioxide

The Mannich-type reaction of imines with (1-methoxy-2-methylpropenyloxy)trimethylsilane and aza-Diels-Alder reaction of imines with Danishefsky's diene can be carried out in scCO₂ in the presence of lithium heptadecafluorooctanesulfonate which offer a way to synthesize β-amino carbonyl compounds and nitrogen-containing six-membered ring compounds under environmentally benign conditions.     

X波段六腔渡越管振荡器的高频特性研究

 从麦克斯韦方程出发，采用时域有限差分法（FDTD）和离散傅里叶变换（DFFT）相结合的方法，通过数值计算得出了六腔开放式谐振腔中前四个谐振频率和场分布，计算出的谐振频率与实验测量结果基本相同。比较了开放腔和封闭腔谐振频率，验证了TEM波吸收边界条件，并在实际编程计算中得以应用。计算结果为六腔渡越管振荡器的机理研究提供了依据。     

On Constraint Qualifications in Nonsmooth Optimization

We introduce extensions of the Mangasarian-Fromovitz and Abadie constraint qualifications to nonsmooth optimization problems with feasibility given by means of lower-level sets. We do not assume directional differentiability, but only upper semicontinuity of the defining functions. By deriving and reviewing primal first-order optimality conditions for nonsmooth problems, we motivate the formulations of the constraint qualifications. Then, we study their interrelation, and we show how they are related to the Slater condition for nonsmooth convex problems, to nonsmooth reverse-convex problems, to the stability of parametric feasible set mappings, and to alternative theorems for the derivation of dual first-order optimality conditions.In the literature on general semi-infinite programming problems, a number of formally different extensions of the Mangasarian-Fromovitz constraint qualification have been introduced recently under different structural assumptions. We show that all these extensions are unified by the constraint qualification presented here.     

On General Mixed Quasivariational Inequalities

In this paper, we suggest and analyze several iterative methods for solving general mixed quasivariational inequalities by using the technique of updating the solution and the auxiliary principle. It is shown that the convergence of these methods requires either the pseudomonotonicity or the partially relaxed strong monotonicity of the operator. Proofs of convergence is very simple. Our new methods differ from the existing methods for solving various classes of variational inequalities and related optimization problems. Various special cases are also discussed.     

Elliptic and parabolic problems in unbounded domains

We consider elliptic and parabolic problems in unbounded domains. We give general existence and regularity results in Besov spaces and semi‐explicit representation formulas via operator‐valued fundamental solutions which turn out to be a powerful tool to derive a series of qualitative results about the solutions. We give a sample of possible applications including asymptotic behavior in the large, singular perturbations, exact boundary conditions on artificial boundaries and validity of maximum principles. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fractions continues de matrices,convergence et applications

The aim of this article is to give some property of continued fraction with matrices arguments, about their convergence and others applications. At the end of this work, we present a resolution of the Algebraic Riccati Equation by giving an explicit continued fraction development of its solution. This revised version was published online in August 2006 with corrections to the Cover Date.     

Artificial boundary conditions for Petrovsky systems of second order in exterior domains and in other domains of conical type

The approximation of solutions to boundary value problems on unbounded domains by those on bounded domains is one of the main applications for artificial boundary conditions. Based on asymptotic analysis, here a new method is presented to construct local artificial boundary conditions for a very general class of elliptic problems where the main asymptotic term is not known explicitly. Existence and uniqueness of approximating solutions are proved together with asymptotically precise error estimates. One class of important examples includes boundary value problems for anisotropic elasticity and piezoelectricity. Copyright © 2004 John Wiley & Sons, Ltd.     

Analysis of finite dimensional approximations to a class of partial differential equations

In this paper, a unified approach for analysing finite dimensional approximations to a class of partial differential equations boundary value problems (second‐kind Fredholm differential equations) is introduced. The approach is shown to be general despite of its extremely simple form. In particular, it is expected to be useful in the convergence analysis of finite element methods for solving PDE problems. Three specific examples are presented to illustrate the broad applicability of the approach. Copyright © 2004 John Wiley & Sons, Ltd.