Symbolic Reachability Computation for Families of Linear Vector Fields Gerardo Lafferriere Department of Mathematical Sciences Portland State University, P.O. Box 751, Portland, OR 97207-0751. [email protected] George J. Pappas Department of Electrical Engineering University of Pennsylvania, 200 South 33rd Street, Philadelphia, PA 19104. [email protected] Sergio Yovine VERIMAG Centre Equat...

We simulate the Kardar-Parisi-Zhang equation in 2+1 dimensions. It is a non linear stochastic di erential equation which describes driven growing interfaces. The Hopf-Cole transformation is used in order to obtain a stable numerical scheme. The two relevant critical exponents are precisely measured. PACS numbers: 64.60.Ht, 05.40.+j, 05.70.Ln, 68.35.Fx

0

There exists a vast literature about the di erentiabil ity of fuzzy valued mappings see for instance Dubois and Prade Puri and Ralescu Goetschel and Voxman or Kaleva One of the main problems in working with di erentials of fuzzy valued mappings is that the usual class of fuzzy sets of R does not con gure a vectorial space with respect to the sum and the product by a scalar induced by Zadeh s Ex...

Network management and control is a complex problem that requires robust, intelligent, control methodologies to obtain satisfactory performance. Active Queue Management (AQM) mechanisms have been introduced for router support to assist the TCP congestion control to perform satisfactorily in all circumstances. However, certain, well-known limitations, identified in the AQM literature, motivates ...

| In this short note we present an observability criterion for systems whose state is governed by a matrix Riccati di erential equation and whose output is given by an a ne transformation.

The following backward stochastic Riccati di erential equation (BSRDE in short) 8>>>>><>>>>>>>>>>>: dK = [AK +KA+ d X i=1 C 0 iKCi +Q+ d X i=1 (C 0 iLi + LiCi)

For xed = (x; t), we consider the solution u(f) to u (x; t) + Au(x; t) = f(x) (x; t); x 2 ; t > 0 u(x; 0) = u(x; 0) = 0; x 2 ; Bju(x; t) = 0; x 2 @ ; t > 0; 1 j m; where u = @u @t , u = @ u @t , R, r 1 is a bounded domain with smooth boundary, A is a uniformly symmetric elliptic di erential operator of order 2m with t-independent smooth coe cients, Bj , 1 j m, are t-independent boundary di eren...

We provide rigorous evidence of the fact that the modified Constantin-Lax-Majda equation modeling vortex and quasi-geostrophic dynamics [22] describes the geodesic flow on the subgroup Diff∞1 (S) of orientation-preserving diffeomorphisms φ ∈ Diff∞(S) such that φ(1) = 1 with respect to right-invariant metric induced by the homogeneous Sobolev space Ḣ(S) and show the local existence of the geodes...

the purpose of this paper is to study the fuzzy fractional differentialequations. we prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. fuzzy derivative is considerin the goetschel-voxman sense and fractional derivative is consider in theriemann liouville sense. at the end, we...