In this paper conditional hidden Markov model (HMM) lters and conditional Kalman lters (KF) are coupled together to improve demodulation of di erential encoded signals in noisy fading channels. We present an indicator matrix representation for di erential encoded signals and the optimal HMM lter for demodulation. The lter requires O(N) calculations per time iteration, where N is the number of m...

Consider the Cauchy problem for an ordinary diierential equation _ x = g(t; x); x(0) = x; t 2 0; T]: (1:1) When g is continuous, the local existence of solutions is provided by Peano's theorem. Several existence and uniqueness results are known also in the case of a discontinuous right hand side 7]. We recall here the classical theorem of Carath eodory 8]: Theorem A. Let g : 0; T] IR n 7 ! IR n...

We deene continual queries as a useful tool for monitoring of updated information. Continual queries are standing queries that monitor the source data and notify the users whenever new data matches the query. In addition to periodic refresh, continual queries include Epsilon Transaction concepts to allow users to specify query refresh based on the magnitude of updates. To support eecient proces...

Here we will provide an overview of the method of nding symmetries of partial di erential equations. First we will discuss some basic facts regarding local groups of transformations, symmetries of algebraic equations and group actions on functions. We will then proceed to a discussion of how to interpret the task of solving a PDE in terms of jet spaces, and the meaning of group actions in this ...

In this survey we recall the results obtained in [16] where we gave a representation theorem for the solutions of stochastic di¤erential equations in Hilbert spaces. Using this representation theorem and the deterministic characterizations of exponential stability and uniform observability obtained in [16], [17], we will prove a result of Datko type concerning the exponential dichotomy of stoch...

Solvability of forward–backward stochastic di erential equations with nonsmooth coe cients is considered using the Four-Step Scheme and some approximation arguments. For the onedimensional case, the existence of an adapted solution is established for the equation which allows the di usion in the forward equation to be degenerate. As a byproduct, we obtain the existence of a viscosity solution t...

In this paper, a numerical method is presented for proving the existence and inclusion of connecting orbits of continuous dynamical systems described by parameterized nonlinear ordinary di erential equations. Taking a certain second order nonlinear ordinary di erential equaiton as an example, the existence of homoclinic bifurcation points is proved by the method.

We study a new class of backward stochastic di€erential equations, which involves the integral with respect to a continuous increasing process. This allows us to give a probabilistic formula for solutions of semilinear partial di€erential equations with Neumann boundary condition, where the boundary condition itself is nonlinear. We consider both parabolic and elliptic equations.

In this paper, we investigate the almost surely asymptotic stability for the nonlinear stochastic di erential delay equations with Markovian switching. Some su0cient criteria on the controllability and robust stability are also established for linear stochastic di erential delay equations with Markovian switching. ? 2003 Elsevier Ltd. All rights reserved.

In this paper we give necessary design principles to be used, when constructing secure Feistel ciphers. We introduce a new concept, practical security against linear and di erential attacks on Feistel ciphers. We give examples of such Feistel ciphers (practically) resistant to di erential attacks, linear attacks and other attacks.