We present an algorithm for the solution of a nontrivial coupled system of algebraic Riccati equations appearing in risk sensitive control problems. Moreover we use comparison methods to derive non blow up conditions for the solutions of a corresponding terminal value problem for coupled systems of Riccati di erential equations.

In this paper we present some results about analytic machines regarding the power of computations over Q or R solutions of di erential equations and the stability problem of dynamical systems We rst explain the machine model which is a kind of Blum Shub Smale machine enhanced by in nite convergent computations Next we com pare the computational power of such machines over the elds Q and R showi...

In this paper we present a new symbolic approach to hybrid systems Hybrid systems are systems con taining both continuous and discrete changing quantities We model hybrid systems using hybrid automata Hybrid automata extend the classical notion of nite state machines by combining di erential equations to model the dynamic behavior of systems with a nite control In contrast to other approaches w...

This paper reviews the formulation and application of optimization techniques based on control theory for aerodynamic shape design in both inviscid and viscous compressible ow. The theory is applied to a system de ned by the partial di erential equations of the ow, with the boundary shape acting as the control. The Frechet derivative of the cost function is determined via the solution of an adj...

Computer simulations of realistic applications usually require solving a set of non-linear partial di erential equations (PDEs) over a nite region. The process of obtaining numerical solutions to the governing PDEs involves solving large sparse linear or eigen systems over the unstructured meshes that model the underlying physical objects. These systems are often solved iteratively, where the s...

In this paper we consider the pair di usion process in more than two spatial dimensions. In this case we are able to prove just a local existence result, since it is not possible to deduce global a priori estimates for the equations as it can be done in the two dimensional case. The model includes a nonlinear system of reaction{ drift{di usion equations, a nonlinear ordinary di erential equatio...

This report presents a new statistical attack on iterative block ciphers called the correlation attack which is a natural generalization of linear cryptanalysis. The attack is based on nding complex-valued functions on the input and the output of a cipher which have a high correlation. Their mutual relation is then exploited to yield information about the nal round key. Introducing the notions ...

In this paper we describe how wavelets may be used to solve partial diierential equations. These problems are currently solved by techniques such as nite diierences, nite elements and multi-grid. The wavelet method, however, ooers several advantages over traditional methods. Wavelets have the ability to represent functions at diierent levels of resolution, thereby providing a logical means of d...

— We present recent existence results of quasi-periodic solutions for Schrödinger equations with a multiplicative potential on T , db 1, finitely di¤erentiable nonlinearities, and tangential frequencies constrained along a pre-assigned direction. The solutions have only Sobolev regularity both in time and space. If the nonlinearity and the potential are in Cl then the solutions are in Cl. The p...

Interval methods for ordinary di erential equations (ODEs) provide guaranteed enclosures of the solutions and numerical proofs of existence and unicity of the solution. Unfortunately, they may result in large over-approximations of the solution because of the loss of precision in interval computations and the wrapping e ect. The main open issue in this area is to nd tighter enclosures of the so...