Hybrid action systems extend a conventional action system with a guarded di erential equation | a di erential action | that de nes evolution of continuous variables while the guard remains true. The new action is given a weakest liberal precondition semantics, which is illustrated by examples from a train model. The example motivates a discussion of priorities in a system of iterated di erentia...

An action system framework is a predicate transformer based method for modelling and analysing distributed and reactive systems. The actions are statements in Dijkstra's guarded command language, and their semantics is given by predicate transformers. We extend conventional action systems with a di erential action consisting of a di erential equation and an evolution guard. The semantics is giv...

We describe some new algorithm and heuristics for computing the polynomial and rational solutions of bounded degree of a class of ordinary di erential equations, which includes generalized Riccati equations. As a consequence, our methods can be used for factoring linear ordinary di erential equations. Since they generate systems of algebraic equations in at most n unknowns, where n is the order...

This paper deals with Hermite matrix polynomials expansions of some relevant matrix functions appearing in the solution of di erential systems. Properties of Hermite matrix polynomials such as the three terms recurrence formula permit an e cient computation of matrix functions avoiding important computational drawbacks of other well-known methods. Results are applied to compute accurate approxi...

In this paper, we study general linear systems of delay di erential-algebraic equations (DDAEs) of arbitrary order. We show that under some consistency conditions, every linear high-order DAE can be reformulated as an underlying high-order ordinary di erential equation (ODE) and that every linear DDAE with single delay can be reformulated as a high-order delay di erential equation (DDE). We der...

Three schemes for linearizing the transconductance of the basic di erential pair in subthreshold CMOS are examined: 1) multiple asymmetric di erential pairs, 2) source degeneration via symmetric di usors, and 3) source degeneration via a single di usor. Using a maximally at optimizing criterion, the linear range of the basic di erential pair can be increased by four-to-eight times.

We introduce and study the Koszul complex for a Hecke R-matrix. Its cohomologies, called the Berezinian, are used to de ne quantum superdeterminant for a Hecke R-matrix. Their behaviour with respect to Hecke sum of R-matrices is studied. Given a Hecke R-matrix in n-dimensional vector space, we construct a Hecke R-matrix in 2n-dimensional vector space commuting with a di erential. The notion of ...

S hur omplement pre onditioning for ellipti systems of partial di erential equations D. Loghin and A. J. Wathen One su essful approa h in the design of solution methods for saddle-point problems requires the eÆ ient solution of the asso iated S hur omplement problem ([26℄, [19℄). In the ase of problems arising from partial di erential equations the fa torization of the symbol of the operator an...

This paper considers the security of iterated block ciphers against the di erential cryptanalysis introduced by Biham and Shamir Di erential cryptanalysis is a chosen plaintext attack on secret key block ciphers that are based on iterating a cryptographically weak function r times e g the round Data Encryption Standard DES It is shown that the success of such attacks on an r round cipher depend...

Transfer functions models of linear systems are a well established tool for the design and analysis of one-dimensional systems. This is not the case for multidimensional physical systems, given in terms of initial boundary value problems. Here, the only mathematical description of widespread use are partial di erential equations. This contribution shows, how the one-dimensional transfer functio...