Many linear boundary value problems arising in computational physics can be formulated in the calculus of differential forms. Discrete differential forms provide a natural and canonical approach to their discretization. However, much freedom remains concerning the choice of discrete Hodge operators, that is, discrete analogues of constitutive laws. A generic discrete Hodge operator is introduce...

In this paper we consider the infinite horizon H2/H∞ control problem for discrete-time timevarying linear systems subject to Markov jump parameters and state-multiplicative noises. A stochastic bounded real lemma is firstly developed for a class of discrete-time time-varying Markov jump systems with stateand disturbance-multiplicative noises. Based on which, a necessary and sufficient condition...

Any discrete differential manifold M (finite set endowed with an algebraic differential calculus) can be represented by appropriate polyhedron P(M). This representation demonstrates the adequacy of the calculus of discrete differential manifolds and links this approach with that based on finitary substitutes of continuous spaces introduced by R.D.Sorkin.

In this paper we present a syntactical approach for the design of real-time embedded systems. The requirement of the system is specified as Duration Calculus formula over continuous state variables. We model discretization at the state level and approximate continuous state variables by discrete ones. The discrete design is formulated as Duration Calculus formula over discrete state variables. ...

The multiplicative coalescent X(t) is a l-valued Markov process representing coalescence of clusters of mass, where each pair of clusters merges at rate proportional to product of masses. From random graph asymptotics it is known (Aldous (1997)) that there exists a standard version of this process starting with infinitesimally small clusters at time −∞. In this paper, stochastic calculus techni...

We give a first-principles description of the context semantics of Gonthier, Abadi, and Lévy, a computer-science analogue of Girard’s geometry of interaction. We explain how this denotational semantics models λ-calculus, and more generally multiplicative-exponential linear logic (MELL), by explaining the call-by-name (CBN) coding of the λcalculus, and proving the correctness of readback, where ...

We reconsider work by Bellin and Scott in the 1990s on R. Milner and S. Abramsky’s encoding of linear logic in the π-calculus and give an account of efforts to establish a tight connection between the structure of proofs and of the cut elimination process in multiplicative linear logic, on one hand, and the input-output behaviour of the processes that represent them, on the other, resulting in ...

These notes survey some aspects of discrete-time chaotic calculus and its applications, based on the chaos representation property for i.i.d. sequences of random variables. The topics covered include the Clark formula and predictable representation, anticipating calculus, covariance identities and functional inequalities (such as deviation and logarithmic Sobolev inequalities), and an applicati...

The notion of multilinear quantum Lie operation appears naturally in connection with a different attempts to generalize the Lie algebras. There are a number of reasons why the generalizations are necessary. First of all this is the demands for a ”quantum algebra” which was formed in the papers by Ju.I. Manin, V.G. Drinfeld, S.L. Woronowicz, G. Lusztig, L.D. Faddeev, and many others. These deman...