. We consider a multivariate continuous time process, generated by a system of linear stochastic di¤erential equations, driven by white noise and involving coe¢ cients that possibly vary over time. The process is observable only at discrete, but not necessarily equally-spaced, time points (though equal spacing signi…cantly simpli…es matters). Such settings represent partial extensions of ones s...

The problem of nding bounds on the H∞-norm of systems with a nite number of point delays and distributed delay is considered. Su cient conditions for the system to possess an H∞-norm which is less or equal to a prescribed bound are obtained in terms of Riccati partial di erential equations (RPDE’s). We show that the existence of a solution to the RPDE’s is equivalent to the existence of a stabl...

We present an overview of intrinsic integration schemes for di erential equations evolving on manifolds, paying particular attention to homogeneous spaces. Various examples of applications are introduced, showing the generality of the methods. Finally we discuss abstract Runge{Kutta methods. We argue that homogeneous spaces are the natural structures for the study and the analysis of these meth...

In this paper we consider the problem of constructing a well-posed state space model for a class of singular integro-diierential equations of neutral type. The work is motivated by the need to develop a framework for the analysis of numerical methods for designing control laws for aeroelastic and other uid/structure systems. Semigroup theory is used to establish existence and well-posedness res...

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 ...

In this paper we derive the sharp long time stability and error estimates of nite element approximations for parabolic integro di erential equations First the exponential decay of the solution as t is studied and then the semi discrete and fully discrete approximations are considered using the Ritz Volterra projection Other related problems are studied as well The main feature of our analysis i...

Much work paralleling the standard theory of linear di erential equations has been done recently for dynamic equations on time scales, providing a uni ed treatment of the continuous and discrete analysis in this area. One area which is less developed is the theory of series solutions, partly due to the lack of suÆcient di erentiability in a general time scale, and also due to the lack of an ana...

Collocation schemes are presented for solving linear fourth order di erential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalen...