In this paper we consider smooth di erential 1-forms and smooth nonlinear control-a ne systems with (n 1)-inputs evolving on an ndimensional manifold with boundary. These systems are called hypersurface systems under the additional assumption that the drift vector eld and control vector elds span the tangent space to the manifold. We locally classify all structurally stable di erential 1-forms ...

This paper describes the design philosophy behind the recent replacement of the NAG Ordinary Di erential Equation (ODE) sti integrators. This replacement was is intended to update the ODE chapter algorithmically but, more importantly in the context of this paper, it provides a more exible interface than has been available in the past. This interface is designed to permit a wide variety of probl...

This paper provides a large deviation principle for Non-Markovian, Brownian motion driven stochastic di↵erential equations with random coe cients. Similar to Gao & Liu [19], this extends the corresponding results collected in Freidlin & Wentzell [18]. However, we use a di↵erent line of argument, adapting the PDE method of Fleming [14] and Evans & Ishii [10] to the pathdependent case, by using b...

Einstein's eld equations for spatially self-similar locally rotationally symmetric perfect uid models are investigated. The eld equations are rewritten as a rst order system of autonomous ordinary di erential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system of di erential equations is reduced as far as possible. The system is subsequ...

A careful analysis of di erential renormalization shows that a distinguished choice of renormalization constants allows for a mathematically more fundamental interpretation of the scheme. With this set of a priori xed integration constants di erential renormalization is most closely related to the theory of generalized functions. The special properties of this scheme are illustrated by applicat...

We present four circuits implemented in subthreshold CMOS which greatly increase the linear range over the basic di erential pair. These circuits are appropriate for low voltage applications since there is no stacking of saturated transistors. The rst circuit topology employs multiple asymmetric di erential pairs. The second is a symmetric \bump" transconductor. The remaining two use source deg...

| We consider di erential equations A(x) _ x = g(x), where A is an n n-matrix of C 1 functions and g is C 1 . We investigate the above di erential equation about singular points x 0 that are standard in the sense of Rabier. In particular, the null space of A(x 0 ) is of dimension 1. We show that there is a C 1 -di eomorphism that transforms the above equation about x 0 into x 1 _ x 1 = 1, _ x 2...

Discussion and examples of holonomic and anholonomic constraints are presented in the languange of exteror di®erential forms.

The e ciency of numerically solving time-dependent partial di erential equations on parallel computers can be greatly improved by computing the solution on many time-levels simultaneously. The theoretical properties of one such method, namely the discrete-time multigrid waveform relaxation method, are investigated for systems of ordinary di erential equations obtained by spatial nite element di...

The present paper gives a new view point for the di erential operators with respect to the coordinates of the quantum matrix space. A special emphasis is put on an inductive construction of these di erential operators from the q-di erence operators de ned on each columns (resp. rows). This idea for understanding our operators provides us with two important applications: (1) a construction of th...