The main topics of this technical report are quaternions, their mathematical properties, and how they can be used to rotate objects. We introduce quaternion mathematics and discuss why quaternions are a better choice for implementing rotation than the well-known matrix implementations. We then treat di erent methods for interpolation between series of rotations. During this treatment we give co...

The paper deals with the analysis of pair di usion models in semiconductor technology. The underlying model contains reaction-drift-di usion equations for the mobile point defects and dopant-defect pairs as well as reaction equations for immobile dopants which are coupled with a nonlinear Poisson equation for the chemical potential of the electrons. For homogeneous structures we present an exis...

We consider di erent situations of blowup in sup norm for hyper bolic equations For scalar conservation laws with a source the asymptotic pro le of the solution close to a blowup point is described in detail Based on an example of Je rey we next show how blowup for ordinary di erential equations can be used to construct examples of blowup for systems of hy perbolic equations Finally we outline ...

An approach for transforming systems of partial di erential equations in order to obtain new formulations which are more accessible to numerical solution is studied. An algorithm is developed for generating such transformations automatically, using symbolic computations employing Gr obner bases. The algorithm is implemented using freely available software. This approach, along with planned dev...

We de ne a discrete (integer-valued) Lyapunov function V for cyclic nearest neighbor systems of di erential delay equations possessing a feedback condition. This extends analogous de nitions for cyclic systems of ODE's, and for scalar di erential delay equations. We relate the values of V to the real parts of the Floquet multipliers for such linear periodic systems, and thereby prove all Floque...

The nite di erence method is a numerical analysis technique used to solve problems involving irregular geometries, complicated boundary conditions, or both. The geometries are represented using partial di erential equations. The solutions to the partial di erential equations can be easily generated with the aid of a computer. As the geometries become increasingly complex, the solutions of the p...

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...

The task of modeling, i.e. of creating a set of equations that can be used to predict the behavior of a physical object, is a key step in engineering analysis. This paper describes a computer system, MSG, for generating mathematical models to analyze physical systems involving heat transfer behavior. MSG is motivated by the need for modeling in an automated design process. The models are sets o...

Novel computing devices are exploited for numerical computation. The solution of a numerical problem is sought, which has been solved many times before, but this time with a di erent set of input data. A table is a classical way to collect the old solutions in order to exploit them to nd the new one. This process is extended to more general problems than the usual function value approximation. ...

This work presents the arguments for the possibility of approximating some discontinuous dynamical systems with continuous or even smooth dynamical systems. The discontinuous di€erential equation, which describes the system, is transformed into a di€erential inclusion and then into a di€erential equation with continuous or smooth right-hand side. As an example a generalization of the equations ...