Differential forms and Clifford analysis

In this paper we use a calculus of differential forms which is defined using an axiomatic approach. We then define integration of differential forms over chains in a new way and we present a short proof of Stokes' formula using distributional techniques. We also consider differential forms in Clifford analysis, vector differentials and their powers. This framework enables an easy proof for a Cauchy's formula on a k-surface. Finally, we discuss how to compute winding numbers in terms of the monogenic Cauchy kernel and the vector differentials with a new approach which does not involve cohomology of differential forms

Modelling of Elastic Gearboxes Using a Generalized Gear Contact Model

The object of this paper is to present an universal model that describes the gear contact between two gears in a planar environment. The model includes elastic effects between the gear wheels. Using this model it is possible to create arbitrary spur gear connections as well as all kinds of epicyclic gearing configurations by supplying the proper external constraints. The presented model is implementated in the Modelica language and Dymola is used for the simulations

A discrete Bochner-Martinelli formula

In the even dimensional case the discrete Dirac equation may be reduced to the so-called discrete isotonic Dirac system in which suitable Dirac operators appear from both sides in half the dimension. This is an appropriated framework for the development of a discrete Martinelli-Bochner formula for discrete holomorphic functions on the simplest of all graphs, the rectangular Z(m) one. Two lower-dimensional cases are considered explicitly to illustrate the closed analogy with the theory of continuous variables and the developed discrete scheme

Supersonic-combustion rocket

A supersonic combustion rocket is provided in which a small rocket motor is substituted for heavy turbo pumps in a conventional rocket engine. The substitution results in a substantial reduction in rocket engine weight. The flame emanating from the small rocket motor can act to ignite non-hypergolic fuels

Harmonic and monogenic functions in superspace

The aim of this work is to further extend the analytic theory of monogenic functions in superspace and to construct a set of operators that allow to construct an explicit basis for the spaces of symplectic spherical harmonics