No abstract

This chapter introduces the maple software package stochastic consisting of maple routines for stochastic calculus and stochastic differential equations and for constructing basic numerical methods for specific stochastic differential equations, with simple examples illustrating the use of the routines. A website address is given from which the software can be downloaded and where up to date information about installment, new developments and literature can be found.

It is shown that for any Petrov type III, shear-free, perfect-fluid solution of Einstein's field equations, in which the perfect fluid satisfies a barotropic equation of state such that , the fluid volume expansion is zero. In addition, the fluid must necessarily be rotating.

No abstract

It is shown that for any Petrov type III, shear-free, perfect fluid solution of Einstein's field equations, in which the perfect fluid satisfies a barotropic equation of state p = p(w) such that , the fluid volume expansion is zero, or the equation of state satisfies . It follows that all such perfect fluids whose equation of state is the gamma law, must have zero fluid volume expansion.