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We study uniformly distributed direction of motion at finite speed where the direction alternations occur according to the renewal epochs of a K-Erlang pdf. At first sight, our generalizations of previous Markovian results appears to be a small step, however, it must be seen as an important non-Markovian case where we have found closed-form expressions for the pdf and the conditional characteristic function of this semi-Markov transport process. We present detailed calculations of a three-dimensional example for the 2-Erlang case, which is important not only from physical applications point of view but also to understand more general models. For instance, in principle the example of the 2-Erlang case can be extended to a K-Erlang case (K = 3, 4, . . .) but some of the mathematical expressions may be cumbersome.

Communicated by W. SprößigGiven a PDE with real or complex partial derivatives and with constant coefficients, we propose a method of assigning to it a set of algebra-valued functions in such a manner that the components of the latter are solutions of the PDE. Copyright

In this article we study the roots or zeros of polynomials with bicomplex coefficients. Bicomplex algebra is a two-dimensional Clifford algebra over C with commutative multiplication, and is a generalization of complex numbers. We present a technique for computing zeros of bicomplex polynomials, and illustrate our main results with some examples.

Abstract-In this paper we study a one-dimensional random motion by having a general Erlang distribution for the sojourn times and we obtain higher order hyperbolic equations for this case. We apply the methodology of random evolutions to find the partial differential equations governing the particle motion and we obtain a factorization of these equations. As a particular case we find the linear biwave equation for the symmetric motion case and 2-Erlang distributions for the sojourn times of a semi-Markov evolution.