Provides society information that may include news, reviews or technical notes should be of interest to practitioners and researchers.

Elliptic pseudoanalytic function theory was considered independently by Bers and Vekua decades ago. In this paper we develop a hyperbolic analogue of pseudoanalytic function theory using the algebra of hyperbolic numbers. We consider the Klein-Gordon equation with a potential. With the aid of one particular solution we factorize the Klein-Gordon operator in terms of two Vekua-type operators. We...

We introduce a new construction of transfinite barycentric coordinates for arbitrary closed sets in 2D. Our method extends weighted Gordon-Wixom interpolation to non-convex shapes and produces coordinates that are positive everywhere in the interior of the domain and that are smooth for shapes with smooth boundaries. We achieve these properties by using the distance to lines tangent to the boun...

An extended ( ′ G )–expansion method is obtained by improving the form of solution in ( G′ G )– expansion method which is proposed in recent years. By using the extended ( ′ G )–expansion method and with the aid of homogeneous balance principle, many explicit and exact travelling wave solutions with two arbitrary parameters to the Klein-Gordon equation are presented, including the hyperbolic so...

Many of us will always remember the distressing scenes from various incidents during the troubles. I have vivid memories of looking after the victims of the Omagh bomb during my second week as JHO in the Royal Victoria Hospital in 1998. In the weeks following the Omagh bomb I re-read Marie by Gordon Wilson and it brought me to tears again. Gordon will always be remembered for forgiving those wh...

In this paper, we are interested to study the Sine-Gordon equation in generalized functions theory introduced by Colombeau, in the first we give result of existence and uniqueness of generalized solution with initial data are distributions (elements of the Colombeau algebra). Then we study the association concept with the classical solution.