As UML 2.0 is evolving into a family of languages with individually specified semantics, there is an increasing need for automated and provenly correct model transformations that (i) assure the integration of local views (different diagrams) of the system into a consistent global view, and, (ii) provide a well–founded mapping from UML models to different semantic domains (Petri nets, Kripke aut...

We are concerned primarily with the task of uncovering the precise mathematical proofs which underlie certain semi-formal arguments. In the area of program development the program transformations [BuD77] are an excellent example of semi-formality, since, as is well known, the calculus of transformations is not, in general, sound1, and it is capable of effecting significant shifts in logical com...

The paper summarizes and generalizes a recently proposed mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics. The framework is based on Hilbert spaces H of functions of four space-time variables x, t, furnished with an additional indefinite inner product invariant under Poincaré transformations, and isomorphisms of these spaces that preserve t...

Hanson et al. [4] described mathematical visualization as “the art of creating concrete understanding from abstract mathematical objects and their transformations.” Such artistry may be difficult to achieve because it demands both mathematical and graphical knowledge in one person, or excellent communication between members of a group of individuals with specific talents. Furthermore, it may al...

In the two papers of this series, we initiate development a new approach to implementing concept symmetry in classical field theory, based on replacing Lie groups/algebras by groupoids/algebroids, which are appropriate mathematical tools describe local symmetries when gauge transformations combined with space-time transformations. second part, shall adapt formalism developed first paper context...

This article is proposed to address the melting heat transfer of a Jeffrey fluid in Blasius and Sakiadis flow caused due to a moving surface. Thermal radiation and a constant free stream are considered in this mathematical model. The non-linear coupled dimensionless equations from the governing equations are attained by employing appropriate similarity transformations. The resulting dimensionle...

This communication influences on magnetohydrodynamic flow of viscoelastic fluid with magnetic field induced by oscillating plate. General solutions have been found out for velocity and shear stress profiles using mathematical transformations (Integral transforms). The governing partial differential equations have been solved analytically under boundary conditions u(0,t)=A_0 H(t)sinΩt and u(0,t)...

It is well known that the parabolic partial differential equations in two or more space dimensions with overspecified boundary data, feature in the mathematical modeling of many phenomena. In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation in general dimensions is considered. Employing some transformations, we change the inverse prob...

The propagation of surface waves in a fluid- saturated porous isotropic layer over a semi-infinite homogeneous elastic medium with an irregularity for free and rigid interfaces have been studied. The rectangular irregularity has been taken in the half-space. The dispersion equation for Love waves is derived by simple mathematical techniques followed by Fourier transformations.  It can be seen t...