As the Model Driven Architecture (MDA) relies on complex and highly automated model transformations between arbitrary modeling languages, the quality of such transformations is of immense importance as it can easily become a bottleneck of a model-driven design process. Automation surely increases the quality of such transformations as errors manually implanted into transformation programs durin...

This paper shows the existence of a critical dimension for finite length nanowires exhibiting shape memory effects. We give a brief survey of phase transformations, their classifications, and provide the basis of mathematical models for the phenomena involving such transformations, focusing on shape memory effects at the nanoscale. Main results are given for the dynamic of square-to-rectangular...

Selected Common Threads and Root Concepts Linking Old to New Sandra L. Arlinghaus* and Joseph Kerski** Introduction In the twentieth century, much of mathematics experienced a well-known paradigm shift in moving from a focus on mathematical objects to a focus on transformations of objects. Thus, one sees, for example, linear algebra courses that focus on matrix vector products as linear transfo...

In software engineering, transformational development is aimed at developing computer systems by transforming a coarse-grained specification of a system to its final code through a series of transformation steps. Transformational development is known to bring benefits such as: correctness by construction, explicit mappings between development steps, and reversibility of transformations. No comp...

The way super- and sub-additive transformations of aggregation functions are introduced involve suprema and infima taken over simplexes whose dimensions may grow arbitrarily. Exact values of such transformations may thus be hard to determine in general. In this note we discuss methods of algorithmic approximation of such transformations.

We prove that any multiple-copy entanglement transformation fS. Bandyopadhyay, V. Roychowdhury, and U. Sen, Phys. Rev. A 65, 052315 s2002dg can be implemented by a suitable entanglement-assisted local transformation fD. Jonathan and M. B. Plenio, Phys. Rev. Lett. 83, 3566 s1999dg. Furthermore, we show that the combination of multiple-copy entanglement transformation and the entanglement-assiste...

In software engineering transformational development aims at developing software systems by transforming a coarse-grained specification to final code (or to a detailed specification) through a sequence of small transformation steps. Transformational development is known to bring benefits such as: correctness-preserving of the development cycle, explicit mappings between development steps, reusa...

In molecular shape analysis and in the analysis of various molecular functions used in modeling chemical reactions and biochemical interactions, it is often useful to generate transformations that interconvert various molecular models into one another. Some of these models are continua whereas some others have disconnected parts or even separated discrete points. The interconversion between suc...

The polyhedral model is a collection of techniques developed around a common intermediate representation of programs : integer polyhedra. Such a mathematical representation of programs inherits nice structural properties. For instance, when loop transformations are represented as affine functions, compositions of transformations are also affine functions due to their closure properties. The pol...

The paper deenes an algebraic tool for manipulating directed acyclic graphs (on short dags). The approach we propose combines two mathematical tools { category theory and universal algebra { and it allows an unitary treating of dags transformations. We show that the speciication, implementation and programming of concurrent systems can be achieved by using this theory.