Abstract: Besides different definitions, in this work is given the so called transformation matrix, which maps the given index space in another index space. Transformation used in this new index space reduces the number of processing elements in the array. We illustrate all possible instances of transformation matrices and we show the importance of using the transformation matrix by comparing t...

Graph transformation provides an intuitive mechanism for capturing model transformations. In the current paper, we investigate and compare various graph transformation tools using a compact practical model transformation case study carried out as part of the AGTIVE 2007 Tool Contest [22]. The aim of this case study is to generate formal CSP processes from high-level UML activity diagrams, which...

In this paper, we focus on a general class of Schrödinger equations that are time-dependent and quadratic in X and P . We transform Schrödinger equations in this class, via a class of time-dependent mass equations, to a class of solvable timedependent oscillator equations. This transformation consists of a unitary transformation and a change in the “time” variable. We derive mathematical constr...

During the design process of dependable computer controlled systems the verification process aiming to assess whether the system fulfils its requirements or needs some re-design is indispensable at each level of abstraction and after each step of system model refinement in order to spare time and resources. When such a refinement step is performed, system characteristics like dependability, tim...

Mathematical assistance systems and proof assistance systems in general have traditionally been developed as large, monolithic systems which are often hard to maintain and extend. In this article we propose a component network architecture as a means to design and implement such systems. Under this view a mathematical assistance system is an integrated knowledge-based system composed as a netwo...

This chapter aims to deepen the idea that one of the crucial aspects of algebraic problem solving is the transformation of the mathematical structure of the problem in order to be able to manage it better, and that anticipation allows the process of transformation to be directed towards simplifying and resolving the task. Different cases of the transformation of the problem (without, before and...

A new computationally efficient framework for vehicle tracking on a mobile platform is proposed. The principal component of the framework is the log-polar transformation applied to video frames captured from a standard uniformly sampled format camera. The log-polar transformation provides two major benefits to real-time vehicle tracking from a mobile vehicle platform moving along a single or mu...

The use of formal verification methods is essential in the design process of dependable computer controlled systems. A complex environment should support the semiformal specification as well as the formal verification of the desired system. The efficiency of applying these formal methods will be highly increased if the underlying mathematical background is hidden from the designer. In such an i...

An important problem in computer vision is to determine how features extracted from images are connected to an existing model. In this paper, we focus on solving the registration problem, i.e. obtaining rigid transformation parameters between several 3D data sets, whether partial or exhaustive. The di culty of this problem is to obtain a method which is robust with respect to outliers and at th...

PQ analysis for detecting power line disturbances in real-time is one of the major challenging techniques that are being explored by many researchers. In order to understand the causes of electronic equipment being damaged due to disturbances in power line, there is a need for a robust and reliable algorithm that can work online for PQ analysis. PQ signal analysis carried out using transformati...