it is well known that the parabolic partial differential equationsin two or more space dimensions with overspecified boundary data,feature in the mathematical modeling of many phenomena. in thisarticle, an inverse problem of determining an unknowntime-dependent source term of a parabolic equation in generaldimensions is considered. employing some transformations, wechange the inverse problem to...

Mathematics requires thinking but also pattern recognition. Recent research indicates that perceptual learning (PL) interventions facilitate discovery of structure and recognition of patterns in mathematical domains, as assessed by tests of mathematical competence. Here we sought direct evidence that a brief perceptual learning module (PLM) produces changes in basic information extraction. Accu...

Wavelet transformation is one of the most practical mathematical transformations in the field of image processing, especially image and signal processing. Depending on the nature of the multiresolution analysis, Wavelet transformation become more accessible and powerful tools. In this paper, we refer to the mathematical foundations of this transformation.   Introduction: The...

The polyhedral model provides techniques to optimize Static Control Programs (SCoP) using some complex transformations which improve data-locality and which can exhibit parallelism. These advanced transformations are now available in both GCC and LLVM. In this paper, we focus on the correctness of these transformations and in particular on the problem of integer overflows. Indeed, the strength ...

On the basis of the Michelson-Morley experiment, the physical models of Einstein’s and Lorentz’s theories are discussed, together with their respective logical and mathematical processes, both leading to the same transformations by Lorentz. Our analysis evidences logical coherence problems between Einstein’s model and the Lorentz transformations, as well as in the “light postulate” itself. Repl...

This paper discusses picture logic, a visual language for the specification of diagrams and diagram transformations. Formal specification techniques for diagrammatic or visual languages have previously mainly been targeted towards static diagrammatic languages. For reasoning about certain types of diagrams, however, formalizing a notion of change is inevitable. This is particularly true of visu...

Convergence problems occur abundantly in all branches of mathematics or in the mathematical treatment of the sciences. Sequence transformations are principal tools to overcome convergence problems of the kind. They accomplish this by converting a slowly converging or diverging input sequence {sn} ∞ n=0 into another sequence {s ′ n }∞ n=0 with hopefully better numerical properties. Padé approxim...

This paper presents a new approach for PLL for synchronization with the public grid phase and frequency of grid-connected single phase inverter. The approach uses trigonometric transformations of the inverter output voltage and the grid voltage. The proposed mathematical model is then studied by means of computer simulation for different voltage amplitudes of the grid voltage as well as the inv...

We consider systems of diffusion equations that have considerable interest in Soil Science and Mathematical Biology and focus upon the problem of finding those forms of this class that can be linearized. In particular we use the equivalence transformations of the second generation potential system to derive forms of this system that can be linearized. In turn, these transformations lead to nonl...

Slowly convergent series and sequences as well as divergent series occur quite frequently in the mathematical treatment of scientific problems. In this report, a large number of mainly nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series are discussed. Some of the sequence transformations of this report as for instance Wynn’s ǫ algorithm o...