Experimenting with Different Approaches to Test Colinearity of Points

The subject of collinearity of 3 points on a line is challenging for 7th- grade students. This article discusses the possibilities to demonstrate different approaches for solving collinearity of three points on a line: straight angle, axiom on the uniform mapping of an angle on a half-plane, parallel axiom, vector method, and homothetic features. The experiment was held using GEONExT to demonstrate by visual methods collinearity of three points on a line a district type of problems.

Solving Differential Equations by Parallel Laplace Method with Assured Accuracy

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Parallel Algorithm for the Local Variations Method

Димитър С. Илиев, Станимир Д. Илиев - Актуално е изследването на поведението на течен менискус в околността на хетерогенна стена. До сега няма получено числено решение за формата на менискуса около стена, която е с хаотична хетерогенност. В настоящата статия е разработен алгоритъм за метода на локалните вариации, който може да се използва на многопроцесорни системи. С този метод е получен за първи път профила на равновесен течен менискус около вертикална стена с хаотична хетерогенност.

Randomized Parallelization – a New Method for Solving Hard Combinatorial Problems

A new method for solving some hard combinatorial optimization problems is suggested, admitting a certain reformulation. Considering such a problem, several different similar problems are prepared which have the same set of solutions. They are solved on computer in parallel until one of them will be solved, and that solution is accepted. Notwithstanding the evident overhead, the whole run-time could be significantly reduced due to dispersion of velocities of combinatorial search in regarded cases. The efficiency of this approach is investigated on the concrete problem of finding short solutions of non-deterministic system of linear logical equations.

The Development of Parallel Resolution Algorithms Using the Graph Representation

The parallel resolution procedures based on graph structures method are presented. OR-, AND- and DCDP- parallel inference on connection graph representation is explored and modifications to these algorithms using heuristic estimation are proposed. The principles for designing these heuristic functions are thoroughly discussed. The colored clause graphs resolution principle is presented. The comparison of efficiency (on the Steamroller problem) is carried out and the results are presented. The parallel unification algorithm used in the parallel inference procedure is briefly outlined in the final part of the paper.

Monte Carlo Algorithm for Solving Integral Equations with Polynomial Non-Linearity. Parallel Implementation

An iterative Monte Carlo algorithm for evaluating linear functionals of the solution of integral equations with polynomial non-linearity is proposed and studied. The method uses a simulation of branching stochastic processes. It is proved that the mathematical expectation of the introduced random variable is equal to a linear functional of the solution. The algorithm uses the so-called almost optimal density function. Numerical examples are considered. Parallel implementation of the algorithm is also realized using the package ATHAPASCAN as an environment for parallel realization.The computational results demonstrate high parallel efficiency of the presented algorithm and give a good solution when almost optimal density function is used as a transition density.