Analysis of the equations of a liquid crystal taking into account moment interaction
Page:369-374
Headings of the journal
"Educational Resources and Technologies"
Educational environmentMethods and technologies of training and educationInformation technologyMathematical cyberneticsMethodological researchManagement in social and economic systemsApplied GeoinformaticsEducation for sustainable developmentAll rubrics
All rubrics
Release: 2016-2 (14)
Keywords: liquid crystal, moment medium, dynamics, finite-difference scheme, parallel computational algorithm, CUDA technology
Annotation: Based on the mathematical model of a liquid crystal in the acoustic approximation, the system of two equations of second-order was obtained for tangential stress and angular velocity. Computational algorithm for numerical solution of boundary-value problems is worked out, implemented as a parallel program in the С language using the CUDA technology
Simulation of the stability of a system by the theory of one-dimensional percolation
Page:374-378
Release: 2016-2 (14)
Keywords: percolation theory, composite material, stability of the system
Annotation: A mathematical model of the system resistance to damage is considered. A new algorithm to determine the stability of damage based on quasi-one-dimensional percolation theory is proposed. The model can be used for interpretation of results in quasi-one-dimensional nanometer systems
The deterministic semantic of the regular expressions
Page:379-386
Release: 2016-2 (14)
Keywords: formal language parser, regular expression, Kleene algebra, finite automaton, deterministic semantic of regular expression
Annotation: The problem of conversion of formal language texts is of considerable practical importance for software reengineering and for the software integration. Pattern matching is technique of searching a text string based on a specific search pattern. The pattern specified by regular expression forms the basis for building a variety of converters. It is proposed to change the traditional model of the language parser by pattern matching based on the finite state machine into the algebra of patterns with side effects. The proposed deterministic semantic of regular expression eliminates the need to switch from the regular expression engine and user code execution environment and back again
Return the one-dimensional problem with an unknown source
Page:387-394
Release: 2016-2 (14)
Keywords: integral transforms, operator, bilinear system of integral equations, uniqueness theorems
Annotation: Investigated the one-dimensional inverse problem with an unknown source and an unknown variable coefficient two known solutions at fixed points in the plane. Inverse problem using the method of integral transforms is reduced to inverse problem of Sturm-Liouville problem. The uniqueness theorems are proved
On the cubature formula with the involving derivatives
Page:400-404
Release: 2016-2 (14)
Keywords: cubature formula, Sobolev function spaces
Annotation: The algorithm of replacing some other lattice nodes to minimize the error functional norm is developed under the concordance condition of the convergence order with lattice step and the smoothness of the function along the selected coordinate directions. The results obtained by the method tested in the control examples