Dr
Sergei Meshveliani
(Program systems institute, Pereslavl-Zalessky, Russia)
07/07/2017, 12:30
It is described a certain provable program for a generic arithmetic
of fractions. This is a small part of the project DoCon-A of provable
programs for a computer algebra library. In this system, functional
programs for known algebraic methods are written together with proofs, and proofs are automatically checked by the compiler (see the Coq and Agda systems). The used language (Agda) is...
Dr
Anatoli Loutsiouk
(Department of Civil Engineering, King Mongkut University of Technology Thonburi, Thailand)
07/07/2017, 12:45
The multiplicity of a weight of an irreducible finite-dimensional representation of a complex semisimple Lie algebra can in principle be evaluated by using the celebrated Kostant multiplicity formula, which employs summation of values of Kostant partition function over the Weyl group of the algebra. While Kostant’s formula is quite elegant, it is usually not suitable for computations due to...
Mikhail Malykh
(RUDN University)
07/07/2017, 13:00
Modern development of computer science revived the old investigations about the solvability of differential equations in the finite terms. There are remarkable differential equations which can be integrated in CAS. In our work we want to speak about remarkable differential equations in another sense: for these equations there are finite difference schemes which conserve algebraic properties of...
Mikhail Malykh
(RUDN University)
07/07/2017, 13:15
Consider a waveguide of a constant simply connected cross-section $S$ with ideally conducting walls. The axis $Oz$ is directed along the cylinder axis, the normal to $\partial S$ will be denoted as $\vec n$, the tangent vector perpendicular to $\vec e_z$ as $\vec \tau$. Let the filling $\epsilon$, $\mu$ of this waveguide have the jump at $z=0$ so this plane is the joint of two waveguide. For a...
Dr
Sergey Perepechko
(Petrozavodsk State University)
07/07/2017, 13:30
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Near-perfect matchings on cylinders $C_m \times P_n$ of odd order
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Abstract:\\
The problem of counting near-perfect matchings on...
Mr
Denis Yanovich
(LIT JINR)
07/07/2017, 13:45
In this paper the author will talk about the problem of computing involutive bases and Gröbner bases of linear systems of difference equations, its importance, applicability for physical and mathematical problems and the algorithm for solving it.
An implementation of the computation algorithm in C will be presented, calculation times will be compared with the competing programs. The parallel...
Ms
Anastasya Demidova
(Peoples’ Friendship University of Russia (RUDN University)), Mr
Migran Gevorkyan
(PFU)
07/07/2017, 14:30
To describe models where the intensity of the interaction between components depends on the concentration of a component, one can use the scheme of interaction from chemical kinetics:
\[
\sum\limits^{n}_{i=1}N^{s}_{i}X_{i} \xleftrightarrow[\;\;k^{-}_{s}\;\;]{\;\;k^{+}_{s}\;\;} \sum\limits^{n}_{i=1}M^{s}_{i}X_{i},\; s = 1,\ldots,S.
\]
Here $X_{i}$ represents the number $i$-th component,...
Konstantin Marinov
(JINR)
07/07/2017, 14:45
In this work we consider Korteveg-de Vries equation and apply to it our approach based on difference elimination by construction of a Groebner basis. As a result, we obtain finite difference approximation with second-order accuracy for the space and time. This scheme is consistent with Korteveg-de Vries equation and stable due to it is implicit. Therefore, our scheme is convergent. We made...
Dr
Dmitry Kulyabov
(PFUR & JINR)
07/07/2017, 15:00
We are studying the process of global synchronization in systems with control. As a control system, we study the continuous model of the active control module of the type RED [1-3]. We apply the method of harmonic linearization. To simplify the model, we applied the following: the model is written in moments; The model describes only the phase of avoiding overloading of the TCP Reno protocol;...
Mr
Viktor Rikhvitsky
(Joint Institute fo Nuclear Research)
07/07/2017, 15:15
Many natural phenomena are described by a system of nonlinear partial differential equations (PDEs) which is often difficult to be solved analytically, as there is no a general theory for completely solving of the nonlinear PDEs.
One of the most useful techniques is the Lie (classical) symmetry method and to obtain the invariant solutions, we focus on the physically interesting situations...
Dr
Dmitry Kulyabov
(PFUR & JINR)
07/07/2017, 15:30
When modeling different physical and technical systems, they can often be modeled in the form of one-step processes. Our group has been developing a formalism of stochastization of one-step processes for quite a long time. We investigated a variety of representations of both the one-step processes, and methods of their stochastization. We have considered representations in the state vectors...
Dr
Alexander Kryukov
(SINP MSU)
07/07/2017, 15:45
Will be presented the computer algebra algorithms of simplification of tensor expressions which based on group-theoretical properties of tensor monoms and multilinear identities like Bianchi.
Dr
Robert Yamaleev
(JINR LIT)
07/07/2017, 16:00
An algorithm of reduction of n-order differential equation into the system of n-order Riccati-type equations is constructed. Solutions of the system of Riccati equations are roots of the polynomial coefficients of which are given by the set of linear independent solutions of n-order differential equation. Interrelations with the Poincare model of hyperbolic space and the general complex...
Dr
A. Raportirenko
(JINR)
07/07/2017, 16:15
It is created the minimal development environment for computer algebra systems
AXIOM, REDUCE and MAXIMA, which includes compilers from С and FORTRAN, standard
libraries libc, libm, ..., utilities lex, yacc, awk, ..., and COMMON LISP
interpreter, which is complete and closed.
It is based on sources of libraries and compilers of the middle of 90-th,
available in internet and belonging to...
