42 research outputs found
A heat transfer with a source: the complete set of invariant difference schemes
In this letter we present the set of invariant difference equations and
meshes which preserve the Lie group symmetries of the equation
u_{t}=(K(u)u_{x})_{x}+Q(u). All special cases of K(u) and Q(u) that extend the
symmetry group admitted by the differential equation are considered. This paper
completes the paper [J. Phys. A: Math. Gen. 30, no. 23 (1997) 8139-8155], where
a few invariant models for heat transfer equations were presented.Comment: arxiv version is already officia
A problem with parameter for the integro-differential equations
The article proposes a numerically approximate method for solving a boundary value problem for an integro-differential equation with a parameter and considers its convergence, stability, and accuracy. The integro-differential equation with a parameter is approximated by a loaded differential equation with a parameter. A new general solution to the loaded differential equation with a parameter is introduced and its properties are described. The solvability of the boundary value problem for the loaded differential equation with a parameter is reduced to the solvability of a system of linear algebraic equations with respect to arbitrary vectors of the introduced general solution. The coefficients and the right-hand sides of the system are compiled through solutions of the Cauchy problems for ordinary differential equations. Algorithms are proposed for solving the boundary value problem for the loaded differential equation with a parameter. The relationship between the qualitative properties of the initial and approximate problems is established, and estimates of the differences between their solutions are given
ENSURING FOOD SAFETY OF THE REPUBLIC OF KAZAKHSTAN
This article analyzes the scientific and technical information, as well as experimental studies on the application of the principles of HACCP. By applying, the HACCP principles for chopped semi-finished products, the description of the investigated product has been developed, which includes following information: product name, composition, quality and safety indicators, main stages of the technological process; packing method; conditions of storage, transportation and sale, as well as information on labeling. the HACCP plan will allow food (meat) industry production of safe and high-quality goods. Thus, the general consumer will not have doubts about the quality of purchased semi-finished products
More efficient use of economic business management techniques
Nowadays economic methods of management pay a lot of attention to the development of people economy and it takes large importance.Халық шаруашылығы дамуының қазіргі кезеңінде басқарудың экономикалық әдістері зор маңыз алып отыр
Symmetry-preserving discrete schemes for some heat transfer equations
Lie group analysis of differential equations is a generally recognized
method, which provides invariant solutions, integrability, conservation laws
etc. In this paper we present three characteristic examples of the construction
of invariant difference equations and meshes, where the original continuous
symmetries are preserved in discrete models. Conservation of symmetries in
difference modeling helps to retain qualitative properties of the differential
equations in their difference counterparts.Comment: 21 pages, 4 ps figure
The sign, linguistic analysis, idioethnic interpretation of communication and linguistic persona
The purpose of the article is to review the theoretical aspects of ethnocultural interpretation of communicative behavior as a part of the national linguistic identity. Logical-semantic and logical-communicative components of an utterance are reviewed regarding the identification of ethnocultural components of an utteranc
Multiscale expansions of difference equations in the small lattice spacing regime, and a vicinity and integrability test. I
We propose an algorithmic procedure i) to study the ``distance'' between an
integrable PDE and any discretization of it, in the small lattice spacing
epsilon regime, and, at the same time, ii) to test the (asymptotic)
integrability properties of such discretization. This method should provide, in
particular, useful and concrete informations on how good is any numerical
scheme used to integrate a given integrable PDE. The procedure, illustrated on
a fairly general 10-parameter family of discretizations of the nonlinear
Schroedinger equation, consists of the following three steps: i) the
construction of the continuous multiscale expansion of a generic solution of
the discrete system at all orders in epsilon, following the Degasperis -
Manakov - Santini procedure; ii) the application, to such expansion, of the
Degasperis - Procesi (DP) integrability test, to test the asymptotic
integrability properties of the discrete system and its ``distance'' from its
continuous limit; iii) the use of the main output of the DP test to construct
infinitely many approximate symmetries and constants of motion of the discrete
system, through novel and simple formulas.Comment: 34 pages, no figur
Structures and waves in a nonlinear heat-conducting medium
The paper is an overview of the main contributions of a Bulgarian team of
researchers to the problem of finding the possible structures and waves in the
open nonlinear heat conducting medium, described by a reaction-diffusion
equation. Being posed and actively worked out by the Russian school of A. A.
Samarskii and S.P. Kurdyumov since the seventies of the last century, this
problem still contains open and challenging questions.Comment: 23 pages, 13 figures, the final publication will appear in Springer
Proceedings in Mathematics and Statistics, Numerical Methods for PDEs:
Theory, Algorithms and their Application
Lie point symmetries of difference equations and lattices
A method is presented for finding the Lie point symmetry transformations
acting simultaneously on difference equations and lattices, while leaving the
solution set of the corresponding difference scheme invariant. The method is
applied to several examples. The found symmetry groups are used to obtain
particular solutions of differential-difference equations
Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach
Five types of blow-up patterns that can occur for the 4th-order semilinear
parabolic equation of reaction-diffusion type
u_t= -\Delta^2 u + |u|^{p-1} u \quad {in} \quad \ren \times (0,T), p>1,
\quad \lim_{t \to T^-}\sup_{x \in \ren} |u(x,t)|= +\iy, are discussed. For
the semilinear heat equation , various blow-up patterns
were under scrutiny since 1980s, while the case of higher-order diffusion was
studied much less, regardless a wide range of its application.Comment: 41 pages, 27 figure