Differencialnie Uravnenia i Protsesy Upravlenia

A discrete dynamic system generated by a diffeomorphism is considered. The task of constructing an invariant decomposition of the tangent space is set. This task is reduced to calculating the components of a chain recurrent set on a projective bundle. A computer-oriented tool for such a calculation is a symbolic image of a dynamic system, which is an oriented graph. The components of the chain recurrent set are determined by calculating the components of the strong connectivity of the symbolic image. A nontrivial example of calculating the desired tangent space decomposition is given.

Georgii Sergeevich Osipenko

Irina Alexeevna Andreeva

Differential Equations and Control Processes

Calculation of the Invariant Decomposition of the Tangent Space

切空间不变分解的计算

The article discusses the process of sublimation of chemically pure ammonium chloride crystals. Instrumental studies were conducted using synchronous thermal analysis, including thermogravimetry and differential scanning calorimetry, under non-isothermal conditions with three different heating rates (3, 5, and 10 В°C/min). The data obtained from the experiments were processed using the Friedman isoconversion method. Based on the assumption that the sublimation process consists of three successive stages that can be modeled by n-th order reaction kinetics, a kinetic model was developed to describe the change in sample mass over time. Statistical and nonlinear regression techniques were used to determine the kinetic triplets for each stage. The model was then applied to predict the progression of the sublimation process under various temperature regimes. The results of the work can be used both in an independent form and in the construction of complex models of chemical processes in which it is necessary to take into account the course of a competing process of sublimation of ammonium chloride.

Maksim Igorevich Kuzmin

David Ilyich Kushniruk

Nikita Sergeevich Romanov

Egor Andreevich Danilov

Anastasia Nikolaevna Babkina

Kinetic model of the ammonium chloride sublimation process

氯化铵升华过程的动力学模型

After introducing some basic mathematical theory on kleinian groups, we discuss both technical features and drawbacks of the classic approach adopted to render the digital representation of diagrams that display either the action of tessellation and the limit sets related to Kleinian groups in one complex variable. We will then follow to illustrating the details of a new approach, based upon numerical base conversion. This discussion will be supported by pseudo-code, in order to explain the implementation guidelines. Finally, we will review the benefits of this algorithm.

Alessandro Rosa

Light and fast renderings of limit sets for Fuchsian and Kleinian groups

Fuchsian和Kleinian群的极限集的轻量快速渲染

Ordinary differential equations of the 2nd and 3rd orders with multiplicative right-hand sides of the 2nd and 3rd orders are studied. A method is considered for reducing the order of equations and obtaining exact solutions of differential equations using transformations that are invariants of generators of cyclic transformations discrete groups closed in the classes of differential equations under consideration. The method of discrete invariants is an alternative to the method of "multiplication" of integrable cases in the class of differential equations under study by using the constructed discrete group of transformations acting in this class of equations. Examples are given to illustrate the method of discrete invariants.

Zilya Nailevna Khakimova

Ajkanush Ashotovna Atojan

Integration of Differential Equations by Using Invariants of Discrete Transformation

使用离散变换不变量整合微分方程

We take a space X of dynamical systems that could be: homeomorphisms or continuous maps of a compact metric space K or diffeomorphisms of a smooth manifold or actions of an amenable group. We demonstrate that a typical dynamical system of X is a continuity point for the set of probability invariant measures considered as a function of a map, let Y be the set of all such continuity points. As a corollary we prove that for typical dynamical systems average values of continuous functions calculated along trajectories do not drastically change if the system is perturbed.

Sergey Kryzhevich

Sets of Invariant Measures and Cesaro Stability

不变测度集与切萨罗稳定性

This paper is concerned with the study of a nonlinear problem involving the fractional p(x)-Laplacian operator. By means of the Berkovits degree theory, we prove the existence of nontrivial weak solutions for this problem. The appropriate functional framework for this problem is the fractional Sobolev spaces with variable exponent.

Mustapha Ait Hammou

Nonlinear Problem Involving the Fractional P(x)-Laplacian Operator by Topological Degree

拓扑度法解决分数阶P(x)-拉普拉斯算子涉及的非线性问题

Publication Information	Publisher: Saint Petersburg State University，Publishing cycle: ，Journal Type: journal，Open Access Journals: No
Basic data	Year of publication: 2019，Proportion of original research papers: 0.00%，Self Citation Rate:N.A.， Gold OA Rate: 0.00%

Differencialnie Uravnenia i Protsesy Upravlenia

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Calculation of the Invariant Decomposition of the Tangent Space

Kinetic model of the ammonium chloride sublimation process

Light and fast renderings of limit sets for Fuchsian and Kleinian groups

Integration of Differential Equations by Using Invariants of Discrete Transformation

Sets of Invariant Measures and Cesaro Stability

Calculation of the Invariant Decomposition of the Tangent Space

Kinetic model of the ammonium chloride sublimation process

Light and fast renderings of limit sets for Fuchsian and Kleinian groups

Integration of Differential Equations by Using Invariants of Discrete Transformation

Nonlinear Problem Involving the Fractional P(x)-Laplacian Operator by Topological Degree

ISSN	1817-2172
h-index	6