The First Lyapunov Method for Strongly Non-linear Systems of Differential Equations

The article is aimed to give a brief review of works published by authors during at least last 10 years and devoted to the construction of solutions of systems of ordinary differential equations in a neighbourhood of a nonelementary criticai point

A Necessary Condition for existence of Lie Symmetries in Quasihomogeneous Systems of Ordinary Differential Equations

Lie symmetries for ordinary differential equations are studied. In systems of ordinary differential equations, there do not always exist non-trivial Lie symmetries around equilibrium points. We present a necessary condition for existence of Lie symmetries analytic in the neighbourhood of an equilibrium point. In addition, this result can be applied to a necessary condition for existence of a Lie symmetry in quasihomogeneous systems of ordinary differential equations. With the help of our main theorem, it is proved that several systems do not possess any analytic Lie symmetries.Comment: 15 pages, no figures, AMSLaTe

APPROACHES TO ANALYSIS OF GENOTYPE AND PHENOTYPE RELATION WITH QTL METHODS

The paper describes methods of QTL-analysis in the research of the genotype influence. QTL-analysis is a statistical method that connects phenotypic data with genotype, enables the determination of the exact localization and gene influence power. The QTL mapping idea is to phenotype observation and identification of the genome region on which the genotype is associated with the phenotype. With the help of molecular-genetic markers, molecular maps of individual chromosomes and genomes are made, genes and QTLs mapping are performed on them. Thus, genes with the greatest connectivity to phenotype were identified. The correlation between genotype and phenotype is studied across the full genome of the individual. The data provided by the Laboratory of Molecular Genetics of the innate immunity of Petrozavodsk State University were the initial data in this research. The essence of the project, carried out jointly with the laboratory, is to study the arrays of genetic information to identify and model the relationships between the genotype and the phenotype of biological organisms. The second-generation mice hybrids of lines C57BL/6 and MOLF were involved in the experiment. Genotyping and phenotyping were conducted based on sequencing data (determination of amino acid and nucleotide sequence) of matrix RNA. The practical result of the work is the identification of chains of activated genes, under the influence of which the cells of the tissues and organs under research die (apoptosis). The result of the study is a technique for analyzing the relationship between a phenotype and a genotype, through which groups of significant phenotypes were identified

ОЦЕНКА РИСКОВ НАРУШЕНИЯ АНТИМОНОПОЛЬНОГО ЗАКОНОДАТЕЛЬСТВА ИСПОЛНИТЕЛЬНЫМИ ОРГАНАМИ ГОСУДАРСТВЕННОЙ ВЛАСТИ

The article deals with a problem of building an anti-trust compliance system in state executive authorities from the point of view of contemporary risk management. The authors expound a well-known instrument based on the bow-tie diagram construction which successfully helps to develop effective measures to prevent violation of anti-trust legislation cases by state executive authorities. They also give some numeric results of statistical modelling of anti-trust legislation violation risks by state executive authorities by means of the Monte-Carlo method.В работе предлагается взгляд на проблематику построения системы антимонопольного комплаенса в исполнительных органах государственной власти с позиции общей философии, теории и практики современного риск-менеджмента. Изложен известный метод анализа рисков, основанный на построении диаграммы «галстук-бабочка», позволяющий осознанно разрабатывать эффективные меры предупреждения рисков нарушения антимонопольного законодательства исполнительными органами государственной власти. Приведены результаты статистического моделирования рисков нарушения антимонопольного законодательства исполнительными органами государственной власти при помощи метода Монте-Карло

Finiteness of integrable nn-dimensional homogeneous polynomial potentials

We consider natural Hamiltonian systems of $n>1$ degrees of freedom with polynomial homogeneous potentials of degree $k$. We show that under a genericity assumption, for a fixed $k$, at most only a finite number of such systems is integrable. We also explain how to find explicit forms of these integrable potentials for small $k$

RISK ASSESSMENT FOR VIOLATION OF ANTI-TRUST LEGISLATION BY STATE EXECUTIVE AUTHORITIES

The article deals with a problem of building an anti-trust compliance system in state executive authorities from the point of view of contemporary risk management. The authors expound a well-known instrument based on the bow-tie diagram construction which successfully helps to develop effective measures to prevent violation of anti-trust legislation cases by state executive authorities. They also give some numeric results of statistical modelling of anti-trust legislation violation risks by state executive authorities by means of the Monte-Carlo method

COMPARISON OF RUSSIAN NATIONAL STANDARD “RISK MANAGEMENT. PRINCIPLES AND GUIDELINES” RELEASES (GOST R ISO 31000:2019 AND GOST R ISO 31000:2010), TAKING INTO ACCOUNT PRIMARY SOURCES

Publication of new releases of professional standards in different areas is always a challenge for experts since usually after such events organizations, which declare following principles formulated in those standards formally or informally, start implementing new processes. That is why it is necessary to understand the difference between the new release of a standard and a previous one. That circumstance is extremely important since risk management standards from the ISO family declare that the risk management has to become an intrinsic essential part of all business processes in an organization. In case of Russian national standards GOST R ISO 31000:2019 and GOST R ISO 31000:2010 Russian professional community didn’t perform the work mentioned above. The reason was the COVID-19 pandemic which influenced the economics in general and activity of all professional communities in particular. The aim of the article under consideration is to fill in that gap

On the polynomial integrability of the Hoyer systems

Agraïments: The second author is supported by FCT through the project PTDC/MAT/117106/2010 and through CAMGSD, Lisbon.The Hoyer polynomial differential systems depend on nine parameters. We provide necessary conditions in order that these systems have two functionally independent polynomial first integrals. We show that these conditions are not sufficient. Additionally, we illustrate how can be computed the polynomial first integrals of these systems using the Kovalevsky exponents

СРАВНЕНИЕ ВЕРСИЙ НАЦИОНАЛЬНОГО СТАНДАРТА РОССИЙСКОЙ ФЕДЕРАЦИИ «МЕНЕДЖМЕНТ РИСКА. ПРИНЦИПЫ И РУКОВОДСТВО» (ГОСТ Р ИСО 31000:2019 И ГОСТ Р ИСО 31000:2010) С УЧЕТОМ ПЕРВОИСТОЧНИКОВ

Publication of new releases of professional standards in different areas is always a challenge for experts since usually after such events organizations, which declare following principles formulated in those standards formally or informally, start implementing new processes. That is why it is necessary to understand the difference between the new release of a standard and a previous one. That circumstance is extremely important since risk management standards from the ISO family declare that the risk management has to become an intrinsic essential part of all business processes in an organization. In case of Russian national standards GOST R ISO 31000:2019 and GOST R ISO 31000:2010 Russian professional community didn’t perform the work mentioned above. The reason was the COVID-19 pandemic which influenced the economics in general and activity of all professional communities in particular. The aim of the article under consideration is to fill in that gap.Выход в свет новых версий профессиональных стандартов для специалистов в соответствующих областях всегда является вызовом, поскольку за этими событиями обычно следует запуск внедрения новых процессов в организациях, декларирующих формальное или неформальное следование принципам, сформулированным в этих стандартах. Поэтому чрезвычайно важно понять, чем же на самом деле отличается предыдущая версия от новой, иначе обновление управленческих процессов в организации может стать безрезультатным. Это обстоятельство особенно важно принимать во внимание для стандартов управления рисками из серии ISO, поскольку стандарты этой серии декларируют неотъемлемость менеджмента риска в отношении всех бизнес-процессов в организации. В случае со стандартами ГОСТ Р ИСО 31000:2019 и ГОСТ Р ИСО 31000:2010 к моменту написания настоящей статьи указанная работа в рассматриваемых аспектах не проводилась, что связано с влиянием пандемии коронавируса COVID-19 на экономику в целом и на деятельность профессиональных сообществ в частности. Цель настоящей статьи – восполнение этого пробела