Temur Ipolite Chilachava

• PhD, Doctor of Physical and Mathematical Sciences (Dr. Habil.) Professor
• Head of Department at Sokhumi State University

In the paper two and three-dimensional nonlinear dynamical systems are offered describing training of scientists. In two-level model two subjects are considered: research associates without degree and the scientists with doctor's degree, and in three-stage model three subjects: research associates without degree, candidates of science and the scien...

In the real model it is supposed that the powerful state with a widespread state language carries out assimilation of the population of less powerful state and the third population talking in two languages, different in prevalence. Carries out assimilation of the population of the state formation with the least widespread language to the turn, less...

In work the new nonlinear mathematical and computer model of nformation warfare with participation of interstate authoritative institutes is offered. The model is described by Cauchy's problem for nonlinear non-homogeneous system of the differential equations. Confronting sides in extend of provocative statements, the third side (the peacekeeping i...

Abstrac: In work the new nonlinear mathematical model describing assimilation of the people (population) with some less widespread language by two states with two different widespread languages is offered. In model three subjects are considered: the population and government institutions with the widespread first language, influencing by means of s...

This work proposes an asymptotic method of solution for a system of nonlinear nonhomogeneous equations of one class of initial-boundary problems with an unknown external boundary in the domain. The system of equations describes an adiabatic spherical and symmetrical motion of a gravitating gas , while a moving detonating wave (a spherical surface w...

Previously, we presented a scenario for the transformation process of the Proto-Kartvelian population into Georgian, Megrelian, Laz, and Svan populations, which considered four periods of this process (from 5000 BC to the present). The results of the mathematical and computer modeling for the first two periods of the transformation were published e...

This paper discusses the two stages of transformation of the Common-Kartvelian-speaking people: the first stage was 5000–2500 BC, when the entire populace spoke the Common Kartvelian language and lived in the South Caucasus; the second stage was 2500–1000 BC, when the entire populace was divided into three parts: Svan, Colchian-Georgian and the thi...

Earlier, we proposed a scenario for the transformation of the Proto-Kartvelian population into the Georgian, Megrelian, Laz and Svan populations. Using mathematical and computer modeling, the first stage (5000-2500 BC) of the dynamics of the Proto-Kartvelian population was studied. In particular cases, exact analytical solutions are obtained, and i...

The mathematical modeling of astrophysics processes is one of the most actual problem of modern applied mathematics. To solve many problems of astrophysics, it is necessary to study the dynamics of gaseous bodies interacting with a gravitational field. The work considers a non-avtomodel problem about the central explosion of nonhomogeneous gas body...

Mathematical modeling of social and political processes, such as globalization, assimilation of peoples, bipolar or multipolar arrangement of the world, is of significant scientific and practical interest. These processes are greatly influenced by the spread and interaction of the main world religions: Christianity (33,9%), Islam (22,7%), Hinduism...

The mathematical modeling of astrophysics processes are one of the most actual problems of modern applied mathematics. To solve many problems of astrophysics, it is necessary to study the dynamics of gaseous bodies interacting with a gravitational field. The work considers a nonavtomodel problem about the central explosion of nonhomogeneous gas bod...

Earlier, we proposed a scenario for the transformation of the Proto-Kartvelian population into the Georgian, Megrelian, Laz and Svan populations [1]. In [1], using mathematical and computer modeling, the first stage (5000-2500 BC) of the dynamics of the Proto-Kartvelian population was studied. In particular cases, exact analytical solutions are o...

The mathematical modeling of astrophysics processes is one of the most actual problem of modern applied mathematics. To solve many problems of astrophysics, it is necessary to study the dynamics of gaseous bodies interacting with a gravitational field [1, 2]. The work considers a nonavtomodel problem about the central explosion of nonhomogeneous ga...

This work discusses the second period of transformation of the Proto-Kartvelian population, when the population divided into three parts: Proto-Svan; speaking the Colchian-Georgian language and the third part was scattered on the European continent. The second period is described by two different mathematical models: a part of the Proto-Kartvelian...

This work discusses the first period (from L to XXX-XXV centuries BC) when the entire population spoke one Proto-Kartvelian language. This period is described by a Pearl-Verhulst-type mathematical model. For the unknown function of variable coefficients in the general case, which determines the number of Proto-Kartvelian speaking population at a gi...

This work discusses two periods of transformation of the Proto-Kartvelian population: the first (L–XXV centuries BC) when the entire population spoke one Proto-Kartvelian language and lived in a relatively large area; the second period – (XXV–X centuries BC), when the population divided into three parts: Proto-Svan; speaking the Colchian-Georgian l...

The Pelasgian tribes spoke the Proto-Kartvelian language and were primarily found in the Peloponnese peninsula, Crete, and other islands, in ancient Asia and the Caucasus. At a certain stage of development (XXX-XXV centuries BC), the Pelasgian tribes experienced strong harassment from nomadic Indo-European and Semitic warlike tribes, as a result...

The Pelasgian tribes spoke the Proto-Kartvelian language and were primarily found in the Peloponnese peninsula, Crete, and other islands, in ancient Asia and the Caucasus. At a certain stage of development (XXX-XXV centuries BC), the Pelasgian tribes experienced strong harassment from nomadic Indo-European and Semitic warlike tribes, as a result of...

The article proposes a new nonlinear mathematical model that describes the process of possibility (instability of the state) or impossibility (stability of the state) of separating the region from the state. The model is described by the Cauchy problem for a nonlinear two-dimensional dynamic system. The model assumes that only two categories of cit...

In this paper, we consider a non-self-similar problem of a central explosion of a homogeneous gaseous three-axis ellipsoid located in its own gravitational field and solid-body rotating around an z axis with a constant ω angular velocity. As initial data, the exact solution of the problem of stationary solid-state rotation of a homogeneous three-ax...

We live in a world of complex epidemiological, environmental, economic, political social processes and apparently their full-scale interdisciplinary mathematical and computer modeling, the only way to qualitative and quantitative predictive zoning of the consequences of these events. Using the example of mathematical modeling in the social sphere (...

Over the past few decades, mathematical modeling of social processes, such as information warfares, language globalization, assimilation of peoples, political conflicts, etc. has been of particular interest. Currently, the ongoing military events related to the Russian invasion of Ukraine are directly related to Russia's desire to change the natura...

To solve many problems of astrophysics, it is necessary to study the dynamics of gaseous bodies interacting with a gravitational field [1, 2]. Numerous observations show that stars rotate. The study of rotating gravitating gaseous bodies has a long history and originates in the classical works of Newton, Maclaurin, Jacobi, Liouville, Dirichlet, Ded...

The work considers a non-self-similar problem about the central explosion of nonhomogeneous gas body (star) bordering vacuum which is in equilibrium in its own gravitational field. To solve the problem, the asymptotic method of thin impact layer has been used. The solution of the problem in the vicinity behind the shock wave (the destruction surfac...

The paper discusses new mathematical models that describe the early stages of the spread of the SARS-CoV-2 virus. The first model considers two groups of people: without healthy immunity and asymptomatic infected. The second model considers three groups of people: without healthy immunity, asymptomatic infected and detected infected. In the first m...

The work proposes a nonlinear mathematical model describing the process of two-level assimilation , taking into account the quadratic terms of self-limiting the growth of populations of three sides talking in languages significantly different in dissemination. Two-level assimilation process considered when in one large region the population speakin...

The paper proposes a new nonlinear mathematical model, describing in a certain politically conflicting region of a certain state the presence of three population groups with different political priorities. One part of the population (unionists) is politically oriented towards the preservation of the region within the former state, the second part o...

The work considers a nonautomodel problem about the central explosion of nonho-mogeneous gas body (star) bordering vacuum, which is in equilibrium in its own gravitational field. Asymptotic method of thin impact layer is used to solve the problem. The solution of the problem in the vicinity behind the shock wave (discontinuity surface of the first...

The work considers a nonavtomodel problem about the central explosion of nonhomogeneous gas body (star) bordering vacuum, which is in equilibrium in its own gravitational field. Asymptotic method of thin impact layer is used to solve the problem. The solution of the problem in the vicinity behind the shock wave (the fracturing surface of the first...

Mathematical modeling of explosive processes in gravitational gas bodies is one of the actual problems in astrophysics. The work considers a nonautomodel problem about the central explosion of nonhomogeneous gas body (star) bordering vacuum, which is in equilibrium in its own gravitational field. Asymptotic method of thin impact layer is used to so...

It is of great interest to predict the extent of the epidemic by creating appropriate mathematical models. Since the beginning of 2020, the incurable infectious disease COVID-19 has spread around the world, which has already killed many people and changed the world (economy, development rate, etc.). Naturally, at this stage, several vaccines have a...

In the paper, a new Integrated Mathematical Model of Information warfare is built. In the suggested model, by selecting continuous intensity coefficients of aggressiveness of the conflicting parties and the peacemaking activity of a third party, it is possible to describe the process of Non-Permanent Information Warfare with restrictions. The Non-P...

The paper proposes a new general nonlinear mathematical model, which describes the process of the possibility of secession of a particular region from a certain state. The model is described by the Cauchy problem for a nonlinear two-dimensional dynamic system. The model assumes that only two categories of citizens live in a particular region of a s...

Abstract: The paper proposes a new general nonlinear mathematical model, which describes the process of the possibility of secession of a particular region from a certain state. The model is described by the Cauchy problem for a nonlinear two-dimensional dynamic system. The model assumes that only two categories of citizens live in a particular reg...

Nonlinear mathematical models of economic cooperation between two politically (non-military confrontation) mutually opposing sides (two countries or a country and its legal region) are proposed, which consider economic cooperation between parts of the population of the sides, aimed at rapprochement of the sides and peaceful settlement of conflicts....

Earlier we proposed mathematical models for resolving political conflicts through economic cooperation between two politically mutually opposing sides (possibly a country or country and its legal subject). In case of constant parameters of models, with some dependencies between coefficients, exact analytical solutions are found and conflict resolut...

The paper proposes a nonlinear mathematical model describing the process of two-level assimilation, taking into account the quadratic terms of self-limiting the growth of populations of three sides talking in languages significantly different in distribution. In the special case, when the coefficients of the model are constant, the first integral o...

In this work a new nonlinear mathematical model of process of three level assimilation which is described by four-dimensional dynamic systems is offered. In case of constancy of coefficients special points of the dynamic system are found. The conditions on constant coefficients for which it is possible to find special points with all four coordinat...

Earlier we proposed mathematical models for resolving political conflicts through economic cooperation between two politically mutually opposing sides (possibly a country or country and its legal subject). In case of constant parameters of models, with some dependencies between coefficients, exact analytical solutions are found and conflict resolut...

The work proposes a new general nonlinear mathematical model describing the social process of two-level assimilation taking into account quadratic members of self-restriction of population growth of three sides. In the case of constant coefficients of the model, the first integral of a three-dimensional dynamic system has been found, which in the p...

Nonlinear mathematical models of economic cooperation between two politically (non-military confrontation) mutually opposing sides (two countries or a country and its legal region) are proposed, which consider economic cooperation between parts of the population of the sides, aimed at rapprochement of the sides and peaceful settlement of conflicts....

This paper considers mathematical models in the general case, when the variation of demographic factors of the sides is taken into account, and over time the coefficients of aggressiveness and cooperation of parts of the population of the sides, respectively, both preventing and facilitating cooperation, are changed. Numerous computer simulations w...

Nonlinear mathematical models of economic cooperation between two politically (non-military confrontation) mutually opposing sides (two countries or a country and its legal region) are proposed, which consider economic cooperation between parts of the population of the sides, aimed at rapprochement of the sides and peaceful settlement of conflicts....

Abstract. Nonlinear mathematical models of economic cooperation between two politically (non-military confrontation) mutually opposing sides (two countries or a country and its legal region) are proposed, which consider economic cooperation between parts of the population of the sides, aimed at rapprochement of the sides and peaceful settlement of...

The paper examines mathematical and computer modeling of the process of resolving political conflict through economic cooperation between two politically mutually opposing sides (possibly a country or country and its subject). Cases of both zero and variable demographic factor are considered. Factors of aggressiveness, cooperation are variable func...

The paper examines mathematical and computer modeling of the process of resolving political conflict through economic cooperation between two politically mutually opposing sides (possibly a country or country and its subject). Cases of both zero and variable demographic factor are considered. Factors of aggressiveness, cooperation are variable func...

In this work new mathematical models are offered where it is meant: in the first case-the governments of both sides, influencing various levers of pressure upon the citizens inclined to mutual economic cooperation, interfere with the process of economic cooperation, and in the second case-the government of one side interferes, and the government of...

In this work the exact solution of a problem on stationary solid-state rotation with a constant angular speed of a homogeneous three-axis gas ellipsoid (the law and speed of the movement of the medium and also thermodynamic characteristics of the medium) which is in its own gravitational field and adjoining on emptiness is found (zero pressure on b...

In this work the problem about solid-state rotation with a constant angular speed of the three axis homogeneous gas ellipsoid which is in own gravitational field and adjoining on emptiness is considered. It is known that in the theory of ellipsoidal figures of balance, a half shaft of a steady three-axis ellipsoid of rotation of Jacobi and also the...

Nonlinear mathematical models of economic cooperation between two politically mutually warring sides which consider economic or other type of cooperation between parts of the population of the sides, directed to rapprochement of the sides and peaceful resolution of the conflicts are offered. In mathematical models it is meant: in the first case tha...

Research of the dynamic systems describing mathematical models of resolution of conflict by means of economic cooperation at bilateral or unilateral counteraction Abstract In work new mathematical models are offered where it is meant: in the first case-the governments of both sides, influencing various levers of pressure upon the citizens inclined...

In this work new mathematical models are offered where it is meant: in the first case-the governments of both sides, influencing various levers of pressure upon the citizens inclined to mutual economic cooperation, interfere with the process of economic cooperation, and in the second case-the government of one side interferes, and the government of...

Mathematical models of information warfares proposed in 2009 by Professor Temur Chilachava are considered. Linear and nonlinear continuous and discrete models are considered

Mathematical and computer modeling of information warfares proposed by professor Temur Chilachava is considered

Mathematical modeling got already into the areas of the social sphere, such as, processes of linguistic globalization. Prof. T. Chilachava offered and we discussed nonlinear mathematical models of economic cooperation for resolution existing political conflict between two opposing political sides. In the given work two nonlinear mathematical models...

Mathematical modeling got already into such areas of the social sphere, such as, processes of linguistic globalization. Prof. T. Chilachava offered and we discussed nonlinear mathematical models of economic cooperation for resolution existing political conflict between two opposing political sides. In the given work are discussed two nonlinear math...

Earlier we considered mathematical models of interference of fundamental and applied researches [1,2] and so two or three-stage trainings of the diplomaed scienti�c experts [3,4]. In this work a nonlinear mathematical model of competition for micro-constraints between two universities (micro model, for one region, where only two choice) is discusse...

In the recent years, mathematical modeling has penetrated into social sphere, such as linguistic globalization processes [1]. Earlier prof. T. Chilachava offered [2] and we discussed nonlinear mathematical models of economic cooperation for resolution existing political conflict between two opposing political sides [3 - 6]. In the given work are di...

Earlier we considered mathematical models of interference of fundamental and applied researches and so two or three-stage trainings of the diplomaed scientific experts. In this work a nonlinear mathematical model of competition for micro-constraints between two universities (micro model, for one region, where only two choice) is discussed. The micr...

In the recent years, mathematical modeling has penetrated into social sphere, such as linguistic globalization processes. Earlier prof. T. Chilachava offered and we discussed nonlinear mathematical models of economic cooperation for resolution existing political conflict between two opposing political sides. In the given work are discussed two nonl...

The concept of "information warfare ", her understanding of the USA, Russia, Great Britain, Germany, France and of China is given. The new direction in the theory of information warfares "Mathematical models of information flows" offered in 2009 by the prof. Temur Chilachava is considered. In particular, T. Chilachava means confrontation by mass me...

New mathematical models of permission of a political conflict between two sides (the countries, the country and its legal region) are presented

Mathematical modeling has been widely recognized in such disciplines as sociology, history, political science and others [1]. In this work the new nonlinear mathematical model of process of three-level assimilation which is described by four-dimensional dynamic system is offered. In case of constancy of coefficients of model special points of dynam...

Mathematical modeling has been widely recognized in such disciplines as sociology, history, political science and others [1]. In this work the new nonlinear mathematical model of process of three-level assimilation which is described by four-dimensional dynamic system is offered. In case of constancy of coefficients of model special points of dynam...

Mathematical modeling has been widely recognized in such disciplines as sociology, history, political science and others [1]. In this work the new nonlinear mathematical model of process of three-level assimilation which is described by four-dimensional dynamic system is offered. In case of constancy of coefficients of model special points of dynam...

New nonlinear mathematical models of economic cooperation between two politically (not military opposition) mutually warring sides (two countries or the country and its legal subject) which consider economic or other type of cooperation between parts of the population of the sides, directed to rapprochement of the sides and peaceful resolution of t...

At the solution of many relevant astrophysical problems connected with the explosive phenomena in gravitating gas bodies of various configuration (a sphere, Maclaurin's spheroid, a three-axis ellipsoid of Jacobi, etc.) and propagation of shock or detonation waves (a surface of a discontinuity of the first kind of solutions) knowledge of the exact s...

The research object of this paper is the study of the election process, within the inter-election period, in the case of the transformation of bipartisan (the ruling party and one opposition party) into three-party elections (ruling and two opposition parties) and a forecast of the election results is made. Some special cases are studied, exact ana...

The research object of this paper is the study of the election process, within the inter-election period, in the case of the transformation of bipartisan (the ruling party and one opposition party) into three-party elections (ruling and two opposition parties) and a forecast of the election results is made. Some special cases are studied, exact ana...

The research object of this paper is the study of the election process, within the inter-election period, in the case of the transformation of bipartisan (the ruling party and one opposition party) into three-party elections (ruling and two opposition parties) and a forecast of the election results is made. Some special cases are studied, exact ana...

The research object of this paper is the study of the election process, within the inter-election period, in the case of the transformation of bipartisan (the ruling party and one opposition party) into three-party elections (ruling and two opposition parties) and a forecast of the election results is made. Some special cases are studied, exact ana...

In this presentation new mathematical models are offered where it is meant: in the first case – the governments of both sides, influencing various levers of pressure upon the citizens inclined to mutual economic cooperation, interfere with the process of economic cooperation, and in the second case – the government of one side interferes, and the g...

Earlier was offered an original approach for creating of new nonlinear mathematical models of economic cooperation between two politically (not military opposition) mutually warring sides (perhaps the countries or the country and its legal subject) which considers economic or other type cooperation between parts of the population of the sides, dire...

Earlier was offered an original approach for creating of new nonlinear mathematical models of economic cooperation between two politically (not military opposition) mutually warring sides (perhaps the countries or the country and its legal subject) which considers economic or other type cooperation between parts of the population of the sides, dire...

At the solution of many relevant astrophysical problems connected with the explosive phenomena in gravitating gas bodies of various configuration (a sphere, Maclaurin's spheroid, a three-axis ellipsoid of Jacobi, etc.) and propagation of shock or detonation waves (a surface of a rupture of the first kind of solutions) knowledge of the exact solutio...

In this presentation new mathematical models are offered where it is meant: in the first case – the governments of both sides, influencing various levers of pressure upon the citizens inclined to mutual economic cooperation, interfere with the process of economic cooperation, and in the second case – the government of one side interferes, and the g...

New nonlinear mathematical models of economic cooperation between two politically (not military opposition) mutually warring sides (two countries or the country and its legal subject) which consider economic or other type of cooperation between parts of the population of the sides, directed to rapprochement of the sides and peaceful resolution of t...

New nonlinear mathematical models of economic cooperation between two politically (not military opposition) mutually warring sides (two countries or the country and its legal subject) which consider economic or other type of cooperation between parts of the population of the sides, directed to rapprochement of the sides and peaceful resolution of t...

New nonlinear mathematical models of economic cooperation between two politically (not military opposition) mutually warring sides (two countries or the country and its legal subject) which consider economic or other type of cooperation between parts of the population of the sides, directed to rapprochement of the sides and peaceful resolution of t...

New nonlinear mathematical models of economic cooperation between two politically (not military opposition) mutually warring sides (two countries or the country and its legal subject) which consider economic or other type of cooperation between parts of the population of the sides, directed to rapprochement of the sides and peaceful resolution of t...

In this paper, we consider a new nonlinear continuous mathematical model of linguistic globalization. Two categories of the world’s population are considered: a category that hinders and a category conducive to the dominant position of the English language.With a positive demographic factor of the population, which prevents globalization and the ne...

The paper considers a nonlinear mathematical model of economic cooperation between two politically mutually opposing sides (possibly a country or a country and its subject) that takes into account economic or other type of cooperation between parts of the population of the sides aimed at convergence and peaceful resolution of the conflict. The mode...

In this paper, the dynamics of the election process in the case of the transformation of bipartisan elections (the ruling party and one opposition party) into three-party (ruling and two opposition parties) in the inter-election period is considered. In the case, with the zero demographic factor of all three political parties, and also with some re...

The paper considers a nonlinear mathematical model of economic cooperation between two politically mutually opposing sides (possibly a country or a country and its subject) that takes into account economic or other type of cooperation between parts of the population of the sides aimed at convergence and peaceful resolution of the conflict. The mode...

In work the new nonlinear mathematical model of economic cooperation between two politically mutually warring sides (perhaps the countries or the country and its subject) which considers economic or other type the cooperation between parts of the population of the sides directed to rapprochement of the sides and peaceful resolution of the conflict...

The paper deals with a nonlinear mathematical model of competition between two universities , which takes into account both competition for a limited contingent of enrollees and the attraction of students due to mobility (the transition of students from one university to another). Dynamic system describing quantitative dynamics (flows) as students...

Earlier we have offered nonlinear mathematical models of processes of bilateral and two-level assimilation [1-4]. In this work the new nonlinear mathematical model of process of three-level assimilation which is described by four-dimensional dynamic system is offered:                           ) () () () () () () () () ()...

The paper deals with a nonlinear mathematical model of competition between two universities, which takes into account both competition for a limited contingent of enrollees and the attraction of students due to mobility (the transition of students from one university to another). Dynamic system describing quantitative dynamics (flows) as students o...

Earlier we have offered nonlinear mathematical models of processes of bilateral and two-level assimilation [1]–[4]. In this work the new nonlinear mathematical model of process of three-level assimilation which is described by four-dimensional dynamic system is offered. In case of constancy of coefficients of model special points of dynamic system...

The paper considers a nonlinear mathematical model of economic cooperation between two politically mutually opposing sides (possibly a country or a country and its subject) that takes into account economic or other type of cooperation between parts of the population of the sides aimed at convergence and peaceful resolution of the conflict. The mode...

At the moment it is actual to create a mathematical model, which would give an opportunity to define the dynamics of change in the number of supporters of different political subjects during the election period and a possible forecast of the election results. The nonlinear mathematical models of two and three party elections were proposed in the wo...

At the moment it is actual to create a mathematical model, which would give an opportunity to define the dynamics of change in the number of supporters of different political subjects during the election period and a possible forecast of the election results. The nonlinear mathematical models of two and three party elections were proposed in the wo...

The paper considers a nonlinear mathematical model of economic cooperation between two politically mutually opposing sides (possibly a country or a country and its subject) that takes into account economic or other type of cooperation between parts of the population of the sides aimed at convergence and peaceful resolution of the conflict. The mode...

In this paper the dynamics of the election process in the case of the transformation of bipartisan elections (the ruling party and one opposition party) into three-party (ruling and two opposition parties) is considered within the inter-election period. Some special case is studied. In the particular case, with a non-zero demographic factor the exa...

In this paper, we have modeled the dynamics of an election process in the case of the transformation of bipartisan (the ruling party and one opposition party) election into three -party (ruling and two opposition parties) election during the inter-election period. Special case is considered. In the particular case, with the zero demographic factor...

In this paper, we have modeled the dynamics of an election process in the case of the transformation of bipartisan (the ruling party and one opposition party) election into three-party (ruling and two opposition parties) election during the inter-election period. Special case is considered. In the particular case, with the zero demographic factor o...

In the work a new nonlinear continuous mathematical model of linguistic globalization (macromodel) is considered. Two categories of the world's population are considered: interfering and conducive to the dominance of the English language (assimilation). It is proved that the linguistic globalization with a positive demographic factor of the populat...

In this paper, we consider a new nonlinear continuous mathematical model of linguistic globalization. Two categories of the world's population are considered: a category that hinders and a category conducive to the dominant position of the certain language. With a positive demographic factor of the population, which prevents globalization and the n...