**SPATIAL MODELLING OF HISTORICAL DYNAMICS**

**A.S.Malkov**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 201-204**

The problems of spatial historical dynamics are concerned. We propose a system of mathematical spatial models describing different aspects of global historical process. Economics, trade, demography, politics, wars and migrations are taken into account. Some problems having both subjective and instrumental nature are analyzed and discussed. (full text)

**
NUMERICAL ALGORITHM FOR TIME SERIES MODELS**

**Olga Martin**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 204-209**

In this paper, a method for the determination of the trend for a time series is presented. A comparative study was made between the seasonal components and the aleatory components, which were computed by this algorithm and these founded by an additive model. (full text)

**
COMPLEX SYSTEM OF NATIONAL MONITORING
AND STRATEGIC PERSPECTIVE OF RUSSIA.**

**I.G. Medvedev and N.A. Mitin**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 209-212**

At a meeting with the leadership of the Russian Academy of Sciences on December 3, 2001, Russian President V.V. Putin set two objectives before the scientific community. The first one is to search for scientifically justify ways of transforming the country’s economy from its present raw-material orientation to an innovative way of development; the second is to scrutinize government decisions and forecast and prevent disasters, catastrophes, and instabilities in the anthropogenic, social, and natural spheres. The first of these tasks is about evaluating the corridor of Russia’s opportunities and choosing a historical perspective; the second involves parrying threats, protecting the country from dangers, and preventing disasters along the historical way that society will choose after solving the objective. (full text)

**
TAX SYSTEM & INTEREST TO NEW INDUSTRIAL CAPACITIES**

**Serge E. Miheev**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 212-217**

It is shown that concurrency and labor consuming of any good elaborated in new production are connected by linear law . Negativity of the parameter means that high labor consuming productions are not concurrent in inner and outer markets. It is proved that , where are local and world taxes on raw materials, mainly on oil and gas, are local an world taxes on ordinary productive activity. Custom taxes and transport expenses perturbs the linearity but common tendency retains. That points a way how to turn an economic orientation from raw production to world workshop. (full text)

**
TOWARDS APPLICATION OF NATURAL SCIENCES
MODELS TO PROBLEMS OF GENERAL POLITOLOGY**

**A.P.Mikhailov**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 217-217**

It is impossible to imagine contemporary science, technology and many other fields of creative activity apart from mathematical modeling. Due to its universality, flexibility and accuracy this methodology won a lot of fields of knowledge from technical systems design and control to analysis of social and political processes. Although nobody can await from mathematical modeling of social life the accuracy and predictability of modeling in natural sciences and in technology, under some conditions the modeling of these supercomplex phenomena may be performed successfully. For this it is necessary to combine efforts of various specialists around some actual problem. One of these problem is relations in the system “Power-Society”. In this paper we represent mathematical model of this system and results of modeling with respect to some important macro-political events in history of Russia in XX-th century. (full text)

**
МОДЕЛИРОВАНИЕ ЛАТЕНТНЫХ ИЗМЕНЕНИЙ
С ПОМОЩЬЮ СТУКРТУРНЫХ УРАВНЕНИЙ**

**O.V.Mitina, M.D.Newcomb**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 217-220**

Latent Growth Modeling allow to study dynamical process in social and humanitarian science. Along with sequential path analysis of repeating measurments of one variable or several ones, which can form associative model or latent factor’s model LGM is a powerful and flexible techniques which allow to study changes in inter- and intra-individual levels. Each of these methods has it unique benefits and limitations. In this paper, we will demonstrate several of them, contrast and apply to analysis of real data from behavior science. (full text)

**
GRAPH THEORY MODEL OF SWAP TRANSACTIONS DEALING**

**L. M. Novozhilova**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 221-223**

Dynamic system consists of several constantly revived projects that are swap transactions on world mixed market. We consider a multistage conversion scheduling as a project realization yielding a premium. An institutional investor has a set of resources, which he invests in projects for a deriving a premium. All projects can be executed at the same time, but the implementation each of them needs different resources. An investment procedure completes by realizations of all projects. Maximal independent nodes set of a constructed graph accords to maximal number of simultaneously projects implementation. Dynamical investment distribution model is suggested in the report too. (full text)

**
MATHEMATICAL METHODS AND PEDAGOGICAL APPROACHES
OF ECONOMIC THINKING DEVELOPMENT OF TECHNICAL
INSTITUTE STUDENTS**

**A.B. Olneva, N.P.Yantsohina**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 237-240**

Current reality makes us treat a new system of education in a quite different way. There is a necessity to develop economic thinking of children, beginning from any age. And we study the development of economic thinking of Technical Institute Students. (full text)

**
GAME THEORETIC FORMALIZATION OF THE HIERARCHICAL
CONTROL OF SUSTAINABLE DEVELOPMENT**

**G.A.Ougolnitsky**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 240-242**

A conception of the hierarchical control of sustainable development based on game theoretic modeling is proposed. The principles of optimality of the hierarchical control of sustainable development as solution sets of the hierarchical game theoretic model are formulated. The organizational and ecological-economic interpretations are discussed. (full text)

**
MODELING OF HIERARCHICAL STATUS CONSIDERING
THE ORGANIZATIONAL STRATIFICATION**

**G.A. Ougolnitsky**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 242-245**

The traditional approach to measuring the hierarchical status in organizations [1-4] treats the status as a one-valued function of the organizational structure. This approach ignores the real dependence of the status value on the social stratification. A proposed new measure function of the hierarchical status takes into account both the organizational structure and an organizational stratification by criteria of sex, age, nationality, and so on. Some formal properties of the measure function are analyzed. A case study using the program implementation of the proposed model is discussed. (full text)

**
COALITION STRUCTURES IN MATCHING PROBLEMS**

**Ipek Ozkal Sanver**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 245-245**

We define two versions of stability and efficiency of partitions and analyze their relationships for some matching rules. The stability and efficiency of a partition depends on the matching rule. The results are stated under various membership property rights axioms. It is shown that in a world where agents can freely exit from and enter coalitions, whenever the matching rule is individually rational and Pareto optimal, the set of stable and efficient partitions coincide and it is unique: the grand coalition. Then we define a weaker version of stability and efficiency, namely specific to a given preference profile and find some negative results for stable matching rules. (full text)

**
РАЗРАБОТКА МЕТОДОЛОГИИ СОЗДАНИЯ ТОРГОВОЙ СИСТЕМЫ
ДЛЯ РОССИЙСКОГО РЫНКА ЦЕННЫХ БУМАГ НА ОСНОВЕ
ТЕХНИЧЕСКОГО АНАЛИЗА И ЕЕ ОПТИМИЗАЦИЯ**

**D.A. Parshin**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 246-249**

There are some theoretical foundations of technical analysis, which are considered in this work. The trading system, which generates signals to buy and sell securities, is based on mathematical method of technical analysis. While making investment decisions at securities market the system of indicators is the subject of research. Shares of the Russian issuer, such as RAO UES, Lukoil, Rostelekom and Surgutneftegaz are regarded as the subject of research. Moden techical analysis computer programs applications were used in this research (Metastock7.0 Professional and Omega Research Prosuite). (full text)

**
TECHNOLOGIES UNIFYING MATHEMATICAL AND
HUMANITARIEN METHODS OF ANALYSIS AND PROGNOSIS**

**Yu.N. Pavlovsky**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 249-252**

The simple processes, systems, phenomena are studied and forecasted by mathematical methods. Complicated processes, systems, phenomena are studied and forecasted by humanitarian methods. The frontier between simple and complicated processes and correspondingly mathematical and humanities methods of prognosis is not fixed and not too accurate. Development of mathematical modeling technologies leads to invasion into not yet explored fields. Opposite process occur: it is necessary “to understand” phenomena, which is subjected to mathematical modeling. Therefore interaction between mathematical and humanities methods have place. Result are forming technologies of analysis and prognosis unifying mathematical and humanitarian methods. (full text)

**
WESTERN ACTIVITY AND ORIENTAL
CONTEMPLATIVENESS: LOGIC OF DIFFERENCE**

**I.V.Petrova, S.Yu.Malkov**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 252-254**

В докладе рассматриваются принципы принятия решений в условиях изменяющихся внешних условий, изложена соответствующая математическая модель. Показано, что в зависимости от характера внешних изменений среды целесообразны различные стратегии поведения, обеспечивающие минимизацию возникающих издержек. На основе полученных результатов предложено объяснение различия западной "философии активности" и восточной "философии недеяния". (full text)

**
ECONOMETRIC ANALYSIS OF ETHNO POLITICAL CONFLICT**

**M.A. Petrova**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 255-258**

Ethnopolitical conflicts are an extremely important problem of the modern Russian Federation, whose population consists of about 150 different ethnic groups. The example of Chechnya showed the world the extent to which such a conflict can evolve. The North Caucasus is one of the most politically active, conflict-ridden areas in the world. Mathematical methods were applied to examine conflict behavior in order to provide a clear picture of the situation and to analyze ways of alleviating the problem. There were some urgent questions that can be answered with the help of detailed econometrics analysis of available data. Results are presented in this paper together with some possible explanations of observed patterns. (full text)

**
REGIME OF LOSSES FROM NATURAL DISASTERS IN
CONNECTION WITH CHARACTERISTICS OF SOCIETY**

**V.F.Pisaremko, M.V.Rodkin**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 259-261**

The amount of losses from natural disasters rapidly increases with time. Being extrapolated in the future this loss values in a few decades will approach the values of the annual economic growth of the world economics eliminating this way the very possibility of the economic development. However, the alternative interpretation of the regime of loss values from natural disasters can be presented. This model and the connection of the regime of losses from natural disasters with social and economical characteristics of society are discussed. (full text)

**
FORECAST OF GRADUATE PUPILS OUTFLOWS ON ASSESSMENT
TO EDUCATIONAL INSTITUTIONS IN VARIOUS UNITS OF RUSSIA
FOR THE MIDDLE-TERM PERSPECTIVE (2015)**

**E. A. Pitukhin, V. A. Gurtov**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 261-263**

Influence of graduate pupils outflow on enrollment to primary, secondary and high educational institutions is forecasted for all 89 Russian units. School-leavers outflow to regional centers, particularly, Saint Petersburg and Moscow is taken into consideration. Graduate pupils outflows during the last years are scrutinized. A discrete dynamic model on graduate pupils outflows to primary, secondary and high educational institutions is built up. (full text)

**
SIMULATION DEVELOPING AND FORECASTS ON THE TURN OVER
OF A TEACHING STUFF IN HIGH EDUCATIONAL INSTITUTIONS**

**E. A. Pitukhin, V. A. Gurtov, I. V. Pennie**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 264-266**

Stuff turn over in professional educational institutions is getting more and more topical. Mathematic model of the teaching stuff turn over inside an institution is being developed. Data on the age groups in Petrozavodsk State University for 1998-2002 are given as an example. 5 group ages from 23 years old till 70 years old are overhauled. Interpolation of an extended data is done by means of cubic spline at compound conditions. A discrete dynamic model in the form of difference linear equation system is a basis of the mathematic model. (full text)

**
DISPROPORTIONALITY INDICES FOR PROPORTIONAL
REPRESENTATION SYSTEMS **

**V.V. Platonov**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 267-268**

The reasons why any electoral system distort the voters’ preferences are discussed. Several well-known disproportionality indices for proportional representation systems are analyzed. Two new disproportionality indices are introduced and calculated for parliaments in several countries. (full text)

**
Theory of the global DEMOGRAPHIC process**

**A.V. Podlazov**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 269-272**

Life-consuming technologies concept based approach to the global demographic process is proposed. The phenomena of population growth and demographic transition are explained and the maximum world population is estimated. (full text)

**
GEOMETRIC MODELING OF THE ECONOMIC PROCESSES**

**V.D. Polezhaev **

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 272-275**

The main problem of approximation for a function is choice of empirical formula. In this work a particular class of the monotonous two-parametric functions is considered for solution of this problem. These functions are pooled to form one class by a common property concerning so-called generalized average. The main advantage of proposed approach is that proposed set of the empirical functions is not accidental but logically justified. It makes it possible to carry out graphical express-analysis of the studied dependences without complicated computations and take into account not only statistical but also analytical information on an economic phenomenon under study. (full text)

**
PRODUCTION MANAGEMENT ON BASIS OF OPTIMIZATION METHODS**

**L.N. Polezhaeva **

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 275-277**

In this work we consider the questions of management for production output on example of one of omsk’s enterprises, concerning with production of the disposable plastic dishes of the broad assortment. The Problem of production management is reduced to determination of such plan of production that total profit from sales of products of each type is maximum, but operation of production reconstruction together with starting-up and adjustment takes minimum time. We have define such mathematical models of the process, solving which, it is possible to determine the optimum plan of production of each type output under specified conditions. (full text)

**
MODELING OF POLITICAL IDEAS COMPETING PROCESSES.**

**Yu. A. Polunin**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 277-279**

The model is suggested that describes the situation of ideas competition under the circumstances of political environment composed of two groups. One group is formed by politically active people who potentially may become supporters of one of competing ideas. The other group is formed by people politically indifferent at the moment under consideration. In general case people may move from one group to another. The ideas compete to attract the maximum number of supporters from politically active group of people. (full text)

**
NONZERO-SUM DUELS **

**L. N. Positselskaya **

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 279-283**

We discuss two-person nonzero-sum games which are generalizations of traditional duels. We describe equilibrium situations for duels of various types (discrete, continuous and mixed). Conditions for Pareto optimal play to be achieved in the equilibrium situation are given. Sufficient conditions for quasi-antagonisticity are found. (full text)

**
SYSTEM ANALYSIS OF DEVELOPING ECONOMY: METHODS, RESULTS, TECHNOLOGY**

**I.G. Pospelov**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 284-289**

The classic model of general intertemporal equilibrium is presented as dynamic system for financial values. There exits the first integral of optimal trajectory of each agent which may be interpreted as the own capital of the agent. The new description of ideal equilibrium may be used as phenomenological base for modeling non ideal economic systems. This result together with the results of analysis of structure of previously built successful model gives the way to the new technology of modeling. (full text)

**
TECHNOLOGY OF BUILDING MACROMODELS OF INTERTEMPORARY
EQUILIBRIUM WITH THE HELP OF THE INTELLECTUAL TOOL ECOMOD**

**L.Ya. Pospelova, M. A. Khokhlov**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 289-293**

The ECOMOD system supports the proper structure of an agent-based macroeconomic model taking into account the natural ambiguity of economic concepts. The system is based on the classification of model relationships and variables which expresses their meaning and supports a) editing relationships; b) syntax control; c) semantic control; d) control of balances of assets; e) dimensionality control (existence of consistent system of measurement units). The technology of modelling provides usage of the universal system of analytical conversions for solution of optimization problems circumscribing behaviour of the agents. The perspectives of development of the means remembering a previous history of each analytically transformed interrelation are discussed. The work is done - with the financial support of the Russian foundation for basic research (project code 04-01-00606) - according to program of State support of leading scientific schools (project code НШ-1843.2003.1). (full text)

**
THE APPROACH TO THE DESCRIPTION OF MAECENAS INFLUENCE
ON ECONOMIC RESULTS OF A BENEFICENT COMPANY**

**O.V. Radzetskaya**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 294-296**

The economic decisions of the beneficent company now gets the special importance, as it will allow to develop the concept of charity. The strategy of charity can be developed after the model of interaction between beneficent company, recipient of grant and the state, as regulating system, will be created. To describe the influence of charity on the Maecenas business activity it is offered to use some disturbing function. This limited in time function increases the investment appeal of the beneficent company. The income dynamics of the beneficent company can be described by the system of differential equations. The solution of these equations allows to make a proposal of charity strategy. (full text)

**
On total conditionally controllability of
singular perturbed descriptor system **

**Raetskaya E.V.**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 296-298**

The necessary and sufficient conditions of total conditionally of system (1) (below) are obtained. (full text)

**
SOCIOLOGICAL CARNO CYCLE**

**R. Raikhlin**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 298-303**

The behaviour of the society is considered like a Carno cycle. Considered variables are enthropy and temperature. (full text)

**
MEASURING SOCIAL INTERACTIONS**

**B. Roehner**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 303-303**

It is shown how it is possible to assess the range of the social interactions between households from migration data. It turns out that the occurrence of "white flight" becomes important at distances of about 100 meters per household. From that observation one can derive the strength and range of the interactions between households. (full text)

**
INFLUENCE OF EQUIPROBABLE DEFLECTIONS OF MARKET
ON STATISTICAL RESULTS OF TRADE SYSTEMS**

**A.N. Romanov**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 303-306**

The fluctuations of prices on exchange market with determined by share of confidence possible to consider equiprobable. However rules of completion of deals such a that exist the certained slantings of results of trade systems, regardless of that, what algorithm they use. However, resting only in suggestion about that that deflections of the prices in one or another side are equiprobable, possible forecasts of statistical results of functioning of the trade systems. (full text)

**
A STATISTICAL ANALYSIS OF POSITIONAL VOTING METHODS**

**E. Rykhlevskaia, M. Regenwetter**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 307-307**

`
In social choice
theory, aggregation of individual preferences can be performed using a variety
of competing methods, including so-called "scoring rules". Depending on the
model for representation, as well as on the method for aggregation of individual
preferences, one can arrive on different conclusions about group preferences
given the same original data. Even within a fixed preference representation
model and aggregation rule, group preference relations derived from a random
sample may or may not reflect "true" population preferences. Tsetlin &
Regenwetter(2003) showed how probabilities of obtaining correct/incorrect
majority preference relations from a random sample can be evaluated using
sampling and Bayesian frameworks. We extend their approach by applying the same
framework to a variety of other (positional) scoring rules, using generalized
definitions of those rules for preferences represented in terms of mixed
probabilities. We use realistic distributions to access empirical probabilities
of "correct" or "incorrect" group outcomes from the various national election
survey data. We discuss how these probabilities and confidence bounds on them
depend on the sample size, preference representation model, and scoring rule. `
(full text)

**
MODELING REPLACEMENT MIGRATION**

**G.L. Safarova, E.M. Il'in, N.G. Kosolapenko**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 308-310**

Complicated demographic situation in Russia is characterized by the negative rate of natural increase (RNI) which is not compensated by positive net migration. Thus, the total population size decreases leading to numerous socio-economical problems, in particular to the labour market problem. As in the middle-term perspective significant fertility increase is not expected, migration increase may be considered as a solution of depopulation problem. Thus, a question concerning migration streams which ensure population non-decrease (so called replacement migration) is raised. Within the framework of Leslie matrix model of population reproduction a problem of regulation replacement migration is considered. (full text)

**
A MINIMAX PROCEDURE FOR ELECTING COMMITTEES**

**M. Remzi Sanver**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 311-311**

A procedure for electing committees, called the minimax procedure, is described. While based on approval voting (AV), it chooses the committee that minimizes the maximum “Hamming distance” to all voters (minimax outcome). Such an outcome may be diametrically opposed to the usual AV outcome, which minimizes the sum of the Hamming distances to all voters (minisum outcome). Computer simulation is used to determine how much, on average, minimax and minisum outcomes diverge. The manipulability and monotonicity of the minimax procedure are also investigated. The minimax procedure is applied to the 2003 Game Theory Society (GTS) election of a council of 12 new members from a list of 24 candidates. (full text)

**
Some generalizations of Condorcet's Jury Theorem**

**D. Derend and L. Sapir**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 311-314**

We study the dichotomous choice model, which goes back more than two centuries ago, as far as [4]. A committee faces two alternatives, of which only one is correct, and decides by the simple majority rule. Condorcet's statement may be phrased as composed of the three parts: A group decision, utilizing the simple majority rule, is more likely to be correct than that of any of the members. The advantage of a group decision increases with the size of the decision body. The probability of the group to make a correct choice using the simple majority rule tends to 1 as the number of members tends to infinity. Condoret's Jury Theorem has been a subject of extensive study for several decades. It provides a theoretical basis of public choice theory and political science theory (cf. [7]). Here we focus on the second part of Condorcet's statement, in particular on the question if a small augmentation of the committee is always an advantage. The answer depends on the interpretation. For a fixed committee and random subcommittees it is unconditionally correct (see [1], [2]). However, this is not necessarily the case in general. (full text)

**
RESULTS OF SIMULATION OF CONSTITUTING PRINCIPLES OF LIVE
AND OF LIVING ACTIVITIES IN RUSSLANDIAN FEDERATION
(IN BROADER SENSE, IN NORTHERN EURASIA)**

**V. Savin**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 314-320**

This article tries to explicitly look at the state, business “society”, religious “societies”, cultural and scientific “societies” etc. as multi-agents (of high hierarchical organizational level) that do live in certain environment. This allows not only to analyze the existing relations between different kinds of multi-agents, but also to try to positively influence or construct conditions for optimizing the relations between these agents with the scope to adequate these relationships to the specific kind of environment. The “philosophical” point of view of this article also permits to build the general goal function for the co-evolution of multi-agents (of high hierarchical organizational level) in their environments. This article is written using the modern northern-american literature to the complex adaptive systems (see references) and is the basis for the modeling work in the Foundation for Monitoring and Forecasting of Developments in Cultural-Territorial Spaces (www.fmprktp.org). (full text)

**
ON MODELING OF DEPENDENCE STRUCTURE OF CLAIMS IN EXCESS-OF-LOSS REINSURANCE**

**E. Yu. Scetinin**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 320-321**

The aim of this work is to analyze the dependence structure between losses and expenses in excess-of-loss reinsurance. In our investigations we used the extreme value copulas and proposed a new asymmetric logistic model of extreme dependence function. Our results could be useful in evaluation of reinsurance premiums. The relevance of our approach was provided by intensive computer mofeling. (full text)

**
mathematical view on the difference between
"Western" and "oriental" agrarian societies**

**A.V.Sergeev, S.Yu.Malkov**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 322-324**

Mathematical model describes typical processes of production, redistribution and consumption of material welfare in agrarian society, taking account of geoclimatic conditions in Europe and Asia. It is shown that geoclimatic factor causes differences in social structure. (full text)

**
Mathematical modeling in structure of displaying
of political object: limits of opportunities**

**O.F.Shabrov**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 325-329**

Mathematical modeling is the most important means of display of objects in a politics. Its using is justified and effective when verbal display becomes insufficient because of big number of parameters or necessities of the quantitative description. In a politics the requirement for mathematical model is especially actual in connection with impossibility of research experiment on real political object. (full text)

**
STUDYING OF CORRUPT HIERARCHY BY MEANS OF MATHEMATICAL MODELLING**

**A. Shamraj**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 329-329**

In article the corruption hierarchy which is a part of the qovernment hierarchy studied in works by A.P.Mihajlov is investigated. The basic postulate of behaviour of the corrupt official is formulated. On his its basis the mathematical model of corruption hierarchy is constructed. Various scripts of development of mutual relations of corrupt bureaucracy and the state are investigated. (full text)

**
FIRM ADAPTATION MANAGEMENT ALGORHYTHMS UPON
THE CHANGE OF THE SITUATION IN THE MARKET**

**J.V. Shiryaev and A.A. Bragina**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 329-332**

The problem of firm parameters optimal means according to its adaptation to market conditions is solved. The evaluation task of adaptation efficiency depending on expenditure guantity of firm parameter change – investments, on the example of food industry enterprises is also solved. (full text)

**
CONSEQUNTIONS OF INCLUDED SUBGROUPS AND MODELING
OF EVOLUTION ANCIENT SOCIETY (RESULTS OF PARALLEL
CALCULATION AND ITS INTERPRETATIONS)**

**V. Shvedovsky**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 332-334**

In this report results of parallel calculations (look at Appendix) for great group gratings for Sn (n³4) are discussed. The model of very old society are presented on the path on group grating. Especially we are interesting in those tracks, which may be considered as, in a sense, minimum path. Finally, some problems which could be described in terms of changes low H(n) = LnL + (n-1)Ln(n) - LnLn(n-1) - n (by W.M.Bechterev) are discussed. (full text)

**
ON A NEW METHOD OF INVESTIGATION
OF DYNAMIC ECONOMIC MODELS**

**P.M. Simonov**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 335-337**

A new approach to research of differential equations with aftereffect is considered in the report. Modifications of some well-known models micro- and macroeconomics are suggested. Effective sufficient stability tests of such models are demonsrated. (full text)

**
COMPARING THE RULES CHAMBERLIN’S WAY**

**G. Pritchard and A. Slinko**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 337-340**

In 1973–75 Gibbard and Satterthwaite published a fundamental impossibility theorem which states that every non-dictatorial social choice function, whose range contains at least three alternatives, at certain profiles can be manipulated by a single individual. After that, the natural question arose: if there are no perfect rules, which ones are the best, i.e. least manipulable? The answer to this question cannot be given in absolute terms. It stipulates introducing a certain index of manipulability of the rule and a certain model for the population. The answer may depend both on the choice of the index and on the choice of the model. (full text)

**
Modelling
of choosing the tax schedules**

**R.O. Smirnov, S.V. Chistyakov**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 341-343**

The article substantiates a new approach to the choice of tax schedules based on several mathematical models. The first model, based on game theory, helps to construct the average tax rates schedule. The second is an optimization model used to construct the marginal tax rates schedule. (full text)

**
Optimal control of distributed systems
and its applications in economics**

**V.I. Soloviev**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 343-346**

Many economical systems are distributed, the most simple example of distributed economical system is illustrated by Beckman’s transportation flow model kf / |f| = grad l, where l is good’s price, k is transportation tariff and f is local transportation flow. We can also illustrate distributed economic systems by Black — Sholes’s derivative instrument pricing model in financial theory, generalized Tiele’s model in insurance theory, etc. The necessary conditions for optimal control of such systems satisfying partial differential equations are formulated as Lagrange — Pontryagin’s maximum principle generalization. The economical and financial applications are discussed. (full text)

**
The society losses from inflation and taxation**

**A. I. Sotskov**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 346-349**

In the standard framework of the macroeconomic model with a representative consumer, producer and government we suggest a definition and a description of structure of the society losses from policy steps of the government. A theorem asserts that the society surplus is added of the consumer’s, producer’s, and the government’s surpluses. In particular, the theorem generalizes the Bailey’s (1956) classical result on costs of inflation. The work contains also some results of comparative statics, and a calculation experiment with a model calibrated on Russian data. (full text)

**
VARIATION INDEX AND LOCAL FRACTAL ANALYSIS**

**M.M. Dubovikov, A.V. Kryanev, N.V. Starchenko**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 349-352**

On the basis of the minimal covers, it is introduced the variation index which extends the applicability of fractal analysis to study of various natural, technological and social chaotic processes. In particular, for the case of financial series, it is shown that the minimal scale which is necessary for determining with an acceptable accuracy, is two orders smaller than the one for computing the Hurst index H. This allows us to consider as a local fractal characteristic and to show that is related to the stability of underlying processes. (full text)

**
AGE STRUCTURE MODEL FOR SECONDARY SCHOOL TEACHERS**

**M. Stepantsov **

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 352-355**

When analyzing the
situation in Russian secondary school. it seems necessary to forecast the
developing tendencies in education under particular social-economical
conditions? and one of the main features here is the age structure of teachers
employed.

This forecast can be made with the help of the proposed mathematical model,
including mail factors that influence the age structure of teachers. The model
is built, considering the main differences between work forces of secondary
school and ones of high school.

The definite parameters of the model can be obtained from the results of social
and statistical studies. The parameters being defined, it is possible to make
forecasts of age structure dynamics and of general social situation in secondary
school under different social-economic scenarios in the country.
(full text)

**
THE REDUCTION TECHNIQUES TO TIME-OPTIMAL CONTROL PROBLEMS
FOR NON-LINEAR SINGULARLY PERTURBED SYSTEMS**

**N.N. Subbotina**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 356-358**

Time-optimal control problems for systems with fast (singularly perturbed) and slow motions are under consideration. There are obtained sufficient conditions for the value function, which is equal to minimal time of arrival to the given target set, to converge as speeds of fast variables tend to infinity. The researches are based on the coincidence of the value function and the unique lower semi-continuous minimax solution to a Dirichlet problem for the Bellman equation. The suggested construction of the limit value function can be considered as a development of the reduction technique. (full text)

**
About optimal contracts with managers of investment funds**

**E.A. Sukhina**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 358-362**

The approach is based on the interpretation of Pliska and Belecky [1],[2] continuous time portfolio optimization model. This model takes into account the fact that the mean return of individual securities or asset categories are explicitly affected by underlying economic factors as dividend yield, a firm’s return on equity, interest rates, unemployment rates, etc. Methods of risk sensitive control theory are employed, using an infinite horizon objective that is natural and features the long run expected growth rate, the asymptotic variance and a single risk aversion parameter. Our approach allows to align interests of managers and investors in the following sense: we find the optimal strategy of the full capital distribution between the managers fee and investors, maximizing the expected growth rate of capital on big enough interval of time, taking into account a manager’s skill to raise the capital of the fond in the risk averse case. Thus it becomes clear, in what situation (at what parameters of activity) the manager should be remunerated and in what sizes and when it is fined and on how many. (full text)

**
Social Processes Forecasting Using
Learning Genetic Algorithm**

**S.V. Sychev**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 363-365**

Social processes forecasting has become more urgent and demanded in modern society. It is usually inconvenient to apply traditional methods to solve the problem, several reasons taken into consideration. In this connection it is recommended to use a comparatively new approach, based on Learning Genetic Algorithm for Prognosis (LGAP). Numerous experiments proved that high degree forecasting can be achieved with the use of the method. (full text)

**
ENDOGENOUS FORMATION OF COALITIONS WITH POPULAR PLAYERS**

**S. Thoron**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 365-367**

A normal form game of coalition formation is presented in which each player's strategy is a list of coalitions she is willing to form. This is an enrichment of the strategies spaces that have been proposed in the literature. Indeed, in the normal form games proposed by Von Neumann and Morgenstern (1944) and Hart and Kurz (83) one player's strategy is to choose the coalition to which she wants to belong. However, "a priori", when a player is willing to negotiate, she knows that she is willing to form different possible coalitions, even if her objective is to reach the best choice available. Hence, for a given strategy profile, the feasible coalitions are coalitions such that they are in the list-strategy of each member. For each strategy profile, we define the feasible set of coalitions and for each individual, her individual feasible set consists of those elements of the feasible set to which she belongs. In general, the coalitions in a feasible set do not form a partition of the set of players. (full text)

**
ON THE POSSIBLE REASONS FOR THE HYPEREXPONENTIAL GROWTH OF THE EARTH POPULATION**

**S.V. Tsirel**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 367-369**

A new model of the Earth population growth is offered. It shows that the hyperbolic growth presents the transition period between zero growth (after filling its own ecological niche) to the exponential one. The difficult problem of explaining the hyperbolic growth in the XVIII-XX cc. is discussed. (full text)

**
SECULAR CYCLES: LONG-TERM OSCILLATIONS IN ECONOMIC
AND SOCIAL STRUCTURES OF AGRARIAN SOCIETIES**

**P. Turchin **

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 370-373**

One particularly interesting dynamic pattern in history is the oscillation of centralization and decentralization of political power, seemingly affecting all hierarchical macrosystems, from systems of chiefdoms to world empires. What sociopolitical mechanisms may explain these dynamics? I will present some mathematical models and data that address this question. (full text)

**
CONCEPT OF TIME-EVENT CONTROLLED PROCESSES — A WAY TO THE MOST
GENERAL FORMULATIONS OF PRODUCTION PLANNING AND REGULATION PROBLEMS**

**A.M.Valuev**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 373-376**

A proposed approach to production planning or regulation problems formulation explicitly takes into consideration the fact that the qualitative state of a production system changes after some events, so instants of these events are treated as ends of plan period stages. To find instants of events of a certain type corresponding relationships are introduced into the model. The general formulation of the new models class is given. These models give the possibility to apply exact optimization techniques for determination of values of some parameters that earlier might be appointed only by experts and to embrace in a sole problem statement a lot of plan problem variants that traditionally may be regarded only separately. Such kind of models may be treated either as deterministic or stochastic that lead to broad possibilities of controlled processing modeling in the context of planning as well as the programmed processed regulation due to various disturbances. (full text)

**
MODELS OF TAX SYSTEM OPTIMIZATION**

**A.A. Vasin, P.A. Vasina**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 376-378**

Creation of the efficient tax system is one of the most important tasks for countries in transition. The present paper aims to discuss the main components of this complicated problem. The first one is the choice of the tax structure and tax rates in order to get the desirable tax revenue. The second problem under consideration is determination of the optimal tax schedule and audit strategy for direct taxes. The paper also discussed several issues related to tax inspection organization and creation incentives for the efficient work of inspectors. Models of interaction between taxpayers and inspectors take into account corruption, audit costs and random mistakes of participants. (full text)

**
ALGEBRAS AND GROUPS LIE – TOOLS FOR MODELLING ECOSYSTEMS**

**Yakovenko G.N.**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 378-382**

The modification of system Lotka - Volterra considered. The modification enables to take into account natural unpredictable influences on ecosystem. The algebraic models, allowing to describe are investigated also dynamics of system to within the description of a variable state. (full text)

**
A MATHEMATICAL MODEL OF A STATE**

**V.K. Zakharov, A.D. Yashin**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 382-385**

In this paper a dynamic model of a state and more generally of a nomós (i.e. a linked vitally active community) is introduced (see also [1]). The vital activity of a nomos is presented in the form of a vitally organizing cycle of streams of results of substantiating, directing, and ensuring activities, linking units and main parts of the nomos with each other and also with the natural environment and the external organized environment. The model describes only a nomos with a constant construction. (full text)

**
APPLICATION OF SYSTEM DYNAMICS FOR MODELING FIRM
FUNCTIONING AND ESTIMATING OF ITS ACTIVITY UNDER UNCERTAINTIES**

**S.V. Zankov and V.I. Shiryaev**

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 385-388**

Nonlinear dynamic mathematic model of a firm is build using approach of system dynamics. The problem of firm activity estimating is solved for purposes of further firm optimization and control. This is the problem of model state and parameters estimation under conditions of imperfect and incomplete data. (full text)

**
ZEROTH RISKS
IN NONCOOPERATIVE GAME**

**L.V. Zhukovskaya **

**Proceedings of the International Conference "Mathematical
Modelling Of Social And Economical Dynamics" (Mmsed-2004), June 23-25, 2004,
Moscow, Russia. - Moscow, RSSU,2004. pp. 388-388**

Noncooperative game under uncertaity is considered. Each payoff function is accomplished by risk function. Properties of this extended game are investigated. (full text)

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