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## THE LABOR IMMIGRATION CONTROL

In this paper we propose a dynamic model of controlled labor immigration. The model can be used as a framework to study the economic impacts of immigration for host countries. The system’s trajectories are analyzed for different parameter values. A control problem formalization is given. Existence of optimal immigration quota is proved.

The design of logistics chain is strategically important issue for almost every company. There is a large variety of model formulations and solving algorithms, which vary in fundamental assumption, mathematical complexity, etc. In this paper classification of models of dislocation of logistic capacities is considered and the multicriteria model of optimum dislocation of warehouses in supply chains is offered.

This study is an attempt to obtain reliable data on the natural history of breast cancer growth. The opportunities for using classical mathematical models (exponential and logistic tumor growth models, Gompertz and von Bertalanffy tumor growth models) were analysed in order to describe growth of the primary tumor and the secondary distant metastases of human breast cancer. Our results suggest a new «Consolidated mathematical growth Model of the Primary tumor and the Secondary distant metastases» (CoMPaS). The CoMPaS is based on exponential tumor growth model and consists of a system of determinate nonlinear and linear equations. The CoMPaS describes correctly the primary tumor growth (parameter T) and the secondary distant metastases growth (parameter M). Also, CoMPaS associates with data of 10–15-year survival in patients with the different tumor stage. Analysis of the metastases «nonvisible period» growth indicate the case of discrepancy between 15-year survival depending on tumor stage. In conclusion, the CoMPaS and supporting computer program were build to improve the accuracy of the forecast on survival of breast cancer and facilitate the optimisation of diagnosing secondary distant metastases. This led to completely original results that show how the growth rate of the metastases can change in relation to the growth rate of the primary tumour, taking into consideration its size and diameter of the tumour.

Proceedings of the III International Conference in memory of V.I. Zubov "Stability and Control Processes (SCP 2015)".

Nowadays the random search became a widespread and effective tool for solving different complex optimization and adaptation problems. In this work, the problem of an average duration of a random search for one object by another is regarded, depending on various factors on a square field. The problem solution was carried out by holding total experiment with 4 factors and orthogonal plan with 54 lines. Within each line, the initial conditions and the cellular automaton transition rules were simulated and the duration of the search for one object by another was measured. As a result, the regression model of average duration of a random search for an object depending on the four factors considered, specifying the initial positions of two objects, the conditions of their movement and detection is constructed. The most significant factors among the factors considered in the work that determine the average search time are determined. An interpretation is carried out in the problem of random search for an object from the constructed model.The important result of the work is that the qualitative and quantitative influence of initial positions of objects, the size of the lattice and the transition rules on the average duration of search is revealed by means of model obtained. It is shown that the initial neighborhood of objects on the lattice does not guarantee a quick search, if each of them moves. In addition, it is quantitatively estimated how many times the average time of searching for an object can increase or decrease with increasing the speed of the searching object by 1 unit, and also with increasing the field size by 1 unit, with different initial positions of the two objects. The exponential nature of the growth in the number of steps for searching for an object with an increase in the lattice size for other fixed factors is revealed. The conditions for the greatest increase in the average search duration are found: the maximum distance of objects in combination with the immobility of one of them when the field size is changed by 1 unit. (that is, for example, with 4x4 at 5x5) can increase the average search duration in e^1,69≈5,42. The task presented in the work may be relevant from the point of view of application both in the landmark for ensuring the security of the state, and, for example, in the theory of mass service.

Religion, ethnicity, and politics are typical explanatory variables of violent conflicts. From an economic point of view, economic growth reduces the risk of civil war, yet the economic determinants of conflict have been little studied. In this article, we empirically study the impact of regional macroeconomic conditions on the number of violent conflicts in Indonesia, a country with potential risks of communal conflict because of the plurality of its society. We use panel data consisting of observations on 16 Indonesian regions from 2004 to 2013 to assess the impact of economic factors on conflict, reevaluating the religion effect using dynamic models (SYS GMM estimator). Our findings suggest that only the inflation rate predicts the conflict growth rate. Economic growth, economic development, poverty, and even religion, do not significantly affect the number of regional conflicts.

The purpose of the article is to compare the models of state regulation of economic growth, connected to market optimization and counter-cyclical regulation, through the prism of their influence on population’s living standards and to determine the most optimal one according to the criterion of maximization of positive influence. Methodology: The authors use the method of regression analysis for determining the dependence of the life quality index in 2018 on the 2007 level, growth rate of GDP (model of market optimization), and depth of decline of GDP in the crisis period (2010) (model of counter-cyclical regulation). The research objects include 16 developed and developing countries that are peculiar for the highest living standards as of 2018–8 countries implement the model of market optimization and 8 countries implement the model of counter-cyclical regulation. Results: It is concluded that maximization of advantages for the global economy, connected to increase of population’s living standards, requires the model of counter-cyclical regulation, which envisages limitation of growth rate of economy in the period of its rise for leveling the following cyclical fluctuations–minimization of crisis in the period of decline. The alternative model of market optimization is undesired, as it hinders the achievement of global goals in the sphere of sustainable development, reducing population’s living standards. Recommendations: It is shown that practical implementation of global goals in the sphere of sustainable development envisages unification of the practice of national state regulation of economic growth for optimizing the growth of the modern global economy. The authors’ recommendations for this are offered.

We investigate the impact of inequality in wealth distribution on the joint dynamics of conflict intensity and pro-growth institutions in the historical perspective. We build a two-sector endogenous growth model with political conflict between the traditional elite and the emerging class of capitalists during the transition from stagnation to growth. First, our model attempts to explain different moments of industrialization worldwide. Second, we capture various paths of conflict intensity: hump-shaped path, almost absent conflict, and other. We show that the distribution of wealth has a non-monotonous impact on the intensity of conflict and institutions supporting industrialization. Namely, higher inequality in land distribution may be detrimental to industrialization, but may lower conflict intensity. In contrast, higher inequality in capital holdings may be growth-enhancing.

Smoking is a problem, bringing signifi cant social and economic costs to Russiansociety. However, ratifi cation of the World health organization Framework conventionon tobacco control makes it possible to improve Russian legislation accordingto the international standards. So, I describe some measures that should be taken bythe Russian authorities in the nearest future, and I examine their effi ciency. By studyingthe international evidence I analyze the impact of the smoke-free areas, advertisementand sponsorship bans, tax increases, etc. on the prevalence of smoking, cigaretteconsumption and some other indicators. I also investigate the obstacles confrontingthe Russian authorities when they introduce new policy measures and the public attitudetowards these measures. I conclude that there is a number of easy-to-implementanti-smoking activities that need no fi nancial resources but only a political will.

One of the most important indicators of company's success is the increase of its value. The article investigates traditional methods of company's value assessment and the evidence that the application of these methods is incorrect in the new stage of economy. So it is necessary to create a new method of valuation based on the new main sources of company's success that is its intellectual capital.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.