Abstract: The object of this research is the border activity, while the subject is the science of border activity – borderology. The article consists of five sections. The first section views border activity as a system of preventive (border prevention and deterrence), security and control (border patrol, border search), and defense-militant measures (special activity, combat activity, operational actions). The second and third sections give detail description to these measures, as well as the typical stages of the cycles of activity. The fourth section is dedicated to description of the structure of borderology – the system of knowledge on ensuring border security, state c of border organizations, preparation and conduct of border activity, and its all-round provision. The fifth section provides a systemic formulation of principles of border activity. Within the framework of development of the concept of “border management system”, the author considers the border activity as a system of measures aimed at ensuring national security in the borders. The science of border activity includes the following disciplines: border art (border policy, border operational art, border tactics), border history, border statistics, mathematical theory of managing border security, legal framework of border security and border activity, philosophy of border security, psychology and sociology of border activity, theory of border training and education, theories of all-round support of border activity, theory of development, application of technical and special means of border activity.   

Abstract: The object of research is the combat and military operations. The subject is the dynamic models of combat operations and functions of victory in the conflict. The first combat model was developed by M. P. Osipov in 1915 based on the analysis of military battles for the hundred-year period. He was first to formulate the principles of combat operations modelling. In recent decades, the economists also joined the analysis of conflicts (contests and auctions). The goal of this work lies in analysis and unification of the two indicated approaches, and provision military leadership with quantitative grounds for decision-making in preparing to the combat operations. Leaning on the statistical analysis of offensive and defensive strategic operations during the Great Patriotic War (forces and means of the parties by the beginning of operation and its outcome), the author verifies the original expansion of conflict model – the function of victory in combat operations and assesses the parameters of the form of model. The scientific novelty of consists in establishing a close connection and dependence between the two approaches to combat operations modeling: based on dynamics of the averages (classical approach) and modeling with the use of conflict functions (econometric approach). The advanced function of victory in combat operations is easy to use and complies with the provisions of military science and the theory of combat potentials.

Abstract: Insufficient economic growth rates, security problems, the expected exit of the UK from the EU prompt further research into the analysis of the processes of integration and disintegration of supra- and interstate entities. The paper presents a security model of the state, consisting of two components - development functions and conservation functions. The development function in the form of a three-factor power production function takes into account the population size of the country, its area, urbanization, gross domestic product per capita and natural population growth. The conservation function operates with variables such as: the share of the state-forming ethnos from the population of the country, the parameters of attraction and ethnic heterogeneity. The verification of the security model was carried out using the example of the EU countries. A model for the security of supra- and interstate political entities (unions) is developed, taking into account the degree of integration between individual countries (the share of state functions transferred to the Union). For the EU countries, an assessment of the heterogeneity parameter relative to the allied country, Germany, has been carried out. Shumov analyzes the network structure model that includes the geographic graph (combination of axes (states) and ridges (boundaries between states)) and sociopolitical graph (arcs are interpeted as the presence of sociopolitical connections). The author offers his definition of admissible coalitions and explains the rule of formation of socio-political network structures: political actors select coalition with the maximum security function. Shumov provides examples of formation of optimal coalitions. Using the network structure model, the author carries out an analysis of the processes of integration and disintegration in the European Union. As the European Union integration develops, disintegratoin processes are expected to reinforce in multinational states, or the states will have to leave the Union. 

Abstract: The research object is the characteristics and factors of development of societies and states. The research subject is the creation of the model and indexes of sovereign development of the key states. The article demonstrates the model that takes into account the following indexes: population size, territory size, and social technologies. Instead of the difficult-to-calculate and difficult-to-evaluate innovation index, the author offers the social technologies index consisting of three indicators: urbanization, GDP per capita, and population size growth rates. The author applies the natural-science approach and mathematical modeling. The author enumerates the key 20 countries in the descending order of the sovereign development index: China, the USA, India, Russia, Brazil, Canada, Indonesia, Mexico, Australia, DR Congo, Nigeria, Argentina, Iran, Pakistan, Algeria, Saudi Arabia, Ethiopia, Egypt, the Republic of South Africa, Turkey. The scientific novelty of the study consists in the application of publicly available statistical data for the calculation of the sovereign development indexes of countries covering long periods of time. 

Abstract: The insufficient economic growth, the security problems and the UK expected leaving of the EU incline to the continuation of the analysis of integration and disintegration processes in the European Union. The research subject is the assessment of the security level of the European Union. Through the dichotomy of the values of development and preservation, the author defines the function of the security of the state and the union of states. Based on the statistical data, the author assesses the security of the Union according to several scenarios. To analyze integration and disintegration processes in the EU, the author uses the system approach, historical and statistical data and mathematic modeling. On the base of the assessment of Russia’s security over the past 200 years, the author assumes that the decrease of the value of the preservation function below 0,5 – 0,6 creates the prerequisites for the possible dissolution or transformation of the state. The author formulates the formal tasks of the search for the optimal composition and structure of the European Union and gives the examples of the calculation of the rational composition of its member-states. 

Abstract: This work explores the factors that significantly affect the security of the constituents of the Russian Federation. For considering in the mathematical model the following factors are being determined: climate factor, socioeconomic factors, level of transnational wellness, and level of integration of the regional national groups into the unified social space of the country. Security is defined through the dichotomy of the values of development and values of preservation. The parameters of the model are being evaluated considering the data on the migration of the population. The author presents calculations on the assessment of the security level in the Russian regions during the peace time and war time (not taking into account the military factors). By using the systemic and historical approaches, along with the methods of mathematical modelling, the author formulates the criterion of regional security, which reflects the values of development (socioeconomic factors) and values of preservation (complementarity of ethnoses, integration of national and regional groups into the country’s social space). The Pareto distribution is used in building of this model; the assessment of parameters is carried out via using the method of least squares. The basic model of regional security can be applied in modelling (expansion of a model): sociopolitical and socioeconomic security, demographical and environmental security, safety in circumstances of emergencies, border security, etc.

Abstract: The subject of this research is the analysis and determination of the key, maximally aggregated and measurable factors that define the level of security of a state (or a coalition of states). The factors affecting the state of national security (population, territory, technologies, and complementarity of the ethnoses) are being studied for the purpose of building a mathematical model of national security. In the interests of verification of the model, the author uses statistical and analytical data that characterizes the security of the nations of the European and Eurasian unions: size of the population, size of the territories, index of innovations, etc. In order to describe the system of international relations, the work employs the typology og the international systems by Morton Kaplan. In structuring the model, the author utilizes production function, power function, and distribution of Pareto. Using this model, the assessment of the security of the European and Eurasian unions is being carried out. The results of the assessment demonstrate that inclusion of Ukraine into the European Union will lower the EU’s level of security. The technologies are the hampering factor of the expansion of the European Union.

Abstract: Scientific, axiological and historical approaches have been used to consider the model of national (public) security, which reflects the dualism of the values of development and preservation, taking into account the following factors: population of the state, area, the level of technological development and its convertation to actions, diversity of population. The parameters are evaluated by the example of participation of a range of countries in the First and Second World wars, as well as the military campaign of the USA in Iraq. The parameters characterising the diversity of population are based on the statistical data of the regions and ethnicities of Russia (USSR). The demonstrated model meaningfully characterises the potentials of states and societies. The convertations of these potentials to real developments depends on multiple factors studied by humanities. The study involves mathematical and statistical methods of analysis of social processes and phenomena. The parameters have been evaluated using the least squares method. Having used the suggested model, the author concludes that the European Union has probably reached the limits of its enlargement, and it is possible that some states may withdraw their membership. Also, function values of sovereignty, preservation and security have been calculated for the countries of G7 (USA, Great Britain, Germany, Japan, France, Canada and Italy) and E7 (China, India, Brazil, Russia, Mexico, Indonesia and Turkey). Total function value of sovereignty for the E7 countries is 1.7, whereas for the G7 states it is 4.6.

Abstract: The article is devoted to national security and the related processes of integration and disintegration of states and political alliances. The author develops the security model defined through the dichotomy of values of development and preservation, cooperation and competition. For the purpose of the model assessment and verification the author uses historical, statistical and analytical data characterizing the security of states and alliances of states and regions: the population size and structure, socio-economic characteristics, innovation index, etc. The author uses the methods of mathematical modeling, mathematical statistics, historical data about the development of states since 1500, and the systems and natural scientific approaches. The security model gives the opportunity to solve several practical tasks:
1. To assess security of China, Russia and the USA for the period from 1500 till 2009. The author shows that social transformations in the society and the state take place when the preservation rate decreases below 0,5 – 0,6.
2. To calculate the security of the European Union according to three scenarios: creation of a commonwealth, a federation or a unitary state. The author supposes that recently the EU has reached its growth limits (and even exceeded them). Its sustainable existence is provided by means of translation of the part of military and political sovereignty to the EU by the USA and the passivity of other geopolitical actors.
3. To calculate the security of the Eastern European Union (unification of 9 states around Russia). With any form of unification the Union will be a sustainable construction. This assessment does not contradict the historical development of Russia. 

Abstract: The article contains the criterion for the frontier security - prevented harm to public good minus the costs of frontier activities. The criterion allows to account for the efficiency of frontier measures and frontier constrainment. Efficiency of frontier measures is evaluated with the use of frontier productive function, efficiency of constrainment is evaluated with the logit model.  The definition of security has value-oriented subjective character, and it is determined by the historical experience of the people. In order to take into account subjective factors, the article contains definition of the view (perception) function and evaluation of adequacy of formal dependencies.  With the use of systemic historical approach the author provides analysis of frontier security of the state in the XX century. Development of the frontier system is regarded as an adaptation. The author reveals adaptation mechanism, showing dependencies between the contents of various stages of the recent frontier history and the dominant perception of value of security among the elites and in the society.  The evaluation of these approaches to frontier security facilitates the formation of an "intellectual" frontier in order to improve security of the state and society from the transborder challenges.

Abstract: The boundary security is analyzed within boundary studies, its object of study is boundary processes, boundary systems, and boundary influences.  This article includes evaluation of approaches towards boundary security modeling from the standpoints of systemic analysis, system science, operation studies.  The article contains three parts.  Part one is devoted to the structure of boundary studies, and its main characteristics, such as norms and principles of boundary activities, functions of boundaries, boundary policy and boundary means, threats in boundary areas, types of boundary influences, etc.   In the second part it is shown that complicated boundary processes may be modelled with the use of hierarchy and chains of models. The author studies 13 modelling levels starting from the physical and geographic level and finishing with the goal-setting level.  The modeling chains are based upon general and specialized cycles of activity and administration.  The last part provides for modeling methods in the sphere of boundary security. Rephrasing William Ashby, one may state that real process models of boundary security guarantees should be no less varied than the variety of real administrative situations. Due to this fact, the model should be multi-level and they should correspond with universal and special cycles of administration and activities.