We construct an example of blow-up in a ”ow of min-plus linear operators arising as solution operators for a Hamilton…Jacobi equation @S/@t+|∇S|/ + U(x, t) = 0, where > 1 and the potential U(x, t) is uniformly bounded together with its gradient. The construction is based on the fact that, for a suitable potential de“ned on a time interval of length T, the absolute value of velocity for a Lagrangian minimizer can be as large as O(log T)2−2/. We also show that this growth estimate cannot be surpassed. Implications of this example for existence of global generalized solutions to randomly forced Hamilton…Jacobi or Burgers equations are discussed.

A multivariate generalization of the classical collective risk model is considered. In this model in which each component is dependent on the others.The exact solutions and asymptotic approximations to the probability of ruin were obtained.

In this paper the modification of McEliece public-key cryptosystem is considered, which uses the codes based on Plotkin construction as the private key, instead of Goppa codes traditionally considered for this purpose. Proposed modification allows strengthening of McEliece cryptosystem by attacks complication based on the secret code structure.

In this paper an attack on McEliece cryptosystem is considered. In this system the private and public keys are generator matrices of equivalent codes, i.e. they differ by fixed (secret) permutation. At the same time it is known that for every code there are the group of permutations preserving the code. Such code's structure may be used for analysis of McEliece cryptosystem.

One of the actively developing approaches of group robotics systems creation is the use of social behavior models. Aggressive behavior is one of the underlying mechanisms forming social behavior. In this paper, the application of aggressive behavior concepts is considered by analogy with animal aggressive behavior that can be used for solving tasks of group robotics. As a role model, an ant – a true social insect – is proposed. It was shown that in aggressive behavior of ants, the numerical factor and imitative behavior play an important role. Agent’s aggressive behavior model depending on accumulated aggression and the number of other nearby agents is proposed. The results of computer experiments for territory defense tasks are presented. The results show that aggression is a stabilizing factor for an approximately equal number of agents in different groups. By an increase in group size, aggression becomes a way of capturing foreign territory.

The conflict measure and index of decreasing of igno-rance in frame of Dempster-Shafer theory are intro-duced. Those functionals are analyzed on the bodies of evidences of special type. It is shown that the great correlation between the bodies of evidence is a sufficient condition of decreasing of ignorance after the applying of combining rule. The relationships between the measure of conflict and the index of decreasing of ignorance in the case of different types of evidences and the application of different combining rules were investigated.

Diffculties concerning the choice of the invariants of the projective transformation groups used for the identification of the shapes of planar objects are illustrated and solutions allowing the derivation of robust identification criteria are discussed.

The chapter is focuses on the research in rural Russia. The empirical materials were studied in the historical context. The chapter helps to understand the consequences of the Russion Revolution 1917.

Our approach to the problem of charge carrier transport in homogeneous polymers assumes carrier hopping on a densely packed manifold of transport (hopping) centers retaining the short-range order of the respective single crystal. The central idea, which distinguishes it from the Bassler’s disorder theory, is that the energy scatter concerns only a small fraction of hopping centers, which begin to act as traps. The majority of isoenergetic centers build up a transfer band with microscopic mobility µ0 equal to that in the respective single crystal. The origin of the energy scatter (and traps themselves) is ascribed to the elementary voids of the fluctuation free volume forming an association with the normal hopping centers.

We consider a fractional 0-1 programming problem arising in manufacturing. The problem consists in clustering of machines together with parts processed on these machines into manufacturing cells so that intra-cell processing of parts is maximized and inter-cell movement is minimized. This problem is called Cell Formation Problem (CFP) and it is an NP-hard optimization problem with Boolean variables and constraints and with a fractional objective function. Because of its high computational complexity there are a lot of heuristics developed for it. In this paper we suggest a branch and bound algorithm which provides exact solutions for the CFP with a variable number of cells and grouping efficacy objective function. This algorithm finds optimal solutions for 21 of the 35 popular benchmark instances from literature and for the remaining 14 instances it finds good solutions close to the best known.

The cell formation problem (CFP) is an NP-hard optimization problem considered for cell manufacturing systems. Because of its high computational complexity several heuristics have been developed for solving this problem. In this paper we present a branch and bound algorithm which provides exact solutions of the CFP. This algorithm finds optimal solutions for 13 problems of the 35 popular benchmark instances from the literature.

The chapter discusses the establishment of diplomatic relations between Spain and Russia and evaluates the role of Peter I in this process. Special attention is paid to the development of trade relations between the two countries. The text used new archival documents.

Students’ grade system is a complex multifactorial process, which usually ends with a numerical estimate. The studying mindset and motivation of the student, which are inextricably interconnected, depend on the objectivity of the estimate. The major problems related to the understanding of estimate as an absolute value or a relative one, which uses comparison, are analysed. Solution methods allowing to combine positive sides of each of the approaches of evaluation are offered. These methods allow to combine both absolute and relative estimate. The following proposed approaches are taken into consideration: a modular system of training, preference of cumulative assessment, the choice of the monitoring procedure form etc. Basic parameters influencing the creation of a «fair» grade system, as well as results of the students survey regarding the factors influencing a grade system are given.

In this article I am offering some critical comments on two of the most important programs of modern social and political philosophy: transcendental pragmatics and communication theory. These considerations will cover two main problems: justification of rational prerequisites of activities, that would be common and universal for all of humanity and universal, and transparent communication, that is common for all representatives of intersubjective commonality. The first problem is the difficulty of removing the fundamental contradiction between "ones" and "someone else's", and the second is the difficulty of simulation of communication unity, that despite its universality, may serve as different packages of values.

Each developing country tries to catch up with the developed world. Unfortunately, only few economies were able to reach this purpose during last sixty years. Well-known Gershenkonђs argument - «advantage of backwardness» - does not work properly in most cases [Gershenkon, 1962]. Though imitations of technologies and governance methods are much cheaper than innovations, the imitation process is also costly and requires sophisticated approaches of choosing and harmonizing different kinds of economic policies.

The presentation considers the problem of the academic heterogeneity among universities freshmen. This problem is widely discussed in circumstances of demographic decline when higher education becomes widespread. As a result differentiation of universities based on the quality of students' freshmen arises: some universities admit predominately high-scored students, while the others have a large variation in students’ preparation level. Universities have to work with non-uniform contingent of students. In Russia the Unified State Exam (USE) is used to admit students to the universities. There are two obligatory exams (Mathematics and Russian language) and different optional exams which students can choose depending on their future direction of study. Scores for USE are the only basis for students’ admission to universities. The points of interest are simultaneously the quality of admission and its heterogeneity. Heterogeneity implies differences in the student’s USE scores in one university. The data base includes USE scores of all students enrolled in all universities in 2011-2012 in the context of different majors. The procedure of academic heterogeneity investigation has been developed with the 5-points scale of heterogeneity levels. There are two types of issues in this research. The first one includes the analysis of academic heterogeneity indicators over years and the classification of universities based on their heterogeneity. The second issue concerns intra-university level and includes the following points: • Identification of factors that influence academic heterogeneity of enrolled students • Analysis of heterogeneity in the context of different majors • Analysis of the dynamics of academic heterogeneity over the years • The university contribution to the dynamics of heterogeneity during the period of education. • Recommendations for dealing with heterogeneous contingent of students. For assessing student’s heterogeneity traditional statistical methods were applied as well as mathematical modeling based on Item Response Theory (IRT). The use of IRT methods allows us to place all the data on the unique metric scale, construct classification of universities on the quality of admission and assess heterogeneity. Despite the differences in the systems of state exams and the academic selectivity in various countries the methods developed can be used to assess the heterogeneity of university freshmen in each country.