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At the beginning of the 20th century, the processes of urbanization were actively taking place in the Russian Empire, but in different regions they went with varying degrees of intensity. Modernization changes in the traditional agricultural and nomadic societies of the Central Asian region began after its final annexation to the Russian Empire, which happened quite late – in the 60-70s of the 19th century. Based on the data of statistical surveys of the Steppe and Turkestan general-governorate’s areas, the authors analyze the urban population’s dynamics, the movement of its class and national composition in order to assess the level of urbanization of the region, as to what extent it reflects the general patterns of modernization and what is its regional specificity. The graphs compiled according to the Surveys show that in all nine areas of the region there was a quantitative increase in the urban population. The main incentives for urban growth were trade and railway construction. At the same time, another trend is observed: the proportion of citizens in the entire population does not increase significantly, but fluctuates in the range of several percentage points. The absence of pronounced dynamics of the urban population outpacing growth over the rural population indicates the initial stage of the Central Asia’s urbanization. The low intensity of urbanization is quite corresponded to the Central Asian economic modernization imperial strategy, which consisted in the development of commodity specialization of agricultural sector for the needs of the metropolitan industry and peasant colonization of the region.

This paper is devoted to hot isostatic pressing (HIP). HIP capsule simulation software has been analysed. Abaqus has been proved the most appropriate simulation tool, which enables finite element analysis and allows users to define their own material properties via a special control program. Specific features of HIP simulation models have been evaluated. Powder densification model has been analysed and implemented. A control program has been developed to factor in elastic and plastic material behaviour. Preliminary simulations have been run for a one-element model and a capsule model.

In the paper explicit functional continuous Runge–Kutta and Runge–Kutta–Nystrom methods for retarded functional differential equations are considered. New methods for first order equations as well as for second order equations of the special form are constructed with the reuse of the last stage of the step. The order conditions for Runge–Kutta–Nystrom methods are derived. Methods of orders three, four and five which require less computations than the known methods are presented. Numerical solution of the test problems confirm the convergence order of the new methods and their lower computational cost is performed.

Peasant (farm) households (P(F)H) in the Altai Krai are quite a significant form of agricultural organizations, their contribution in the crop-growing is particularly high. P(F)H account for more than 30% of arable land of the region, and they also give comparable results in crop production in general, as well as in certain categories of crops (for example, about 38% in cereals). However, in the context of administrative districts there are significant differences in the proportion of products produced by this type of households. Statistical data analysis reflects specialization of P(F)H in the production of cereals and leguminous crops (production of wheat is leading). The leaders in the production of these crops are the steppe districts (Klyuchevskiy – 77.6%, Uglovskiy – 72.6%, Volchikhinskiy – 69.8%), which have the most favorable combination of natural and climatic conditions for growing hard varieties wheat (durum wheat) which are most valuable. When moving from the west to the east of the region, there is a general tendency to a decrease in the role of P(F)H in the production of cereals and leguminous crops. Along with the increase in the share of large farms that produce a significant part of cereals and leguminous crops, there is a wider range of crop production and an increase in the share of animal husbandry, as well as the emergence of consumer-oriented sub-sectors (garden and berry crops). Low rates of cereals and leguminous crops production belong to the districts that are relatively close to large enterprises that consume cereals (poultry farms), as well as areas of the suburban zone of the cities of Barnaul and Biysk; larger and more stable enterprises (limited liability company, open joint stock company, closed joint stock company), focused on a large consumer, are concentrated here.

The relevance of assessment of effectiveness of various directions of state policy (particularly in the demographic sphere) is caused by unevenness of demographic development of regions of the country and low degree of controllability of demographic processes. The analysis of regional programs in the sphere of population policy showed that in most cases the expected result of realization of administrative influences is formulated indistinctly that predetermines impossibility of its unambiguous assessment after the term of implementation of the program or its separate stages. Application of typological approach to assessment of results of demographic policy of territorial subjects of the Russian Federation can become one of possible solutions of the designated problem. Application of typological approach to the analysis of features of demographic development of territorial subjects of the Russian Federation has scientific and administrative value thanks to a possibility of consideration of a contribution of certain territories to change of a demographic portrait of the country, spatial features and long-term trends of development of the population. For the purpose of the typological analysis of demographic development the Federal State Statistics Service divides territories into six groups on the basis of components of change of population. The offered group is a basis for assessment of effectiveness of the realized population policy.

We propose stabilized explicit stochastic Runge–Kutta methods of strong order one half for Ito stochastic delay differential equations with one fixed delay. The family of the methods is constructed by embedding Runge–Kutta–Chebyshev methods of order one for ordinary differential equations. The values of a damping parameter of the methods are determined appropriately in order to obtain excellent mean square stability properties. Numerical experiments are carried out to confirm their order of convergence and stability properties.

Structure based partitioning of a system of ordinary differential equations is considered. A general form of the explicit multischeme Runge–Kutta type method for such systems is presented. Order conditions and simplifying conditions are written down. An algorithm of derivation of the sixth order method with seven stages and reuse with two free parameters is given. It embeds a fourth order error estimator. Numerical comparison to the Dormand–Prince method with the same computation cost but of lower order is performed.

An algorithm to construct a differentiable control function guaranteeing the transfer nonlinear stationary systems of ordinary differential equations from the initial state to a given final state of the phase space such that restrictions for the control are satisfied is proposed. The proposed algorithm is convenient for numerical implementation and is applicable to a broad class of systems. A sufficient condition of the existence of a desired transfer function is constructed. A certain practical problem is considered and simulated numerically by means of the presented method.

The hydrothermal reaction of NaN3 with Cu(Phen)Cl2 in acetonitrile solutions results in the formation of two complexes: new d9 mononuclear cis-[CuII(Phen)2(mtz)2]·H2O and d10 coordination polymer catena-[CuI(Phen)(μ-CN)]n (mtz is 5-methyltetrazolate anion and Phen is 1,10-phenanthroline). The process involves in situ formation of mtz ligand via cycloaddition of acetonitrile and azide (in the case of [CuII(Phen)2(mtz)2]) and cleavage of acetonitrile C–C bond (in the case of [CuI(Phen)(μ-CN)]n). Both complexes were fully characterized by a comprehensive set of methods, including the single crystal X-ray diffraction data.

An attempt to construct fast Runge–Kutta methods for delay differential equations with distributed delays is made. As a starting point functional continuous methods for general retarded functional differential equations are considered. New explicit methods of order three and four are constructed, which are more effective than functional continuous Runge–Kutta methods of the same order. Numerical tests confirm the convergence order of the new methods. Comparison to closely related Runge–Kutta methods for Volterra integro-differential equations is made.

Structural partitioning of systems of ordinary differential equations is made on base of right-hand side dependencies on the unknown variables. It is used to construct fully explicit Runge–Kutta methods with several computational schemes applied to different parts of the system. The constructed structural methods require fewer right-hand side evaluations (stages) per step for some parts of the system than classic explicit Runge–Kutta methods of the same order. The full structural form of the system is presented, which after permutation of variables can be applied to any system of ordinary differential equation. For such structure a multischeme method is formulated and conditions of the sixth order are written down. We present simplifying conditions and reduce the system to a solvable smaller system. A particular computational scheme, that requires seven stages for a group without special structure and only six stages for other equations, is presented. Its sixth order is confirmed by a numerical convergence test.

Numerical methods for solving retarded functional differential equations of the second order with right-hand side independent of the function derivative are considered. The approach used by E. Nyström for second-order ordinary differential equations with the mentioned property is applied for construction of effective functional continuous methods. Order conditions are formulated, and example methods are constructed. They have fewer stages than Runge–Kutta type methods of the same order. Application of the constructed methods to test problems confirms their declared orders of convergence.

A theorem was originally proposed to deal with the stochastic theta methods when they are applied to a linear test equation with delay and non-delay in a diffusion term. We extend the theorem to a proposition in a general form, and use it for stability analysis of stochastic orthogonal Runge-Kutta-Chebyshev methods when the methods are applied to the test equation., International Conference on Numerical Analysis and Applied Mathematics 2019 (ICNAAM-2019), 23–28 September, 2019, Rhodes, Greece

Pathfinding is a widespread task in many domains, including computer games, robotics and road maps. This paper describes the work of JPS+ algorithm and puts forward its modifications allowing to reduce pathfinding time. We propose to use a visibility graph to modify the map pre-processing logic at the stage of Primary Jump Points calculation. The paper also puts forward modifications in the shortest path algorithm solved for two points: the logic of Target Jump Points work and Primary Jump Points filtering has been altered to deal with obstacles. We propose an open-source software solution that accommodates the modifications.

Strength analysis problems are those engineering tasks that aim to calculate strength properties of structures. The modelling in this sphere is of such complexity that it is often difficult to integrate a geometric model (CAD) and the analysis of physical impact exerted on it (FEM).This paper describes a prototype of an open-source system that integrates CAD and FEM. The strength analysis task is used to illustrate the integration. The system is deployed by means of the Docker platform and uses Jupyter Notebook for strength analysis.

In this paper we study a system of delay differential equations from the viewpoint of a finite time blow-up of the solution. We prove that the system admits blow-up solutions, no matter how small the length of the delay is. In the non-delay system every solution approaches to a stable unit circle in the plane, thus time delay induces blow-up of solutions, which we call “delay-induced blow-up” phenomenon. Furthermore, it is shown that the system has a family of infinitely many periodic solutions, while the non-delay system has only one stable limit cycle. The system studied in this paper is an example that arbitrary small delay can be responsible for a drastic change of the dynamics. We show numerical examples to illustrate our theoretical results.

Two families of structural four-stage Runge–Kutta methods of order five are considered. The choice of the scheme with the best numerical properties in each family is justified. The comparison of classical and Runge–Kutta–Nystrom fifth order methods is shown and the better performance for some test problems is demonstrated.Two families of structural four-stage Runge–Kutta methods of order five are considered. The choice of the scheme with the best numerical properties in each family is justified. The comparison of classical and Runge–Kutta–Nystrom fifth order methods is shown and the better performance for some test problems is demonstrated.

Diagonally implicit Runge–Kutta type methods are considered for retarded functional differential equations. Methods are constructed to be L-stable when applied to ordinary differential equations. Two approached are used: complete diagonally implicit methods and methods with first explicit stage. It is shown that the latter lets construction of methods of desired orders with fewer stages.

An algorithm for constructing a control function that transfers a wide class of stationary nonlinear systems of ordinary differential equations from an initial state to a final state under certain control restrictions is proposed. The algorithm is designed to be convenient for numerical implementation. A constructive criterion of the desired transfer possibility is presented. The problem of an interorbital flight is considered as a test example and it is simulated numerically with the presented method., Comment: 9 pages, 2 figures

The so-called structural methods for systems of partitioned ordinary differential equations studied by Olemskoy are considered. An ODE system partitioning is based on special structure of right-hand side dependencies on the unknown functions. The methods are generalization of Runge–Kutta–Nystrom methods and as the latter are more efficient than classical Runge–Kutta schemes for a wide range of systems. Polynomial interpolants for structural methods that can be used for dense output and in standard approach to solve delay differential equations are constructed. The proposed methods take fewer stages than the existing most general continuous Runge–Kutta methods. The orders of the constructed methods are checked with constant step integration of test delay differential equations. Also the global error to computational costs ratios are compared for new and known methods by solving the problems with variable time-step.

We construct here an embedded Dormand–Prince pair of explicit methods of orders 6 and 4 for systems of ordinary differential equations with special structure, namely with two parts, in which the right-hand sides are dependent only on the unknown functions from the other group. The number of stages is six, which is fewer than for general explicit Runge–Kutta methods. The comparison to Dormand–Prince method of the same computation cost is made showing the higher accuracy of the suggested method.

We consider here numerical methods for systems of retarded functional differential equations of two equations in which the right-hand sides are cross-dependent of the unknown functions, i.e. the derivatives of unknowns don’t depend on the same unknowns. It is shown that using the special structure of the system one can construct functional continuous methods of Runge–Kutta type with fewer stages than it is necessary in case of general Runge–Kutta functional continuous methods. Order conditions and example methods of orders three and four are presented. Test problems are solved, demonstrating the declared convergence order of the new methods.

An explicit embedded method of the Dormand-Prince type designed for integrating systems of ordinary differential equations of special form is examined. A family of economical fifth-order numerical schemes for integrating systems of structurally separated ordinary differential equations is constructed.

An explicit Runge-Kutta type method for systems of ordinary differential equations with special structure is considered. For partitioned systems a family of explicit methods of order six with just six stages is constructed, which makes them more efficient than classic Runge-Kutta methods of order six. It is shown that second order differential equations, which right-hand side doesn't depend on the first derivative, can be rewritten as the considered partitioned systems. Direct application of the constructed methods to them generates two different families of Runge-Kutta-Nystrom methods. The comparison of constructed methods with known methods of order six is held.

An explicit embedded pair of methods for systems of second order ordinary equations with special structure is considered. Two-parametric families of methods of orders four and three with automatic step-size control are constructed. The numeric comparison to known embedded Runge-Kutta pairs of the same order is held.

When solving delay differential equations (DDEs) with state-dependent delays the problem of breaking point detection is important. Points where the solution is not smooth enough to provide the order of the method must be included into the computational mesh, otherwise a reduction in the order of the solution will result. The problem, however is to detect and compute such points efficiently. Breaking points arise every time a delay falls on a previous breaking point (either of the calculated solution or in the history function). In the case of retarded DDEs the new breaking point is (at least) one order smoother than the previous breaking point that gave rise to it. For fixed or time-dependent delays the breaking points can be precomputed independent of the solution, but for state-dependent delays the positions of the breaking points depend on the computed solution. If a breaking point is detected and the step-size is changed in order to incorporate the point into the mesh, then the new step-size generates a new solution and the breaking point moves. Consequently, breaking point detection is traditionally performed iteratively, and is computationally expensive. The same breaking point can also be detected multiple times. In the current work we propose a fast non-iterative method for finding breaking points with sufficient precision to preserve the order of up to third or fourth order methods. Our method makes use of analytic continuation of the solution across breaking points (including possible breaking points in the initial history function), and we explain how we handle this carefully to attain the desired order. Test results are presented for Explicit Functional Continuous Runge–Kutta methods, showing that they retain their order of convergence when the solutions have breaking points.

Рассматривается одноканальная система массового обслуживания с общим законом распределения времён обслуживания. Общий закон предлагается приближать двухфазным распределением, первая фаза которого детерминированная, а вторая экспоненциальная. Показано, что выбором параметров такого двухфазного распределения можно получить сколь угодно маленький коэффициент вариации. Представлены уравнения для переходного режима и для стационарного распределения вероятностей. Переходный процесс описывается системой дифференциальных уравнений с запаздывающим аргу-ментом. Результаты имитационного моделирования срав-ниваются с решением системы на стационарные вероятно-сти., A one-server queuing system with general distribution of service time is considered. An approximation to the general distribution with two-stage law the where first stage is deterministic and the second is exponential is suggested. It is shown that the coefficient of variation can be made arbitrarily small by choosing the parameters of the suggested distribution. The steady-state and transient equations are presented. The transient behavior is described with a system of delay-differential equations. Imitation results are compared to the obtained steady-state equations solution.