Modeling the dynamic semantics of a computer program

Purpose of the study.The aim is to create a technique targeted at the development of simulation skills in higher education environment, where students are competent in applying information technologies in economics. The relevance of the research lies in the fact that the existing methodological developments often focus on a specific software tool or methodology that cannot respond to all economic problems. A specialist in simulation modeling should possess integrative interdisciplinary knowledge from related scientific fields, for example, probability theory and mathematical statistics, higher mathematics, be familiar with other methods of solving economic problems: linear, nonlinear, dynamic programming, optimization; show proficiency in structural and functional analysis; be able to explore complex processes and systems comprehensively.Materials and methods.The following pedagogical approaches and teaching methods were implemented in this research: ● a systematic approach to solving complex problems based on the modelling economic objects as systems operating in a certain environment, ● activity approach to develop students’ professional competences in the process of creation, debugging and optimization of computer models of economic systems; ● problem teaching method in the framework of research and analysis of educational problems of the subject area; ● implemented interactive teaching methods; ● multimedia methods in the content of teaching materials of the discipline, including electronic manuals, educational videos, as well as multimedia presentations. The research also utilized information technologies, in which computers, communication equipment and software environments are: ● means to provide educational material to students for the transfer of knowledge; ● tools for designing, developing and conducting simulation experiments. In addition, we used the following special professional technologies, methods and tools in the process of teaching students: ● structural and functional modeling methodology; ● discrete-event approach to simulation methodology; ● special software for development and research of simulation models of economic processes and systems: Arena 15.0, AnyLogic 8.3.2.According to the requirements of the new educational standards, the student must master a sufficiently large amount of general cultural, professional and specialized competencies included in the curriculum. The application of the proposed approaches and methods allows to provide effective development of skills of simulation modeling of educational programs for bachelors of «Applied Informatics» and «Business Informatics».Results.The study created a method of teaching students the skills of simulation modeling. The research also established the model of formation of readiness of the IT specialist to the development of simulation models of economic processes and systems in higher school. We also identified important methodological conditions for the formation of professional competencies of students in the field of modeling, such as: ● application of a systematic approach to the analysis of domain problems, as well as for the synthesis of mathematical simulation models of business processes and economic systems; ● practical orientation of the content of training (selection and research in the educational process of the most characteristic, typical problems of the economy); ● integration of interdisciplinary knowledge, methods and approaches to solve complex problems.Conclusion.The method can equip students with skills of simulation modeling with various areas of practical application. First, this technique can be used by university students who are engaged in pursuing practical skills and basic system knowledge in the field of simulation. Secondly, teachers can use it, conducting courses: “Computer modeling”, “Mathematical and simulation modeling”, “Modeling of processes and systems” in the educational process of the University to improve the professional competence of students training simulation modeling. Third, the outcomes may be of interest to managers of educational programs in the areas of: “Applied Informatics”, “Business Informatics”, etc. to improve the structure and sequence of disciplines of competence-oriented curricula. Finally, the application of the proposed methodology in the educational process of the University will enhance professional expertise of young specialists and undoubtedly address the needs of potential employers.

Microtasking versus Message Passing Parallelisation of the 3D-Combustion Code AIOLOS on the NEC SX-4

Providing growing economic needs is impossible without economic development. Economic development is associated with qualitative and structural changes in the economy, education, science, and culture. In accordance with the changes in society, the purpose of economic science also changes. There is a transition from observing the economy to influencing economic processes, their management, planning, forecasting, implementation of specific tasks at individual enterprises within certain terms in accordance with the general goals and interests of the national economy. The level of influence on economic phenomena varies from recommendations to specific methods of quantitative calculation, which provide an objective choice of an economic decision. Scientific management of economic processes can be carried out only on the basis of the application of precise mathematical methods in all spheres of the economy – from the distribution of minerals to the demand for consumer goods and household services, labor needs, planning of logistical tasks, etc. Therefore, the subject of the research is conducting mathematical modeling of an economic phenomenon, analysis of economic processes, using the methodology of economic-mathematical modeling and mathematical programming, with the aim of forecasting and studying one or another aspect of its development in the planning and management system, in information provision, in the possibility taking into account the dynamics of economic processes. The study of various economic phenomena with the help of economic-mathematical models, which are a simplified description and take into account the most significant and determining factors of the studied phenomenon, involves the use of mathematics for a formal description of the most significant relationships between economic variables and objects: conclusions can be obtained by the method of deduction, which are adequate for the object under study; methods of mathematics and statistics make it possible to obtain new knowledge about the researched object; the use of mathematical terminology allows you to accurately and compactly express the statements of economic theory, formulate its concepts and conclusions. The analysis of previous studies shows that the problems of organizing the teaching of mathematical disciplines in higher educational institutions, taking into account modern requirements, were taken care of by scientists: I.P. Vasylchenko, L.P. Husak, G.Ya. Dutka, T.V. Krylova, O.V. Levchuk, L.I. Nichugovska, V.A. Petruk et al. The need to build a holistic methodology for the introduction of higher mathematics, the theory of probabilities and mathematical statistics, mathematical modeling and optimization of economic processes is the key task of the article on the use of economic and mathematical models for the development and implementation of optimal projects for the development of the production and services market. Conclusion: to solve effectively a wide class of problems with appropriate solution methods, covering various problems of development and functioning of real economic systems, it is convenient to develop economic and mathematical models, which, in combination with powerful, high-speed computing equipment and modern software products, will make up decision-making support systems in various sectors of the economy.

In this work a new nonlinear mathematical model of process of three level assimilation which is described by four-dimensional dynamic systems is offered. In case of constancy of coefficients special points of the dynamic system are found. The conditions on constant coefficients for which it is possible to find special points with all four coordinates non-negative are determined. Introducing some dependence among coefficients of the system, two first integrals are derived, and the four-dimensional system is reduced to a two-dimensional one.The sign-variable divergence theorem of a two-dimensional vector field in some one-coherent area of the first quadrant of the phase plane is proved. According to Bendixon’s criterion it is possible to have a closed integral curve completely lying in this area.Introduction. Mathematical modeling of physical processes has a long history. Mathematical modeling of physical processes involves the model adequacy, which is validated by Newton’s non-relative five laws of classical mechanics: mass conservation law; law of conservation of impulse; the law of conservation the momentum of impulse; the first law of thermodynamics, i.e. energy conservation law; the second law of thermodynamics, i.e. entropy conservation law [, , , , ].Creation of mathematical models is more original in social sphere, because, they are more difficult to substantiate [, , ].We created a new direction of mathematical modeling, i.e. “Mathematical Modeling of Information Warfare” [, , ]. In these models two antagonistic sides waging with each other information warfare and also the third peacekeeping side trying to extinguish information warfare are considered. Conditions on model parameters at which the third side will be able to force the conflicted sides to completion of information warfare are found.We also offered mathematical models of forecasting the results of political elections in case of two or three parties. Also models in case of change of selective subjects before the next elections have been considered [, , , , ].We proposed to create new nonlinear mathematical models of economic cooperation between two politically (not military opposition) mutually warring sides (two countries or a country and its legal region) which consider economic or other type of cooperation between different parts of population aimed to the peaceful resolution of conflicts [, ].Taking into consideration the important tendencies in the world, it is important to study demographic and assimilation of social processes through mathematical modeling.In [] we considered a new nonlinear continuous mathematical model of linguistic globalization. Two categories of the world’s population are considered: a category that hinders and a category leading to the dominant position of the English language. With a positive demographic factor of the population, which prevents globalization or a negative demographic factor of the population contributing to globalization, it is shown that the dynamic systems describing these processes allow the existence of two topologically not equivalent phase portraits (a stable node, a limit cycle).It is known that, in the world, a social process of assimilation of languages is hidden. This process, as a rule, considers expansion of an area of the dominating languages (state languages of economically powerful states) at the expenses of less widespread languages (state languages economically of rather weak states).According to this point of view, today, for less widespread languages (including classic languages) the conditions under which there will be no disappearance of the major languages are important, i.e. there will be no full assimilation of people talking in these languages.

While GPUs are increasingly popular for high-performance computing, optimizing the performance of GPU programs is a time-consuming and non-trivial process in general. This complexity stems from the low abstraction level of standard GPU programming models such as CUDA and OpenCL: programmers are required to orchestrate low-level operations in order to exploit the full capability of GPUs. In terms of software productivity and portability, a more attractive approach would be to facilitate GPU programming by providing high-level abstractions for expressing parallel algorithms.OpenMP is a directive-based shared memory parallel programming model and has been widely used for many years. From OpenMP 4.0 onwards, GPU platforms are supported by extending OpenMP's high-level parallel abstractions with accelerator programming. This extension allows programmers to write GPU programs in standard C/C++ or Fortran languages, without exposing too many details of GPU architectures.However, such high-level parallel programming strategies generally impose additional program optimizations on compilers, which could result in lower performance than fully hand-tuned code with low-level programming models. To study potential performance improvements by compiling and optimizing high-level GPU programs, in this paper, we 1) evaluate a set of OpenMP 4.× benchmarks on an IBM POWER8 and NVIDIA Tesla GPU platform and 2) conduct a comparable performance analysis among hand-written CUDA and automatically-generated GPU programs by the IBM XL and clang/LLVM compilers.

Location of cross-docking centers and vehicle routing scheduling under uncertainty: A fuzzy possibilistic–stochastic programming model

This thesis is concerned with different topics in multi-parametric programming and explicit model predictive control, with particular emphasis on hybrid systems. The main goal is to extend the applicability of these concepts to a wider range of problems of practical interest, and to propose algorithmic solutions to challenging problems such as constrained dynamic programming of hybrid linear systems and nonlinear explicit model predictive control. The concepts of multi-parametric programming and explicit model predictive control are presented in detail, and it is shown how the solution to explicit model predictive control may be efficiently computed using a combination of multi-parametric programming and dynamic programming. A novel algorithm for constrained dynamic programming of mixed-integer linear problems is proposed and illustrated with a numerical example that arises in the context of inventory scheduling. Based on the developments on constrained dynamic programming of mixed-integer linear problems, an algorithm for explicit model predictive control of hybrid systems with linear cost function is presented. This method is further extended to the design of robust explicit controllers for hybrid linear systems for the case when uncertainty is present in the model. The final part of the thesis is concerned with developments in nonlinear explicit model predictive control. By using suitable model reduction techniques, the model captures the essential nonlinear dynamics of the system, while the achieved reduction in dimensionality allows the use of nonlinear multi-parametric programming methods.

Nasal cavity volume changes after rapid maxillary expansion in adolescents evaluated with 3-dimensional simulation and modeling programs

A mathematical model and operational program complex for neutron physics processes in the BN-350 reactor

This paper studies the stable model semantics of logic programs with (abstract) constraint atoms and their properties. We introduce a succinct abstract representation of these constraint atoms in which a constraint atom is represented compactly. We show two applications. First, under this representation of constraint atoms, we generalize the Gelfond–Lifschitz transformation and apply it to define stable models (also called answer sets) for logic programs with arbitrary constraint atoms. The resulting semantics turns out to coincide with the one defined by Son et al. (2007), which is based on a fixpoint approach. One advantage of our approach is that it can be applied, in a natural way, to define stable models for disjunctive logic programs with constraint atoms, which may appear in the disjunctive head as well as in the body of a rule. As a result, our approach to the stable model semantics for logic programs with constraint atoms generalizes a number of previous approaches. Second, we show that our abstract representation of constraint atoms provides a means to characterize dependencies of atoms in a program with constraint atoms, so that some standard characterizations and properties relying on these dependencies in the past for logic programs with ordinary atoms can be extended to logic programs with constraint atoms.

Portfolio selection is one of the most important financial and investment issues. Portfolio selection seeks to allocate a predetermined capital (wealth) over one or multiple time periods between assets and stocks in a such way that the wealth of investor (portfolio owner) is maximized the risks are minimized. In the paper, we first propose a mathematical programming model for Portfolio selection to maximize the minimum amount Sharpe ratios of portfolio in all periods (max-min problem). Then, due to the uncertain property of the input parameters of such a problem, a robust possibilistic programming model (based on necessity theory) has been developed, which is capable of adjusting the robust degree of output decisions to the uncertainty of the parameters. The proposed model has been tested on 27 companies active in the Tehran stock market. At the end, the results of the model demonestrate the good performance of the robust possibilistic programming model.

The paper describes the application of the author’s mathematical model of gas-dynamic processes for a marine piston engine based on a computer program. The developed mathematical and numerical model is designed to conduct simulation diagnostics. Therefore, it is possible to carry out calculations for motors in different technical conditions and observing influence of changes in technical condition on selected parameters of its work. Simulation of changes in technical condition is carried out by modifying parameters of structure’s model object. The article contains a detailed description of each options of the computer program. From the main program window, user can select type of engine model (supercharging method, cylinder number, work order, stroke and piston diameter and a number of other parameters). Through a window of simulation of known and recognizable damages such as: change in fuel dose for each cylinder, change in intake and outlet valves, leakage of piston-ring-cylinder system, change of injector hole cross section. Final windows show results of calculations in form of mileage parameters of engine as a function of crank angle.

Mathematical models of competitive processes in the economy using known universal models that describe the behavior of counterparties in the market are found in this article. The object of research is to build mathematical models of competitive processes in a pair – secondhand dealer, and to process and convert the economic parameters that are necessary for the models. The methods of research use analysing and solving equations for the known and improved universal models that describe the behaviour of contractors in the market. Mathematical package for construction of schedules of dependences is used. The goals are to construct and research the modified model on the basis of mathematical model by Lotka- Volterra and its further development, and to create software product for statistical processing the economic information. Results – the mathematical model manufacturer – secondhand dealer is created, its modified version is received, and with the help of mathematical package Mathcad, researches of models were done. Prospects of the further improvement of models are revealed. The software product is developed, allowing to process the statistical economic information. On the basis of mathematical model by Lotka-Volterra and its further development a mathematical model of several producers and one middleman is created. Its modified version is studied using mathematical package Mathcad. The nonstable behavior of the counterparties is found. For this model some prospects for further improvements is identified.

This paper considers processes of electric arc damping by automatic switches in the short-circuit mode. Certain conditions for facilitating a successful short-circuit arc damping are shown, such as the limitation of the short-circuit current amplitude by its active resistance, the reduction of the phase shift between current and voltage, and the amplitude loss in returning and restoring voltages. The article features oscillograms of currents and voltages in the short-circuit mode. Anode heating processes are also described within the framework of the process of arc burning (heat saturation mode) and after the change of polarity current transition through zero processes at the cathode in the temperature equalization mode. Mathematical models of processes at the cathode took into account the thermal flows of the ionic component and evaporation. The calculations were carried out with the average values of thermal coefficients for copper, as the arc base moves from contacts to contact holders, which are made of copper and its alloys. The results of the calculations proved the validity of the considered mathematical models of thermal processes at both the cathode and the anode.

This article gives a brief description of the principles of organization of Internet education in the teaching of “Mathematical modeling of information technology and processes” to students on the basis of “Moodle LMS” system distance learning at the Tashkent Pharmaceutical Institute and shows its main features and advantages. Extensive use of educational technologies, optimization, humanization and innovation in the National Program of Personnel Training to solve the tasks of training and educating young people to be highly moral, spiritual and enlightened, conscientious at work, deeply aware of their responsibilities to society and family, competitive, qualified professionals. The organization, management and control of the learning process on the basis of methods is relevant. Nowadays, a wide range of opportunities are being created for students to have fast, plentiful, reliable information and to acquire knowledge independently. In particular, electronic systems allow students to use important information related to science at any distance, depending on their capabilities. “Moodle” open source software complex is a system designed specifically for the management of the educational process using the Internet (Learning management system - LMS). Distance learning is a modern form of organizing the learning process using distance learning technologies. Its development was due to the increase in the number of Internet users, the availability and quality of open learning electronic resources. The use of distance learning technologies undoubtedly has a wide range of advantages: the organization of the learning process in an Internet environment, so the student location does not prevent high-quality training, regardless of the location of the educational institution. Distance learning is based on the principle of independent preparation of students through teacher guidance and allows you to choose a convenient time for lessons. It includes interactive communication between teachers and students, information resources of the educational institution and information resources of the Internet, the rapid delivery of the Internet in electronic form.