№ 116(2), February, 2016
Public date: 29.02.2016
Archive of journal: Articles count 106, 245 kb
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01.00.00 Physical-mathematical sciences
LIMIT THEOREMS IN STATISTICAL CONTROL
01.00.00 Physical-mathematical sciences
Description
The article analyzes the development of the theory of statistical control (from the XVIII century to the present). Prof. M.V. Ostrogradskii (1846) clearly describes the practical needs (ie, arising from the quality assurance of large quantities of bags of flour or pieces of cloth), to meet whom he spent his research. At the same time Simpson was among the ideas of probability theory XVIII century. Therefore prof. M.V. Ostrogradskii may be regarded as the founder of the theory of statistical process control (not only in our country but all over the world). Limit theorems of probability theory and mathematical statistics have provided a number of asymptotic results in problems of statistical quality control, offer based on these best practices. However, we must find out how much interest among specialists characteristics are different from limit for finite sample sizes. Such research for the synthesis algorithm control plan on the basis of the limit average output level of defects is made in this article, and for the synthesis algorithm control plan on the basis of the acceptance and the rejection levels of defects - not yet (clarification of the conditions of applicability of this algorithm - unsolved problem of applied mathematics). We have briefly reviewed the development of our researches on the statistical control. Control units can be not only some units of production, but also documents (with internal and external audit), and standard units of air, water and soil in the environmental monitoring. One of the achievements can be regarded as the transfer of statistical control of production for environmental monitoring
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MODERN ECONOMETRIC METHODS - INTELLECTUAL TOOLS OF ENGINEERS, MANAGERS AND ECONOMISTS
01.00.00 Physical-mathematical sciences
Description
Statistical methods are widely used in domestic feasibility studies. However, for most managers, economists and engineers, they are exotic. This is because modern statistical methods are not taught in the universities. We discuss the situation, focusing on the statistical methods for economic and feasibility studies, ie, econometrics. In the world of science, econometrics has a rightful place. There are scientific journals in econometrics, Nobel Prizes in Economics are awarded to series of researches in econometrics. The situation in the field of scientific and practical work and especially the teaching of econometrics in Russia is disadvantaged. Often, individual particular constructions replace econometrics in general, such as those related to regression analysis. In econometrics we select three types of scientific and applied activities: development and study of methods of applied statistics, taking into account the specifics of economic data; development and study of econometric models, in accordance with the specific needs of economic science and practice; the use of econometric methods for statistical analysis of specific economic data. This article describes these three types of scientific and applied activities. We discuss the specificity of economic data. We show the importance of economic non-numeric values. We discuss the statistics of interval data - scientific direction at the joint of metrology and statistics. We give the representation of the econometric models. Problems of application of econometric methods are considered as an example of inflation. We discuss the statistics and econometrics as the field of scientific and practical activities. We have examined econometric methods in practical and training activities
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THE INVERSE PROBLEM OF A REPRODUCTION MODEL OF NATIONAL INCOME
01.00.00 Physical-mathematical sciences
Description
In practice, there were developed and tested some mathematical models of balance relationships (balance model), economic growth, expanding economy, labour market, theories of consumption, production, competitive equilibrium models of the economy in conditions of imperfect competition and others. The basis of these models were based on linear algebra, mathematical analysis, mathematical programming, differential equations, optimization methods, optimal control theory, probability theory, stochastic processes, operations research, game theory, statistical analysis. The inverse problem in various models of mathematical Economics was considered quite rare. These tasks were sufficiently investigated in the study of physical processes. As shown by the analysis of the theoretical and applied studies of economic processes, they represent considerable interest for practice. Therefore, the considered in the study inverse problems of the mathematical model, as it is shown by the already introduced results of other mathematical models, are of considerable interest in applied and theoretical research. In this article, the authors have formulated and investigated an inverse problem for a model of economic growth. For its solution the authors propose to build a system of algebraic equations, using a reproduction model of national income; then, using methods of quadratic programming, to find the best average quadratic estimates of the model parameter
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DYNAMICS OF RELATIVISTIC PARTICLES IN THE GALAXY METRIC
01.00.00 Physical-mathematical sciences
Description
In this study we investigate the dynamics of relativistic particles in the axially symmetric metrics. We have built metric having axial symmetry and contains two centers of gravity and a logarithmic singularity. The application received metrics to the movement of particles in galaxies is described. It is established that there are stable orbit in the metric with two centers of gravity, the particle velocity at which reaches the value v/ c ≈ 7.0 . Orbit radius varies widely, but remains substantially flat orbit. Unstable same movements are completed so that the particles leave the system. The hypothesis that this kind of relativistic objects can serve as sources of the magnetic fields of the planets, stars and galaxies has been proposed. The question of the realization in the galaxy metric of Einstein's hypothetical elevator in which there is a uniform gravitational field, simulating the accelerated movement of the elevator is described. A homogeneous gravitational field in a limited region of space was numerical simulated. It has been shown that this kind of accelerated objects generate relativistic effect in the form of a log potential, not diminishing with distance from the center of the system. It is assumed that such capabilities can be associated with the Higgs field responsible for the occurrence of the inertial mass of the elementary particles
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DYNAMICAL MODEL OF ELECTROMAGNETIC DRIVE
01.00.00 Physical-mathematical sciences
Description
The article discusses the dynamic model of the rocket motor electromagnetic type, consisting of a source of electromagnetic waves of radio frequency band and a conical cavity in which electromagnetic waves are excited. The processes of excitation of electromagnetic oscillations in a cavity with conducting walls, as well as the waves of the YangMills field have been investigated. Multi-dimensional transient numerical model describing the processes of establishment of electromagnetic oscillations in a cavity with the conducting wall was created Separately, the case of standing waves in the cavity with conducting walls been tested. It is shown that the oscillation mode in the conducting resonator different from that in an ideal resonator, both in the steady and unsteady processes. The mechanism of formation of traction for the changes in the space-time metric, the contribution of particle currents, the Yang-Mills and electromagnetic field proposed. It is shown that the effect of the Yang-Mills field calls change the dielectric properties of vacuum, which leads to a change in capacitance of the resonator. Developed a dynamic model, which enables optimal traction on a significant number of parameters. It was found that the thrust increases in the Yang-Mills field parameters near the main resonance frequency. In the presence of thermal fluctuations and the Yang-Mills field as well the traction force changes sign, indicating the presence of various oscillation modes
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GENERAL RELATIVITY AND DYNAMICAL MODEL OF ELECTROMAGNETIC DRIVE
01.00.00 Physical-mathematical sciences
Description
The article discusses the dynamic model of the rocket motor electromagnetic type, consisting of a source of electromagnetic waves of radio frequency band and a conical cavity in which electromagnetic waves are excited. The processes of excitation of electromagnetic oscillations in a cavity with conducting walls, as well as the waves of the YangMills field are investigated. The multi-dimensional transient numerical model describing the processes of electromagnetic oscillations in a cavity with conducting wall created. Separately, the case of standing waves in the cavity with conducting walls considered. It is shown that the oscillations mode in the conducting resonator different from that in an ideal resonator, both in steady and unsteady processes. The mechanism of formation of traction for the changes in the space-time metric, the contribution of particle currents, the Yang-Mills and electromagnetic field proposed. It is shown that the Yang-Mills field calls the change of the dielectric constant, which leads to a change in the capacitance of the resonator. Thus, the parametric resonance occurs in the system, which leads to a strengthening of the Yang-Mills amplitude, and to the emergence of traction. We have developed a dynamic model, which enables optimal traction on a significant number of parameters. It was found that the thrust increases in the Yang-Mills field near the main resonance frequency. A model describing the excitation and emission of nonlinear waves of the Yang-Mills field was proposed. It is shown that nonlinear waves of the Yang-Mills field more effectively carry the momentum from the system in comparison with electromagnetic waves, and it explains the significant increase by several orders of thrust in the engines of the electromagnetic type, compared with the photon rocket
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