№ 107(3), March, 2015
Public date: 31.03.2015
Archive of journal: Articles count 114, 263 kb
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01.00.00 Physical-mathematical sciences
ECONOMETRIC TOOLS OF CONTROLLING
01.00.00 Physical-mathematical sciences
DescriptionEconometrics is one of the most effective mathematical tools of controlling. The article deals with general problems of application of econometric methods in solving problems of controlling. Econometric methods - is primarily a statistical analysis of concrete economic data, of course, with the help of computers. In our country, they are still relatively little known, even though we have the most powerful scientific school in the foundations of econometrics - the probability theory. The article shows that to decide the problems of controlling is necessary to apply econometric methods. Classification of econometric tools can be carried out on various grounds: on methods, by type of data, in tasks, etc. Mass introduction of software products, including modern econometric analysis tools of concrete economic data can be regarded as one of the most effective ways to accelerate scientific and technological progress. The whole arsenal currently used econometric and statistical techniques (methods) can be divided into three streams: high econometric (statistical) technology; classical econometric (statistical) technology, low (inadequate, obsolete) econometric (statistical) technology. The main problem of modern econometrics is to ensure that the concrete econometric and statistical studies used only the first two types of technology. To get a broader representation of the use of econometric methods in the management of production organization we analyze basic textbook "Organization and planning of engineering production (production management)," prepared by the Department of "Economics and organization of production" of the Bauman Moscow State Technical University. It has more than 20 times using econometric methods and models that testify to the effectiveness of such a tool of manager as econometrics
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GEOMETRIC TURBULENCE IN GENERAL RELATIVITY
01.00.00 Physical-mathematical sciences
DescriptionThe article presents the simulation results of the metric of elementary particles, atoms, stars and galaxies in the general theory of relativity and Yang-Mills theory. We have shown metrics and field equations describing the transition to turbulence. The problems of a unified field theory with the turbulent fluctuations of the metric are considered. A transition from the Einstein equations to the diffusion equation and the Schrödinger equation in quantum mechanics is shown. Ther are examples of metrics in which the field equations are reduced to a single equation, it changes type depending on the equation of state. These examples can be seen as a transition to the geometric turbulence. It is shown that the field equations in general relativity can be reduced to a hyperbolic, elliptic or parabolic type. The equation of parabolic type describing the perturbations of the gravitational field on the scale of stars, galaxies and clusters of galaxies, which is a generalization of the theory of gravitation Newton-Poisson in case of Riemannian geometry, taking into account the curvature of space-time has been derived. It was found that the geometric turbulence leads to an exchange between regions of different scale. Under turbulent exchange material formed of two types of clusters, having positive and negative energy density that corresponds to the classical and quantum particle motion respectively. These results allow us to answer the question about the origin of the quantum theory
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METRIC OF ACCELERATING AND ROTATING REFERENCE SYSTEMS IN GENERAL RELATIVITY
01.00.00 Physical-mathematical sciences
DescriptionMetric describing the accelerated and rotating reference system in general relativity in the case of an arbitrary dependence of acceleration and angular velocity on time has been proposed. It is established that the curvature tensor in such metrics is zero, which corresponds to movement in the flat spaces. It is shown that the motion of test bodies in the metric accelerated and rotating reference system in general relativity is similarly to the classical motion in non-inertial reference frame. Consequently, there exist a metric in general relativity, in which the Coriolis theorem and classic velocity-addition formula are true. This means that classical mechanics is accurate rather than approximate model in general relativity. A theory of potential in non-inertial reference systems in general relativity is considered. The numerical model of wave propagation in non-inertial reference frames in the case when potential depending of one, two and three spatial dimensions has been developed. It is shown in numerical experiment that the acceleration of the reference system leads to retardation effects, as well as to a violation of the symmetry of the wave front, indicating that there is local change of wave speed
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A CLASSICAL PROBLEM FOR LOADED HYPERBOLIC-PARABOLIC EQUATION OF SECOND ORDER
01.00.00 Physical-mathematical sciences
DescriptionThe investigated and correct boundary value problem for mixed hyperbolic-parabolic equation of second order in a bounded domain is posed and studied in this work. Boundary conditions are of a classical nature. On line of type changes, which is also the line of the parabolic degeneracy for hyperbolic equations considered in the lower half-plane, a continuous bonding condition for the function itself and the breaking condition for the trace of the derivative is given. The main result is the proof of its unique solvability in the required class of functions. In particular, based on the properties of the operators of fractional integro-differentiation and in view of the ratio of the first boundary value problem for the heat equation, the question of the solvability of the original problem was equivalently reduced to the problem of solvability of the corresponding integral equation of the Voltaire second kind. In the hyperbolic part of the region, the question of solvability of the problem has also been reduced to the problem of solvability of the integral equation Voltaire second kind. The properties of the hypergeometric function of Gauss, as well as classical methods of integral equations were used. Thus it is proved the uniqueness and the existence of classical solution to the initial problem