01.00.00 Physical-mathematical sciences
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PHASE TRANSITION FOR GLUON FIELD: A QUALITATIVE ANALYSIS
01.00.00 Physical-mathematical sciences
DescriptionThe phase transition for US(3) gauge field (without quarks) is considered. It is shown that the phase transition is due to the fact that at high temperatures the partition function should be calculated as for a gas of gluons, whereas at low temperatures as the sum over energy levels of correlated quantum states of SU(3) gauge field. A correlated quantum state for strongly interacting fields is defined as a nonperturbative quantum state of strongly interacting fields. The energy spectrum of these quantum states are discrete one. A lower bound of the phase transition temperature by comparing of the average energy for the perturbative and nonperturbative regimes is estimated (for glueball being in thermal equilibrium with the thermostat). It is shown that this quantity is associated with a mass gap. In a scalar model of glueball its energy is calculated. It is shown that this energy is the mass gap. If we set the glueball mass ~ 1.5•10³MeV then it is found that the corresponding value of coupling constant lies in the nonperturbative region
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HEEDING OF HETEROGENEITY OF ENVIRONMENT WHEN CALCULATING A MAGNETIC FIELD
01.00.00 Physical-mathematical sciences
DescriptionThe formula for definition of magnitude and direction of secondary sources of a field as surface currents for the registration of heterogeneity of environment is found. We have shown that it is possible to solve non-linear field problems, using the mathematical deduc-tions shown in this article
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CLARIFICATION OF A MODEL OF A BALANCING ROBOT BY LOGICAL AND EMPIRICAL METHODS
01.00.00 Physical-mathematical sciences
DescriptionThis work studies the mathematical model of the object “inverted pendulum” on the example of the unstable electromechanical devices which is balancing robot on wheel couple. Unfortunately, many details of object model are unknown. Logical and empirical method offers hypotheses about the difference between the actual object model from its mathematical approximation based on logical analysis with subsequent refinement of this model and testing of the hypothesis with modeling of the systems with the updated model. As a result, the amendments to the model have been found containing nonlinear components. With the help of these amendments, the dynamic characteristics of the actuator, filters, friction and the tendency of the object to fluctuations are better taken into account
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STABILITY OF STATIONARY CONDITIONS OF KINETICS OF LEYKOPOEZ
01.00.00 Physical-mathematical sciences
DescriptionThe results of the research of stability of the model of neutrophilomonocytegenesis are shown in the article. With the criterion of Routh-Hurwitz it's calculated that the system of the differential equations of cells growing is asymptotically steady. Threshold values of parameters of model at which the system becomes unstable are defined
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01.00.00 Physical-mathematical sciences
DescriptionThe article presents a project of the Yang-Mills amplifier. Amplifier model is a multilayer spherical shell with increasing density towards the center. In the center of the amplifier is the core of high-density material. It is shown that in such a system, the amplitude of the Yang-Mills waves rises from the periphery to the center of several orders of magnitude. The role of the Yang-Mills field in the processes occurring in the nuclei of galaxies, stars and planets is discussed. The data modeling to strengthen the Yang-Mills field in the bowels of the planet, with an atomic explosion, and in some special devices such as the voltaic pile. To describe the mechanism of amplification chromodynamics field used as accurate results in Yang-Mills theory and numerical models developed based on an average and the exact equations as well. Among the exact solutions of the special role played by the centralsymmetric metric describing the contribution of the Yang-Mills field in the speed of recession of galaxies. Among the approximate numerical models can be noted the eight-scalar model we have developed for the simulation of non-linear color oscillations and chaos in the Yang-Mills theory. Earlier models were investigated spatio-temporal oscillations of the YangMills theory in the case of three and eight colors. The results of numerical simulation show that the nonlinear interaction does not lead to a spatial mixing of colors as it might be in the case of turbulent diffusion. Depending on the system parameters there is a suppression of the amplitude of the oscillations the first three by five colors or vice versa. The kinetic energy fluctuations or shared equally between the color components, or dominated by the kinetic energy of repressed groups of colors. In the present study, we found that amplification chromodynamic field leads to a sharp increase in the amplitude of the suppressed color, which can lead to an increase in entropy, excitation of nuclear reactions and decays particles
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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. Maxwell's equations and Yang-Mills theory are converted to the moving axes in metric describes the acceleration and rotating reference frame in the general relativity in the case of an arbitrary dependence of acceleration and angular velocity of the system from time. The article discusses the known effects associated with acceleration and (or) the rotation of the reference frame - the Sagnac effect, the effect of the Stewart-Tolman and other similar effects. 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 has been 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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01.00.00 Physical-mathematical sciences
DescriptionThe drawbacks of the existing ontology languages and problems of their practical application are discussed in this paper. The requirements for the process of ontologies creating are laid down. A simplified method of constructing the ontological domain model on the basis of the original language SXML is proposed
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MANAGEMENT OF THE FINANCIAL AND THE ECONOMIC STATE OF A COMPANY USING A MATHEMATICAL MODEL
01.00.00 Physical-mathematical sciences
DescriptionThis article focuses on the mathematical modeling of evaluation of financial and economic activities of a company and on definition (based on this model) of such balance settings (line F1 and F2) which would make financial-economic indicators of the activities of the organization optimal, and the total cumulative score was the maximum. The knowledge and the use of the optimal parameters of the balance will allow the managers to plan strategy for the future development of the company. The article analyzes the dependencies of each of the 15 basic indicators (profitability, turnover, financial stability, liquidity and solvency) of financial and economic activity of the organization on the balance parameters. The optimal values of the parameters of the balance and the main indicators of financial and economic activities of the organization have been found. We have also built a mathematical model of optimal control of financial and economic indicators in the form of a problem of mathematical programming. For example, for the company called "Nika" it is shown the possibility of improving estimation of financial and economic condition of the organization. Knowledge of the optimal parameters of the balance will allow the managers to plan strategy for the future development of the organization. To solve this problem we have used the method of generalized reduced gradient implemented in Excel, with which there was found a maximum of the objective function for the article restrictions. The article describes the analysis algorithm of the optimization problem. A common assessment was carried out in stages, based on the calculation algorithm of sequentially improved target functions
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THE GROWTH POINTS OF STATISTICAL METHODS
01.00.00 Physical-mathematical sciences
DescriptionOn the basis of a new paradigm of applied mathematical statistics, data analysis and economic-mathematical methods are identified; we have also discussed five topical areas in which modern applied statistics is developing as well as the other statistical methods, i.e. five "growth points" – nonparametric statistics, robustness, computer-statistical methods, statistics of interval data, statistics of non-numeric data
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PREONS CURRENTS AND WIRELESS POWER TRANSFER
01.00.00 Physical-mathematical sciences
DescriptionIn this article, a model of preons electric currents caused by the motion of preons in the electron shells and nuclear shells is proposed. It is assumed that preons currents may contribute to the conductivity of the material. A closed model of electrodynamics, which describes the diffusion of the vector potential due to the contribution to the conductivity of preons currents, is formulated. An analogy of hydrodynamics and electrodynamics of continuous media with preons currents is considered. A model of the wireless transmission of electricity is proposed