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PHYSICS AND MATHEMATICS

ISSN 2227-6017 (ONLINE), ISSN 2303-9868 (PRINT), DOI: 10.18454/IRJ.2227-6017
ЭЛ № ФС 77 - 80772, 16+

DREAMS’ MOTIVTIONS

Posted in 2013, Issue № 9(16) September 2013, PHYSICS AND MATHEMATICS | 0 comments

It was shown that a dream is a mental model of a future state of a part of surrounding world, important for individual, presented in the shape of possible development scenarios. Over a hundred thousand years, creating such scenarios has become one of the basic human needs. A mathematical model for determining an individual’s tendency to dream in different periods of life was elaborated and investigated.

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MODELING OF RECTILINEAR TRAJECTORY-WAVE MOTION OF AN OBJECT

Posted in 2021, Issue №8 (110) August 2021, PHYSICS AND MATHEMATICS | 0 comments

The current study formulates the local variational principle (LVP), the theorem on the necessary and sufficient condition for the existence of a V-function, the wave and trajectory theorem, examines the direct and inverse problems of dynamics in a new formulation, which are the essence of the V-function method. The V-function method indicates that the wave motion of an object is inextricably linked with its trajectory motion. The trajectory motion of an object is described by a system of ordinary differential equations, and the wave motion is modeled by a second-order partial differential equation. On the basis of the V-function method, the optical-mechanical analogy receives a new continuation. It is shown that in the physical sense, the wave amplitude is determined by an action that manifests itself in the movement of an object (particle). It is established that the energy levels obtained using the V-function method for the case of rectilinear uniform motion of a quantum object completely coincide with the classical Schrodinger results for a harmonic oscillator.

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ON THE STUDY OF A SYSTEM CLOSE TO A HARMONIC OSCILLATOR VIA APPROXIMATE POINT MAPPING

Posted in 2021, Issue №8 (110) August 2021, PHYSICS AND MATHEMATICS | 0 comments

The theory of nonlinear oscillations is one of the most important components of modern science. Nonlinear oscillation is a term usually applied to oscillatory phenomena that occur in nonlinear dynamical systems. The most accessible for research are oscillatory systems with low nonlinearity, for which various asymptotic methods have been developed. Moreover, the study of nonlinear systems close to a harmonic oscillator is still of particular interest. The current study assesses the possibility of studying a system close to harmonic oscillators by via approximate point mapping, both equations of which contain nonlinear terms. The article provides explicitly defined functions of the sequence of a point map, in the construction of which asymptotic methods are used, as well as the results of their analysis.

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STM PARAMETERS OF SEMICONDUCTOR COLLOIDAL QUANTUM DOTS

Posted in 2021, Issue №8 (110) August 2021, PHYSICS AND MATHEMATICS | 0 comments

Based on the studies of the tunnel-emission volt-ampere characteristics of colloidal quantum dots CdSe, PbS, InSb and the single-electron transport model, the article determines the most important parameters of quantum dots such as the effective mass of the electron, the permittivity, the energy of the potential tunneling barrier, the linear size of the quantum-limited resonant electron motion (the size of the quantum dot). A comparison of the obtained parameters of quantum dots with similar ones for bulk semiconductors shows their good correspondence, which may indicate both the validity of the obtained parameters and the possibility of using models and properties of bulk semiconductors in relation to quantum dots. Based on the data obtained and with the continuation of the research, it is possible to create a method along with a software and hardware complex for industrial control of the main parameters of quantum dots.

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ON THE DIAGONALIZABILITY CONDITIONS OF A PERTURBED DIFFERENCE OPERATOR IN SOME SPACES

Posted in 2021, Issue №7 (109) July 2021, PHYSICS AND MATHEMATICS | 0 comments

The current paper uses the method of similar operators to obtain the conditions for reducing the matrix of a difference operator of the form 03-09-2021 10-27-01 to a diagonal or block-diagonal form in the standard basis of space 03-09-2021 10-27-11 and estimates its spectral characteristics. The paper presents the main definitions of the method used. In accordance with the method of such operators, the operator A is represented in the form 03-09-2021 10-27-24 where the matrix operator 03-09-2021 10-27-34 has a diagonal structure, and B is the perturbation operator. The conditions for the perturbation operator are considered in cases when this operator belongs to three different spaces. The asymptotic representation of eigenvalues, estimates of eigenvectors, and elements of matrices of spectral projectors are also obtained.

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CALCULATION OF FACTORS IN PONDEROMOTIVE ELEKTROPLASTICHNOSTI MONOCRYSTAL SB.

Posted in 2013, Issue October 2013, PHYSICS AND MATHEMATICS | 0 comments

In this paper the calculations of the intrinsic magnetic field of the current sample of antimony.

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DEVELOPMENT OF CONTENTS AND ACTIVITIES FOR IMPROVING THE EFFICIENCY OF THE PROBLEM OF SOFTWARE AND HARDWARE “DISPLAY STAND”

Posted in 2013, Issue October 2013, PHYSICS AND MATHEMATICS | 0 comments

In the article – the creation of «Display stand», increasing sales efficiency by reducing staff while increasing the quality of the advertising information.

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SOLUTION OF THE EFFICIENCY OF SALE SHOP BY IMPROVING THE HARDWARE “DISPLAY STANDS”

Posted in 2013, Issue October 2013, PHYSICS AND MATHEMATICS | 0 comments

The paper considers the problem of increasing the effectiveness of sales shop and an improved hardware complex “Display stand”.

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OPTIMAL OPERATION MODES OF DUAL MAGNETRONS FOR DEPOSITION TiO2 THIN FILMS

Posted in 2013, Issue October 2013, PHYSICS AND MATHEMATICS | 0 comments

The investigation of optical properties of TiO2 thin films, obtained by a dual magnetron sputtering system (MSS), shows that optical characteristics of films depend on their structure and determine by operation mode and configuration of the magnetic field of the magnetron.

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STRUCTURE AND THERMODYNAMICS PROPERTIES OF EXPLOSIVE TATB, PETN AND TATT

Posted in 2013, Issue October 2013, PHYSICS AND MATHEMATICS | 0 comments

One of the most perspective ways in increasing the safety of explosive works, in particular, in coal-mining industry, is the use of laser initiation technologies, which is able to eliminate the possibility of functioning of the system of initiation in unauthorized cases, and its assured functioning in the sanctioned ones. In this work the substances meeting the practical requirements are being researched. Such substances are TATB, PETN and TATT. The research reveals the geometrical and thermodynamics properties of these molecules.

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DIELECTRIC STUDY OF COMPOSITE MATERIALS FILLED WITH FERROELECTRIC CERAMICS

Posted in 2013, Issue October 2013, PHYSICS AND MATHEMATICS | 0 comments

The paper views the results of the study of temperature and frequency dependence of the dielectric parameters in polymer composites based on polyethylene and barium titanate. With the introduction of ferroelectric into the polymer matrix an increase in the dielectric constant and dielectric loss tangent was found.

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HEAT EXCHANGE BETWEEN THE PLASMA TORCH JET AND THE HEATED SURFACE OF THE ALUMINA MELT FOR NITROGEN, ARGON AND HYDROGEN

Posted in 2021, Issue №7 (109) July 2021, PHYSICS AND MATHEMATICS | 0 comments

The article evaluates the efficiency of heat transfer between the plasma torch jet and the heated surface of the alumina melt in order to select the optimal working gas for the production technology of pure white corundum. This technology is being developed for the purpose of its industrial application with a corundum capacity of 50 kg per hour. According to this technology, corundum crystals are obtained by melting alumina powder in a reactor with a plasma torch jet. Nitrogen, argon, and hydrogen are considered as the working gas of the plasma torch. The calculations use estimates of the thermophysical characteristics of nitrogen, argon, and hydrogen at the operating temperature of the plasma torch, which approximately amounts to 8000K. The jet velocity and Nusselt numbers characterizing heat transfer were calculated taking into account the required performance. According to the results of calculations, the most effective gas for heating and melting alumina is nitrogen because of its incomplete dissociation at the operating temperature of the plasma torch and, as a result, higher thermal conductivity and specific enthalpy.

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AN INVESTIGATION OF THE FORMATION OF THERMOELECTRIC EMF IN AQUEOUS SOLUTIONS OF ELECTROLYTES

Posted in 2021, Issue №7 (109) July 2021, PHYSICS AND MATHEMATICS | 0 comments

The current article analyzes the process of thermoelectric EMF formation on the basis of equations describing the electric potential differences fixed by electrodes in an electrolyte solution under non-isothermal conditions. The authors also conduct an analysis of the contributions to the measured signal from various effects and their changes over time. A method for measuring the thermoelectric EMF is proposed, which allows identifying individual components of the resulting potential difference. Based on the analysis of the obtained experimental results, the article demonstrates that the main contribution to the measured difference of thermoelectric potentials, in the narrow sens, is made by the thermodiffusion difference of electric potentials, which is formed in the initial state.

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MATHEMATICAL MODEL OF MELANOMA

Posted in 2021, Issue №7 (109) July 2021, PHYSICS AND MATHEMATICS | 0 comments

The current article introduces a mathematical model of a growing four-stage surface melanoma. The model is represented by the Cauchy problem for a system of four ordinary differential equations. The stages of the disease are modeled by chambers of various capacities with the movement of malignant cells from chamber to chamber. The chemotherapy model takes into account the direct effect of drugs on tumor cells at a given time interval. Using a statistical approach, the authors develop a model for constructing the distribution of patients by the time of diagnosis, the duration of treatment, and the time of relapse. Also, the article provides an estimation of the drugs to be consumed for treatment to a given required level of survival. The model parameters are determined based on clinical data on the growth rate of the neoplasm, the time interval of treatment.

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AN INVESTIGATION OF THE STRUCTURAL AND PHYSICAL PROPERTIES OF COLLOIDAL QUANTUM DOTS OF NARROW-BAND SEMICONDUCTORS VIA ELECTRON AND SCANNING PROBE MICROSCOPY

Posted in 2021, Issue №7 (109) July 2021, PHYSICS AND MATHEMATICS | 0 comments

Based on variations in the parameters of the synthesis of quantum dots and measurements on electron and probe microscopes, the study establishes that the crystallization rate during their colloidal synthesis is the determining factor for the structural and physical properties of quantum dots. At the same time, with the slow growth of crystals, the histogram of the size distribution has two maxima, which is probably due to the thermodynamic anisotropy of crystallization. The study of the tunnel-emission properties of quantum dots makes it possible to estimate the values of the effective mass of their conduction electrons and to assume the applicability of its method to quantum dots. At the same time, the values of the potential emission barrier are determined by the characteristic of the differential tunneling conductivity (dI/dV)/(I/V).

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FEATURES OF MULTICRYSTALLINE TRANSPORT OF ELECTRONS OF COLLOIDAL QUANTUM POINTS OF InSb AND PbS

Posted in 2021, Issue №7 (109) July 2021, PHYSICS AND MATHEMATICS | 0 comments

On samples in the structure of a multi-grained layer of colloidal quantum dots of narrow-gap semiconductors of indium antimonide and lead sulfide, electrons are transported in intergranular nanogaps during current flow by thermal emission from quantum dots without a shell and tunnel emission from quantum dots with a shell. Electrons are injected into quantum dots by tunneling emission and flight through the shell. For the variant without a shell, the current is limited by space charge, similar to the Coulomb blockade. The results are discussed using the streamline model across the layer. According to the characteristics, it is calculated that there are 100-200 quantum dots in the streamlines.

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A MATHEMATICAL MODEL OF ACNE

Posted in 2021, Issue №6 (108) June 2021, PHYSICS AND MATHEMATICS | 0 comments

The current study develops a mathematical model of acne. The model takes into account the characteristics of the appearance, maturation, and spread of pustules on the system of sweat glands of the skin. The process of bacterial population growth is described by a system of discrete-time equations. The treatment model assumes the direct effect of chemicals on the pustules. The statistical-probabilistic approach is applied in the model of the distribution of patients by the time of the onset of the stages of the condition and in the models of the distribution by the duration of treatment. The parameters that characterize the kinetics of pustule growth and the rate of their spread over the surface are determined based on clinical data. The treatment model assumes that the drugs affect all the pustules simultaneously.

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SKIN EFFECT IN A CYLINDRICAL CIRCULAR CONDUCTOR WITH A RECTANGULAR PULSE SHAPE

Posted in 2021, Issue №6 (108) June 2021, PHYSICS AND MATHEMATICS | 0 comments

The article deals with the case of the skin effect in a conductor with a rectangular shape of the current pulse based on the Maxwell’s equations. The study determines the value of the voltage loss in a cylindrical conductor in the case of a sharp skin effect along with obtaining an expression for the effective depth of current penetration for a rectangular pulse of a given duration. Based on the obtained expressions, the study presents a specific example of a sharp skin effect for a cylindrical copper conductor. It is shown that in the case of a sharp skin effect, the requirements for the choice of the conductor material are reduced, while the change in the pulse duration has a low effect. The resulting expressions can also be applied to an annular conductor.

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EXCEL VBA FUNCTIONS FOR NUMERICAL SOLUTION OF A CAUCHY PROBLEM OF THE FIRST-ORDER ODE SYSTEM

Posted in 2021, Issue №6 (108) June 2021, PHYSICS AND MATHEMATICS | 0 comments

The current study presents program codes of custom VBA Excel functions that implement numerical methods for solving the Cauchy problem for a system of 1st order ordinary differential equations using the Euler and Runge-Kutta 4th order methods. The parameters of the functions are the initial and final values of the independent variable, an array of initial values of the dependent variables, and the number of steps. Program codes use dynamic arrays. Custom functions can be applied to the Cauchy problem and one of the 1st order differential equations. All of the custom functions have descriptions that explain their purpose. The article demonstrates the use of custom functions using specific examples of numerical solutions to the Cauchy problem of 1st order differential equations system and individual 1st-order differential equations.

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GAS DISCHARGE WITH A LIQUID ELECTROLYTE CATHODE IN CREATING A FLOW OF STEAM WATER PLASMA

Posted in 2021, Issue №6 (108) June 2021, PHYSICS AND MATHEMATICS | 0 comments

The current article presents the results of an experimental study of a gas discharge with a flowing liquid electrolyte cathode under combustion conditions inside a chamber with walls made of refractory material. The copper anode was located above the cathode. The interelectrode distance was 20 cm. Aqueous solutions of sodium chloride with a concentration of 0.2-0.3 mol / l were used as an electrolyte. The electric power source was a three-phase rectifier with an output voltage of 2100 V. The discharge burned steadily without a ballast resistor in the power range of 25-30 kW. As a result, the researchers obtained a flow of steam water plasma with a mass velocity of 1.0-1.7 g/s. The total heat loss through the electrodes did not exceed 30% of the overall power consumption.

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