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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+

КВАНТОВАЯ КРИПТОГРАФИЯ: КВАНТОВОЕ РАСПРЕДЕЛЕНИЕ КЛЮЧЕЙ

Posted in 2012, PHYSICS AND MATHEMATICS, Выпуск № 5(5) Октябрь 2012 | 0 comments

В статье рассмотрена система квантового распределения ключей, ее алгоритм, достоинства и недостатки, сформулированы перспективы развития таких систем.

Поставлены следующие задачи:

Изучить теорию квантового распределения ключей.
Проанализировать QKD и выявить его преимущество и недостатки.
Изучить перспективы развития квантового распределения ключей.

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PONTRYAGIN’S MAXIMUM PINCIPLE FOR A STATE-CONSTRAINED OPTIMAL CONTROL PROBLEM GOVERNED BY A BIHARMONIC EQUATION

Posted in 2022, Issue № 5 (119) May 2022, PHYSICS AND MATHEMATICS | 0 comments

The article considers the problem of optimal control of biharmonic equation with constraint on the state. The necessary condition of optimality in the form of the Pontryagin’s maximum principle was formulated and proved. This result can be useful both for organizing a subsequent computational procedure of successive approximations method, and for qualitative analysis of the problem, perhaps not leading to a final answer, but establishing important components of the solution, meaming an optimal process. It must also be noted that the biharmonic equations describing the features of the optimal control object constantly arise in problems of the mathematical theory of elasticity and related problems of optimization. Phase limitations in setting the optimal control within the problem in question, tend to make it difficult to find a solution.

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DEVELOPMENT OF TECHNOLOGY FOR DETECTING STRESS CORROSION CRACKING ON PIPELINES VIA NEURAL NETWORKS

Posted in 2022, Issue № 04 (118) April 2022, PHYSICS AND MATHEMATICS | 0 comments

The current article describes a technique for modeling the propagation of stress corrosion cracking in sections of main gas pipelines. The methodology is based on a predictive model for predicting the appearance of corrosion defects on a gas pipeline. The presented algorithm was created using the principles of neural network modeling. The model is based on a multilayer perceptron, a standard tool for solving binary classification problems. Additionally, the paper examines one of the existing methods for detecting corrosion defects in pipelines, which is a point-factor analysis. The paper points out the disadvantages of this technique and suggests comparing it with a neural network model. The study also provides an economic comparison of the two methods based on some sections of a main gas pipeline.

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AN EVALUATION OF THE POSSIBILITY OF USING A VACUUM LAYER IN SOUNDPROOFING PANELS

Posted in 2022, Issue № 03(117) March 2022, PHYSICS AND MATHEMATICS | 0 comments

One of the current problems of modern life is protection from noise on the ways of its propagation. Currently, there is a need in reducing noise in various fields of human activity. The noise of short-term exposure does not make any significant changes in the human body; the problem is mainly with prolonged negative sounds, which can be tackled through various methods and approaches. In the trajectory of noise control, various solutions to the problem were proposed. The study distinguishes method of applying vacuum to protect against noise. From the standpoint of physics, a vacuum is an ideal medium that prevents the propagation of sound waves. However, many attempts to apply vacuum in the design of sound protection devices have not shown good results. Currently, the researchers continue the search for devices that use a vacuum layer to protect against noise.

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MATHEMATICAL MODELING OF CANCER TREATMENT

Posted in 2022, Issue № 03(117) March 2022, PHYSICS AND MATHEMATICS | 0 comments

The current study develops a mathematical model of neoplasm growth taking into account the immune response of the body. Mathematical models of treatment include chemotherapy, external intervention and immunotherapy. Mathematical models are based on the Cauchy problem for ordinary differential equations. The authors conduct an analysis of stationary states and obtain the conditions for the “destruction” of the neoplasm. The study also introduces a model for the purposes of constructing the distribution of conditional patients according to the stages of the disease and the duration of treatment. The “dose-effect” dependencies for various treatment programs are also constructed.

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ON THE STUDY OF ROBUST STABILITY AND APERIODICITY OF CONTINUOUS AND DISCRETE SYSTEMS

Posted in 2022, Issue № 03(117) March 2022, PHYSICS AND MATHEMATICS | 0 comments

At present, there is no need to justify the importance of the study of robust stability (i.e., the preservation of stability by the system under conditions of uncertainty). If the model describes a physical object (mechanical, physical, economic, etc.), then, as a rule, its parameters are not known exactly, although the equations describing the operation of the system are known. That is, there is always uncertainty in real tasks. The article discusses some approaches to the study of both stability and aperiodicity of interval-indeterminate continuous and discrete systems using the Mikhailov criterion. The study provides examples of concrete calculations of robust stability boundaries for continuous systems of the third and fourth order.

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DIFFERENTIAL PROPERTIES OF THE FUNCTIONS

Posted in 2022, Issue № 02(116) February 2022, PHYSICS AND MATHEMATICS | 0 comments

The first integral representation of the functions of many variables defined in the regions (star regions relative to the points of a given ball) GMEn belongs to academician S.L. Sobolev. S.L.Sobolev developed a method of integral representations of functions from well-known functional spaces constructed by him 1and proved the basic theorems of embedding these spaces with further applications to the theory of partial differential equations.

Further development of the method of integral representations of the theory of spaces of differentiable functions of many variables is associated with the name of V.P. Ilyin. He proved a fundamentally new integral representation of functions of many variables at any point xOEn.

The study investigates the “weight” spaces of functions 1, points of many bundles of variables 1definedinthedomain satisfyingthecondition “variable 1 -semihorn”. These constructed “weight” spaces of the type of generalized B-spaces depend on the parameter 1, which in the case s=1 generalize the known “weight” spaces 1-O.V.Besov, and in the case s=1, generalize the known spaces of 1functions with a dominant shifted derivative, in the case of power “weights” given in the works of A.J.Dzhabrailov.

A.D.Dzhabrailov proved new integral representations of functions of many variables, with the help of which he managed to build a general theory of spaces of functions with a dominant mixed derivative 1, with further development of the method of integral representations in the theory of the embedding theorem of these spaces.

A new functional space is also constructed by the method of integral representations [1] based on a new integral representation of smooth functions at points 1.

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Evaluating Fractal Properties of Nanostructures from Microscopic Images

Posted in 2022, Issue № 02(116) February 2022, PHYSICS AND MATHEMATICS | 0 comments

The article investigates a method for analyzing fractal properties of images based on their structural function and proposes an extension of this method in order to analyze local fractal features. The authors investigate a method for synthesizing images with spectral self-similarity properties and propose a method for modifying images into fractal ones with a self-similar structural function based on wavelet transformations. Also, the authors introduce a software tool for fractal analysis of microscopic images using the methods featured in the study. The effectiveness of these methods is shown by means of their verification on modeled fractal images. The study proposes the application of the developed fractal analysis tools in the field of electron and optical microscopy.

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PREDATOR-PREY MODEL ON A LINEAR TERRITORY

Posted in 2022, Issue № 02(116) February 2022, PHYSICS AND MATHEMATICS | 0 comments

The current article carries out a study of the Rosenzweig-MacArthur predator-prey model on a straight line segment. The authors provide an analysis of stationary solutions and obtain the conditions for the existence of periodic solutions in a spatial variable. The study provides variants of possible distributions of the numbers of predators and victims in the territory. The model is extended for the interaction of populations under anthropogenic pressure. It is also based on statistical data on the contaminated area in the vicinity of a copper-nickel plant. The research features an assessment of the possible decrease in the number of predator and prey populations depending on the degree of contamination. With the use of simulation modeling, the study constructs the distributions of predators and victims depending on the anthropogenic load.

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AN INVESTIGATION OF OPTICAL AND ELECTRICAL PROPERTIES OF THE TlGaSe 2 SINGLE CRYSTAL

Posted in 2021, Issue № 12 (114) December 2021, PHYSICS AND MATHEMATICS | 0 comments

In order to determine the nature of optical transitions, the authors conducted studies in the self-absorption edge of TlGaSe 2; transmission and reflection were measured at 300 K and 77 K, the authors also calculated the absorption coefficient. The results are in good agreement with the calculations of the Brillouin zone. It is shown that the long-wave edge of the proper absorption band is formed by indirect transitions (Y→D). At 4.2 K in the spectrum, an intense absorption line λ = 579.5 nm (2,138 eV) is observed in the absorption spectrum. It can be concluded that in TlGaSe 2, the self-absorption edge is formed by a direct exciton transition, which is preceded by an indirect optical transition. Studies of transitions corresponding to the TlGaSe 2self-absorption edge show that the edge is formed by a transition between extreme points of the Brillouin zone that have polarization features. Transitions occur from several levels located in close proximity to each other. TlGaSe 2 crystallizes in a monoclinic structure with the Cc space-group, which indicates that these crystals have a single element of symmetry – the reflection plane σ perpendicular to the layers. However, the experimental results obtained are not explained by this symmetry of the crystal.

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NUMERICAL SIMULATION OF LAVA FLOWS IN MODELS OF ISOTHERMAL VISCOUS MULTIPHASE INCOMPRESSIBLE FLUID

Posted in 2021, Issue № 12 (114) December 2021, PHYSICS AND MATHEMATICS | 0 comments

A lava flow begins to form when molten rock erupts onto the surface of the Earth and slowly spreads to the surface from a fissure vent. Eruptions create different lava flows (for example, flows of a different structure and flow velocity) under the influence of gravity, depending on the chemical composition, temperature of igneous rocks, and the topography of the surface over which the lava flows. Despite the fact that volcanic lava flows do not have a significant impact on people’s lives, their danger is considerable, since hot lava kills vegetation, destroys infrastructure, and can cause flooding due to melting snow/ice. Following the development of computing resources, numerical modeling of lava flows over the past few decades has moved from modeling one-dimensional flows to modeling three-dimensional flows, which is most adequately able to reflect real natural processes. In order to investigate the dynamics and interaction of lava flows, the current article develops three-dimensional numerical models of flows of an isothermal viscous Newtonian multiphase fluid on various surfaces under the influence of gravity. A complete simulation of a lava flow is a challenging task from a physical, mathematical, and numerical point of view. The mathematical model includes the Navier-Stokes equation, the incompressibility equation, and the phase transfer equations with corresponding initial and boundary conditions. The finite volume method is used for numerical approximation of the mathematical model. The program codes are implemented in the ANSYS Fluent package in C. When conducting numerical experiments, a parallel-acting computer was used. The article demonstrates the results of calculations of the model experiment. Lava flow reconstruction models can provide significant assistance in the design of barriers reflecting lava flows. The availability of technological and scientific data (such as satellite monitoring data, high-speed calculation algorithms, and realistic models) will allow for integrating data into models with traditional methods of studying volcanic activity, which will allow more efficient use of the results.

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SOLUTION TO THE PROBLEM OF CREEP OF CURVILINEAR-ANISOTROPIC MEDIA BY THE RUNGE-KUTTA-FEHLBERG METHOD OF 5-6 ORDER

Posted in 2022, Issue № 01(115) January 2022, PHYSICS AND MATHEMATICS | 0 comments

The article proposes a method for preliminary analysis of the composition and assessment of the dynamics of layers of deep-lying rock formations, physical knowledge of which is insufficient or cannot be obtained experimentally without the stage of development and launch of wells, mines and quarries. This method is based on modeling the stress-strain state of rocks taking into account block-curved anisotropy and creep. The paper proposes a method for an effective numerical solution of the stress-strain state problem taking into account block-curved anisotropy and creep. The developed software is offered on the basis of the Scientific and Educational Center “Supercomputer engineering modeling and development of software complexes” of the Bauman Moscow State Technical University to create, describe, solve, analyze soil models and other mathematical models.

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PREDATOR-PREY MATHEMATICAL MODEL IN A POLLUTED AREA

Posted in 2022, Issue № 01(115) January 2022, PHYSICS AND MATHEMATICS | 0 comments

The current article conducts an analysis of the Rosenzweig-MacArthur local predator-prey model and determines the conditions for the “death” of the predator, the frequency of damped oscillation in the number of populations. The authors develop a model of anthropogenic pressure that takes into account a decrease in the birth rate of victims, a decrease in the amount of trophic resource, and a decrease in the capacity of the environment. Possible distributions of the number of victims and predators are constructed depending on various factors determining the interaction of populations taking into account anthropogenic pressure.

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APPLICATION OF THE POTENTIAL METHOD IN GRAVIMETRIC EXPLORATION

Posted in 2021, Issue № 12 (114) December 2021, PHYSICS AND MATHEMATICS | 0 comments

Determination of the mass of the components of the Earth by gravimetric measurements is important for the search for minerals and the modelling of a geoid. Of the most interest is the magnitude of the masses in the near-surface layer of several kilometers. The article presents a numerical method for determining the values of these masses in a space of differentiable functions using the mathematical method of potential. Unlike most of the known algorithms, the method leads to the solution of a correctly posed problem with a single solution. The described algorithm generalizes the previously proposed method for determining the masses of the components of the Earth in the space of differentiable functions from the global to the regional level. Based on the results of the global calculation, it is possible to obtain initial data for calculating the refined values of the masses of the components composing the Earth in the near-surface layer, the depth of which is determined by the area of field measurements. The increase in the area of field measurements makes it possible to use the proposed approximation at a greater depth and determine the mass values with a given accuracy.

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Modeling of Psychological and Pedagogical Portraits of Teachers and Students

Posted in 2021, Issue № 12 (114) December 2021, PHYSICS AND MATHEMATICS | 0 comments

The introduction of digital methods into the educational process makes the use of mathematical methods and models relevant. The mathematical description of the characteristics of students and teachers who form their psychological and pedagogical portraits is an important problem. Their vector characteristics and matrix representation are chosen as portrait models. For mathematical matching of digital portraits with vector description, it is proposed to apply the magnitude of their scalar product. The article introduces a method of finding the proportions of the elements of the structural matrix of portraits, in which the characteristics of teachers and students in this educational team will be balanced. The method is based on the analysis of the eigenvalue of the structural matrix of the model.

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NUMERICAL METHOD FOR CALCULATING RIEMANN INTEGRALS USING ASYMPTOTIC POLYNOMIALS BASED ON THE FIRST-KIND CHEBYSHEV POLYNOMIALS. A PROGRAM BASED ON MICROSOFT EXCEL

Posted in 2021, Issue № 12 (114) December 2021, PHYSICS AND MATHEMATICS | 0 comments

The standard method for calculating Riemann integrals using the Newton-Leibniz formula involves finding a primitive subintegral function. However, this method does not always work. There are multiple numerical methods for calculating certain integrals from functions that do not have a primitive. The current article presents a numerical method for calculating approximate values of certain integrals using asymptotic polynomials based on the first-kind Chebyshev polynomials. The study also shows a program based on Microsoft Excel, the use of which will allow for calculating any Riemann integral without intermediate calculations and requiring a minimum amount of time.

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L-CURVE METHOD FOR EVALUATING THE OPTIMAL PARAMETER OF A SMOOTHING CUBIC SPLINE

Posted in 2021, Issue № 11 (113) November 2021, PHYSICS AND MATHEMATICS | 0 comments

A universal device for filtering measuring noise is a smoothing cubic spline of defect 1. The magnitude of the filtering error (smoothing) is mostly determined by the value of the smoothing parameter. With the optimal smoothing parameter value, the smoothing error value takes a minimum value. In practice, there is no a priori information on the exact (not noisy) values of the signal, and it is impossible to calculate the value of the optimal smoothing parameter. In this regard, the algorithms used to solve practical problems for choosing the optimal parameter allow for estimating only acceptable smoothing errors, which sometimes significantly exceed the minimum values. The estimation of the optimal smoothing parameter with an unknown variance of the noise measurement of experimental data presents particular difficulty. The current article constructs and examines in detail an algorithm for estimating the optimal parameter based on the L-curve method. This method is used to select the regularization parameter in algorithms for solving incorrectly set tasks. Particular attention is paid to the estimation of the optimal parameter in conditions of correlated noise. Based on the results of these studies, the authors provide practical recommendations for the application of this selection algorithm in the practice of processing experimental data.

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IDEMPOTENT MODEL OF THE CLASSICAL ASSIGNMENT PROBLEM

Posted in 2013, Issue №6 (13) June 2013, PHYSICS AND MATHEMATICS | 0 comments

The main principle of idempotent algebra is observed in this article, the main advantages of idempotent approach are given. An idempotent model of a classical assignment problem is given, this model makes even non-linear assignment problems become linear ones.

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A NEW THEORY OF MAGNETISM

Posted in 2013, Issue №6 (13) June 2013, PHYSICS AND MATHEMATICS | 0 comments

In this article the – criticism of Maxwell’s theory, called the cause of terrestrial magnetism, discovered a new magnetic force, and drew an analogy between the magnetic field and the gravitational field, amended in Newton’s law of universal gravitation.

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THE HYDROACOUSTIC RECEPTION EXTENDED PARAMETRICAL ARRAY

Posted in 2013, Issue №6 (13) June 2013, PHYSICS AND MATHEMATICS | 0 comments

In work use of the flexible extended array on the basis of a wave guide in the form of a flexible wave guide with filling with any liquid is offered, distribution of acoustic fluctuations to a round wave guide is considered. Change of phase speed in a wave guide is analyzed at
influence on it of a low-frequency signal. Schemes of processing signals are considered.

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