Pub Date : 1900-01-01DOI: 10.20948/mathmon-2019-44-6
A. Mikhailov, A. Petrov, O. Proncheva
{"title":"\"Power-Information-Society\" model","authors":"A. Mikhailov, A. Petrov, O. Proncheva","doi":"10.20948/mathmon-2019-44-6","DOIUrl":"https://doi.org/10.20948/mathmon-2019-44-6","url":null,"abstract":"","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129826388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.20948/mathmontis-2021-52-6
M. Zhukovskiy, V. Egorova
Algorithms for supercomputer modeling of the radiation electromagnetic field in heterogeneous materials of a complex finely-dispersed structure are constructed. A geometric model of a heterogeneous medium is created using Stilinger-Lubachevsky algorithms for multimodal structures. The model includes a system of detectors for statistical evaluation of functionals on the space of solutions of the photon-electron cascade transport equations. Algorithms for the three-dimensional approximation of the results of modeling the radiation transport in a fine-dispersed medium to an electrodynamic difference grid are developed. The approximation methods based on the technology of neural networks. The method of numerical solution of the complete system of Maxwell's equations for calculating the electromagnetic field in a fine-dispersed medium is worked out. The results of demonstration calculations of the electromagnetic field are presented. The results of the calculations show that the spatial distribution of the radiation electromagnetic field has a sharply inhomogeneous structure caused by the presence of boundaries of materials with different radiation properties.
{"title":"Modeling of the radiation induced electromagnetic field in finely-disperse media","authors":"M. Zhukovskiy, V. Egorova","doi":"10.20948/mathmontis-2021-52-6","DOIUrl":"https://doi.org/10.20948/mathmontis-2021-52-6","url":null,"abstract":"Algorithms for supercomputer modeling of the radiation electromagnetic field in heterogeneous materials of a complex finely-dispersed structure are constructed. A geometric model of a heterogeneous medium is created using Stilinger-Lubachevsky algorithms for multimodal structures. The model includes a system of detectors for statistical evaluation of functionals on the space of solutions of the photon-electron cascade transport equations. Algorithms for the three-dimensional approximation of the results of modeling the radiation transport in a fine-dispersed medium to an electrodynamic difference grid are developed. The approximation methods based on the technology of neural networks. The method of numerical solution of the complete system of Maxwell's equations for calculating the electromagnetic field in a fine-dispersed medium is worked out. The results of demonstration calculations of the electromagnetic field are presented. The results of the calculations show that the spatial distribution of the radiation electromagnetic field has a sharply inhomogeneous structure caused by the presence of boundaries of materials with different radiation properties.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131140857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.20948/MATHMONTIS-2019-46-9
M. Demin, V. Mazhukin, A. A. Aleksashkina
Of all the metals, gold is the most well-known and widely used material in scientific research, industrial production and, more recently, in biomedicine problems. In the temperature range 300 ≤ T ≤ 2000 K, including the region of the melting – crystallization phase transition, the results of modeling the phonon thermal conductivity of gold are presented. Phonon thermal conductivity plays an important role in modeling the mechanisms of interaction of pulsed laser radiation with gold in the framework of the two-temperature continuum model. In the region of the phase transition, overheating-undercooling of the solid phase occurs, the substance changes its structure. These phenomena are associated with changes in the phonon subsystem of gold, therefore, for mathematical modeling of heatingcooling, it is necessary to know the characteristic of heat transfer as the thermal conductivity of the phonon subsystem of gold. Obtaining the temperature dependence of phonon thermal conductivity in such a wide temperature range from experiment is problematic. In this work, phonon thermal conductivity was obtained by the direct non-equilibrium method in the framework of molecular dynamics modeling using the EAM potential.
{"title":"Molecular dynamic calculation of lattice thermal conductivity of gold in the melting-crystallization region","authors":"M. Demin, V. Mazhukin, A. A. Aleksashkina","doi":"10.20948/MATHMONTIS-2019-46-9","DOIUrl":"https://doi.org/10.20948/MATHMONTIS-2019-46-9","url":null,"abstract":"Of all the metals, gold is the most well-known and widely used material in scientific research, industrial production and, more recently, in biomedicine problems. In the temperature range 300 ≤ T ≤ 2000 K, including the region of the melting – crystallization phase transition, the results of modeling the phonon thermal conductivity of gold are presented. Phonon thermal conductivity plays an important role in modeling the mechanisms of interaction of pulsed laser radiation with gold in the framework of the two-temperature continuum model. In the region of the phase transition, overheating-undercooling of the solid phase occurs, the substance changes its structure. These phenomena are associated with changes in the phonon subsystem of gold, therefore, for mathematical modeling of heatingcooling, it is necessary to know the characteristic of heat transfer as the thermal conductivity of the phonon subsystem of gold. Obtaining the temperature dependence of phonon thermal conductivity in such a wide temperature range from experiment is problematic. In this work, phonon thermal conductivity was obtained by the direct non-equilibrium method in the framework of molecular dynamics modeling using the EAM potential.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128130844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.20948/mathmontis-2022-53-7
O. Feodoritova, N. Novikova, M. M. Krasnov, V. Zhukov
An approach to numerical simulation of three-dimensional electrical and thermal fields in high-temperature superconductors is described. In such a semiconductor, the phenomena of superconductivity are observed at high temperatures above the temperature of liquid nitrogen. The absence of a generally accepted theory of superconductivity leads to the need to study physical processes in semiconductor structures using mathematical simulations. The main attention is paid to the calculation of temperature and electric current distributions in large-size mesas with a self-heating effect. An efficient algorithm for solving the equations describing these distributions is constructed. The basis of the algorithm is an adaptive multigrid method on structured Cartesian grids. The adaptability is based on the Chebyshev iterative method for constructing the smoothing procedures at each grid level and for solving the coarsest grid equations. The adaptive technique allows us to realistically simulate the anisotropic phenomena. The functionality of the algorithm is demonstrated along with an example of solving an anisotropic model problem with discontinuous coefficients.
{"title":"Multigrid method for numerical modelling of high temperature superconductors","authors":"O. Feodoritova, N. Novikova, M. M. Krasnov, V. Zhukov","doi":"10.20948/mathmontis-2022-53-7","DOIUrl":"https://doi.org/10.20948/mathmontis-2022-53-7","url":null,"abstract":"An approach to numerical simulation of three-dimensional electrical and thermal fields in high-temperature superconductors is described. In such a semiconductor, the phenomena of superconductivity are observed at high temperatures above the temperature of liquid nitrogen. The absence of a generally accepted theory of superconductivity leads to the need to study physical processes in semiconductor structures using mathematical simulations. The main attention is paid to the calculation of temperature and electric current distributions in large-size mesas with a self-heating effect. An efficient algorithm for solving the equations describing these distributions is constructed. The basis of the algorithm is an adaptive multigrid method on structured Cartesian grids. The adaptability is based on the Chebyshev iterative method for constructing the smoothing procedures at each grid level and for solving the coarsest grid equations. The adaptive technique allows us to realistically simulate the anisotropic phenomena. The functionality of the algorithm is demonstrated along with an example of solving an anisotropic model problem with discontinuous coefficients.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124537525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.20948/mathmon-2019-44-12
B. Chetverushkin, A. Aptekarev, V. Mazhukin, O. Koroleva, M. Demin, A. Mazhukin
The article is dedicated to the 100th anniversary of the outstanding Soviet and Russian scientist, Academician of the USSR Academy of Sciences and the Russian Academy of Sciences Alexander Andreevich Samarskii, the founder of the Soviet and Russian school of mathematical modeling, the creator of the fundamental general theory of difference schemes, an outstanding teacher who brought up more than one generation of famous scientists , an active organizer and a bright advocate of science. Scientific activities of academician A.A. Samarskii is strongly associated with the Keldysh Institute of Applied Mathematics of Academy of Sciences of the USSR and the Russian Academy of Sciences and the Institute of Mathematical Modeling of the Russian Academy of Sciences, which he headed. A brilliant scientist and an excellent organizer, he laid down the potential to keep the world level of Russian science in the most important area of mathematical modeling for our country. 1. A.A. SAMARSKII THE FOUNDER OF THE NATIONAL SCHOOL OF MATHEMATICAL MODELING Alexander Andreevich Samarskii was born on February 19, 1919 in the village of NovoIvanovskoye, Donetsk-Amvrosievsky District, Donetsk Region, into a peasant family. He began his education at the village school, and then attended the secondary school named after A.P. Chekhov in Taganrog, which in 1936 he graduated with honors. After school, A.A. Samarskii entered the Faculty of Physics of the Lomonosov Moscow State University. In 1939 he began working in the scientific seminar of professor A.N. Tikhonov, a brilliant mathematician, a future academic, world-famous scientist. Since that time, the collaboration of two eminent scientists, which lasted for many decades, began.
{"title":"Life long scientific feat. On the occasion of centenary of the birth of academician of RAS A.A. Samarskii","authors":"B. Chetverushkin, A. Aptekarev, V. Mazhukin, O. Koroleva, M. Demin, A. Mazhukin","doi":"10.20948/mathmon-2019-44-12","DOIUrl":"https://doi.org/10.20948/mathmon-2019-44-12","url":null,"abstract":"The article is dedicated to the 100th anniversary of the outstanding Soviet and Russian scientist, Academician of the USSR Academy of Sciences and the Russian Academy of Sciences Alexander Andreevich Samarskii, the founder of the Soviet and Russian school of mathematical modeling, the creator of the fundamental general theory of difference schemes, an outstanding teacher who brought up more than one generation of famous scientists , an active organizer and a bright advocate of science. Scientific activities of academician A.A. Samarskii is strongly associated with the Keldysh Institute of Applied Mathematics of Academy of Sciences of the USSR and the Russian Academy of Sciences and the Institute of Mathematical Modeling of the Russian Academy of Sciences, which he headed. A brilliant scientist and an excellent organizer, he laid down the potential to keep the world level of Russian science in the most important area of mathematical modeling for our country. 1. A.A. SAMARSKII THE FOUNDER OF THE NATIONAL SCHOOL OF MATHEMATICAL MODELING Alexander Andreevich Samarskii was born on February 19, 1919 in the village of NovoIvanovskoye, Donetsk-Amvrosievsky District, Donetsk Region, into a peasant family. He began his education at the village school, and then attended the secondary school named after A.P. Chekhov in Taganrog, which in 1936 he graduated with honors. After school, A.A. Samarskii entered the Faculty of Physics of the Lomonosov Moscow State University. In 1939 he began working in the scientific seminar of professor A.N. Tikhonov, a brilliant mathematician, a future academic, world-famous scientist. Since that time, the collaboration of two eminent scientists, which lasted for many decades, began.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127737915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.20948/mathmontis-2023-56-7
B. Davvaz, F. F. Kareem, Wisam K. Awad
An intuitionistic fuzzy set was exhibited by Atanassov in 1986 as a generalization of the fuzzy set. So, we introduce cubic intuitionistic structures on a KU-semigroup as a generalization of the fuzzy set of a KU-semigroup. A cubic intuitionistic k-ideal and some related properties are introduced. Also, a few characterizations of a cubic intuitionistic k-ideal are discussed and new cubic intuitionistic fuzzy sets in a KU-semigroup are defined.
{"title":"Cubic intuitionistic structures of a semigroup in KU-algebra","authors":"B. Davvaz, F. F. Kareem, Wisam K. Awad","doi":"10.20948/mathmontis-2023-56-7","DOIUrl":"https://doi.org/10.20948/mathmontis-2023-56-7","url":null,"abstract":"An intuitionistic fuzzy set was exhibited by Atanassov in 1986 as a generalization of the fuzzy set. So, we introduce cubic intuitionistic structures on a KU-semigroup as a generalization of the fuzzy set of a KU-semigroup. A cubic intuitionistic k-ideal and some related properties are introduced. Also, a few characterizations of a cubic intuitionistic k-ideal are discussed and new cubic intuitionistic fuzzy sets in a KU-semigroup are defined.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127124067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.20948/MATHMON-2019-44-11
Luka Bulatović, Anđela Mijanović, Balša Asanović, Nikola Trajković, V. Bozovic
In this paper, we propose new method for automated cryptanalysis of substitution cryptosystem using Hill climbing algorithm. New heuristic function is proposed in order to drastically improve overall fitness of the standard Hill climbing algorithm. Several fitness functions have been tested and we try to detremine which of them perform better in specific situations using our suggested time-dependent measure goodness. We conclude which of those functions should be used in case we are dealing with short or long texts.
{"title":"Automated cryptanalysis of substitution cipher using Hill climbing with well designed heuristic function","authors":"Luka Bulatović, Anđela Mijanović, Balša Asanović, Nikola Trajković, V. Bozovic","doi":"10.20948/MATHMON-2019-44-11","DOIUrl":"https://doi.org/10.20948/MATHMON-2019-44-11","url":null,"abstract":"In this paper, we propose new method for automated cryptanalysis of substitution cryptosystem using Hill climbing algorithm. New heuristic function is proposed in order to drastically improve overall fitness of the standard Hill climbing algorithm. Several fitness functions have been tested and we try to detremine which of them perform better in specific situations using our suggested time-dependent measure goodness. We conclude which of those functions should be used in case we are dealing with short or long texts.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127964485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.20948/MATHMON-2019-44-7
Y. Nemirovsky, N. Feodorova
{"title":"Modeling limit states for curvilinearly reinforced rotated disks","authors":"Y. Nemirovsky, N. Feodorova","doi":"10.20948/MATHMON-2019-44-7","DOIUrl":"https://doi.org/10.20948/MATHMON-2019-44-7","url":null,"abstract":"","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"206 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116395468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.20948/mathmontis-2022-53-4
Ilias Laib, Nadir Rezzoug
A sequence of strictly positive integers is said to be primitive if none of its terms divides the others and is said to be homogeneous if the number of prime factors of its terms counted with multiplicity is constant. In this paper, we construct primitive sequences A of degree d, for which the Erdős’s analogous conjecture for translated sums is not satisfied.
{"title":"On a sum over primitive sequences of finite degree","authors":"Ilias Laib, Nadir Rezzoug","doi":"10.20948/mathmontis-2022-53-4","DOIUrl":"https://doi.org/10.20948/mathmontis-2022-53-4","url":null,"abstract":"A sequence of strictly positive integers is said to be primitive if none of its terms divides the others and is said to be homogeneous if the number of prime factors of its terms counted with multiplicity is constant. In this paper, we construct primitive sequences A of degree d, for which the Erdős’s analogous conjecture for translated sums is not satisfied.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124145313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.20948/mathmontis-2021-52-4
Ilias Laib
A sequence A of strictly positive integers is said to be primitive if none of its term divides another. Z. Zhang proved a result, conjectured by Erdős and Zhang in 1993, on the primitive sequences whose the number of the prime factors of its terms counted with multiplicity is at most 4. In this paper, we extend this result to the primitive sequences whose the number of the prime factors of its terms counted with multiplicity is at most 5.
{"title":"The degree of primitive sequences and Erdős conjecture","authors":"Ilias Laib","doi":"10.20948/mathmontis-2021-52-4","DOIUrl":"https://doi.org/10.20948/mathmontis-2021-52-4","url":null,"abstract":"A sequence A of strictly positive integers is said to be primitive if none of its term divides another. Z. Zhang proved a result, conjectured by Erdős and Zhang in 1993, on the primitive sequences whose the number of the prime factors of its terms counted with multiplicity is at most 4. In this paper, we extend this result to the primitive sequences whose the number of the prime factors of its terms counted with multiplicity is at most 5.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131687579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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