Pub Date : 1900-01-01DOI: 10.20948/mathmontis-2021-52-3
V. E. Berezovskii, J. Mikeš, Ž. Radulović
We consider almost geodesic mappings π1* of spaces with affine connections. This mappings are a special case of first type almost geodesic mappings. We have found the objects which are invariants of the mappings π1*. The fundamental equations of these mappings are in Cauchy form. We study π1* mappings of constant curvature spaces.
{"title":"Almost geodesic mappings of type π1* of spaces with affine connection","authors":"V. E. Berezovskii, J. Mikeš, Ž. Radulović","doi":"10.20948/mathmontis-2021-52-3","DOIUrl":"https://doi.org/10.20948/mathmontis-2021-52-3","url":null,"abstract":"We consider almost geodesic mappings π1* of spaces with affine connections. This mappings are a special case of first type almost geodesic mappings. We have found the objects which are invariants of the mappings π1*. The fundamental equations of these mappings are in Cauchy form. We study π1* mappings of constant curvature spaces.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"70 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":"130071064","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-2022-55-4
Nabil Tahmi, Laid Elkhiri, Abdallah Derbal
In this paper, we gave some new identities and super-congruences involving binomial coefficient, and some interesting congruences related to Fibonacci and Lucas sequence.
{"title":"Congruences involving the binomial coefficient and some applications","authors":"Nabil Tahmi, Laid Elkhiri, Abdallah Derbal","doi":"10.20948/mathmontis-2022-55-4","DOIUrl":"https://doi.org/10.20948/mathmontis-2022-55-4","url":null,"abstract":"In this paper, we gave some new identities and super-congruences involving binomial coefficient, and some interesting congruences related to Fibonacci and Lucas sequence.","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":"125409456","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-2022-53-1
Brahim Mittou
Recently the author and Derbal introduced and studied some elementary properties of arithmetic functions related the greatest common divisor. New properties of them are given in this paper.
{"title":"New properties of an arithmetic function","authors":"Brahim Mittou","doi":"10.20948/mathmontis-2022-53-1","DOIUrl":"https://doi.org/10.20948/mathmontis-2022-53-1","url":null,"abstract":"Recently the author and Derbal introduced and studied some elementary properties of arithmetic functions related the greatest common divisor. New properties of them are given in this paper.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"1 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":"129040980","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-2023-56-1
Ž. Pavićević, V. Mazhukin
The article is dedicated to the 30th anniversary of the publication of the journal Mathematica Montisnigri. The founders of the journal are the Association of Mathematicians and Physicists of Montenegro and the Faculty of Sciences and Mathematics of University of Montenegro, Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences (KIAM). The chief editors of the journal are prof. Žarkop Pavićević (University of Montenegro) and prof. V.I. Mazhukin (KIAM). The first issue of the magazine was published in May 1993. The history of the organization of the institution and the publication of the journal is traced. The role of the rector of Lomonosov Moscow State University аcademician V.A. Sadovnichy and prof. of the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University V.I. Gavrilov in creating the journal. The development of the journal and the role of mathematicians of the University of Montenegro and mathematicians of the Keldysh Institute of Applied Mathematics of RAS in this process.
{"title":"Mathematica Montisnigri journal is 30","authors":"Ž. Pavićević, V. Mazhukin","doi":"10.20948/mathmontis-2023-56-1","DOIUrl":"https://doi.org/10.20948/mathmontis-2023-56-1","url":null,"abstract":"The article is dedicated to the 30th anniversary of the publication of the journal Mathematica Montisnigri. The founders of the journal are the Association of Mathematicians and Physicists of Montenegro and the Faculty of Sciences and Mathematics of University of Montenegro, Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences (KIAM). The chief editors of the journal are prof. Žarkop Pavićević (University of Montenegro) and prof. V.I. Mazhukin (KIAM). The first issue of the magazine was published in May 1993. The history of the organization of the institution and the publication of the journal is traced. The role of the rector of Lomonosov Moscow State University аcademician V.A. Sadovnichy and prof. of the Faculty of Mechanics and Mathematics of Lomonosov Moscow State University V.I. Gavrilov in creating the journal. The development of the journal and the role of mathematicians of the University of Montenegro and mathematicians of the Keldysh Institute of Applied Mathematics of RAS in this process.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"2 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":"117031328","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-2022-53-5
N. Yilmaz
The main object of the present paper is to consider the matrix polynomials for the generalized bivariate Fibonacci and Lucas polynomials. Working with matrix properties for these new matrix polynomials, some identities of the generalized bivariate Fibonacci and Lucas polynomials will be researched. Finally, we build the relationships between the generalized bivariate Fibonacci and Lucas matrix polynomials
{"title":"The generalized bivariate Fibonacci and Lucas matrix polynomials","authors":"N. Yilmaz","doi":"10.20948/mathmontis-2022-53-5","DOIUrl":"https://doi.org/10.20948/mathmontis-2022-53-5","url":null,"abstract":"The main object of the present paper is to consider the matrix polynomials for the generalized bivariate Fibonacci and Lucas polynomials. Working with matrix properties for these new matrix polynomials, some identities of the generalized bivariate Fibonacci and Lucas polynomials will be researched. Finally, we build the relationships between the generalized bivariate Fibonacci and Lucas matrix polynomials","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"75 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":"117233146","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-2019-46-13
V. Mazhukin
The 18th International Scientific Seminar "Mathematical Models and Modeling in LaserPlasma Processes & Advanced Scientific Technologies" (LPPM3-2019) was held from September 29 to October 5, 2019 in the city of Petrovac (Montenegro). Figure 1 shows a photograph of the participants of the LPPM3-2019 workshop on the opening day. The Seminar organizers: M.V. Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, A.M. Prokhorov Institute of General Physics of the Russian Academy of Sciences, University of Montenegro (Podgorica), Forum of Professors and Researchers of Montenegro, Scientific journal "Mathematica Montisnigri". The seminar in 2019 coincided with the 100th anniversary of the birth of an outstanding Soviet and Russian scientist, academician of the Academy of Sciences of the USSR and the Russian Academy of Sciences Alexander Andreevich Samarskii (Fig. 2). Academician A.A. Samarskii is the founder of the Soviet and Russian schools 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 propagandist of science. Scientific activity of academician A.A. Samarskii is firmly connected with the M.V. Keldysh Institute of Applied Mathematics, 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 the potential to preserve the world level of Russian science in the most important field of mathematical modeling for our country. The 18th International Scientific Seminar LPPM3 celebrated the 10th anniversary of its holding in Montenegro. The seminar "Mathematical models and modeling in laser-plasma processes and advanced scientific technologies" (LPPM3) was founded in 2004. The first five years, the organizers of the Seminar were two institutes of the Russian Academy of Sciences:
{"title":"Information analytical review. 18th International Scientific Seminar \"Mathematical Models and Modeling in Laser-Plasma Processes and Advanced Scientific Technologies\" (LPPM3-2019)","authors":"V. Mazhukin","doi":"10.20948/MATHMONTIS-2019-46-13","DOIUrl":"https://doi.org/10.20948/MATHMONTIS-2019-46-13","url":null,"abstract":"The 18th International Scientific Seminar \"Mathematical Models and Modeling in LaserPlasma Processes & Advanced Scientific Technologies\" (LPPM3-2019) was held from September 29 to October 5, 2019 in the city of Petrovac (Montenegro). Figure 1 shows a photograph of the participants of the LPPM3-2019 workshop on the opening day. The Seminar organizers: M.V. Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, A.M. Prokhorov Institute of General Physics of the Russian Academy of Sciences, University of Montenegro (Podgorica), Forum of Professors and Researchers of Montenegro, Scientific journal \"Mathematica Montisnigri\". The seminar in 2019 coincided with the 100th anniversary of the birth of an outstanding Soviet and Russian scientist, academician of the Academy of Sciences of the USSR and the Russian Academy of Sciences Alexander Andreevich Samarskii (Fig. 2). Academician A.A. Samarskii is the founder of the Soviet and Russian schools 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 propagandist of science. Scientific activity of academician A.A. Samarskii is firmly connected with the M.V. Keldysh Institute of Applied Mathematics, 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 the potential to preserve the world level of Russian science in the most important field of mathematical modeling for our country. The 18th International Scientific Seminar LPPM3 celebrated the 10th anniversary of its holding in Montenegro. The seminar \"Mathematical models and modeling in laser-plasma processes and advanced scientific technologies\" (LPPM3) was founded in 2004. The first five years, the organizers of the Seminar were two institutes of the Russian Academy of Sciences:","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"83 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":"115841931","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-2022-54-4
H. Fettouch, S. Hamouda
In this paper, we investigate the [p,q]-order of growth of solutions to certain linear differential equations with entire coefficients and analytic coefficients in the unit disc by using the Nevanlinna theory of meromorphic functions. This work is an improvement and generalization of some previous results by the second author.
{"title":"Double order of growth of solutions to linear differential equations with analytic coefficients","authors":"H. Fettouch, S. Hamouda","doi":"10.20948/mathmontis-2022-54-4","DOIUrl":"https://doi.org/10.20948/mathmontis-2022-54-4","url":null,"abstract":"In this paper, we investigate the [p,q]-order of growth of solutions to certain linear differential equations with entire coefficients and analytic coefficients in the unit disc by using the Nevanlinna theory of meromorphic functions. This work is an improvement and generalization of some previous results by the second author.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"10 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":"126325028","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-2022-54-2
Sasa Vujosevic
A cactus chain is a connected graph in which all blocks are cycles, each cycle has at most two cut-vertices and each cut-vertex is shared by exactly two cycles. In this paper we give exact values of edge PI index and vertex PI index of an arbitrary cactus chain and vertex Szeged index of some special types of cactus chains.
{"title":"Computation of edge Pi index, vertex Pi index and Szeged index of some cactus chains","authors":"Sasa Vujosevic","doi":"10.20948/mathmontis-2022-54-2","DOIUrl":"https://doi.org/10.20948/mathmontis-2022-54-2","url":null,"abstract":"A cactus chain is a connected graph in which all blocks are cycles, each cycle has at most two cut-vertices and each cut-vertex is shared by exactly two cycles. In this paper we give exact values of edge PI index and vertex PI index of an arbitrary cactus chain and vertex Szeged index of some special types of cactus chains.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"34 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":"126528988","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-2019-46-8
E. Strebkova, M. Krivosheina, Ya. V. Mayer
The processes of elastoplastic deformation in single-crystal alloys characterized by cubic symmetry of properties are investigated. Using the heat-resistant single-crystal alloy VZhM8 used to create gas turbine engine blades by directional crystallization as an example, the dependences of deformation processes on the orientation of loading directions with respect to crystallographic axes are shown. Significant anisotropy of mechanical properties, including the presence of negative Poisson’s ratios, in heat-resistant nickel alloys is maintained up to a temperature of 1150 C. Therefore, over the entire range of operating temperatures, the propagation velocities of elastic and plastic waves in single-crystal heat-resistant nickel alloys depend on the propagation direction. On the example of a VZhM8 single-crystal alloy under dynamic loading in a three-dimensional formulation, the differences in the processes of deformation realized in a single crystal under loading along the [011], [111] and [001] axes are investigated.
{"title":"Features of the processes of elastic deformation in cubic crystals","authors":"E. Strebkova, M. Krivosheina, Ya. V. Mayer","doi":"10.20948/mathmontis-2019-46-8","DOIUrl":"https://doi.org/10.20948/mathmontis-2019-46-8","url":null,"abstract":"The processes of elastoplastic deformation in single-crystal alloys characterized by cubic symmetry of properties are investigated. Using the heat-resistant single-crystal alloy VZhM8 used to create gas turbine engine blades by directional crystallization as an example, the dependences of deformation processes on the orientation of loading directions with respect to crystallographic axes are shown. Significant anisotropy of mechanical properties, including the presence of negative Poisson’s ratios, in heat-resistant nickel alloys is maintained up to a temperature of 1150 C. Therefore, over the entire range of operating temperatures, the propagation velocities of elastic and plastic waves in single-crystal heat-resistant nickel alloys depend on the propagation direction. On the example of a VZhM8 single-crystal alloy under dynamic loading in a three-dimensional formulation, the differences in the processes of deformation realized in a single crystal under loading along the [011], [111] and [001] axes are investigated.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"24 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":"126532240","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-2023-56-9
A. Kolesnichenko
In this paper we constructed thermo-hydrodynamics for relativistic fluid (taking into account the second order of deviation from equilibrium for dissipative heat and viscosity flows) on the basis of extended irreversible thermodynamics. EIT formalism, providing adequate mod-eling of systems close to the equilibrium state, goes beyond the local equilibrium hypothesis by expanding the number of basic independent variables (including dissipative flows), as well as by modifying such conceptual concepts as entropy, temperature and pressure. The evolutionary laws for the main nonequilibrium field quantities of the relativistic system are postulated: 4-vector particle flux, 4-vector energy-momentum and 4-vector entropy flux. In order to derive the consti-tutive equations, a nonlocal Gibbs covariance relation and a nonlocal form of the second princi-ple of thermodynamics with a source of entropy due to additional variables-dissipative flows-were obtained. The defining equations of the hyperbolic type, forbidding superluminal velocities, modified by relaxation terms, have been obtained. The construction of relativistic thermodynam-ics is carried out using the hydrodynamic 4-speed defined by Eckart. The constructed relativistic hydrodynamics has its applications in such important fields of science as nuclear physics, astro-physics and cosmology.
{"title":"Toward the construction of relativistic thermo-hydrodynamics of an ideal fluid by the method of extended irreversible thermodynamics","authors":"A. Kolesnichenko","doi":"10.20948/mathmontis-2023-56-9","DOIUrl":"https://doi.org/10.20948/mathmontis-2023-56-9","url":null,"abstract":"In this paper we constructed thermo-hydrodynamics for relativistic fluid (taking into account the second order of deviation from equilibrium for dissipative heat and viscosity flows) on the basis of extended irreversible thermodynamics. EIT formalism, providing adequate mod-eling of systems close to the equilibrium state, goes beyond the local equilibrium hypothesis by expanding the number of basic independent variables (including dissipative flows), as well as by modifying such conceptual concepts as entropy, temperature and pressure. The evolutionary laws for the main nonequilibrium field quantities of the relativistic system are postulated: 4-vector particle flux, 4-vector energy-momentum and 4-vector entropy flux. In order to derive the consti-tutive equations, a nonlocal Gibbs covariance relation and a nonlocal form of the second princi-ple of thermodynamics with a source of entropy due to additional variables-dissipative flows-were obtained. The defining equations of the hyperbolic type, forbidding superluminal velocities, modified by relaxation terms, have been obtained. The construction of relativistic thermodynam-ics is carried out using the hydrodynamic 4-speed defined by Eckart. The constructed relativistic hydrodynamics has its applications in such important fields of science as nuclear physics, astro-physics and cosmology.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"18 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":"132137455","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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