Pub Date : 2021-08-01DOI: 10.20948/mathmontis-2021-51-5
D. Khan, A. Rehman, Saleem Iqbal, Ali Ahmed, Sana Jafar, M. Baloch
In this manuscript we recommend a new description of the modified Fourier transform for a function which is absolutely integrable, having finite number of maxima and minima and finite number of discontinuities which further takes the form of simple Fourier transform for substituting α = e where α > 0 and α ≠ 1. Moreover we prove various results of the modified Fourier transform and also we show that the set that consists of whole modified Fourier transformable functions under the convolution operation is a commutative semi group as well as form an abelian group under the operation of addition
{"title":"Modified Fourier transform and its properties","authors":"D. Khan, A. Rehman, Saleem Iqbal, Ali Ahmed, Sana Jafar, M. Baloch","doi":"10.20948/mathmontis-2021-51-5","DOIUrl":"https://doi.org/10.20948/mathmontis-2021-51-5","url":null,"abstract":"In this manuscript we recommend a new description of the modified Fourier transform for a function which is absolutely integrable, having finite number of maxima and minima and finite number of discontinuities which further takes the form of simple Fourier transform for substituting α = e where α > 0 and α ≠ 1. Moreover we prove various results of the modified Fourier transform and also we show that the set that consists of whole modified Fourier transformable functions under the convolution operation is a commutative semi group as well as form an abelian group under the operation of addition","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115012374","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 : 2021-08-01DOI: 10.20948/mathmontis-2021-51-7
V. S. Zakharov, M. Zhukovskiy, S. Zakharov, M. Markov
Data on processes of electron scattering on ions and neutral atoms are required in fundamental studies and in applied research in such fields as astro- and laser physics, low density plasma simulations, kinetic modeling etc. Experimental and computational data on elastic and inelastic electron scattering in a wide range of electron energies is available mostly for the electron interaction with neutral atoms, but are very limited for the scattering on ions, notably for elastic processes. In present work the calculational approaches for the cross-section computation of electron elastic and inelastic scattering on neutral atoms and ions are considered. The atomic and ion properties obtained in quantum-statistical Hartree-Fock-Slater model are used in the direct computation of electron elastic scattering and ionization cross-sections by a partial waves method, semiclassical and distorted-wave approximations. Calculated cross-sections for elastic scattering on nitrogen and oxygen atoms and ions, and electron ionisation cross-sections are compared with the available experimental data and widely used approximations and propose consistent results. Considering applicability of Hartree-Fock-Slater model in wide scope of temperatures and densities, such approach to the cross-section calculation can be used in a broad range of energies and ion charges.
{"title":"Electron scattering cross-sections for particle transport modeling in a weakly ionized air plasma","authors":"V. S. Zakharov, M. Zhukovskiy, S. Zakharov, M. Markov","doi":"10.20948/mathmontis-2021-51-7","DOIUrl":"https://doi.org/10.20948/mathmontis-2021-51-7","url":null,"abstract":"Data on processes of electron scattering on ions and neutral atoms are required in fundamental studies and in applied research in such fields as astro- and laser physics, low density plasma simulations, kinetic modeling etc. Experimental and computational data on elastic and inelastic electron scattering in a wide range of electron energies is available mostly for the electron interaction with neutral atoms, but are very limited for the scattering on ions, notably for elastic processes. In present work the calculational approaches for the cross-section computation of electron elastic and inelastic scattering on neutral atoms and ions are considered. The atomic and ion properties obtained in quantum-statistical Hartree-Fock-Slater model are used in the direct computation of electron elastic scattering and ionization cross-sections by a partial waves method, semiclassical and distorted-wave approximations. Calculated cross-sections for elastic scattering on nitrogen and oxygen atoms and ions, and electron ionisation cross-sections are compared with the available experimental data and widely used approximations and propose consistent results. Considering applicability of Hartree-Fock-Slater model in wide scope of temperatures and densities, such approach to the cross-section calculation can be used in a broad range of energies and ion charges.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130675432","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 : 2021-08-01DOI: 10.20948/mathmontis-2021-51-6
A. Kolesnichenko
A logical scheme for constructing thermodynamics of anomalous stochastic systems based on the nonextensive two-parameter (κ, ς) -entropy of Sharma–Taneja–Mittal (SHTM) is considered. Thermodynamics within the framework (2 - q) -statistics of Tsallis was constructed, which belongs to the STM family of statistics. The approach of linear nonequilibrium thermodynamics to the construction of a family of nonlinear equations of Fokker−Planck−Kolmogorov (FPK), is used, correlated with the entropy of the STM, in which the stationary solution of the diffusion equation coincides with the corresponding generalized Gibbs distribution obtained from the extremality (κ, ς) - entropy condition of a non-additive stochastic system. Taking into account the convexity property of the Bregman divergence, it was shown that the principle of maximum equilibrium entropy is valid for (κ, ς) - systems, and also was proved the H - theorem determining the direction of the time evolution of the non-equilibrium state of the system. This result is extended also to non-equilibrium systems that evolve to a stationary state in accordance with the nonlinear FPK equation. The method of the ansatz- approach for solving non-stationary FPK equations is considered, which allows us to find the time dependence of the probability density distribution function for non-equilibrium anomalous systems. Received diffusive equations FPК can be used, in particular, at the analysis of diffusion of every possible epidemics and pandemics. The obtained diffusion equations of the FPK can be used, in particular, in the analysis of the spread of various epidemics and pandemics.
{"title":"On the construction of a family of anomalous-diffusion Fokker–Planck−Kolmogorov’s equations based on the Sharma–Taneja–Mittal entropy functional","authors":"A. Kolesnichenko","doi":"10.20948/mathmontis-2021-51-6","DOIUrl":"https://doi.org/10.20948/mathmontis-2021-51-6","url":null,"abstract":"A logical scheme for constructing thermodynamics of anomalous stochastic systems based on the nonextensive two-parameter (κ, ς) -entropy of Sharma–Taneja–Mittal (SHTM) is considered. Thermodynamics within the framework (2 - q) -statistics of Tsallis was constructed, which belongs to the STM family of statistics. The approach of linear nonequilibrium thermodynamics to the construction of a family of nonlinear equations of Fokker−Planck−Kolmogorov (FPK), is used, correlated with the entropy of the STM, in which the stationary solution of the diffusion equation coincides with the corresponding generalized Gibbs distribution obtained from the extremality (κ, ς) - entropy condition of a non-additive stochastic system. Taking into account the convexity property of the Bregman divergence, it was shown that the principle of maximum equilibrium entropy is valid for (κ, ς) - systems, and also was proved the H - theorem determining the direction of the time evolution of the non-equilibrium state of the system. This result is extended also to non-equilibrium systems that evolve to a stationary state in accordance with the nonlinear FPK equation. The method of the ansatz- approach for solving non-stationary FPK equations is considered, which allows us to find the time dependence of the probability density distribution function for non-equilibrium anomalous systems. Received diffusive equations FPК can be used, in particular, at the analysis of diffusion of every possible epidemics and pandemics. The obtained diffusion equations of the FPK can be used, in particular, in the analysis of the spread of various epidemics and pandemics.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"48 16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123559411","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 : 2021-08-01DOI: 10.20948/mathmontis-2021-51-2
M. Pikula, D. Nedić, Ismet Kalco, Ljiljanka Kvesić
This paper is dedicated to solving of the direct and inverse spectral problem for Sturm Liouville type of operator with constant delay from 𝜋/2 to 𝜋, non-zero initial function and Robin’s boundary conditions. It has been proved that two series of eigenvalues unambiguously define the following parameters: delay, coefficients of delay within boundary conditions, the potential on the segment from the point of delay to the right-hand side of the distance and the product of the starting function and potential from the left end of the distance to the delay point.
{"title":"Inverse spectral boundary problem Sturm Liouville type with constant delay and non-zero initial function","authors":"M. Pikula, D. Nedić, Ismet Kalco, Ljiljanka Kvesić","doi":"10.20948/mathmontis-2021-51-2","DOIUrl":"https://doi.org/10.20948/mathmontis-2021-51-2","url":null,"abstract":"This paper is dedicated to solving of the direct and inverse spectral problem for Sturm Liouville type of operator with constant delay from 𝜋/2 to 𝜋, non-zero initial function and Robin’s boundary conditions. It has been proved that two series of eigenvalues unambiguously define the following parameters: delay, coefficients of delay within boundary conditions, the potential on the segment from the point of delay to the right-hand side of the distance and the product of the starting function and potential from the left end of the distance to the delay point.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"91 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124661151","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 : 2021-08-01DOI: 10.20948/mathmontis-2021-51-3
Yesım Akuzum, O. Deveci
In the present investigation, we define the arrowhead-Jacobsthal sequence by the arrowhead matrix defined with the help of the characteristic polynomial of the generalized order-k Jacobsthal numbers. Next, we derive various properties of the arrowhead-Jacobsthal sequence by using its generating matrix. Also, we give connections between Fibonacci, Jacobsthal, Pell and arrowhead-Jacobsthal numbers.
{"title":"The arrowhead-Jacobsthal sequence","authors":"Yesım Akuzum, O. Deveci","doi":"10.20948/mathmontis-2021-51-3","DOIUrl":"https://doi.org/10.20948/mathmontis-2021-51-3","url":null,"abstract":"In the present investigation, we define the arrowhead-Jacobsthal sequence by the arrowhead matrix defined with the help of the characteristic polynomial of the generalized order-k Jacobsthal numbers. Next, we derive various properties of the arrowhead-Jacobsthal sequence by using its generating matrix. Also, we give connections between Fibonacci, Jacobsthal, Pell and arrowhead-Jacobsthal numbers.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"74 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133719314","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 : 2021-08-01DOI: 10.20948/mathmontis-2021-51-1
Ž. Pavićević, Valerian Ivanovich Gavrilov
In this paper we formulate classical theorems Plesner and Meyer on the boundary behavior of meromorphic functions and their refinement and strengthening - Gavrilov's and Kanatnikov's theorems. An application of these theorems to classes of meromorphic functions with integrable spherical derivative and annular holomorphic functions is presented. Collingwood's theorem on boundary singularities of the Tsuji function as well as Kanatnikov's theorems are formulated. Kanatnikov's theorems strengthen and generalize Collingwood's theorem to broader classes of meromorphic functions with summable spherical derivatives. Special attention is paid to the boundary properties of annular holomorphic functions. The behavior of annular holomorphic functions on the boundary of the unit circle is considered. It is shown that Gavrilov's P-sequences play an important role in the study of the boundary properties of holomorphic and meromorphic functions.
{"title":"Boundary characteristics of meromorphic functions with summable spherical derivation and annular functions. Consideration","authors":"Ž. Pavićević, Valerian Ivanovich Gavrilov","doi":"10.20948/mathmontis-2021-51-1","DOIUrl":"https://doi.org/10.20948/mathmontis-2021-51-1","url":null,"abstract":"In this paper we formulate classical theorems Plesner and Meyer on the boundary behavior of meromorphic functions and their refinement and strengthening - Gavrilov's and Kanatnikov's theorems. An application of these theorems to classes of meromorphic functions with integrable spherical derivative and annular holomorphic functions is presented. Collingwood's theorem on boundary singularities of the Tsuji function as well as Kanatnikov's theorems are formulated. Kanatnikov's theorems strengthen and generalize Collingwood's theorem to broader classes of meromorphic functions with summable spherical derivatives. Special attention is paid to the boundary properties of annular holomorphic functions. The behavior of annular holomorphic functions on the boundary of the unit circle is considered. It is shown that Gavrilov's P-sequences play an important role in the study of the boundary properties of holomorphic and meromorphic functions.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122034167","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 : 2021-08-01DOI: 10.20948/mathmontis-2021-51-4
Sadaf Saleem, F. Hussain, B. Davvaz, M. T. Rahim
In this paper, we investigate some properties of homomorphisms and deductive systems of generalized BE-semigroups. In particular, we show that through every deductive system, we may get factor generalized BE-semigroup.
{"title":"Factor generalized BE-semigroups through deductive systems","authors":"Sadaf Saleem, F. Hussain, B. Davvaz, M. T. Rahim","doi":"10.20948/mathmontis-2021-51-4","DOIUrl":"https://doi.org/10.20948/mathmontis-2021-51-4","url":null,"abstract":"In this paper, we investigate some properties of homomorphisms and deductive systems of generalized BE-semigroups. In particular, we show that through every deductive system, we may get factor generalized BE-semigroup.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134021948","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 : 2018-10-24DOI: 10.20948/mathmon-2019-46-2
M. Kostic
In the paper under review, we analyze the invariance of Doss almost periodicity and Besicovitch-Doss almost periodicity under the actions of convolution products. We thus continue our recent research studies cite{fedorov-novi} and cite{NSJOM-besik} by investigating the case in which the solution operator family $(R(t))_{t>0}$ under our consideration has special growth rates at zero and infinity. In contrast to cite{NSJOM-besik}, the results obtained in this paper can be incorporated in the qualitative analysis of solutions to abstract (degenerate) inhomogeneous fractional differential equations in Banach spaces.
{"title":"Doss almost periodic functions, Besicovitch-Doss almost periodic functions and convolution products","authors":"M. Kostic","doi":"10.20948/mathmon-2019-46-2","DOIUrl":"https://doi.org/10.20948/mathmon-2019-46-2","url":null,"abstract":"In the paper under review, we analyze the invariance of Doss almost periodicity and Besicovitch-Doss almost periodicity under the actions of convolution products. We thus continue our recent research studies cite{fedorov-novi} and cite{NSJOM-besik} by investigating the case in which the solution operator family $(R(t))_{t>0}$ under our consideration has special growth rates at zero and infinity. In contrast to cite{NSJOM-besik}, the results obtained in this paper can be incorporated in the qualitative analysis of solutions to abstract (degenerate) inhomogeneous fractional differential equations in Banach spaces.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128524196","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 : 2018-06-05DOI: 10.20948/mathmontis-2020-47-1
A. Sahami, R. Lotfikar, Ahmad Soltanmohamadi
In this paper, we study the notion of $phi$-biflatness, $phi$-biprojectivity, approximate biprojectivity and Johnson pseudo-contractibility for a new class of Banach algebras. Using this class of Banach algebras we give some examples which are approximately biprojective. Also some Banach algebras are given among matrix algebras which are never Johnson pseudo-contractible.
{"title":"On (approximate) homological notions of certain Banach algebras","authors":"A. Sahami, R. Lotfikar, Ahmad Soltanmohamadi","doi":"10.20948/mathmontis-2020-47-1","DOIUrl":"https://doi.org/10.20948/mathmontis-2020-47-1","url":null,"abstract":"In this paper, we study the notion of $phi$-biflatness, $phi$-biprojectivity, approximate biprojectivity and Johnson pseudo-contractibility for a new class of Banach algebras. Using this class of Banach algebras we give some examples which are approximately biprojective. Also some Banach algebras are given among matrix algebras which are never Johnson pseudo-contractible.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133478803","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-2019-45-1
N. Mihaljevic
{"title":"The existence and the uniqueness of solutions of integral equations for the capacity q and functions of late α","authors":"N. Mihaljevic","doi":"10.20948/mathmontis-2019-45-1","DOIUrl":"https://doi.org/10.20948/mathmontis-2019-45-1","url":null,"abstract":"","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"32 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":"124801235","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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