Pub Date : 1900-01-01DOI: 10.20948/mathmontis-2022-53-2
B. Benaissa
In this paper, we have shown that in the article entitled “New Riemann-Liouville generalizations for some inequalities of Hardy type” the Theorem 3.3 is false and that a necessary condition on the order α must be in Theorem 3.1 and Theorem 3.2. Additionally, the correct Theorem 3.3 and a new result with negative parameter are given; these results will prove using the Hölder inequality, and reverse Hölder inequality.
{"title":"Discussions on Hardy-type inequalities via Riemann-Liouville fractional integral inequality","authors":"B. Benaissa","doi":"10.20948/mathmontis-2022-53-2","DOIUrl":"https://doi.org/10.20948/mathmontis-2022-53-2","url":null,"abstract":"In this paper, we have shown that in the article entitled “New Riemann-Liouville generalizations for some inequalities of Hardy type” the Theorem 3.3 is false and that a necessary condition on the order α must be in Theorem 3.1 and Theorem 3.2. Additionally, the correct Theorem 3.3 and a new result with negative parameter are given; these results will prove using the Hölder inequality, and reverse Hölder inequality.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"695 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":"116096563","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-2019-44-10
S. Ershov, D. D. Zhdanov, A. G. Voloboy
{"title":"Calculation of luminance of scattering medium by MCRT using multiple integration spheres","authors":"S. Ershov, D. D. Zhdanov, A. G. Voloboy","doi":"10.20948/mathmon-2019-44-10","DOIUrl":"https://doi.org/10.20948/mathmon-2019-44-10","url":null,"abstract":"","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"54 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114042599","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-2019-44-2
M. F. Jalalvand, N. J. Rad, M. Ghorani
An exact 1-step dominating set in a graph G is a subset S of vertices of G such that ( ) 1 N v S for every vertex ( ) v V G . A graph is an exact 1-step domination graph if it contains an exact 1-step dominating set. In this paper, we obtain new upper bounds on the size of exact 1-step domination graphs. We also present an upper bound on the total domination number of an exact 1-step domination tree and characterize trees achieving equality for this bound.
图G中的一个精确的1步支配集是G的顶点的子集S，使得()1 N v S对于每个顶点()v v G。如果一个图包含一个精确1步控制集，那么它就是一个精确1步控制图。本文给出了精确1步控制图大小的新上界。我们还给出了精确1步控制树的总控制数的上界，并描述了在该上界上达到相等的树。
{"title":"Some results on the exact 1-step domination graphs","authors":"M. F. Jalalvand, N. J. Rad, M. Ghorani","doi":"10.20948/MATHMON-2019-44-2","DOIUrl":"https://doi.org/10.20948/MATHMON-2019-44-2","url":null,"abstract":"An exact 1-step dominating set in a graph G is a subset S of vertices of G such that ( ) 1 N v S for every vertex ( ) v V G . A graph is an exact 1-step domination graph if it contains an exact 1-step dominating set. In this paper, we obtain new upper bounds on the size of exact 1-step domination graphs. We also present an upper bound on the total domination number of an exact 1-step domination tree and characterize trees achieving equality for this bound.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"81 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":"129250601","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-2019-46-12
{"title":"On the occasion of the 80th anniversary of the academician of the Russian Academy of Sciences, rector of Moscow State University M.V. Lomonosov V. A Sadovnichy","authors":"","doi":"10.20948/mathmontis-2019-46-12","DOIUrl":"https://doi.org/10.20948/mathmontis-2019-46-12","url":null,"abstract":"","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":"128099107","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-2019-45-5
S. Ershov, D. D. Zhdanov, A. G. Voloboy
We investigate new method for calculation of radiance of scattering medium by bi-directional Monte-Carlo ray tracing with photon maps. Usually photons are collected by an integration spheres at the ends of camera ray segments, or a cylinder along that segments. Meanwhile in our method several integration spheres are distributed at random along the first camera ray segment. The rest segments do not collecting photons. The method optimal for a particular scene is the one which produces the least noise, so one need to be able to estimate it. In this paper an analytic calculation of noise in the general bi-directional Monte-Carlo ray tracing is derived and then applied to the proposed method. Then the analytic estimates of noise can be used to find optimal parameters and/or to choose between single integration sphere, multiple integration spheres and integration cylinders.
{"title":"Estimation of noise in calculation of scattering medium luminance by MCRT","authors":"S. Ershov, D. D. Zhdanov, A. G. Voloboy","doi":"10.20948/mathmontis-2019-45-5","DOIUrl":"https://doi.org/10.20948/mathmontis-2019-45-5","url":null,"abstract":"We investigate new method for calculation of radiance of scattering medium by bi-directional Monte-Carlo ray tracing with photon maps. Usually photons are collected by an integration spheres at the ends of camera ray segments, or a cylinder along that segments. Meanwhile in our method several integration spheres are distributed at random along the first camera ray segment. The rest segments do not collecting photons. The method optimal for a particular scene is the one which produces the least noise, so one need to be able to estimate it. In this paper an analytic calculation of noise in the general bi-directional Monte-Carlo ray tracing is derived and then applied to the proposed method. Then the analytic estimates of noise can be used to find optimal parameters and/or to choose between single integration sphere, multiple integration spheres and integration cylinders.","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":"125486453","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-2022-54-6
A. Kroshilin, V. E. Kroshilin
At present, to describe the two-velocity flow of a multiphase mixture, either a two-fluid model is used; or a drift model using simplified momentum equations that do not take into account inertial forces. The corresponding system of equations for a two-fluid model with the same phase pressure without special, postulated, stabilizing terms is non-hyperbolic. This can lead to difficulties in finding a solution. Accounting for the difference in phase pressure in this model can lead to instability of solutions, which can also complicate the search for a solution. The drift model, which is the subject of this work, does not have this shortcoming. The case of N phase velocities (N > 2), considered in this article, has not been studied so far, although it has a large area of practical applications, for example, a three-velocity flow of a dispersed-film flow in the energy and chemical industries, and others. Hyperbolicity and characteristics are investigated. The characteristic equation of the system, which has N-1 degree, is analyzed. It is proved that there is one eigenvalue between neighboring speeds. If the k phases have the same speed, then the k-1 eigenvalue is equal to that same speed. So, if there are no coinciding phase velocities, or the number of phases with the same speed does not exceed 2, then all eigenvalues are real and different, which means that the system is hyperbolic. If the number of phases with the same speed exceeds 2, then all eigenvalues are also real, but there are multiples among them. An additional study carried out for this case showed that the system is also hyperbolic. An analytical solution of the discontinuity decay problem for a three-velocity flow (N=3) is found. It is assumed that the speed difference between the first and second phases is much greater than the speed difference between the second and third phases. Without this assumption, the solution can be found numerically. For the case of two phase velocities (N = 2), an analytical solution is found that describes the transition from a continuous distribution to a jump. This solution describes the flow for a given dependence of the slip rate on the regime parameter.
{"title":"A drift model N of a velocity mixture and the evolution of a discontinuous solution of a two-velocity drift model","authors":"A. Kroshilin, V. E. Kroshilin","doi":"10.20948/mathmontis-2022-54-6","DOIUrl":"https://doi.org/10.20948/mathmontis-2022-54-6","url":null,"abstract":"At present, to describe the two-velocity flow of a multiphase mixture, either a two-fluid model is used; or a drift model using simplified momentum equations that do not take into account inertial forces. The corresponding system of equations for a two-fluid model with the same phase pressure without special, postulated, stabilizing terms is non-hyperbolic. This can lead to difficulties in finding a solution. Accounting for the difference in phase pressure in this model can lead to instability of solutions, which can also complicate the search for a solution. The drift model, which is the subject of this work, does not have this shortcoming. \u0000The case of N phase velocities (N > 2), considered in this article, has not been studied so far, although it has a large area of practical applications, for example, a three-velocity flow of a dispersed-film flow in the energy and chemical industries, and others. Hyperbolicity and characteristics are investigated. The characteristic equation of the system, which has N-1 degree, is analyzed. It is proved that there is one eigenvalue between neighboring speeds. If the k phases have the same speed, then the k-1 eigenvalue is equal to that same speed. So, if there are no coinciding phase velocities, or the number of phases with the same speed does not exceed 2, then all eigenvalues are real and different, which means that the system is hyperbolic. If the number of phases with the same speed exceeds 2, then all eigenvalues are also real, but there are multiples among them. An additional study carried out for this case showed that the system is also hyperbolic. An analytical solution of the discontinuity decay problem for a three-velocity flow (N=3) is found. It is assumed that the speed difference between the first and second phases is much greater than the speed difference between the second and third phases. Without this assumption, the solution can be found numerically. \u0000For the case of two phase velocities (N = 2), an analytical solution is found that describes the transition from a continuous distribution to a jump. This solution describes the flow for a given dependence of the slip rate on the regime parameter.","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":"121955617","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-2019-45-3
A. Kolesnichenko
{"title":"To development of the non-additive thermodynamics of the quantum systems on basis statistics of Tsallis","authors":"A. Kolesnichenko","doi":"10.20948/mathmontis-2019-45-3","DOIUrl":"https://doi.org/10.20948/mathmontis-2019-45-3","url":null,"abstract":"","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"107 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":"133665262","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-2019-44-4
A. Kolesnichenko
Аннотация. В рамках неэкстенсивной статистической механики Тсаллиса выведены соотношения симметрии Онзагера для кинетических коэффициентов в линейных уравнениях регрессии для чётных и нечётных (при изменении направления скоростей элементарных частиц) малых флуктуаций макроскопических параметров состояния. Эти соотношения отражают на макроскопическом уровне инвариантность микроскопических уравнений движения относительно обращения времени. Также как в случае классической статистики Гиббса предложенный в статье вывод опирается на теорию равновесных флуктуаций динамических переменных, характеризующих систему, и на свойстве инвариантности флуктуаций относительно обращения времени. Кроме этого использован постулат Онзагера, согласно которому затухание равновесных флуктуаций термодинамических параметров состояния описывается линейными дифференциальными уравнениями первого порядка. Традиционные соотношения взаимности для экстенсивных систем получаются из выведенных соотношений в случае, когда параметр деформации q , входящий в параметрический
{"title":"To the substantiation in the framework of nonextensive Tsallis statistics of Onsager's reciprocity relations for kinetic coefficients","authors":"A. Kolesnichenko","doi":"10.20948/mathmon-2019-44-4","DOIUrl":"https://doi.org/10.20948/mathmon-2019-44-4","url":null,"abstract":"Аннотация. В рамках неэкстенсивной статистической механики Тсаллиса выведены соотношения симметрии Онзагера для кинетических коэффициентов в линейных уравнениях регрессии для чётных и нечётных (при изменении направления скоростей элементарных частиц) малых флуктуаций макроскопических параметров состояния. Эти соотношения отражают на макроскопическом уровне инвариантность микроскопических уравнений движения относительно обращения времени. Также как в случае классической статистики Гиббса предложенный в статье вывод опирается на теорию равновесных флуктуаций динамических переменных, характеризующих систему, и на свойстве инвариантности флуктуаций относительно обращения времени. Кроме этого использован постулат Онзагера, согласно которому затухание равновесных флуктуаций термодинамических параметров состояния описывается линейными дифференциальными уравнениями первого порядка. Традиционные соотношения взаимности для экстенсивных систем получаются из выведенных соотношений в случае, когда параметр деформации q , входящий в параметрический","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":"115082533","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-2022-55-5
Meriem Moulay, M. Mihoubi
In this paper, using a combinatorial approach, we give a combinatorial interpretation of sequences of numbers related to the partial Bell polynomials. Some recurrence relations for these polynomials may be deduced.
本文利用组合方法，给出了与部分贝尔多项式有关的数列的组合解释。可以推导出这些多项式的一些递推关系。
{"title":"Some combinatorial interpretation related to partial Bell polynomials","authors":"Meriem Moulay, M. Mihoubi","doi":"10.20948/mathmontis-2022-55-5","DOIUrl":"https://doi.org/10.20948/mathmontis-2022-55-5","url":null,"abstract":"In this paper, using a combinatorial approach, we give a combinatorial interpretation of sequences of numbers related to the partial Bell polynomials. Some recurrence relations for these polynomials may be deduced.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"22 5 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":"126119185","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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