Pub Date : 2023-03-17DOI: 10.20948/mathmontis-2023-56-3
P. V. Dovbush
In this paper, as an application of Zalcman's lemma in ℂn, we give a sufficient condition for normality of holomorphic functions of several complex variables, which generalizes previous known one-dimensional criterion of A.J. Lohwater and Ch. Pommerenke.
{"title":"Generalization of Lohwater-Pommerenke's theorem","authors":"P. V. Dovbush","doi":"10.20948/mathmontis-2023-56-3","DOIUrl":"https://doi.org/10.20948/mathmontis-2023-56-3","url":null,"abstract":"In this paper, as an application of Zalcman's lemma in ℂn, we give a sufficient condition for normality of holomorphic functions of several complex variables, which generalizes previous known one-dimensional criterion of A.J. Lohwater and Ch. Pommerenke.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114209233","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 : 2023-01-04DOI: 10.20948/mathmontis-2022-55-1
Khristo N. Boyadzhiev
We present a summation rule using Mellin’s transform to give short proofs of some important classical relations between special functions and Bernoulli and Euler polynomials. For example, the values of the Hurwitz zeta function at the negative integers are expressed in terms of Bernoulli polynomials. We also show identities involving exponential and Hermite polynomials.
{"title":"Several classical identities via Mellin’s transform","authors":"Khristo N. Boyadzhiev","doi":"10.20948/mathmontis-2022-55-1","DOIUrl":"https://doi.org/10.20948/mathmontis-2022-55-1","url":null,"abstract":"We present a summation rule using Mellin’s transform to give short proofs of some important classical relations between special functions and Bernoulli and Euler polynomials. For example, the values of the Hurwitz zeta function at the negative integers are expressed in terms of Bernoulli polynomials. We also show identities involving exponential and Hermite polynomials.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123846436","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}
Bidirectional Monte Carlo ray tracing with photon maps is a powerful method for rendering images. But stochastic noise is inherent in it. However, this noise can be reduced using the multiple importance sampling technique which combines the weighted results of different strategies. The optimal weights allow you to minimize the noise functional and, thus, render the image of the best quality. In this paper, we determine the optimal weights using a system of integral equations derived and solved by us. This system has several qualitative differences from the case of mixing two strategies investigated previously. But further increasing the number of strategies does not change the qualitative features of the system. The system can be solved in a closed form, i.e. as an algebraic formula that includes several integrals of known functions. They can be calculated during ray tracing. Therefore, application of the optimal weights in Monte Carlo ray tracing results in faster rendering of high quality realistic images.
{"title":"Optimal MIS weights in case of mixing 3 strategies for bidirectional MCRT with photon maps","authors":"Sergey Valentinovich Ershov, Mikhail Sergeevich Kopylov, Sergey Georgievich Pozdnyakov, Alexey Gennadievich Voloboy","doi":"10.20948/mathmontis-2023-57-5","DOIUrl":"https://doi.org/10.20948/mathmontis-2023-57-5","url":null,"abstract":"Bidirectional Monte Carlo ray tracing with photon maps is a powerful method for rendering images. But stochastic noise is inherent in it. However, this noise can be reduced using the multiple importance sampling technique which combines the weighted results of different strategies. The optimal weights allow you to minimize the noise functional and, thus, render the image of the best quality. In this paper, we determine the optimal weights using a system of integral equations derived and solved by us. This system has several qualitative differences from the case of mixing two strategies investigated previously. But further increasing the number of strategies does not change the qualitative features of the system. The system can be solved in a closed form, i.e. as an algebraic formula that includes several integrals of known functions. They can be calculated during ray tracing. Therefore, application of the optimal weights in Monte Carlo ray tracing results in faster rendering of high quality realistic images.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136047428","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 : 2023-01-01DOI: 10.20948/mathmontis-2023-57-4
Bahar Kuloğlu, Engin Özkan
In this article, we have developed a new method for codingdecoding the Jacobsthal and Jacobsthal-Lucas sequences via matrix representations. In this method, codingdecoding is done by transforming the messages into a square matrix. This process aims to not only increase the reliability of information security technology but also to provide the ability to verify information at a high rate.
{"title":"Applications of Jacobsthal and Jacobsthal-Lucas numbers in coding theory","authors":"Bahar Kuloğlu, Engin Özkan","doi":"10.20948/mathmontis-2023-57-4","DOIUrl":"https://doi.org/10.20948/mathmontis-2023-57-4","url":null,"abstract":"In this article, we have developed a new method for codingdecoding the Jacobsthal and Jacobsthal-Lucas sequences via matrix representations. In this method, codingdecoding is done by transforming the messages into a square matrix. This process aims to not only increase the reliability of information security technology but also to provide the ability to verify information at a high rate.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136048999","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 : 2023-01-01DOI: 10.20948/mathmontis-2023-57-6
Vladimir Ivanovich Mazhukin, Mikhail Mikhailovich Demin, Aleksandr Viktorovich Shapranov, Olga Nikolaevna Koroleva, Alexander Vladimirovich Mazhukin
The article is devoted to the problem of constructing equations of state with deep entry into metastable regions (overheating/undercooling) of the molten and crystalline phases of aluminum. For mathematical modeling of hydrodynamic processes, the knowledge of the equations of state is the source of the most important information about the dependence of the thermodynamic properties of a substance on the microscopic internal structure. Moreover, for modeling, the equations of state are required in the form of smooth analytical dependencies with the characteristics of metastable states. Molecular dynamics simulation was used as the main tool for obtaining the equations of state. Based on the results of molecular dynamics calculations, the work obtained mutually consistent single-phase equations of state for molten and crystalline aluminum in tabular form. For tabular values, the approximating analytical dependences of low degrees were obtained. The results are presented in the form of tables and graphs. The thermodynamic consistency of the resulting equations is investigated. The simulation results of this work are compared with the equations of state for aluminum obtained by other authors.
{"title":"Equations of state of the molten and crystalline phases of aluminum with deep entry into metastable regions","authors":"Vladimir Ivanovich Mazhukin, Mikhail Mikhailovich Demin, Aleksandr Viktorovich Shapranov, Olga Nikolaevna Koroleva, Alexander Vladimirovich Mazhukin","doi":"10.20948/mathmontis-2023-57-6","DOIUrl":"https://doi.org/10.20948/mathmontis-2023-57-6","url":null,"abstract":"The article is devoted to the problem of constructing equations of state with deep entry into metastable regions (overheating/undercooling) of the molten and crystalline phases of aluminum. For mathematical modeling of hydrodynamic processes, the knowledge of the equations of state is the source of the most important information about the dependence of the thermodynamic properties of a substance on the microscopic internal structure. Moreover, for modeling, the equations of state are required in the form of smooth analytical dependencies with the characteristics of metastable states. Molecular dynamics simulation was used as the main tool for obtaining the equations of state. Based on the results of molecular dynamics calculations, the work obtained mutually consistent single-phase equations of state for molten and crystalline aluminum in tabular form. For tabular values, the approximating analytical dependences of low degrees were obtained. The results are presented in the form of tables and graphs. The thermodynamic consistency of the resulting equations is investigated. The simulation results of this work are compared with the equations of state for aluminum obtained by other authors.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136047430","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 : 2023-01-01DOI: 10.20948/mathmontis-2023-57-7
Alexander Evgen`evich Kroshilin, Vladimir Evgen`evich Kroshilin
During the oil well usage its flow rate inevitably lessens. As a result the oil production enterprises must solve the most important problem of the oil extraction intensification. When solving filtration problems (there is a great set of problems; here we will deal with one of them including physical processes, difficulties and problem setting-up) ordinarily use well-known problems. However, in many cases, for example, when describing thermogas-chemica modification (TGCM) there capacity is insufficient. For example, one needs describing of more than two phases, taking into account chemical reactions and so on. We produced a program which clears this trouble. This program can model main features of the TGCM case: many-phase and non-isothermal process, non-one-dimensional flow. As a result we can better tune calculation programs for specific deposits by taking into consideration of geologic peculiarities and near-well zone defects occurred as a result of previous usage.
{"title":"Numerical model of oil, water and gas flow in oil pools","authors":"Alexander Evgen`evich Kroshilin, Vladimir Evgen`evich Kroshilin","doi":"10.20948/mathmontis-2023-57-7","DOIUrl":"https://doi.org/10.20948/mathmontis-2023-57-7","url":null,"abstract":"During the oil well usage its flow rate inevitably lessens. As a result the oil production enterprises must solve the most important problem of the oil extraction intensification. When solving filtration problems (there is a great set of problems; here we will deal with one of them including physical processes, difficulties and problem setting-up) ordinarily use well-known problems. However, in many cases, for example, when describing thermogas-chemica modification (TGCM) there capacity is insufficient. For example, one needs describing of more than two phases, taking into account chemical reactions and so on. We produced a program which clears this trouble. This program can model main features of the TGCM case: many-phase and non-isothermal process, non-one-dimensional flow. As a result we can better tune calculation programs for specific deposits by taking into consideration of geologic peculiarities and near-well zone defects occurred as a result of previous usage.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136048989","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 : 2023-01-01DOI: 10.20948/mathmontis-2023-57-3
El Hadi Ait Dads, Benaouda Hedia
This paper studies the existence of solutions for nonlocal fractional differential equations on the half-line in a special Banach space. The main result is based on a fixed point theorem combining with a suitable measure of non-compactness for condensing operator, an example is given to illustrate our approach.
{"title":"Fractional differential equations with nonlocal conditions on weight space","authors":"El Hadi Ait Dads, Benaouda Hedia","doi":"10.20948/mathmontis-2023-57-3","DOIUrl":"https://doi.org/10.20948/mathmontis-2023-57-3","url":null,"abstract":"This paper studies the existence of solutions for nonlocal fractional differential equations on the half-line in a special Banach space. The main result is based on a fixed point theorem combining with a suitable measure of non-compactness for condensing operator, an example is given to illustrate our approach.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136049023","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 : 2023-01-01DOI: 10.20948/mathmontis-2023-57-2
Feroudja Aumorassi, Mouloud Goubi, Farida Slimi
In this paper we are interested by the inversion of any stationary and causal autoregressive process of order p, we give some recurrence relations satisfied by the coefficients of the infinite moving average process representation in the sense of Wold decomposition. We compute explicit formula of these coefficients and the corresponding auto-covariance function and we give the minimal value of q in mean square approximation of this autoregressive process with a moving average process of order q-1. The obtained results are explained by examples from the literature and our choice.
{"title":"On the inversion of an autoregressive process of finite order","authors":"Feroudja Aumorassi, Mouloud Goubi, Farida Slimi","doi":"10.20948/mathmontis-2023-57-2","DOIUrl":"https://doi.org/10.20948/mathmontis-2023-57-2","url":null,"abstract":"In this paper we are interested by the inversion of any stationary and causal autoregressive process of order p, we give some recurrence relations satisfied by the coefficients of the infinite moving average process representation in the sense of Wold decomposition. We compute explicit formula of these coefficients and the corresponding auto-covariance function and we give the minimal value of q in mean square approximation of this autoregressive process with a moving average process of order q-1. The obtained results are explained by examples from the literature and our choice.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136049014","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 : 2023-01-01DOI: 10.20948/mathmontis-2023-57-1
Ali Khalouta
In this paper, we suggest a new integral transform called the Khalouta transform, which is a generalization of many integral transforms having exponential type kernel. We discuss certain results on the inverse and the existence of this integral transform. We present useful properties of the Khalouta transform and their applications to solve differential equations. Furthermore, we prove the duality between the Khalouta transform and other transforms such as the Laplace-Carson transform, Sumudu transform, ZZ transform, ZMA transform, Elzaki transform, Aboodh transform, Natural transform and Shehu transform. Finally, we ensure the efficiency and accuracy of the Khalouta transform by solving various examples of both ordinary, integro and partial differential equations.
{"title":"A new exponential type Kernel integral transform: Khalouta transform and its applications","authors":"Ali Khalouta","doi":"10.20948/mathmontis-2023-57-1","DOIUrl":"https://doi.org/10.20948/mathmontis-2023-57-1","url":null,"abstract":"In this paper, we suggest a new integral transform called the Khalouta transform, which is a generalization of many integral transforms having exponential type kernel. We discuss certain results on the inverse and the existence of this integral transform. We present useful properties of the Khalouta transform and their applications to solve differential equations. Furthermore, we prove the duality between the Khalouta transform and other transforms such as the Laplace-Carson transform, Sumudu transform, ZZ transform, ZMA transform, Elzaki transform, Aboodh transform, Natural transform and Shehu transform. Finally, we ensure the efficiency and accuracy of the Khalouta transform by solving various examples of both ordinary, integro and partial differential equations.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"2020 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136049024","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 : 2022-12-01DOI: 10.20948/mathmontis-2022-54-1
K. Boyadzhiev
We prove a short general theorem which immediately implies some classical results of Hasse, Guillera and Sondow, Paolo Amore, and also Alzer and Richards. At the end we obtain a new representation for Euler’s constant γ. The theorem transforms every Taylor series into a series depending on a parameter.
{"title":"Representation of functions in series with parameter","authors":"K. Boyadzhiev","doi":"10.20948/mathmontis-2022-54-1","DOIUrl":"https://doi.org/10.20948/mathmontis-2022-54-1","url":null,"abstract":"We prove a short general theorem which immediately implies some classical results of Hasse, Guillera and Sondow, Paolo Amore, and also Alzer and Richards. At the end we obtain a new representation for Euler’s constant γ. The theorem transforms every Taylor series into a series depending on a parameter.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"246 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116143462","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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