Pub Date : 2022-07-01DOI: 10.56415/basm.y2022.i1.p99
S. Dukhnovsky
In this article, we consider the one--dimensional kinetic system of Carleman equations. The Carleman system is the kinetic Boltzmann equation. This system describes a monatomic rarefied gas consisting of two groups of particles. One particle from the first group, interacting with a particle of the first group, transforms into two particles of the second group. Similarly, two particles of the second group, interacting with themselves, transform into two particles of the first group, respectively. We found traveling wave solutions by using the tanh--function method for nonlinear partial differential system. The results of the work can be useful for mathematical modeling in various fields of science and technology: kinetic theory of gases, gas dynamics, autocatalysis. The obtained exact solutions are new.
{"title":"A self-similar solution and the tanh-function method for the kinetic Carleman system","authors":"S. Dukhnovsky","doi":"10.56415/basm.y2022.i1.p99","DOIUrl":"https://doi.org/10.56415/basm.y2022.i1.p99","url":null,"abstract":"In this article, we consider the one--dimensional kinetic system of Carleman equations. The Carleman system is the kinetic Boltzmann equation. This system describes a monatomic rarefied gas consisting of two groups of particles. One particle from the first group, interacting with a particle of the first group, transforms into two particles of the second group. Similarly, two particles of the second group, interacting with themselves, transform into two particles of the first group, respectively. We found traveling wave solutions by using the tanh--function method for nonlinear partial differential system. The results of the work can be useful for mathematical modeling in various fields of science and technology: kinetic theory of gases, gas dynamics, autocatalysis. The obtained exact solutions are new.","PeriodicalId":102242,"journal":{"name":"Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132740916","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 : 2022-07-01DOI: 10.56415/basm.y2022.i1.p3
O. Pichugina, S. Yakovlev
In this paper, we introduce a concept of the Euclidean combinatorial configuration as a mapping of a set of certain objects into a point of Euclidean space. We classify Euclidean combinatorial configurations sets based on their structure and constraints. The proposed typology forms the basis for studying continuous functional representations of combinatorial configurations. Special classes of functional extensions are introduced, their properties are described, and corresponding examples are given.
{"title":"Continuous Extensions On Euclidean Combinatorial Configurations","authors":"O. Pichugina, S. Yakovlev","doi":"10.56415/basm.y2022.i1.p3","DOIUrl":"https://doi.org/10.56415/basm.y2022.i1.p3","url":null,"abstract":"In this paper, we introduce a concept of the Euclidean combinatorial configuration as a mapping of a set of certain objects into a point of Euclidean space. We classify Euclidean combinatorial configurations sets based on their structure and constraints. The proposed typology forms the basis for studying continuous functional representations of combinatorial configurations. Special classes of functional extensions are introduced, their properties are described, and corresponding examples are given.","PeriodicalId":102242,"journal":{"name":"Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133016374","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 : 2022-07-01DOI: 10.56415/basm.y2022.i1.p22
Anessa Oshah, M. Darus
In the present paper, we study the operator defined by using Ruscheweyh derivative $mathcal{R}^m$ and new generalized multiplier transformation $$ mathcal{D}^{m}_{lambda_{1},lambda_{2},ell,d }f(z) =z+sum_{k=n+1}^{infty}left[dfrac{ell(1+(lambda_{1}+lambda_{2})(k-1))+d}{ell(1+lambda_{2}(k-1))+d}right]^m a_kz^{k}$$ denoted by $mathcal{R}mathcal{D}^{m,alpha}_{lambda_{1},lambda_{2},ell,d }:mathcal{A}_nrightarrow mathcal{A}_n$, $ mathcal{R}mathcal{D}^{m,alpha}_{lambda_{1},lambda_{2},ell,d }f(z)=(1-alpha) mathcal{R}^mf(z)+ alphamathcal{D}^{m}_{lambda_{1},lambda_{2},ell,d }f(z) $, where $ mathcal{A}_{n}=left{fin mathcal{H}(mathbb{U}), f(z) =z+a_{n+1}z^{n+1} +a_{n+2}z^{n+2}+...,zinmathbb{U}right}$ is the class of normalized analytic functions with $mathcal{A}_{1}=mathcal{A}$. We obtain several differential subordinations associated with the operator $mathcal{R}mathcal{D}^{m,alpha}_{lambda_{1},lambda_{2},ell,d }f(z)$. Further, sandwich-type results for this operator are considered.
{"title":"Subordination and superordination for certain analytic functions associated with Ruscheweyh derivative and a new generalised multiplier transformation","authors":"Anessa Oshah, M. Darus","doi":"10.56415/basm.y2022.i1.p22","DOIUrl":"https://doi.org/10.56415/basm.y2022.i1.p22","url":null,"abstract":"In the present paper, we study the operator defined by using Ruscheweyh derivative $mathcal{R}^m$ and new generalized multiplier transformation $$ mathcal{D}^{m}_{lambda_{1},lambda_{2},ell,d }f(z) =z+sum_{k=n+1}^{infty}left[dfrac{ell(1+(lambda_{1}+lambda_{2})(k-1))+d}{ell(1+lambda_{2}(k-1))+d}right]^m a_kz^{k}$$ denoted by $mathcal{R}mathcal{D}^{m,alpha}_{lambda_{1},lambda_{2},ell,d }:mathcal{A}_nrightarrow mathcal{A}_n$, $ mathcal{R}mathcal{D}^{m,alpha}_{lambda_{1},lambda_{2},ell,d }f(z)=(1-alpha) mathcal{R}^mf(z)+ alphamathcal{D}^{m}_{lambda_{1},lambda_{2},ell,d }f(z) $, where $ mathcal{A}_{n}=left{fin mathcal{H}(mathbb{U}), f(z) =z+a_{n+1}z^{n+1} +a_{n+2}z^{n+2}+...,zinmathbb{U}right}$ is the class of normalized analytic functions with $mathcal{A}_{1}=mathcal{A}$. We obtain several differential subordinations associated with the operator $mathcal{R}mathcal{D}^{m,alpha}_{lambda_{1},lambda_{2},ell,d }f(z)$. Further, sandwich-type results for this operator are considered.","PeriodicalId":102242,"journal":{"name":"Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128553979","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 : 2022-07-01DOI: 10.56415/basm.y2022.i1.p66
V. Arnautov, G. Ermakova
When studying unrefinable chains of ring topologies, it is natural to find out how neighborhoods of zero of ring topologies in such chains are related to each other. newline It is proved that for any ideal the restrictions of these topologies to the ideal coincides, or the sum of any neighborhood of zero in the stronger topology with the intersection of the ideal with any neighborhood of zero in the weaker topology is a neighborhood of zero in the weaker topology. We construct a ring and two ring topologies which form an unrefinable chain in the lattice of all ring topologies that a basis of filter of neighborhoods of zero which consists of subgroups of the additive group of the ring and restriction of these topologies to some ideal of the ring is no longer a unrefinable chain. This example shows that the given in [4] conditions under which the properties of a unrefinable chain of ring topologies, are preserved under taking the supremum are essential.
{"title":"Properties of coverings in lattices of ring topologies","authors":"V. Arnautov, G. Ermakova","doi":"10.56415/basm.y2022.i1.p66","DOIUrl":"https://doi.org/10.56415/basm.y2022.i1.p66","url":null,"abstract":"When studying unrefinable chains of ring topologies, it is natural to find out how neighborhoods of zero of ring topologies in such chains are related to each other. newline It is proved that for any ideal the restrictions of these topologies to the ideal coincides, or the sum of any neighborhood of zero in the stronger topology with the intersection of the ideal with any neighborhood of zero in the weaker topology is a neighborhood of zero in the weaker topology. We construct a ring and two ring topologies which form an unrefinable chain in the lattice of all ring topologies that a basis of filter of neighborhoods of zero which consists of subgroups of the additive group of the ring and restriction of these topologies to some ideal of the ring is no longer a unrefinable chain. This example shows that the given in [4] conditions under which the properties of a unrefinable chain of ring topologies, are preserved under taking the supremum are essential.","PeriodicalId":102242,"journal":{"name":"Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica","volume":"315 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122869293","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 : 2022-07-01DOI: 10.56415/basm.y2022.i1.p83
A. Kashu
The preradicals and closure operators in module categories are studied. The concordance is shown between the mappings connecting the classes of preradicals and of closure operators of two module categories $R$-Mod and $S$-Mod in the case of a Morita context $(R,, _{ind R},U_{ind S},, _{ind S}V_{ind R},S)$, using the functors $Hom_{ind R}(U,mbox{-})$ and $Hom_{ind S}(V,mbox{-})$.
{"title":"Euclidean Combinatorial Configurations: Typology, Continuous Extensions and Representations","authors":"A. Kashu","doi":"10.56415/basm.y2022.i1.p83","DOIUrl":"https://doi.org/10.56415/basm.y2022.i1.p83","url":null,"abstract":"The preradicals and closure operators in module categories are studied. The concordance is shown between the mappings connecting the classes of preradicals and of closure operators of two module categories $R$-Mod and $S$-Mod in the case of a Morita context $(R,, _{ind R},U_{ind S},, _{ind S}V_{ind R},S)$, using the functors $Hom_{ind R}(U,mbox{-})$ and $Hom_{ind S}(V,mbox{-})$.","PeriodicalId":102242,"journal":{"name":"Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127954641","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 : 2022-07-01DOI: 10.56415/basm.y2022.i1.p75
D. Lozovanu, Stefan Pickl
The problem of the existence and determining equilibria in pure stationary strategies for a two-player zero-sum average stochastic positional game is considered. We show that for such a game there exists the value and players may achieve the value by applying pure stationary strategies of choosing the actions in their positions. Based on a constructive proof of these results we propose an algorithmic approach for determining the optimal pure stationary strategies of the players.
{"title":"Equilibria in Pure Strategies for a Two-Player Zero-Sum Average Stochastic Positional Game","authors":"D. Lozovanu, Stefan Pickl","doi":"10.56415/basm.y2022.i1.p75","DOIUrl":"https://doi.org/10.56415/basm.y2022.i1.p75","url":null,"abstract":"The problem of the existence and determining equilibria in pure stationary strategies for a two-player zero-sum average stochastic positional game is considered. We show that for such a game there exists the value and players may achieve the value by applying pure stationary strategies of choosing the actions in their positions. Based on a constructive proof of these results we propose an algorithmic approach for determining the optimal pure stationary strategies of the players.","PeriodicalId":102242,"journal":{"name":"Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126241911","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 : 2022-07-01DOI: 10.56415/basm.y2022.i1.p56
A. Moldovyan, D. Moldovyan
A new method for developing signature schemes on finite non-commutative associative algebras is introduced. A signature algorithm is developed on a 4-dimensional algebra defined over the ground field $GF(p)$. The public key element and one of the signature elements represent vectors calculated using exponentiation operations in a hidden commutative group. Decomposition of the algebra into commutative subalgebras is taken into account while designing the algorithm. The method extends the class of algebraic digital signature schemes and opens up the possibility of developing a number of practical post-quantum digital signature algorithms, the main merit of which is comparatively small size of the public key, secret key, and signature.
{"title":"A New Method for Developing Signature Algorithms on Finite Non-commutative Algebras","authors":"A. Moldovyan, D. Moldovyan","doi":"10.56415/basm.y2022.i1.p56","DOIUrl":"https://doi.org/10.56415/basm.y2022.i1.p56","url":null,"abstract":"A new method for developing signature schemes on finite non-commutative associative algebras is introduced. A signature algorithm is developed on a 4-dimensional algebra defined over the ground field $GF(p)$. The public key element and one of the signature elements represent vectors calculated using exponentiation operations in a hidden commutative group. Decomposition of the algebra into commutative subalgebras is taken into account while designing the algorithm. The method extends the class of algebraic digital signature schemes and opens up the possibility of developing a number of practical post-quantum digital signature algorithms, the main merit of which is comparatively small size of the public key, secret key, and signature.","PeriodicalId":102242,"journal":{"name":"Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130239226","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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