The concept of quasi-ordered residuated system was introduced in 2018 by Bonzio and Chajda. The author introduced and analyzed the concept of filters as well as some types of filters in such an algebraic system. Additionally, the author also dealt with a strong quasi-ordered residuated system in which he determined prime and irreducible filters. In this paper, the author introduce three types of prime filters in a strong quasi-ordered residuated system and analyze their interconnections.
{"title":"Three types of prime filters in strong quasi-ordered residuated system","authors":"D. Romano","doi":"10.52846/ami.v49i1.1522","DOIUrl":"https://doi.org/10.52846/ami.v49i1.1522","url":null,"abstract":"The concept of quasi-ordered residuated system was introduced in 2018 by Bonzio and Chajda. The author introduced and analyzed the concept of filters as well as some types of filters in such an algebraic system. Additionally, the author also dealt with a strong quasi-ordered residuated system in which he determined prime and irreducible filters. In this paper, the author introduce three types of prime filters in a strong quasi-ordered residuated system and analyze their interconnections.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":"52 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83165709","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}
In this paper, we introduce and investigate the notion of lacunary statistical convergence of sequences in gradual normed linear spaces. We study some of its basic properties and some inclusion relations. In the end, we introduce the notion of lacunary statistical Cauchy sequences and prove that it is equivalent to the notion of lacunary statistical convergence.
{"title":"On lacunary statistical convergence of sequences in gradual normed linear spaces","authors":"C. Choudhury, S. Debnath","doi":"10.52846/ami.v49i1.1518","DOIUrl":"https://doi.org/10.52846/ami.v49i1.1518","url":null,"abstract":"In this paper, we introduce and investigate the notion of lacunary statistical convergence of sequences in gradual normed linear spaces. We study some of its basic properties and some inclusion relations. In the end, we introduce the notion of lacunary statistical Cauchy sequences and prove that it is equivalent to the notion of lacunary statistical convergence.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":"16 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84702210","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}
The aim of this paper is to prove the existence result of viable solutions for the differential inclusion x ̇(t)ϵF(t,T(t)x) where F is a set-valued map with closed graph. We consider the case when the constraint is moving.
本文的目的是证明F为闭图集值映射的微分包含x (t)ϵF(t, t (t)x)可行解的存在性结果。我们考虑约束移动的情况。
{"title":"Viability for functional differential inclusions without convexity","authors":"M. Aitalioubrahim","doi":"10.52846/ami.v49i1.1516","DOIUrl":"https://doi.org/10.52846/ami.v49i1.1516","url":null,"abstract":"The aim of this paper is to prove the existence result of viable solutions for the differential inclusion x ̇(t)ϵF(t,T(t)x) where F is a set-valued map with closed graph. We consider the case when the constraint is moving.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":"5 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88516854","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}
In this paper, we propose a new algorithm to restore blurred and noisy images based on the total variation regularization, where the discrete associated Euler-Lagrange problem is solved by exploiting the structure of the matrices and transforming the initial problem to a generalized Sylvester linear matrix equation by using a special Kronecker product approximation. Afterwards, global Krylov subspace methods are used to solve the linear matrix equation. Numerical experiments are given to illustrate the effectiveness of the proposed method.
{"title":"Kronecker product approximation for the total variation regularization in image restoration","authors":"A. Bentbib, A. Bouhamidi, K. Kreit","doi":"10.52846/ami.v49i1.1511","DOIUrl":"https://doi.org/10.52846/ami.v49i1.1511","url":null,"abstract":"In this paper, we propose a new algorithm to restore blurred and noisy images based on the total variation regularization, where the discrete associated Euler-Lagrange problem is solved by exploiting the structure of the matrices and transforming the initial problem to a generalized Sylvester linear matrix equation by using a special Kronecker product approximation. Afterwards, global Krylov subspace methods are used to solve the linear matrix equation. Numerical experiments are given to illustrate the effectiveness of the proposed method.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":"9 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89777572","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}
The concept of statistical convergence plays a very prominent role in the study of sequence spaces. In this treatise, we extend the research on different types of statistical convergence viz., statistical convergence in mean, in measure, in distribution, in almost surely and with respect to uniformly almost surely of complex uncertain triple sequences in a given uncertainty space. We emphasize to focus on characterizing statistical convergence of complex uncertain triple sequence in some extent. Moreover, we initiate the notion of complex uncertain Cauchy triple sequence and establish the interconnection of it with a statistically convergent triple sequence.
{"title":"Some results on statistically convergent triple sequences in an uncertainty space","authors":"Birojit Das, B. Tripathy, P. Debnath","doi":"10.52846/ami.v49i1.1520","DOIUrl":"https://doi.org/10.52846/ami.v49i1.1520","url":null,"abstract":"The concept of statistical convergence plays a very prominent role in the study of sequence spaces. In this treatise, we extend the research on different types of statistical convergence viz., statistical convergence in mean, in measure, in distribution, in almost surely and with respect to uniformly almost surely of complex uncertain triple sequences in a given uncertainty space. We emphasize to focus on characterizing statistical convergence of complex uncertain triple sequence in some extent. Moreover, we initiate the notion of complex uncertain Cauchy triple sequence and establish the interconnection of it with a statistically convergent triple sequence.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":"13 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82649487","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}
In this paper, by considering the notion of effect algebra and by using of a new ideal in an effect algebra E, we construct a topology τ on E, and we show that (E,τ) is a topological effect algebra. Then we obtain some conditions under which that (E,τ) is a Hausdorff space. Also, we obtain some results about connected components of this topological space, and we construct a quotient topological effect algebra.
{"title":"New results on topological effect algebras","authors":"S. Saidi Goraghani, R. Borzooei","doi":"10.52846/ami.v49i1.1482","DOIUrl":"https://doi.org/10.52846/ami.v49i1.1482","url":null,"abstract":"In this paper, by considering the notion of effect algebra and by using of a new ideal in an effect algebra E, we construct a topology τ on E, and we show that (E,τ) is a topological effect algebra. Then we obtain some conditions under which that (E,τ) is a Hausdorff space. Also, we obtain some results about connected components of this topological space, and we construct a quotient topological effect algebra.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":"8 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87900931","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}
M. López-García, Alberto Pena-García, Luz de Teresa
In this paper we present some results regarding insensitizing controls for finite dimensional systems. The concept was introduced by J. L. Lions in the context of partial differential equations and, as far as we know, is a problem that has not been treated in literature for ordinary differential equations. The concept in this situation arises in a natural way when treating the semidiscrete one for the heat equation. We present some results in the linear framework.
{"title":"Insensitizing controls for linear ODE's","authors":"M. López-García, Alberto Pena-García, Luz de Teresa","doi":"10.52846/ami.v49i1.1636","DOIUrl":"https://doi.org/10.52846/ami.v49i1.1636","url":null,"abstract":"In this paper we present some results regarding insensitizing controls for finite dimensional systems. The concept was introduced by J. L. Lions in the context of partial differential equations and, as far as we know, is a problem that has not been treated in literature for ordinary differential equations. The concept in this situation arises in a natural way when treating the semidiscrete one for the heat equation. We present some results in the linear framework.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":"96 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74245863","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}
In this work we develop a new Reservoir-People (RP) transmission network model to simulate the potential transmission of the COVID-19 virus in the population of Morocco. Our model is original in the sense that it contains parameters that depend on the confinement phases that Morocco has adopted so far. After developing the mathematical model COVID-19-Morocco we define a cost function to minimize with respect to the parameters. We then use genetic algorithms to optimize this functional. The numerical results we obtain confirm that our model is robust and can predict the evolution of the virus in Morocco.
{"title":"Development and simulation of a mathematical model to simulate the phase transmissibility ofCOVID19 in Morocco","authors":"H. Alaa, Eddine Alaa Alaa, F. Aqel","doi":"10.52846/ami.v49i1.1489","DOIUrl":"https://doi.org/10.52846/ami.v49i1.1489","url":null,"abstract":"In this work we develop a new Reservoir-People (RP) transmission network model to simulate the potential transmission of the COVID-19 virus in the population of Morocco. Our model is original in the sense that it contains parameters that depend on the confinement phases that Morocco has adopted so far. After developing the mathematical model COVID-19-Morocco we define a cost function to minimize with respect to the parameters. We then use genetic algorithms to optimize this functional. The numerical results we obtain confirm that our model is robust and can predict the evolution of the virus in Morocco.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":"101 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79506488","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}
In this paper, we investigate and study the notions of statistical product convergence and statistical product summability via deferred Cesàro and deferred Nörlund product means for martingale sequences of random variables. We then establish an inclusion theorem concerning the relation between these two beautiful and definitively useful concepts. Also, based upon our proposed ideas, we demonstrate new thoughtful approximation of Korovkin-type theorems for a martingale sequence over a Banach space. Moreover, we establish that our theorems effectively extend and improve most (if not all) of the previously existing outcomes (in statistical and classical versions). Finally, by using the generalized Bernstein polynomials, we present an illustrative example of a martingale sequence in order to demonstrate that our established theorems are quite stronger than the traditional and statistical versions of different theorems existing in the literature.
{"title":"A certain class of statistical convergence of martingale sequences and its applications to Korovkin-type approximation","authors":"B. Jena, S. K. Paikray","doi":"10.52846/ami.v49i1.1523","DOIUrl":"https://doi.org/10.52846/ami.v49i1.1523","url":null,"abstract":"In this paper, we investigate and study the notions of statistical product convergence and statistical product summability via deferred Cesàro and deferred Nörlund product means for martingale sequences of random variables. We then establish an inclusion theorem concerning the relation between these two beautiful and definitively useful concepts. Also, based upon our proposed ideas, we demonstrate new thoughtful approximation of Korovkin-type theorems for a martingale sequence over a Banach space. Moreover, we establish that our theorems effectively extend and improve most (if not all) of the previously existing outcomes (in statistical and classical versions). Finally, by using the generalized Bernstein polynomials, we present an illustrative example of a martingale sequence in order to demonstrate that our established theorems are quite stronger than the traditional and statistical versions of different theorems existing in the literature.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":"38 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87217986","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}
Using generalized Taylor's formula, this work investigate the superstability for a class of fractional differential equations with Caputo derivative. In this way, some interesting results are generalized.
{"title":"Superstability of higher-order fractional differential equations","authors":"Bennis Abdellatif","doi":"10.52846/ami.v49i1.1419","DOIUrl":"https://doi.org/10.52846/ami.v49i1.1419","url":null,"abstract":"Using generalized Taylor's formula, this work investigate the superstability for a class of fractional differential equations with Caputo derivative. In this way, some interesting results are generalized.","PeriodicalId":43654,"journal":{"name":"Annals of the University of Craiova-Mathematics and Computer Science Series","volume":"3 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74342244","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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