We will start this article by proving a crucial concept, which will allow us to overcome a set of obstacles we encountered in previous articles concerning the commutativity of near-ring involving homoderivations and Jordan ideals. Furthermore, we present examples to show that limitations imposed in the hypothesis of our results are necessary.
{"title":"On zero-power valued homoderivations in 3-prime near-rings","authors":"A. En-guady, S. Mouhssine, A. Boua","doi":"10.5269/bspm.62741","DOIUrl":"https://doi.org/10.5269/bspm.62741","url":null,"abstract":"We will start this article by proving a crucial concept, which will allow us to overcome a set of obstacles we encountered in previous articles concerning the commutativity of near-ring involving homoderivations and Jordan ideals. Furthermore, we present examples to show that limitations imposed in the hypothesis of our results are necessary.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45232876","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}
Let (G, P) be a quasi-lattice ordered group. In [2] we constructed a universal covariant representation (A,U) for (G, P) in a way that avoids some of the intricacies of the other approaches in [11] and [8]. Then we showed if (G, P) is amenable, true representations of (G, P) generate C∗-algebras which are canonically isomorphic to the C∗-algebra generated by the universal covariant representation. In this paper, we discuss characterizations of amenability in a comparatively simple and natural way to introduce this formidable property. Amenability of (G, P) can be established by investigating the behavior of ΦU on the range of a positive, faithful, linear map rather than the whole algebra.
{"title":"Amenable quase-lattice ordered groups and true representations","authors":"M-Alamin A. H. Ahmed","doi":"10.5269/bspm.62552","DOIUrl":"https://doi.org/10.5269/bspm.62552","url":null,"abstract":"Let (G, P) be a quasi-lattice ordered group. In [2] we constructed a universal covariant representation (A,U) for (G, P) in a way that avoids some of the intricacies of the other approaches in [11] and [8]. Then we showed if (G, P) is amenable, true representations of (G, P) generate C∗-algebras which are canonically isomorphic to the C∗-algebra generated by the universal covariant representation. In this paper, we discuss characterizations of amenability in a comparatively simple and natural way to introduce this formidable property. Amenability of (G, P) can be established by investigating the behavior of ΦU on the range of a positive, faithful, linear map rather than the whole algebra.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47757030","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}
Ahmed Kourrad, Anime Alabkari, K. Adnaoui, F. Lahmidi, Y. Tabit, Abderrahim El Adraoui
In this paper, we proposed and analyzed a non-linear mathematical model for scholar Drop out and we advanced an optimal control policy for this model by considering three variables namely the numbers of school-age children who are in school, school-age children who are out of school, and school-age children in non-formal education. The model is examined using the stability theory of differential equations. The optimal control analysis for the proposed scholar Drop out model is performed using Pontryagin's maximum principle. The conditions for optimal control of the problem with effective use of implemented policies to counter this scourge are derived and analyzed.
{"title":"A mathematical model and optimal control analysis for scholar Drop out","authors":"Ahmed Kourrad, Anime Alabkari, K. Adnaoui, F. Lahmidi, Y. Tabit, Abderrahim El Adraoui","doi":"10.5269/bspm.62650","DOIUrl":"https://doi.org/10.5269/bspm.62650","url":null,"abstract":"In this paper, we proposed and analyzed a non-linear mathematical model for scholar Drop out and we advanced an optimal control policy for this model by considering three variables namely the numbers of school-age children who are in school, school-age children who are out of school, and school-age children in non-formal education. The model is examined using the stability theory of differential equations. The optimal control analysis for the proposed scholar Drop out model is performed using Pontryagin's maximum principle. The conditions for optimal control of the problem with effective use of implemented policies to counter this scourge are derived and analyzed.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44463546","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}
Elhoussain Arhrrabi, M. Elomari, S. Melliani, L. S. Chadli
In this paper, the existence, uniqueness and controllability of solutions for fuzzy neutral stochastic differential equations $($FNSDEs$)$ with impulses are considered based on the Banach fixed point theorem.
{"title":"Existence and controllability results for fuzzy neutral stochastic differential equations with impulses","authors":"Elhoussain Arhrrabi, M. Elomari, S. Melliani, L. S. Chadli","doi":"10.5269/bspm.62765","DOIUrl":"https://doi.org/10.5269/bspm.62765","url":null,"abstract":"In this paper, the existence, uniqueness and controllability of solutions for fuzzy neutral stochastic differential equations $($FNSDEs$)$ with impulses are considered based on the Banach fixed point theorem.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42905023","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 consider the problem of recovering solutions for matrix factorizations of the Helmholtz equation in a three-dimensional bounded domain from their values on a part of the boundary of this domain, i.e., the Cauchy problem. An approximate solution to this problem is constructed based on the Carleman matrix method.
{"title":"Cauchy problem for matrix factorizations of the Helmholtz equation in the space R^m","authors":"Davron Aslonqulovich Juraev, M. Cavalcanti","doi":"10.5269/bspm.62831","DOIUrl":"https://doi.org/10.5269/bspm.62831","url":null,"abstract":"In this paper, we consider the problem of recovering solutions for matrix factorizations of the Helmholtz equation in a three-dimensional bounded domain from their values on a part of the boundary of this domain, i.e., the Cauchy problem. An approximate solution to this problem is constructed based on the Carleman matrix method.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43132322","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 main objective of this work is to study the existence, uniqueness and stability of positive periodic solutions for a first-order neutral differential equation with iterative terms which models the regulation of red blood cell production under a harvesting strategy. Benefiting from the Krasnoselskii's fixed point theorem as well as some properties of an obtained Green's function, we establish the existence of the solutions and taking advantage of the Banach fixed point theorem, we prove that the proposed equation has exactly one solution that depends continuously on parameters. Finally, two examples are exhibited to show the efficiency and application of our findings which are completely new and enrich the existing literature.
{"title":"Existence and uniqueness results for a neutral erythropoiesis model with iterative production and harvesting terms","authors":"Marwa Khemis, Ahlème Bouakkaz","doi":"10.5269/bspm.62529","DOIUrl":"https://doi.org/10.5269/bspm.62529","url":null,"abstract":"The main objective of this work is to study the existence, uniqueness and stability of positive periodic solutions for a first-order neutral differential equation with iterative terms which models the regulation of red blood cell production under a harvesting strategy. Benefiting from the Krasnoselskii's fixed point theorem as well as some properties of an obtained Green's function, we establish the existence of the solutions and taking advantage of the Banach fixed point theorem, we prove that the proposed equation has exactly one solution that depends continuously on parameters. Finally, two examples are exhibited to show the efficiency and application of our findings which are completely new and enrich the existing literature.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41990598","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 study the analyticity of mild solutions to the Debye-Huckel system with small initial data in critical Fourier-Besov-Morrey spaces. Specifically, by using the Fourier localization argument, the Littlewood-Paley theory and bilinear-type fixed point theory, we prove that global-in-time mild solutions are Gevrey regular. As a consequence of analyticity, we get time decay of mild solutions in Fourier-BesovMorrey spaces. Finally, we show a blow-up criterion of the local-in-time mild solutions of the Debye-Huckel system.
{"title":"Gevrey class regularity and stability for the Debye-H¨uckel system in critical Fourier-Besov-Morrey spaces","authors":"Achraf Azanzal, C. Allalou, S. Melliani","doi":"10.5269/bspm.62517","DOIUrl":"https://doi.org/10.5269/bspm.62517","url":null,"abstract":"In this paper, we study the analyticity of mild solutions to the Debye-Huckel system with small initial data in critical Fourier-Besov-Morrey spaces. Specifically, by using the Fourier localization argument, the Littlewood-Paley theory and bilinear-type fixed point theory, we prove that global-in-time mild solutions are Gevrey regular. As a consequence of analyticity, we get time decay of mild solutions in Fourier-BesovMorrey spaces. Finally, we show a blow-up criterion of the local-in-time mild solutions of the Debye-Huckel system.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49555398","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}
Hasnae El Hammar, Mohamed El Ouaarabi, C. Allalou, S. Melliani
We establish the existence of weak solution for a class of $p(x)$-Kirchhoff type problem for the $p(x)$-Laplacian-like operators with Dirichlet boundary condition and with gradient dependence (convection) in the reaction term. Our result is obtained using the topological degree for a class of demicontinuous operators of generalized $(S_{+})$ type and the theory of the variable exponent Sobolev spaces. Our results extend and generalize several corresponding results from the existing literature.
{"title":"Variable exponent $p(cdot)$-Kirchhoff type problem with convection in variable exponent Sobolev spaces","authors":"Hasnae El Hammar, Mohamed El Ouaarabi, C. Allalou, S. Melliani","doi":"10.5269/bspm.62976","DOIUrl":"https://doi.org/10.5269/bspm.62976","url":null,"abstract":"We establish the existence of weak solution for a class of $p(x)$-Kirchhoff type problem for the $p(x)$-Laplacian-like operators with Dirichlet boundary condition and with gradient dependence (convection) in the reaction term. Our result is obtained using the topological degree for a class of demicontinuous operators of generalized $(S_{+})$ type and the theory of the variable exponent Sobolev spaces. Our results extend and generalize several corresponding results from the existing literature.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44728334","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}
We consider a first-order delay differential equation involving iterative terms. We prove the existence of positive periodic and bounded solutions by utilizing the Schauder's fixed point theorem combined with the Green's functions method. Furthermore, by virtue of the Banach contraction principle, the uniqueness and stability of the solution are also analyzed. Our new results are illustrated with two examples that show the feasibility of our main findings.
{"title":"On periodic solutions of a recruitment model with iterative terms and a nonlinear harvesting","authors":"Lynda Mezghiche, R. Khemis","doi":"10.5269/bspm.62662","DOIUrl":"https://doi.org/10.5269/bspm.62662","url":null,"abstract":"We consider a first-order delay differential equation involving iterative terms. We prove the existence of positive periodic and bounded solutions by utilizing the Schauder's fixed point theorem combined with the Green's functions method. Furthermore, by virtue of the Banach contraction principle, the uniqueness and stability of the solution are also analyzed. Our new results are illustrated with two examples that show the feasibility of our main findings.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42067923","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}
A bounded linear operator $T$ on a complex Banach space $mathcal{X}$ is said to be full if $overline{Tmathcal{M}}=mathcal{M}$ for every invariant subspace $mathcal{M}$ of $mathcal{X}$. It is nearly full if $overline{Tmathcal{M}}$ has finite codimension in $mathcal{M}$. In this paper, we focus our attention to characterize full and nearly full operators in complex Banach spaces, showing that some valid results in complex Hilbert spaces can be generalized to this context.
{"title":"On full and nearly full operators in complex Banach spaces","authors":"S. Al-Sa'di, Wilson Pacheco","doi":"10.5269/bspm.62340","DOIUrl":"https://doi.org/10.5269/bspm.62340","url":null,"abstract":"A bounded linear operator $T$ on a complex Banach space $mathcal{X}$ is said to be full if $overline{Tmathcal{M}}=mathcal{M}$ for every invariant subspace $mathcal{M}$ of $mathcal{X}$. It is nearly full if $overline{Tmathcal{M}}$ has finite codimension in $mathcal{M}$. In this paper, we focus our attention to characterize full and nearly full operators in complex Banach spaces, showing that some valid results in complex Hilbert spaces can be generalized to this context.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44374724","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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