This paper presents an analytical and numerical study of a new integro-differential Fredholm-Chandrasekhar equation of the second type. We suggest the conditions that ensure the existence and uniqueness of the nonlinear problem's solution. Then, we create a numerical technique based on the Nystr"{o}m's method. The numerical application illustrates the efficiency of the proposed process.
{"title":"On a new nonlinear integro-differential Fredholm-Chandrasekhar equation","authors":"A. Khellaf, M. Benssaad, S. Lemita","doi":"10.5269/bspm.63023","DOIUrl":"https://doi.org/10.5269/bspm.63023","url":null,"abstract":"This paper presents an analytical and numerical study of a new integro-differential Fredholm-Chandrasekhar equation of the second type. We suggest the conditions that ensure the existence and uniqueness of the nonlinear problem's solution. Then, we create a numerical technique based on the Nystr\"{o}m's method. The numerical application illustrates the efficiency of the proposed process.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42609134","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 prove the existence and uniqueness results of an entropy solution to a class of nonlinear degenerate parabolic problem with Dirichlet-type boundary condition and L1 data. The main tool used here is the Rothe's time-discretization approach combined with the theory of weighted Sobolev spaces.
{"title":"Entropy solution for a nonlinear degenerate parabolic problem in weighted Sobolev space via Rothe's time-discretization approach","authors":"Abdelali Sabri, A. Jamea","doi":"10.5269/bspm.63558","DOIUrl":"https://doi.org/10.5269/bspm.63558","url":null,"abstract":"In this paper, we prove the existence and uniqueness results of an entropy solution to a class of nonlinear degenerate parabolic problem with Dirichlet-type boundary condition and L1 data. The main tool used here is the Rothe's time-discretization approach combined with the theory of weighted Sobolev spaces.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46165408","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}
Hermite transform involves weigth function and Hermite polynomial as its kernel is discussed. The Hermite transform and its basic properties are extended to the distribution spaces and to the space of integrable Boehmian
{"title":"Hermite transform for distribution and Boehmian space","authors":"Deshna Loonker","doi":"10.5269/bspm.62584","DOIUrl":"https://doi.org/10.5269/bspm.62584","url":null,"abstract":"Hermite transform involves weigth function and Hermite polynomial as its kernel is discussed. The Hermite transform and its basic properties are extended to the distribution spaces and to the space of integrable Boehmian","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45700632","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 the boundary value problem for a fourth order nonlinear p-Laplacian difference equation and to prove the existence of at least two nontrivial solutions. Our approach is mainly based on the variational method and critical point theory. One example is included to illustrate the result.
{"title":"Existence of solutions to a discrete problems for fourth order nonlinear p-Laplacian via variational method","authors":"O. Hammouti, Abdelrachid El Amrouss","doi":"10.5269/bspm.63267","DOIUrl":"https://doi.org/10.5269/bspm.63267","url":null,"abstract":"We consider the boundary value problem for a fourth order nonlinear p-Laplacian difference equation and to prove the existence of at least two nontrivial solutions. Our approach is mainly based on the variational method and critical point theory. One example is included to illustrate the result.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48283322","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}
This paper introduces a class of rings called left nil zero semicommutative rings ( LNZS rings ), wherein a ring R is said to be LNZS if the left annihilator of every nilpotent element of R is an ideal of R. It is observed that reduced rings are LNZS but not the other way around. So, this paper provides some conditions for an LNZS ring to be reduced and among other results, it is proved that R is reduced if and only if the ring of upper triangular matrices over R is LNZS. Furthermore, it is shown that the polynomial ring over an LNZS may not be LNZS and so is the case of the skew polynomial over an LNZS ring. Therefore, this paper investigates the LNZS property over the polynomial extension and skew polynomial extension of an LNZS ring with some additional conditions.
{"title":"Left Nil Zero Semicommutative rings","authors":"Sanjiv Subba, T. Subedi","doi":"10.5269/bspm.62926","DOIUrl":"https://doi.org/10.5269/bspm.62926","url":null,"abstract":"This paper introduces a class of rings called left nil zero semicommutative rings ( LNZS rings ), wherein a ring R is said to be LNZS if the left annihilator of every nilpotent element of R is an ideal of R. It is observed that reduced rings are LNZS but not the other way around. So, this paper provides some conditions for an LNZS ring to be reduced and among other results, it is proved that R is reduced if and only if the ring of upper triangular matrices over R is LNZS. Furthermore, it is shown that the polynomial ring over an LNZS may not be LNZS and so is the case of the skew polynomial over an LNZS ring. Therefore, this paper investigates the LNZS property over the polynomial extension and skew polynomial extension of an LNZS ring with some additional conditions.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49662509","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 the present paper, a Carleman matrix is constructed and, on the basis of this matrix, an approximate solution of the Cauchy problem in a multidimensional unbounded domain is found in an explicit form.
{"title":"The Cauchy problem for matrix factorization of the Helmholtz equation in a multidimensional unbounded domain","authors":"Davron Aslonqulovich Juraev","doi":"10.5269/bspm.63779","DOIUrl":"https://doi.org/10.5269/bspm.63779","url":null,"abstract":"In the present paper, a Carleman matrix is constructed and, on the basis of this matrix, an approximate solution of the Cauchy problem in a multidimensional unbounded domain is found in an explicit form.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46968903","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, new closed-form formulas for the matrix exponential are provided using certain polynomials which areconstructed with the help of a generalization of Hermite's interpolation formula. Our method is direct and elementary, it gives tractable and manageable formulas not current inthe extensive literature on this essential subject. Moreover, others are recuperated and generalized. Several particular cases and examples are formulated to illustrate the method presented in this paper.
{"title":"Explicit formulas for the matrix exponential","authors":"M. Mouçouf, S. Zriaa","doi":"10.5269/bspm.63692","DOIUrl":"https://doi.org/10.5269/bspm.63692","url":null,"abstract":"In this work, new closed-form formulas for the matrix exponential are provided using certain polynomials which areconstructed with the help of a generalization of Hermite's interpolation formula. Our method is direct and elementary, it gives tractable and manageable formulas not current inthe extensive literature on this essential subject. Moreover, others are recuperated and generalized. Several particular cases and examples are formulated to illustrate the method presented in this paper.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45155150","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 study the following quasilinear Neumann boundary-value problem$$left{begin{array}{ll}displaystyle -sum^{N}_{i=1} D^{i}(a_{i}(x,u,nabla u))+|u|^{p_{0}-2} u= f(x,u,nabla u) & mbox{in } quad Omega,displaystyle sum^{N}_{i=1} a_{i}(x,u,nabla u)cdot n_{i} = g(x) & mbox{on } quad partialOmega,end{array}right.$$where $Omega$ is a bounded open domain in $>I!!R^{N}$, $(Ngeq 2)$. We prove the existence of a weak solution for $f in L^{infty}(Omega)$ and $gin L^{infty}(partialOmega)$ and the existence of renormalized solutions for $L^{1}$-data $f$ and $g$. The functional setting involves anisotropic Sobolev spaces with constants exponents.
{"title":"Weak and renormalized solutions for anisotropic Neumann problems with degenerate coercivity","authors":"M. B. Benboubker, Hayat Benkhalou, H. Hjiaj","doi":"10.5269/bspm.62362","DOIUrl":"https://doi.org/10.5269/bspm.62362","url":null,"abstract":"In this work, we study the following quasilinear Neumann boundary-value problem$$left{begin{array}{ll}displaystyle -sum^{N}_{i=1} D^{i}(a_{i}(x,u,nabla u))+|u|^{p_{0}-2} u= f(x,u,nabla u) & mbox{in } quad Omega,displaystyle sum^{N}_{i=1} a_{i}(x,u,nabla u)cdot n_{i} = g(x) & mbox{on } quad partialOmega,end{array}right.$$where $Omega$ is a bounded open domain in $>I!!R^{N}$, $(Ngeq 2)$. We prove the existence of a weak solution for $f in L^{infty}(Omega)$ and $gin L^{infty}(partialOmega)$ and the existence of renormalized solutions for $L^{1}$-data $f$ and $g$. The functional setting involves anisotropic Sobolev spaces with constants exponents.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48975351","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 [17], A. chillali et al introduce a new cryptographic method based on matrices over a finite field Fpn , where p is a prime number. In this paper, we will generate this method in a new group of square block matrices based on an elliptic curve, called "elliptic" matrices.
{"title":"The \"Elliptic\" matrices and a new kind of cryptography","authors":"Zakariae Cheddour, A. Chillali, A. Mouhib","doi":"10.5269/bspm.62377","DOIUrl":"https://doi.org/10.5269/bspm.62377","url":null,"abstract":"In [17], A. chillali et al introduce a new cryptographic method based on matrices over a finite field Fpn , where p is a prime number. In this paper, we will generate this method in a new group of square block matrices based on an elliptic curve, called \"elliptic\" matrices.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42939193","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 examine super-recurrence and super-rigidity of composition operators acting on $H(mathbb{D})$ the space of holomorphic functions on the unit disk $mathbb{D}$ and on $H^2(mathbb{D})$ the Hardy-Hilbert space. We characterize the symbols that generate super-recurrent and super-rigid composition operators acting on $H(mathbb{D})$ and $H^2(mathbb{D})$.
{"title":"On compositional dynamics on hardy space","authors":"Otmane Benchiheb, N. Karim, M. Amouch","doi":"10.5269/bspm.62921","DOIUrl":"https://doi.org/10.5269/bspm.62921","url":null,"abstract":"In this work, we examine super-recurrence and super-rigidity of composition operators acting on $H(mathbb{D})$ the space of holomorphic functions on the unit disk $mathbb{D}$ and on $H^2(mathbb{D})$ the Hardy-Hilbert space. We characterize the symbols that generate super-recurrent and super-rigid composition operators acting on $H(mathbb{D})$ and $H^2(mathbb{D})$.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49459603","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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