Pub Date : 2021-03-19DOI: 10.52737/18291163-2021.13.1-1-21
I. Yengui, Faten Ben Amor
We propose to give an algorithm for computing the R-saturation of a finitely-generated submodule of a free module E over a Prüfer domain R. To do this, we start with the local case, that is, the case where R is a valuation domain. After that, we consider the global case (R is a Prüfer domain) using the dynamical method. The proposed algorithm is based on an algorithm given by Ducos, Monceur and Yengui in the case E=R[X]m which is reformulated here in a more general setting in order to reach a wider audience. The last section is devoted to the case where R is a Bézout domain. Particular attention is paid to the case where R is a principal ideal domain (Z as the main example).
{"title":"Saturation of finitely-generated submodules of free modules over Prüfer domains","authors":"I. Yengui, Faten Ben Amor","doi":"10.52737/18291163-2021.13.1-1-21","DOIUrl":"https://doi.org/10.52737/18291163-2021.13.1-1-21","url":null,"abstract":"We propose to give an algorithm for computing the R-saturation of a finitely-generated submodule of a free module E over a Prüfer domain R. To do this, we start with the local case, that is, the case where R is a valuation domain. After that, we consider the global case (R is a Prüfer domain) using the dynamical method. The proposed algorithm is based on an algorithm given by Ducos, Monceur and Yengui in the case E=R[X]m which is reformulated here in a more general setting in order to reach a wider audience. The last section is devoted to the case where R is a Bézout domain. Particular attention is paid to the case where R is a principal ideal domain (Z as the main example).","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41421280","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 : 2020-12-29DOI: 10.52737/18291163-2020.12.12-1-21
D. Shahnazaryan, S. Davidov
In this paper, using hyperidentities with permutations we obtained characterization invertible algebras of various types of linearity.
本文利用具有置换的超恒等式，得到了各种线性类型的刻画可逆代数。
{"title":"Hyperidentities with permutations in invertible binary algebras","authors":"D. Shahnazaryan, S. Davidov","doi":"10.52737/18291163-2020.12.12-1-21","DOIUrl":"https://doi.org/10.52737/18291163-2020.12.12-1-21","url":null,"abstract":"In this paper, using hyperidentities with permutations we obtained characterization invertible algebras of various types of linearity.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42570956","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 : 2020-12-25DOI: 10.52737/18291163-2020.12.11-1-16
F. Hayrapetyan
For weighted $L^p$-classess of $C^1$-functions in the unit disc with weight function of the type $|w|^{2gamma}cdot(1-|w|^{2rho})^{alpha}$, we obtain a family of weighted $overline{partial}$-integral representations of the type $f = P(f) - T(overline{partial} f)$.
{"title":"On a family of weighted $overlinepartial$-integral representations in the unit disc","authors":"F. Hayrapetyan","doi":"10.52737/18291163-2020.12.11-1-16","DOIUrl":"https://doi.org/10.52737/18291163-2020.12.11-1-16","url":null,"abstract":"For weighted $L^p$-classess of $C^1$-functions in the unit disc with weight function of the type $|w|^{2gamma}cdot(1-|w|^{2rho})^{alpha}$, we obtain a family of weighted $overline{partial}$-integral representations of the type $f = P(f) - T(overline{partial} f)$.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44389972","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 : 2020-10-30DOI: 10.52737/18291163-2020.12.10-1-27
A. Poghosyan, Lusine Poghosyan, R. Barkhudaryan
Trigonometric approximation or interpolation of a non-smooth function on a finite interval has poor convergence properties. This is especially true for discontinuous functions. The case of infinitely differentiable but non-periodic functions with discontinuous periodic extensions onto the real axis has attracted interest from many researchers. In a series of works, we discussed an approach based on quasi-periodic trigonometric basis functions whose periods are slightly bigger than the length of the approximation interval. We proved validness of the approach for trigonometric interpolations. In this paper, we apply those ideas to classical Fourier expansions.
{"title":"On some quasi-periodic approximations","authors":"A. Poghosyan, Lusine Poghosyan, R. Barkhudaryan","doi":"10.52737/18291163-2020.12.10-1-27","DOIUrl":"https://doi.org/10.52737/18291163-2020.12.10-1-27","url":null,"abstract":"Trigonometric approximation or interpolation of a non-smooth function on a finite interval has poor convergence properties. This is especially true for discontinuous functions. The case of infinitely differentiable but non-periodic functions with discontinuous periodic extensions onto the real axis has attracted interest from many researchers. In a series of works, we discussed an approach based on quasi-periodic trigonometric basis functions whose periods are slightly bigger than the length of the approximation interval. We proved validness of the approach for trigonometric interpolations. In this paper, we apply those ideas to classical Fourier expansions.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44617787","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 : 2020-09-25DOI: 10.52737/18291163-2020.12.9-1-19
T. Sow
In this paper, we introduce and study a new iterative method based on the generalized viscosity explicit methods (GVEM) for solving the inclusion problem with an infinite family of multivalued accretive operators in real Banach spaces. Applications to equilibrium and to convex minimization problems involving an infinite family of semi-continuous and convex functions are included. Our results improve important recent results.
{"title":"An iterative algorithm based on the generalized viscosity explicit methods for an infinite family of accretive operators","authors":"T. Sow","doi":"10.52737/18291163-2020.12.9-1-19","DOIUrl":"https://doi.org/10.52737/18291163-2020.12.9-1-19","url":null,"abstract":"In this paper, we introduce and study a new iterative method based on the generalized viscosity explicit methods (GVEM) for solving the inclusion problem with an infinite family of multivalued accretive operators in real Banach spaces. Applications to equilibrium and to convex minimization problems involving an infinite family of semi-continuous and convex functions are included. Our results improve important recent results.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42817683","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 : 2020-08-28DOI: 10.52737/18291163-2020.12.7-1-8
Dipankar Saha, M. Sen, Nimai Sarkar, Subhankar Saha
This article is entirely devoted to the application of the measure of noncompactness defined in the Holder space. Here the emphasis is on the study of the nonlinear functional integral equation with changed arguments. Precisely, the existence of a solution is obtained by employing the Darbo fixed point theorem under certain hypotheses. Finally, we provide a tangible example which supports our results.
{"title":"Existence of a solution in the Holder space for a nonlinear functional integral equation","authors":"Dipankar Saha, M. Sen, Nimai Sarkar, Subhankar Saha","doi":"10.52737/18291163-2020.12.7-1-8","DOIUrl":"https://doi.org/10.52737/18291163-2020.12.7-1-8","url":null,"abstract":"This article is entirely devoted to the application of the measure of noncompactness defined in the Holder space. Here the emphasis is on the study of the nonlinear functional integral equation with changed arguments. Precisely, the existence of a solution is obtained by employing the Darbo fixed point theorem under certain hypotheses. Finally, we provide a tangible example which supports our results.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42963611","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 : 2020-08-18DOI: 10.52737/18291163-2020.12.6-1-17
Chul Woo Lee, Jae Won Lee
We study generic lightlike submanifolds M of an indefinite Kaehler manifold ¯M or an indefinite complex space form ¯M(c) with an (ℓ,m)-type metric connection subject such that the characteristic vector field ζ of ¯M belongs to our screen distribution S(TM) of M.
{"title":"Generic lightlike submanifolds of an indefinite Kaehler manifold with an (ℓ,m)-type metric connection","authors":"Chul Woo Lee, Jae Won Lee","doi":"10.52737/18291163-2020.12.6-1-17","DOIUrl":"https://doi.org/10.52737/18291163-2020.12.6-1-17","url":null,"abstract":"We study generic lightlike submanifolds M of an indefinite Kaehler manifold ¯M or an indefinite complex space form ¯M(c) with an (ℓ,m)-type metric connection subject such that the characteristic vector field ζ of ¯M belongs to our screen distribution S(TM) of M.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45063737","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 : 2020-08-02DOI: 10.52737/18291163-2020.12.8-1-15
X. Krasniqi
In this article, we have presented the necessary and sufficient conditions for the power integrability with a weight of the sum of sine and cosine series whose coefficients belong to the $RBVS_{+,omega}^{r,delta }$ class.
{"title":"On the power integrability with a weight of trigonometric series from $RBVS_{+,omega}^{r,delta }$ class","authors":"X. Krasniqi","doi":"10.52737/18291163-2020.12.8-1-15","DOIUrl":"https://doi.org/10.52737/18291163-2020.12.8-1-15","url":null,"abstract":"In this article, we have presented the necessary and sufficient conditions for the power integrability with a weight of the sum of sine and cosine series whose coefficients belong to the $RBVS_{+,omega}^{r,delta }$ class.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46449346","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 : 2020-07-17DOI: 10.52737/18291163-2020.12.5-1-9
Masao Okazaki
In "Higher descent on Pell conics. III. The first 2-descent", Lemmermeyer introduced the canonical heights on the groups of rational points on Pell conics, which are analogues of the canonical heights on elliptic curves. In this paper, we generalize this: We introduce the canonical heights on the groups of Q-rational points on Pell conics over number fields.
{"title":"Canonical heights on Pell conics over number fields","authors":"Masao Okazaki","doi":"10.52737/18291163-2020.12.5-1-9","DOIUrl":"https://doi.org/10.52737/18291163-2020.12.5-1-9","url":null,"abstract":"In \"Higher descent on Pell conics. III. The first 2-descent\", Lemmermeyer introduced the canonical heights on the groups of rational points on Pell conics, which are analogues of the canonical heights on elliptic curves. In this paper, we generalize this: We introduce the canonical heights on the groups of Q-rational points on Pell conics over number fields.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43567398","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 : 2020-06-20DOI: 10.52737/18291163-2020.12.4-1-12
M. Khan, J. Pečarić
In this manuscript, we propose new refinements for the Jensen-Mercer as well as variant of the Jensen-Mercer inequalities associated to certain positive tuples. We give some related integral version and present applications for different means. At the end, further generalizations are given which are associated to m finite sequences.
{"title":"New refinements of the Jensen-Mercer inequality associated to positive n-tuples","authors":"M. Khan, J. Pečarić","doi":"10.52737/18291163-2020.12.4-1-12","DOIUrl":"https://doi.org/10.52737/18291163-2020.12.4-1-12","url":null,"abstract":"In this manuscript, we propose new refinements for the Jensen-Mercer as well as variant of the Jensen-Mercer inequalities associated to certain positive tuples. We give some related integral version and present applications for different means. At the end, further generalizations are given which are associated to m finite sequences.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2020-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42697906","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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