Pub Date : 2023-07-10DOI: 10.46300/91019.2023.10.4
Ardhendu Kumar Nandi, S. Nath, Niva Rani Nath
A compromise between the concept of graph and hypergraph is semigraph. This paper introduced the concept of minimum covering matrix and minimum covering energy of a semigraph G. The minimum covering energy is the summation of singular values of the minimum covering matrix. Upper and lower bounds for minimum covering energy are established and also derive some relationship between minimum covering energy and energy of semigraph G.
{"title":"On Minimum Covering Energy of Semigraph","authors":"Ardhendu Kumar Nandi, S. Nath, Niva Rani Nath","doi":"10.46300/91019.2023.10.4","DOIUrl":"https://doi.org/10.46300/91019.2023.10.4","url":null,"abstract":"A compromise between the concept of graph and hypergraph is semigraph. This paper introduced the concept of minimum covering matrix and minimum covering energy of a semigraph G. The minimum covering energy is the summation of singular values of the minimum covering matrix. Upper and lower bounds for minimum covering energy are established and also derive some relationship between minimum covering energy and energy of semigraph G.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"104 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79535120","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 : 2023-06-14DOI: 10.46300/91019.2023.10.3
Carlos Hernán López Zapata
This article showcases significant progress in solving two renowned problems in the calculus of series: the Flint Hills and Cookson Hills series. For almost twenty years, a long-standing question has remained unanswered in regard to their convergence. Mainly, proving the convergence of the Flint Hills series would significantly impact the redefinition of the upper bound for the irrationality measure of the number π. One of the results presented in this article is that the Flint Hills series converges to 30.3144... which leads to a redefinition of the upper bound for the irrationality measure of π, specifically μ(π)≤ 2.5. This work proposes a transformation that solves the mystery of the Flint Hills and Cookson Hills series. It is based on a summation formula developed by mathematicians Adamchik and Srivastava. By leveraging a specialized series supported by the Riemann zeta function, this approach successfully transforms the original Flint Hills and Cookson Hills series into novel convergent versions with unique significance. The resulting sequences linked to these series are positive and bounded and satisfy convergence. Moreover, this article extends the Flint Hills series when the cosecant function has an arbitrary complex argument n+iβ, with i=√(-1), establishing a new series representation based on the polylogarithm 〖Li〗_3 (e^i2k), with k=1,2,3,…, e the Euler’s number, which bears resemblance to the famous integral of the Bose-Einstein distribution as a relevant finding. This is a never-seen-before link between the Flint Hills series and polylogarithms. Furthermore, a relationship between the Apéry constant and the Flint Hills and Cookson Hills series has been established. This article presents a significant breakthrough in the calculus of series by introducing a new method based on the Riemann Zeta function and logarithmical expressions derived from the Adamchik and Srivastava summation formula. The novel approach extends the analysis of convergence criteria for series, addressing ambiguous cases characterized by abrupt jumps. Thus, the Flint Hills series converges to 30.3144... and the Cookson Hills series to 42.9949... as proved in this article.
{"title":"Finding on Convergence of the Flint Hills and Cookson Hills Series based on a Summation Formula of Adamchik and Srivastava involving the Riemann Zeta Function","authors":"Carlos Hernán López Zapata","doi":"10.46300/91019.2023.10.3","DOIUrl":"https://doi.org/10.46300/91019.2023.10.3","url":null,"abstract":"This article showcases significant progress in solving two renowned problems in the calculus of series: the Flint Hills and Cookson Hills series. For almost twenty years, a long-standing question has remained unanswered in regard to their convergence. Mainly, proving the convergence of the Flint Hills series would significantly impact the redefinition of the upper bound for the irrationality measure of the number π. One of the results presented in this article is that the Flint Hills series converges to 30.3144... which leads to a redefinition of the upper bound for the irrationality measure of π, specifically μ(π)≤ 2.5. This work proposes a transformation that solves the mystery of the Flint Hills and Cookson Hills series. It is based on a summation formula developed by mathematicians Adamchik and Srivastava. By leveraging a specialized series supported by the Riemann zeta function, this approach successfully transforms the original Flint Hills and Cookson Hills series into novel convergent versions with unique significance. The resulting sequences linked to these series are positive and bounded and satisfy convergence. Moreover, this article extends the Flint Hills series when the cosecant function has an arbitrary complex argument n+iβ, with i=√(-1), establishing a new series representation based on the polylogarithm 〖Li〗_3 (e^i2k), with k=1,2,3,…, e the Euler’s number, which bears resemblance to the famous integral of the Bose-Einstein distribution as a relevant finding. This is a never-seen-before link between the Flint Hills series and polylogarithms. Furthermore, a relationship between the Apéry constant and the Flint Hills and Cookson Hills series has been established. This article presents a significant breakthrough in the calculus of series by introducing a new method based on the Riemann Zeta function and logarithmical expressions derived from the Adamchik and Srivastava summation formula. The novel approach extends the analysis of convergence criteria for series, addressing ambiguous cases characterized by abrupt jumps. Thus, the Flint Hills series converges to 30.3144... and the Cookson Hills series to 42.9949... as proved in this article.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"39 20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91539086","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 : 2023-05-23DOI: 10.46300/91019.2023.10.2
Joshue G. Derecho, Katrina Belleza Fuentes
This paper introduces the notion of the JDB-semigroup, an extended study of dual B-algebra by applying the concept of semigroup. Some properties and characteristics of sub JDBsemigroup, units, unity, JD-field, and JD-ideal in a JDB-semigroup are presented in this study.
{"title":"Sub JDB-semigroup, JD-field, and JD-ideal","authors":"Joshue G. Derecho, Katrina Belleza Fuentes","doi":"10.46300/91019.2023.10.2","DOIUrl":"https://doi.org/10.46300/91019.2023.10.2","url":null,"abstract":"This paper introduces the notion of the JDB-semigroup, an extended study of dual B-algebra by applying the concept of semigroup. Some properties and characteristics of sub JDBsemigroup, units, unity, JD-field, and JD-ideal in a JDB-semigroup are presented in this study.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89501273","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 : 2023-04-11DOI: 10.46300/91019.2023.10.1
In this research work, we aim to find and describe all the classical solutions of the homogeneous linear singular differential equation of order l in the space of K' distributions. Recall that in our previous research, the results of which have been published in some journals, we had undertaken similar studies in the case of a singular differential equation of the Euler type of second order, when the conditions were carried out. That said, our intentions in this article are therefore to generalize the results obtained and recently published, focusing our research on the situation of the homogeneous singular linear differential equation of order l of Euler type. In this orientation, we base ourselves on the classical theory of ordinary linear differential equations and look for the particular solution to the equation considered in the form of the distribution with a parameter to be determined, which we replace in the latter. Depending on the nature of the roots of the characteristic polynomial of the homogeneous equation we identify, case by case, all the solutions indicated in the sense of distributions in the space K'. In this same work, we return to the non-homogeneous equation of order l of the same Euler type, whose second member consists only of the derivative of order s of the Dirac-delta distribution studied in our previous work, to fully describe all the solutions of the latter in the sense of distributions in the space K'. We finalize this work by making an important remark emphasizing the interest in undertaking research of the same objective of finding a general solution, by studying the singular differential equations of the same higher-order l with the particularity of being of Euler types on the left and Euler on the right in the space of distributions K’.
{"title":"On Classical and Distributional Solutions of a Higher Order Singular Linear Differential Equation in the Space K’","authors":"","doi":"10.46300/91019.2023.10.1","DOIUrl":"https://doi.org/10.46300/91019.2023.10.1","url":null,"abstract":"In this research work, we aim to find and describe all the classical solutions of the homogeneous linear singular differential equation of order l in the space of K' distributions. Recall that in our previous research, the results of which have been published in some journals, we had undertaken similar studies in the case of a singular differential equation of the Euler type of second order, when the conditions were carried out. That said, our intentions in this article are therefore to generalize the results obtained and recently published, focusing our research on the situation of the homogeneous singular linear differential equation of order l of Euler type. In this orientation, we base ourselves on the classical theory of ordinary linear differential equations and look for the particular solution to the equation considered in the form of the distribution with a parameter to be determined, which we replace in the latter. Depending on the nature of the roots of the characteristic polynomial of the homogeneous equation we identify, case by case, all the solutions indicated in the sense of distributions in the space K'. In this same work, we return to the non-homogeneous equation of order l of the same Euler type, whose second member consists only of the derivative of order s of the Dirac-delta distribution studied in our previous work, to fully describe all the solutions of the latter in the sense of distributions in the space K'. We finalize this work by making an important remark emphasizing the interest in undertaking research of the same objective of finding a general solution, by studying the singular differential equations of the same higher-order l with the particularity of being of Euler types on the left and Euler on the right in the space of distributions K’.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73749438","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 : 2022-10-07DOI: 10.46300/91019.2022.9.16
Gerima Tefera Dejen
The concept of homomorphisms on implication algebra is introduced. The notion of sub algebras, normal subalgebras in an implication algebra are investigated. Quotient implication algebras and kernels in an implication algebra ,and Homomorphisms and isomorphism theorems are elaborated.
{"title":"Properties of Homomorphism and Quotient Implication Algebra on Implication Algebras","authors":"Gerima Tefera Dejen","doi":"10.46300/91019.2022.9.16","DOIUrl":"https://doi.org/10.46300/91019.2022.9.16","url":null,"abstract":"The concept of homomorphisms on implication algebra is introduced. The notion of sub algebras, normal subalgebras in an implication algebra are investigated. Quotient implication algebras and kernels in an implication algebra ,and Homomorphisms and isomorphism theorems are elaborated.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81754425","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 : 2022-09-29DOI: 10.46300/91019.2022.9.15
M. Yaremenko
{"title":"General Periodic Functions and Generalization of Fourier analysis","authors":"M. Yaremenko","doi":"10.46300/91019.2022.9.15","DOIUrl":"https://doi.org/10.46300/91019.2022.9.15","url":null,"abstract":"","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"234 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74508790","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 : 2022-09-22DOI: 10.46300/91019.2022.9.14
Omelebele Jude. A., Udoaka Otobong. G., Udoakpan Itoro. U
The identity difference transformation semigroup was examined for idempotent rank and the combinatorial results for idempotent ranks of IDT_n,IDO_n,IDI_n,and IDPOI_n were obtained.
{"title":"Idempotent Rank Identity Difference Transformation Semigroup","authors":"Omelebele Jude. A., Udoaka Otobong. G., Udoakpan Itoro. U","doi":"10.46300/91019.2022.9.14","DOIUrl":"https://doi.org/10.46300/91019.2022.9.14","url":null,"abstract":"The identity difference transformation semigroup was examined for idempotent rank and the combinatorial results for idempotent ranks of IDT_n,IDO_n,IDI_n,and IDPOI_n were obtained.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89100970","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 : 2022-06-01DOI: 10.46300/91019.2022.9.13
F. Akpan, Udoaka Otobong Gabriel
{"title":"Finite Semi-group Modulo and Its Application to Symmetric Cryptography","authors":"F. Akpan, Udoaka Otobong Gabriel","doi":"10.46300/91019.2022.9.13","DOIUrl":"https://doi.org/10.46300/91019.2022.9.13","url":null,"abstract":"","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90259105","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 : 2022-03-30DOI: 10.46300/91019.2022.9.10
Omelebele Jude. A., Udoaka O. G., U. I. U.
This study focuses on the ranks of identity difference transformation semigroup. The ideals of all the (sub) semigroups; identity difference full transformation semigroup (IDT_n), identity difference order preserving transformation semigroup, (IDO_n), identity difference symmetric inverse transformation semigroup( IDI_n), identity difference partial order preserving symmetric inverse transformation semigroup( IDPOI_n) and identity difference partial order preserving transformation semigroup ( IDPO_n) were investigated for rank and their combinatorial results obtained respectively.
{"title":"Ranks of Identity Difference Transformation Semigroup","authors":"Omelebele Jude. A., Udoaka O. G., U. I. U.","doi":"10.46300/91019.2022.9.10","DOIUrl":"https://doi.org/10.46300/91019.2022.9.10","url":null,"abstract":"This study focuses on the ranks of identity difference transformation semigroup. The ideals of all the (sub) semigroups; identity difference full transformation semigroup (IDT_n), identity difference order preserving transformation semigroup, (IDO_n), identity difference symmetric inverse transformation semigroup( IDI_n), identity difference partial order preserving symmetric inverse transformation semigroup( IDPOI_n) and identity difference partial order preserving transformation semigroup ( IDPO_n) were investigated for rank and their combinatorial results obtained respectively.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"45 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72624135","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 systems of weakening of intuitionistic negation logic mZ, introduced in [1], [2], which are developed in the spirit of da Costa's approach. We take a particular attention on the philosophical considerations of the paraconsistent mZ logic w.r.t. the constructive semantics of the intuitionistic logic, and we show that mZ is a subintuitionistic logic. Hence, we present the relationship between intuitionistic and paraconsistent subintuitionistic negation used in mZ. Then we present a significant number of examples for this subintuitionistic and paraconsistent mZ logics: Logic Programming with Fiting's fixpoint semantics for paraconsistent weakening of 3-valued Kleene's and 4-valued Belnap's logics. Moreover, we provide a canonical construction of infinitary-valued mZ logics and, in particular, the paraconsistent weakening of standard Zadeh's fuzzy logic and of the Godel-Dummet t-norm intermediate logics.
{"title":"Paraconsistent da Costa Weakening of Intuitionistic Negation: What does it mean?","authors":"Z. Majkic","doi":"10.46300/91019.2022.9.9","DOIUrl":"https://doi.org/10.46300/91019.2022.9.9","url":null,"abstract":"In this paper we consider the systems of weakening of intuitionistic negation logic mZ, introduced in [1], [2], which are developed in the spirit of da Costa's approach. We take a particular attention on the philosophical considerations of the paraconsistent mZ logic w.r.t. the constructive semantics of the intuitionistic logic, and we show that mZ is a subintuitionistic logic. Hence, we present the relationship between intuitionistic and paraconsistent subintuitionistic negation used in mZ. Then we present a significant number of examples for this subintuitionistic and paraconsistent mZ logics: Logic Programming with Fiting's fixpoint semantics for paraconsistent weakening of 3-valued Kleene's and 4-valued Belnap's logics. Moreover, we provide a canonical construction of infinitary-valued mZ logics and, in particular, the paraconsistent weakening of standard Zadeh's fuzzy logic and of the Godel-Dummet t-norm intermediate logics.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89195704","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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