In 2016 Hakeem A. Othman and Md. Hanif Page introduced a new notion of set in general topology called an infra -α- open set and investigated its fundamental properties and studied the relationship between infra -α- open set and other topological sets. The objective of this paper is to introduce the new concepts called infra -α- compact space, countably infra -α- compact space, infra -α- Lindelof space, almost infra -α- compact space, mildly infra -α- compact space and infra -α- connected space in general topology and investigate several properties and characterizations of these new concepts in topological spaces.
2016年，Hakeem a . Othman和Md. Hanif Page在一般拓扑中引入了一个新的集合概念，称为infra -α-开集，并研究了其基本性质，研究了infra -α-开集与其他拓扑集之间的关系。本文的目的是在一般拓扑中引入次-α-紧空间、可数次-α-紧空间、次-α- Lindelof空间、几乎次-α-紧空间、温和次-α-紧空间和次-α-连通空间等新概念，并研究这些新概念在拓扑空间中的若干性质和表征。
{"title":"Infra -α- Compact and Infra -α- Connected Spaces","authors":"Raja Mohammad Latif","doi":"10.46300/91019.2021.8.6","DOIUrl":"https://doi.org/10.46300/91019.2021.8.6","url":null,"abstract":"In 2016 Hakeem A. Othman and Md. Hanif Page introduced a new notion of set in general topology called an infra -α- open set and investigated its fundamental properties and studied the relationship between infra -α- open set and other topological sets. The objective of this paper is to introduce the new concepts called infra -α- compact space, countably infra -α- compact space, infra -α- Lindelof space, almost infra -α- compact space, mildly infra -α- compact space and infra -α- connected space in general topology and investigate several properties and characterizations of these new concepts in topological spaces.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"82 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85810709","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 study fuzzy extensions of some covering properties defined by L. Kalantan as a modification of some kinds of paracompactness-type properties due to A.V.Arhangels'skii and studied later by other authors. In fact, we obtain that: if (X,T) is a topological space and A is a subset of X, then A is Lindelöf in (X,T) if and only if its characteristic map χ_{A} is a Lindelöf subset in (X,ω(T)). If (X,τ) is a fuzzy topological space, then, (X,τ) is fuzzy Lparacompact if and only if (X,ι(τ)) is L-paracompact, i.e. fuzzy L-paracompactness is a good extension of L-paracompactness. Fuzzy L₂-paracompactness is a good extension of L₂- paracompactness. Every fuzzy Hausdorff topological space (in the Srivastava, Lal and Srivastava' or in the Wagner and McLean' sense) which is fuzzy locally compact (in the Kudri and Wagner' sense) is fuzzy L₂-paracompact
{"title":"On Fuzzy L-paracompact Topological Spaces","authors":"F. Lupiáñez","doi":"10.46300/91019.2021.8.5","DOIUrl":"https://doi.org/10.46300/91019.2021.8.5","url":null,"abstract":"The aim of this paper is to study fuzzy extensions of some covering properties defined by L. Kalantan as a modification of some kinds of paracompactness-type properties due to A.V.Arhangels'skii and studied later by other authors. In fact, we obtain that: if (X,T) is a topological space and A is a subset of X, then A is Lindelöf in (X,T) if and only if its characteristic map χ_{A} is a Lindelöf subset in (X,ω(T)). If (X,τ) is a fuzzy topological space, then, (X,τ) is fuzzy Lparacompact if and only if (X,ι(τ)) is L-paracompact, i.e. fuzzy L-paracompactness is a good extension of L-paracompactness. Fuzzy L₂-paracompactness is a good extension of L₂- paracompactness. Every fuzzy Hausdorff topological space (in the Srivastava, Lal and Srivastava' or in the Wagner and McLean' sense) which is fuzzy locally compact (in the Kudri and Wagner' sense) is fuzzy L₂-paracompact","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81147745","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 2016 A. Devika and A. Thilagavathi introduced a new class of sets called M*-open sets and investigated some properties of these sets in topological spaces. In this paper, we introduce and study a new class of spaces, namely M*-irresolute topological vector spaces via M*-open sets. We explore and investigate several properties and characterizations of this new notion of M*-irresolute topological vector space. We give several characterizations of M*-Hausdorff space. Moreover, we show that the extreme point of the convex subset of M*-irresolute topological vector space X lies on the boundary.
{"title":"M – STAR – Irresolute Topological Vector Spaces","authors":"Raja Mohammad Latif","doi":"10.46300/91019.2020.7.4","DOIUrl":"https://doi.org/10.46300/91019.2020.7.4","url":null,"abstract":"In 2016 A. Devika and A. Thilagavathi introduced a new class of sets called M*-open sets and investigated some properties of these sets in topological spaces. In this paper, we introduce and study a new class of spaces, namely M*-irresolute topological vector spaces via M*-open sets. We explore and investigate several properties and characterizations of this new notion of M*-irresolute topological vector space. We give several characterizations of M*-Hausdorff space. Moreover, we show that the extreme point of the convex subset of M*-irresolute topological vector space X lies on the boundary.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91068869","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 p be an odd prime. Algebraic lattices of full diversity in dimension p are obtained from ramified cyclic extensions of degree p. The 3, 5, and 7-dimensional lattices are optimal with respect to sphere packing density and therefore are isometric to laminated lattices in those dimensions. AMS Subject Classification: 11H31, 11R18, 11H50, 94B75
{"title":"FULLY-DIVERSE LATTICES FROM RAMIFIED CYCLIC EXTENSIONS OF PRIME DEGREE","authors":"J. Interlando","doi":"10.12732/ijam.v33i6.4","DOIUrl":"https://doi.org/10.12732/ijam.v33i6.4","url":null,"abstract":"Let p be an odd prime. Algebraic lattices of full diversity in dimension p are obtained from ramified cyclic extensions of degree p. The 3, 5, and 7-dimensional lattices are optimal with respect to sphere packing density and therefore are isometric to laminated lattices in those dimensions. AMS Subject Classification: 11H31, 11R18, 11H50, 94B75","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"33 1","pages":"1009"},"PeriodicalIF":0.0,"publicationDate":"2021-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84761871","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 geometry of n Yn space is generated congruently together by the metric tensor and the torsion tensor. In the presented article has been obtained an analog of the Dаrbоuх theory in the n Yn space, also studied the deduction of the equation of the geodesic lines on the hypersurface that embedded in such spaces, showed that in the n Yn space the structure of the curvature tensor has special features and for curvature tensor obtained Ricci - Jacobi identity. We establish that the equations of the geodesics have additional summands, which are caused by the presence of torsion in the space. In n Yn space, the variation of the length of the geodesic lines is proportional to the product of metric and torsion tensors gijSjpk. We have introduced the second fundamental tensor παβ for the hypersurface n Yn-1 and established its structure, which is fundamentally different from the case of the Riemannian spaces with zero torsion. Furthermore, the results on the structure of the curvature tensor have been obtained.
n - Yn空间的几何是由度规张量和扭转张量全等地生成的。本文得到了在n Yn空间中对d_ (r_)理论的类比，并研究了嵌入在该空间中的超曲面上测地线方程的推导，证明了在n Yn空间中曲率张量的结构具有特殊的特征，并得到了曲率张量的Ricci - Jacobi恒等式。我们建立了测地线方程有额外的和，这是由空间中存在扭转引起的。在n Yn空间中，测地线长度的变化与度规张量和扭转张量的乘积成正比。我们引入了nn -1超曲面的第二个基本张量παβ，并建立了它的结构，这与零扭转的黎曼空间有本质的不同。在此基础上，对曲率张量的结构进行了研究。
{"title":"The Dаrbоuх Theory and Geodesics in the Metric Space with Torsion","authors":"","doi":"10.46300/91019.2020.7.3","DOIUrl":"https://doi.org/10.46300/91019.2020.7.3","url":null,"abstract":"The geometry of n Yn space is generated congruently together by the metric tensor and the torsion tensor. In the presented article has been obtained an analog of the Dаrbоuх theory in the n Yn space, also studied the deduction of the equation of the geodesic lines on the hypersurface that embedded in such spaces, showed that in the n Yn space the structure of the curvature tensor has special features and for curvature tensor obtained Ricci - Jacobi identity. We establish that the equations of the geodesics have additional summands, which are caused by the presence of torsion in the space. In n Yn space, the variation of the length of the geodesic lines is proportional to the product of metric and torsion tensors gijSjpk. We have introduced the second fundamental tensor παβ for the hypersurface n Yn-1 and established its structure, which is fundamentally different from the case of the Riemannian spaces with zero torsion. Furthermore, the results on the structure of the curvature tensor have been obtained.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"161 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78107102","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}
F. Dom 'inguez-Mota, J. S. L. 'inez, G. Tinoco-Guerrero
Abstract: This work presents the use of a schemes in generalized finitedifferences for the calculation of a numeric solution associated to a stationary, advection-diffusion problem, and the usage of such schemes in the study of an inverse problem related to this one, in which a non-linear, regularized leastsquares adjustment is employed to determine certain coefficients involved in the problem.
{"title":"A GENERALIZED FINITE-DIFFERENCES SCHEME USED IN MODELING OF A DIRECT AND AN INVERSE PROBLEM OF ADVECTION-DIFFUSION","authors":"F. Dom 'inguez-Mota, J. S. L. 'inez, G. Tinoco-Guerrero","doi":"10.12732/ijam.v33i4.5","DOIUrl":"https://doi.org/10.12732/ijam.v33i4.5","url":null,"abstract":"Abstract: This work presents the use of a schemes in generalized finitedifferences for the calculation of a numeric solution associated to a stationary, advection-diffusion problem, and the usage of such schemes in the study of an inverse problem related to this one, in which a non-linear, regularized leastsquares adjustment is employed to determine certain coefficients involved in the problem.","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"25 1","pages":"599"},"PeriodicalIF":0.0,"publicationDate":"2020-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75099117","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}
Well-rounded lattices have been a topic of recent studies with applications in wiretap channels and in cryptography. A lattice of full rank in Euclidean space is called well-rounded if its set of minimal vectors spans the whole space. In this paper, we investigate the well-roundedness of lattices coming from polynomials with integer coefficients and real roots. AMS Subject Classification: 11H31, 11H06, 11H71
{"title":"WELL-ROUNDED LATTICES VIA POLYNOMIALS WITH REAL ROOTS","authors":"C. Alves, W.L.S. Pinto, A. A. Andrade","doi":"10.12732/ijam.v33i4.10","DOIUrl":"https://doi.org/10.12732/ijam.v33i4.10","url":null,"abstract":"Well-rounded lattices have been a topic of recent studies with applications in wiretap channels and in cryptography. A lattice of full rank in Euclidean space is called well-rounded if its set of minimal vectors spans the whole space. In this paper, we investigate the well-roundedness of lattices coming from polynomials with integer coefficients and real roots. AMS Subject Classification: 11H31, 11H06, 11H71","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"29 1","pages":"663"},"PeriodicalIF":0.0,"publicationDate":"2020-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72947344","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}
Two of the main flaws of Benford’s law will be discussed in this article: (i) the first one, which leads the observer to consider an experimental dataset as the result of a single random variable rather than several, makes this law so mysterious; (ii) the second one is that Benford’s probabilities have long been considered as perfect values: this is obviously not the case. AMS Subject Classification: 60E05
{"title":"LIMITS OF BENFORD'S LAW IN EXPERIMENTAL FIELD","authors":"S. B. D. Silva","doi":"10.12732/ijam.v33i4.12","DOIUrl":"https://doi.org/10.12732/ijam.v33i4.12","url":null,"abstract":"Two of the main flaws of Benford’s law will be discussed in this article: (i) the first one, which leads the observer to consider an experimental dataset as the result of a single random variable rather than several, makes this law so mysterious; (ii) the second one is that Benford’s probabilities have long been considered as perfect values: this is obviously not the case. AMS Subject Classification: 60E05","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"16 1","pages":"685"},"PeriodicalIF":0.0,"publicationDate":"2020-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76806089","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}
{"title":"PROBABILISTIC $varphi$-CONTRACTION IN $b$-MENGER SPACES WITH FULLY CONVEX STRUCTURE","authors":"A. Mbarki, R. Oubrahim","doi":"10.12732/ijam.v33i4.7","DOIUrl":"https://doi.org/10.12732/ijam.v33i4.7","url":null,"abstract":"","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"65 6 1","pages":"621"},"PeriodicalIF":0.0,"publicationDate":"2020-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83667627","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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