The purpose of this paper is to study the principal fibre bundle (P, M, G, πp ) with Lie group G, where M admits Lorentzian almost paracontact structure (Ø, ξp, ηp, g) satisfying certain condtions on (1, 1) tensor field J, indeed possesses an almost product structure on the principal fibre bundle. In the later sections, we have defined trilinear frame bundle and have proved that the trilinear frame bundle is the principal bundle and have proved in Theorem 5.1 that the Jacobian map π* is the isomorphism.
本文的目的是研究具有李群G的主纤维束(P, M, G， πp)，其中M承认在(1,1)张量场J上满足一定条件的洛伦兹几乎副接触结构(Ø， ξp， ηp, G)，在主纤维束上确实具有一个几乎积结构。在后面的章节中，我们定义了三线系系束，证明了三线系系束是主束，并在定理5.1中证明了雅可比映射π*是同构的。
{"title":"The Principal Fibre Bundle on Lorentzian Almost R-para Contact Structure","authors":"L. Das, Mohammad Nazrul Islam Khan","doi":"10.1556/314.2020.00003","DOIUrl":"https://doi.org/10.1556/314.2020.00003","url":null,"abstract":"The purpose of this paper is to study the principal fibre bundle (P, M, G, πp ) with Lie group G, where M admits Lorentzian almost paracontact structure (Ø, ξp, ηp, g) satisfying certain condtions on (1, 1) tensor field J, indeed possesses an almost product structure on the principal fibre bundle. In the later sections, we have defined trilinear frame bundle and have proved that the trilinear frame bundle is the principal bundle and have proved in Theorem 5.1 that the Jacobian map π* is the isomorphism.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134427895","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 solves an enumerative problem which arises naturally in the context of Pascal’s hexagram. We prove that a general Desargues configuration in the plane is associated to six conical sextuples via the theorems of Pascal and Kirkman. Moreover, the Galois group associated to this problem is isomorphic to the symmetric group on six letters.
{"title":"Pascal’s Hexagram and Desargues Configurations","authors":"J. Chipalkatti","doi":"10.1556/314.2020.00004","DOIUrl":"https://doi.org/10.1556/314.2020.00004","url":null,"abstract":"This paper solves an enumerative problem which arises naturally in the context of Pascal’s hexagram. We prove that a general Desargues configuration in the plane is associated to six conical sextuples via the theorems of Pascal and Kirkman. Moreover, the Galois group associated to this problem is isomorphic to the symmetric group on six letters.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130594865","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}
Infinite matroids have been defined by Reinhard Diestel and coauthors in such a way that this class is (together with the finite matroids) closed under dualization and taking minors. On the other hand, Andreas Dress introduced a theory of matroids with coefficients in a fuzzy ring which is – from a combinatorial point of view – less general, because within this theory every circuit has a finite intersection with every cocircuit. Within the present paper, we extend the theory of matroids with coefficients to more general classes of matroids, if the underlying fuzzy ring has certain properties to be specified.
{"title":"Dual Pairs of Matroids with Coefficients in Finitary Fuzzy Rings of Arbitrary Rank","authors":"W. Wenzel","doi":"10.1556/314.2020.00006","DOIUrl":"https://doi.org/10.1556/314.2020.00006","url":null,"abstract":"Infinite matroids have been defined by Reinhard Diestel and coauthors in such a way that this class is (together with the finite matroids) closed under dualization and taking minors. On the other hand, Andreas Dress introduced a theory of matroids with coefficients in a fuzzy ring which is – from a combinatorial point of view – less general, because within this theory every circuit has a finite intersection with every cocircuit. Within the present paper, we extend the theory of matroids with coefficients to more general classes of matroids, if the underlying fuzzy ring has certain properties to be specified.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"31 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120859047","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 X be a topological space. For any positive integer n, we consider the n-fold symmetric product of X, ℱn(X), consisting of all nonempty subsets of X with at most n points; and for a given function ƒ : X → X, we consider the induced functions ℱn(ƒ): ℱn(X) → ℱn(X). Let M be one of the following classes of functions: exact, transitive, ℤ-transitive, ℤ+-transitive, mixing, weakly mixing, chaotic, turbulent, strongly transitive, totally transitive, orbit-transitive, strictly orbit-transitive, ω-transitive, minimal, I N, T T++, semi-open and irreducible. In this paper we study the relationship between the following statements: ƒ ∈ M and ℱn(ƒ) ∈ M.
{"title":"Conceptions of Topological Transitivity on Symmetric Products","authors":"Franco Barragán, S. Macías, A. Rojas","doi":"10.1556/314.2020.00007","DOIUrl":"https://doi.org/10.1556/314.2020.00007","url":null,"abstract":"Let X be a topological space. For any positive integer n, we consider the n-fold symmetric product of X, ℱn(X), consisting of all nonempty subsets of X with at most n points; and for a given function ƒ : X → X, we consider the induced functions ℱn(ƒ): ℱn(X) → ℱn(X). Let M be one of the following classes of functions: exact, transitive, ℤ-transitive, ℤ+-transitive, mixing, weakly mixing, chaotic, turbulent, strongly transitive, totally transitive, orbit-transitive, strictly orbit-transitive, ω-transitive, minimal, I N, T T++, semi-open and irreducible. In this paper we study the relationship between the following statements: ƒ ∈ M and ℱn(ƒ) ∈ M.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123730467","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}
Many combinatorial optimization problems can be expressed in terms of zero-one linear programs. For the maximum clique problem the so-called edge reformulation is applied most commonly. Two less frequently used LP equivalents are the independent set and edge covering set reformulations. The number of the constraints (as a function of the number of vertices of the ground graph) is asymptotically quadratic in the edge and the edge covering set LP reformulations and it is exponential in the independent set reformulation, respectively. F. D. Croce and R. Tadei proposed an approach in which the number of the constraints is equal to the number of the vertices. In this paper we are looking for possible tighter variants of these linear programs.
{"title":"Some Zero-One Linear Programming Reformulations for the Maximum Clique Problem","authors":"Ákos Beke, S. Szabó, Bogdán Zaválnij","doi":"10.1556/314.2020.00005","DOIUrl":"https://doi.org/10.1556/314.2020.00005","url":null,"abstract":"Many combinatorial optimization problems can be expressed in terms of zero-one linear programs. For the maximum clique problem the so-called edge reformulation is applied most commonly. Two less frequently used LP equivalents are the independent set and edge covering set reformulations. The number of the constraints (as a function of the number of vertices of the ground graph) is asymptotically quadratic in the edge and the edge covering set LP reformulations and it is exponential in the independent set reformulation, respectively. F. D. Croce and R. Tadei proposed an approach in which the number of the constraints is equal to the number of the vertices. In this paper we are looking for possible tighter variants of these linear programs.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121768500","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 ƒ be analytic in the unit disk B and normalized so that ƒ (z) = z + a2z2 + a3z3 +܁܁܁. In this paper, we give upper bounds of the Hankel determinant of second order for the classes of starlike functions of order α, Ozaki close-to-convex functions and two other classes of analytic functions. Some of the estimates are sharp.
设在单位圆盘B中为解析式并归一化，使f (z) = z + a2z2 + a3z3 +܁܁܁。本文给出了一类α阶星形函数、Ozaki近凸函数和另外两类解析函数的二阶Hankel行列式的上界。其中一些估计是尖锐的。
{"title":"Hankel Determinant of Second Order for Some Classes of Analytic Functions","authors":"M. Obradovic, N. Tuneski","doi":"10.1556/314.2021.00009","DOIUrl":"https://doi.org/10.1556/314.2021.00009","url":null,"abstract":"Let ƒ be analytic in the unit disk B and normalized so that ƒ (z) = z + a2z2 + a3z3 +܁܁܁. In this paper, we give upper bounds of the Hankel determinant of second order for the classes of starlike functions of order α, Ozaki close-to-convex functions and two other classes of analytic functions. Some of the estimates are sharp.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123995940","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 linear operator on a Hilbert space , in the classical approach of von Neumann, must be symmetric to guarantee self-adjointness. However, it can be shown that the symmetry could be omitted by using a criterion for the graph of the operator and the adjoint of the graph. Namely, S is shown to be densely defined and closed if and only if .In a more general setup, we can consider relations instead of operators and we prove that in this situation a similar result holds. We give a necessary and sufficient condition for a linear relation to be densely defined and self-adjoint.
{"title":"On Self-Adjoint Linear Relations","authors":"P'eter Berkics","doi":"10.1556/314.2020.00001","DOIUrl":"https://doi.org/10.1556/314.2020.00001","url":null,"abstract":"A linear operator on a Hilbert space , in the classical approach of von Neumann, must be symmetric to guarantee self-adjointness. However, it can be shown that the symmetry could be omitted by using a criterion for the graph of the operator and the adjoint of the graph. Namely, S is shown to be densely defined and closed if and only if .In a more general setup, we can consider relations instead of operators and we prove that in this situation a similar result holds. We give a necessary and sufficient condition for a linear relation to be densely defined and self-adjoint.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114332990","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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