Pub Date : 2020-06-01DOI: 10.1556/012.2020.57.2.1461
Ritu Dhankhar, N. Govil, Prasanna Kumar
Let be a polynomial of degree n. Further, let and . Then according to the well-known Bernstein inequalities, we have and . It is an open problem to obtain inequalities analogous to these inequalities for the class of polynomials satisfying p(z) ≡ znp(1/z). In this paper we obtain some inequalites in this direction for polynomials that belong to this class and have all their coefficients in any sector of opening γ, where 0 γ < π. Our results generalize and sharpen several of the known results in this direction, including those of Govil and Vetterlein [3], and Rahman and Tariq [12]. We also present two examples to show that in some cases the bounds obtained by our results can be considerably sharper than the known bounds.
{"title":"On sharpening of inequalities for a class of polynomials satisfying p(z)≡znp(1/z)","authors":"Ritu Dhankhar, N. Govil, Prasanna Kumar","doi":"10.1556/012.2020.57.2.1461","DOIUrl":"https://doi.org/10.1556/012.2020.57.2.1461","url":null,"abstract":"Let be a polynomial of degree n. Further, let and . Then according to the well-known Bernstein inequalities, we have and . It is an open problem to obtain inequalities analogous to these inequalities for the class of polynomials satisfying p(z) ≡ znp(1/z). In this paper we obtain some inequalites in this direction for polynomials that belong to this class and have all their coefficients in any sector of opening γ, where 0 γ < π. Our results generalize and sharpen several of the known results in this direction, including those of Govil and Vetterlein [3], and Rahman and Tariq [12]. We also present two examples to show that in some cases the bounds obtained by our results can be considerably sharper than the known bounds.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"1 1","pages":"255-266"},"PeriodicalIF":0.7,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83697408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-06-01DOI: 10.1556/012.2020.57.2.1458
Bing-Ling Wu, Xiao-Hui Yan
Let Hn be the n-th harmonic number and let vn be its denominator. It is known that vn is even for every integer . In this paper, we study the properties of Hn and prove that for any integer n, vn = en(1+o(1)). In addition, we obtain some results of the logarithmic density of harmonic numbers.
{"title":"Some properties of harmonic numbers","authors":"Bing-Ling Wu, Xiao-Hui Yan","doi":"10.1556/012.2020.57.2.1458","DOIUrl":"https://doi.org/10.1556/012.2020.57.2.1458","url":null,"abstract":"Let Hn be the n-th harmonic number and let vn be its denominator. It is known that vn is even for every integer . In this paper, we study the properties of Hn and prove that for any integer n, vn = en(1+o(1)). In addition, we obtain some results of the logarithmic density of harmonic numbers.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"7 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72526023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let X be a smooth projective K3 surface over the complex numbers and let C be an ample curve on X. In this paper we will study the semistability of the Lazarsfeld-Mukai bundle EC,A associated to a line bundle A on C such that |A| is a pencil on C and computes the Clifford index of C. We give a necessary and sufficient condition for EC,A to be semistable.
{"title":"Lazarsfeld-Mukai Bundles on K3 Surfaces Associated with a Pencil Computing the Clifford Index","authors":"Sarbeswar Pal","doi":"10.1556/012.2022.01518","DOIUrl":"https://doi.org/10.1556/012.2022.01518","url":null,"abstract":"Let X be a smooth projective K3 surface over the complex numbers and let C be an ample curve on X. In this paper we will study the semistability of the Lazarsfeld-Mukai bundle EC,A associated to a line bundle A on C such that |A| is a pencil on C and computes the Clifford index of C. We give a necessary and sufficient condition for EC,A to be semistable.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"20 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82261102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The symbol S(X) denotes the hyperspace of finite unions of convergent sequences in a Hausdor˛ space X. This hyper-space is endowed with the Vietoris topology. First of all, we give a characterization of convergent sequence in S(X). Then we consider some cardinal invariants on S(X), and compare the character, the pseudocharacter, the sn-character, the so-character, the network weight and cs-network weight of S(X) with the corresponding cardinal function of X. Moreover, we consider rank k-diagonal on S(X), and give a space X with a rank 2-diagonal such that S(X) does not Gδ -diagonal. Further, we study the relations of some generalized metric properties of X and its hyperspace S(X). Finally, we pose some questions about the hyperspace S(X).
{"title":"Hyperspace of finite unions of convergent sequences","authors":"Jingling Lin, Fucai Lin, Chuan Liu","doi":"10.1556/012.2021.01510","DOIUrl":"https://doi.org/10.1556/012.2021.01510","url":null,"abstract":"The symbol S(X) denotes the hyperspace of finite unions of convergent sequences in a Hausdor˛ space X. This hyper-space is endowed with the Vietoris topology. First of all, we give a characterization of convergent sequence in S(X). Then we consider some cardinal invariants on S(X), and compare the character, the pseudocharacter, the sn-character, the so-character, the network weight and cs-network weight of S(X) with the corresponding cardinal function of X. Moreover, we consider rank k-diagonal on S(X), and give a space X with a rank 2-diagonal such that S(X) does not Gδ\u0000 -diagonal. Further, we study the relations of some generalized metric properties of X and its hyperspace S(X). Finally, we pose some questions about the hyperspace S(X).","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"286 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80287802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-23DOI: 10.1556/012.2020.57.2.1457
Elif Kizildere, M. Le, G. Soydan
Let l,m,r be fixed positive integers such that 2| l, 3lm, l > r and 3 | r. In this paper, using the BHV theorem on the existence of primitive divisors of Lehmer numbers, we prove that if min{rlm2 − 1,(l − r)lm2 + 1} > 30, then the equation (rlm2 − 1)x + ((l − r)lm2 + 1)y = (lm)z has only the positive integer solution (x,y,z) = (1,1,2).
{"title":"A note on the ternary purely exponential diophantine equation Ax + By = Cz with A + B = C2","authors":"Elif Kizildere, M. Le, G. Soydan","doi":"10.1556/012.2020.57.2.1457","DOIUrl":"https://doi.org/10.1556/012.2020.57.2.1457","url":null,"abstract":"<jats:p>Let <jats:italic>l,m,r</jats:italic> be fixed positive integers such that 2<jats:inline-formula />| <jats:italic>l</jats:italic>, 3<jats:inline-formula /><jats:italic>lm</jats:italic>, <jats:italic>l > r</jats:italic> and 3 | <jats:italic>r</jats:italic>. In this paper, using the BHV theorem on the existence of primitive divisors of Lehmer numbers, we prove that if min{<jats:italic>rlm</jats:italic><jats:sup>2</jats:sup> − 1<jats:italic>,</jats:italic>(<jats:italic>l</jats:italic> − <jats:italic>r</jats:italic>)<jats:italic>lm</jats:italic><jats:sup>2</jats:sup> + 1} <jats:italic>></jats:italic> 30, then the equation (<jats:italic>rlm</jats:italic><jats:sup>2</jats:sup> − 1)<jats:sup><jats:italic>x</jats:italic></jats:sup> + ((<jats:italic>l</jats:italic> − <jats:italic>r</jats:italic>)<jats:italic>lm</jats:italic><jats:sup>2</jats:sup> + 1)<jats:sup><jats:italic>y</jats:italic></jats:sup> = (<jats:italic>lm</jats:italic>)<jats:sup><jats:italic>z</jats:italic></jats:sup> has only the positive integer solution (<jats:italic>x,y,z</jats:italic>) = (1<jats:italic>,</jats:italic>1<jats:italic>,</jats:italic>2).</jats:p>","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"20 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90068855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-01DOI: 10.1556/012.2020.57.1.1451
W. Xing, Cheng Quanguo, Wang Ding-guo
We study certain subgroups of the full group of Hopf algebra automorphisms of twisted tensor biproducts.
研究了扭曲张量双积的Hopf代数自同构满群的若干子群。
{"title":"Characterization of automorphisms of twisted tensor biproducts","authors":"W. Xing, Cheng Quanguo, Wang Ding-guo","doi":"10.1556/012.2020.57.1.1451","DOIUrl":"https://doi.org/10.1556/012.2020.57.1.1451","url":null,"abstract":"\u0000 We study certain subgroups of the full group of Hopf algebra automorphisms of twisted tensor biproducts.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"21 1","pages":"116-137"},"PeriodicalIF":0.7,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74909549","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-01DOI: 10.1556/012.2020.57.1.1455
H. Ghahramani, S. Sattari
Let X be a Hilbert C*-module over a C*-algebra B. In this paper we introduce two classes of operator algebras on the Hilbert C*-module X called operator algebras with property and operator algebras with property ℤ, and we study the first (continuous) cohomology group of them with coefficients in various Banach bimodules under several conditions on B and X. Some of our results generalize the previous results. Also we investigate some properties of these classes of operator algebras.
{"title":"The first cohomology group of some operator algebras on Hilbert C*-modules","authors":"H. Ghahramani, S. Sattari","doi":"10.1556/012.2020.57.1.1455","DOIUrl":"https://doi.org/10.1556/012.2020.57.1.1455","url":null,"abstract":"\u0000 Let X be a Hilbert C*-module over a C*-algebra B. In this paper we introduce two classes of operator algebras on the Hilbert C*-module X called operator algebras with property and operator algebras with property ℤ, and we study the first (continuous) cohomology group of them with coefficients in various Banach bimodules under several conditions on B and X. Some of our results generalize the previous results. Also we investigate some properties of these classes of operator algebras.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"193 1","pages":"54-67"},"PeriodicalIF":0.7,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79697449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-01DOI: 10.1556/012.2020.57.1.1450
László Remete
Let m ≠ 0, ±1 and n ≥ 2 be integers. The ring of algebraic integers of the pure fields of type is explicitly known for n = 2, 3,4. It is well known that for n = 2, an integral basis of the pure quadratic fields can be given parametrically, by using the remainder of the square-free part of m modulo 4. Such characterisation of an integral basis also exists for cubic and quartic pure fields, but for higher degree pure fields there are only results for special cases. In this paper we explicitly give an integral basis of the field , where m ≠ ±1 is square-free. Furthermore, we show that similarly to the quadratic case, an integral basis of is repeating periodically in m with period length depending on n.
{"title":"Integral bases of pure fields with square-free parameter","authors":"László Remete","doi":"10.1556/012.2020.57.1.1450","DOIUrl":"https://doi.org/10.1556/012.2020.57.1.1450","url":null,"abstract":"\u0000 Let m ≠ 0, ±1 and n ≥ 2 be integers. The ring of algebraic integers of the pure fields of type is explicitly known for n = 2, 3,4. It is well known that for n = 2, an integral basis of the pure quadratic fields can be given parametrically, by using the remainder of the square-free part of m modulo 4. Such characterisation of an integral basis also exists for cubic and quartic pure fields, but for higher degree pure fields there are only results for special cases.\u0000 In this paper we explicitly give an integral basis of the field , where m ≠ ±1 is square-free. Furthermore, we show that similarly to the quadratic case, an integral basis of is repeating periodically in m with period length depending on n.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"28 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90540982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-01DOI: 10.1556/012.2020.57.1.1449
T. Gadjiev, V. Guliyev, Konul G. Suleymanova
In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.
{"title":"The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces","authors":"T. Gadjiev, V. Guliyev, Konul G. Suleymanova","doi":"10.1556/012.2020.57.1.1449","DOIUrl":"https://doi.org/10.1556/012.2020.57.1.1449","url":null,"abstract":"\u0000 In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"2 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73463952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-03-01DOI: 10.1556/012.2020.57.1.1452
W. Chu
Two classes of trigonometric sums about integer powers of secant function are evaluated that are closely related to Jordan's totient function.
计算了两类与Jordan的全等函数密切相关的正割函数的整数幂的三角和。
{"title":"Jordan's totient function and trigonometric sums","authors":"W. Chu","doi":"10.1556/012.2020.57.1.1452","DOIUrl":"https://doi.org/10.1556/012.2020.57.1.1452","url":null,"abstract":"\u0000 Two classes of trigonometric sums about integer powers of secant function are evaluated that are closely related to Jordan's totient function.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"82 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73045386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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