Several naturally defined lower separation axioms for bitopological spaces obtained by modifying the axioms T0, T1, and R0 appear in the literature. We introduce and study analogous separation axioms for bitopogenous spaces. In particular, we investigate relationships between the axioms and discuss the conditions under which the relationships are similar to those between the corresponding separation axioms for bitopological spaces.
文献中出现了几条通过修改公理 T 0、T 1 和 R 0 而自然定义的位元空间下层分离公理。我们引入并研究了位元空间的类似分离公理。我们特别研究了这些公理之间的关系，并讨论了这些关系与位元论空间相应分离公理之间关系相似的条件。
{"title":"Lower separation axioms in bitopogenous spaces","authors":"Tom Richmond, Josef Šlapal","doi":"10.1515/ms-2024-0037","DOIUrl":"https://doi.org/10.1515/ms-2024-0037","url":null,"abstract":"Several naturally defined lower separation axioms for bitopological spaces obtained by modifying the axioms <jats:italic>T</jats:italic> <jats:sub>0</jats:sub>, <jats:italic>T</jats:italic> <jats:sub>1</jats:sub>, and <jats:italic>R</jats:italic> <jats:sub>0</jats:sub> appear in the literature. We introduce and study analogous separation axioms for bitopogenous spaces. In particular, we investigate relationships between the axioms and discuss the conditions under which the relationships are similar to those between the corresponding separation axioms for bitopological spaces.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"64 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article is devoted to the study of mappings defined in the plane domain. Under certain conditions, the upper estimate of the distortion of the modulus of families of paths is obtained. Similarly, the upper estimate of the modulus of the families of paths in the pre-image under the mapping is also obtained.
{"title":"On direct and inverse Poletsky inequalities with a tangential dilatation","authors":"Evgeny Sevost’yanov, Valery Targonskii","doi":"10.1515/ms-2024-0007","DOIUrl":"https://doi.org/10.1515/ms-2024-0007","url":null,"abstract":"This article is devoted to the study of mappings defined in the plane domain. Under certain conditions, the upper estimate of the distortion of the modulus of families of paths is obtained. Similarly, the upper estimate of the modulus of the families of paths in the pre-image under the mapping is also obtained.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"103 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we solve the question completely raised by Feng Qi and Dongkyu Lim in paper “Monotonicity properties for a ratio of finite many gamma functions” published in Advances in Difference Equations and get some properties about ratios of finitely many gamma functions such as complete monotonicity, logarithmically complete monotonicity, the Bernstein function property, null point and extreme value.
{"title":"Complete monotonicity for a ratio of finitely many gamma functions","authors":"Hai-Sheng Chen, Ye-Cheng Zhu, Jia-Hui Wang","doi":"10.1515/ms-2024-0027","DOIUrl":"https://doi.org/10.1515/ms-2024-0027","url":null,"abstract":"In this paper, we solve the question completely raised by Feng Qi and Dongkyu Lim in paper “<jats:italic>Monotonicity properties for a ratio of finite many gamma functions</jats:italic>” published in Advances in Difference Equations and get some properties about ratios of finitely many gamma functions such as complete monotonicity, logarithmically complete monotonicity, the Bernstein function property, null point and extreme value.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"28 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this correspondence, we prove the von Bahr–Esseen moment inequality for pairwise independent random vectors in Hilbert spaces. Our constant in the von Bahr–Esseen moment inequality is better than that obtained for the real-valued random variables by Chen et al. [The von Bahr–Esseen moment inequality for pairwise independent random variables and applications, J. Math. Anal. Appl. 419 (2014), 1290–1302], and Chen and Sung [Generalized Marcinkiewicz–Zygmund type inequalities for random variables and applications, J. Math. Inequal. 10(3) (2016), 837–848]. The result is then applied to obtain mean convergence theorems for triangular arrays of rowwise and pairwise independent random vectors in Hilbert spaces. Some results in the literature are extended.
在这篇论文中，我们证明了希尔伯特空间中成对独立随机向量的 von Bahr-Esseen 矩不等式。我们在 von Bahr-Esseen 矩不等式中的常数优于 Chen 等人在实值随机变量中得到的常数[The von Bahr-Esseen moment inequality for pairwise independent random variables and applications, J. Math. Analys.Anal.419 (2014), 1290-1302] 以及 Chen 和 Sung [Generalized Marcinkiewicz-Zygmund type inequalities for random variables and applications, J. Math. Inequal.Inequal.10(3) (2016), 837-848].然后应用该结果获得希尔伯特空间中行独立和成对独立随机向量三角阵列的均值收敛定理。文献中的一些结果得到了扩展。
{"title":"On the von Bahr–Esseen inequality for pairwise independent random vectors in Hilbert spaces with applications to mean convergence","authors":"Nguyen Chi Dzung, Nguyen Thi Thanh Hien","doi":"10.1515/ms-2024-0016","DOIUrl":"https://doi.org/10.1515/ms-2024-0016","url":null,"abstract":"In this correspondence, we prove the von Bahr–Esseen moment inequality for pairwise independent random vectors in Hilbert spaces. Our constant in the von Bahr–Esseen moment inequality is better than that obtained for the real-valued random variables by Chen et al. [<jats:italic>The von Bahr–Esseen moment inequality for pairwise independent random variables and applications</jats:italic>, J. Math. Anal. Appl. 419 (2014), 1290–1302], and Chen and Sung [<jats:italic>Generalized Marcinkiewicz–Zygmund type inequalities for random variables and applications</jats:italic>, J. Math. Inequal. 10(3) (2016), 837–848]. The result is then applied to obtain mean convergence theorems for triangular arrays of rowwise and pairwise independent random vectors in Hilbert spaces. Some results in the literature are extended.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"19 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mohammad Sababheh, Cristian Conde, Hamid Reza Moradi
The classical Bohr inequality for scalars was extended to the non-commutative case of Hilbert space operators in the literature. The sole goal of this article is to discuss the operator Bohr inequality and present some of its new variants. This includes fresh reverses and refinements of this inequality with applications towards an operator’s real and imaginary parts, not to forget the new discussion of different domains of the parameters. One further application towards the operator Dunkl-Williams inequality will be presented too. While the new results are interesting, we emphasize that the approach used to explore these inequalities differs from the existing literature methods for this context.
{"title":"Operator Bohr-type inequalities","authors":"Mohammad Sababheh, Cristian Conde, Hamid Reza Moradi","doi":"10.1515/ms-2024-0035","DOIUrl":"https://doi.org/10.1515/ms-2024-0035","url":null,"abstract":"The classical Bohr inequality for scalars was extended to the non-commutative case of Hilbert space operators in the literature. The sole goal of this article is to discuss the operator Bohr inequality and present some of its new variants. This includes fresh reverses and refinements of this inequality with applications towards an operator’s real and imaginary parts, not to forget the new discussion of different domains of the parameters. One further application towards the operator Dunkl-Williams inequality will be presented too. While the new results are interesting, we emphasize that the approach used to explore these inequalities differs from the existing literature methods for this context.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"abs/0907.0001 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let (Pm)m≥0 be the sequence of Pell numbers given by P0 = 0, P1 = 1, and Pm+2 = 2Pm+1 + Pm for all m ≥ 0. In this paper, for an integer d ≥ 2 which is square free, we show that there is at most one value of the positive integer x participating in the Pell equation x2 − dy2 = ± 1, which is a product of two Pell numbers.
让 (Pm ) m≥0 是由 P 0 = 0、P 1 = 1 和 P m+2 = 2P m+1 + Pm 对所有 m ≥ 0 给出的佩尔数序列。在本文中，对于无平方差的整数 d ≥ 2，我们证明最多有一个正整数 x 的值参与佩尔方程 x 2 - dy 2 = ± 1，这是两个佩尔数的乘积。
{"title":"On the x-coordinates of Pell equations that are products of two Pell numbers","authors":"Mahadi Ddamulira, Florian Luca","doi":"10.1515/ms-2024-0004","DOIUrl":"https://doi.org/10.1515/ms-2024-0004","url":null,"abstract":"Let (<jats:italic>P<jats:sub>m</jats:sub> </jats:italic>)<jats:sub> <jats:italic>m</jats:italic>≥0</jats:sub> be the sequence of Pell numbers given by <jats:italic>P</jats:italic> <jats:sub>0</jats:sub> = 0, <jats:italic>P</jats:italic> <jats:sub>1</jats:sub> = 1, and <jats:italic>P</jats:italic> <jats:sub> <jats:italic>m</jats:italic>+2</jats:sub> = 2<jats:italic>P</jats:italic> <jats:sub> <jats:italic>m</jats:italic>+1</jats:sub> + <jats:italic>P<jats:sub>m</jats:sub> </jats:italic> for all <jats:italic>m</jats:italic> ≥ 0. In this paper, for an integer <jats:italic>d</jats:italic> ≥ 2 which is square free, we show that there is at most one value of the positive integer <jats:italic>x</jats:italic> participating in the Pell equation <jats:italic>x</jats:italic> <jats:sup>2</jats:sup> − <jats:italic>dy</jats:italic> <jats:sup>2</jats:sup> = ± 1, which is a product of two Pell numbers.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"32 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we introduce the concept of Hadamard 𝔇-hom-der on Banach algebras. Further, we apply the fixed point method to prove the stability of the Hadamard 𝔇-hom-der on Banach algebras.
{"title":"A fixed point technique to the stability of Hadamard 𝔇-hom-der in Banach algebras","authors":"Mehdi Dehghanian, Yamin Sayyari","doi":"10.1515/ms-2024-0011","DOIUrl":"https://doi.org/10.1515/ms-2024-0011","url":null,"abstract":"In this paper, we introduce the concept of Hadamard 𝔇-hom-der on Banach algebras. Further, we apply the fixed point method to prove the stability of the Hadamard 𝔇-hom-der on Banach algebras.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"58 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let 𝔔 be a reduced left-sided and left-stable quantale without zero divisors. This paper shows how the systematic use of the «quantization» of 2 viewed as a regular and strict right 𝔔-subalgebra of 𝔔 can both strengthen and simplify the rather complicated construction of quantale-enriched topologies given for semi-unital and semi-integral quantales in the original paper [3]. The underlying structure for this new construction is an adjoint situation between the dual category of semi-unital, semi-integral quantales and quantized topological spaces.
{"title":"Right algebras in Sup and the topological representation of semi-unital and semi-integral quantales, revisited","authors":"Javier Gutiérrez García, Ulrich Höhle","doi":"10.1515/ms-2024-0020","DOIUrl":"https://doi.org/10.1515/ms-2024-0020","url":null,"abstract":"Let 𝔔 be a reduced left-sided and left-stable quantale without zero divisors. This paper shows how the systematic use of the «quantization» of 2 viewed as a regular and strict right 𝔔-subalgebra of 𝔔 can both strengthen and simplify the rather complicated construction of quantale-enriched topologies given for semi-unital and semi-integral quantales in the original paper [3]. The underlying structure for this new construction is an adjoint situation between the dual category of semi-unital, semi-integral quantales and quantized topological spaces.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"16 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study Hermite interpolation for the space of polynomials of total degree in ℝN and the space of homogeneous polynomials in ℝN+1. We investigate the relations between the two types of Hermite interpolation. We show that they have the same regularity and continuity property.
我们研究了 ℝ N 中总阶数多项式空间和 ℝ N+1 中同质多项式空间的赫米特插值法。我们研究了这两种赫米特插值法之间的关系。我们证明它们具有相同的正则性和连续性。
{"title":"Hermite interpolation of type total degree associated with certain spaces of polynomials","authors":"Le Ngoc Cuong, Ta Thi Thanh Mai, Phung Van Manh","doi":"10.1515/ms-2024-0009","DOIUrl":"https://doi.org/10.1515/ms-2024-0009","url":null,"abstract":"We study Hermite interpolation for the space of polynomials of total degree in ℝ<jats:sup> <jats:italic>N</jats:italic> </jats:sup> and the space of homogeneous polynomials in ℝ<jats:sup> <jats:italic>N</jats:italic>+1</jats:sup>. We investigate the relations between the two types of Hermite interpolation. We show that they have the same regularity and continuity property.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"18 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Paolo de Lucia passed away on March 18, 2022 in Nyon, Switzerland. He was undoubtedly one of the most respected experts on Real Analysis and Measure Theory, but most of us miss him first of all as a scientific role model, colleague and fatherly friend. Last year, some of his coauthors, students and friends attended the ‘ Measure Theory and Applications: a symposium remembering Paolo de Lucia’s contributions’, held in Naples on March 30–31, 2023, and contributed orally with lectures and speeches in the section ‘Memories’. For this reason, this year we wish to commemorate him by transcribing our two contributions and keeping them unchanged, albeit without the familiar context of the symposium, because unchanged is the sorrow for his loss and the weight of his absence for those who knew him. So, despite an unbridgeable distance, we can imagine him blushing slightly, smiling and saying ironically “At last, for me even a jurist agrees to publish in a mathematics journal”.
{"title":"In memory of Paolo","authors":"Antonio Cavaliere, Paola Cavaliere","doi":"10.1515/ms-2024-0019","DOIUrl":"https://doi.org/10.1515/ms-2024-0019","url":null,"abstract":"Paolo de Lucia passed away on March 18, 2022 in Nyon, Switzerland. He was undoubtedly one of the most respected experts on Real Analysis and Measure Theory, but most of us miss him first of all as a scientific role model, colleague and fatherly friend. Last year, some of his coauthors, students and friends attended the ‘ Measure Theory and Applications: a symposium remembering Paolo de Lucia’s contributions’, held in Naples on March 30–31, 2023, and contributed orally with lectures and speeches in the section ‘Memories’. For this reason, this year we wish to commemorate him by transcribing our two contributions and keeping them unchanged, albeit without the familiar context of the symposium, because unchanged is the sorrow for his loss and the weight of his absence for those who knew him. So, despite an unbridgeable distance, we can imagine him blushing slightly, smiling and saying ironically “At last, for me even a jurist agrees to publish in a mathematics journal”.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"16 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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