Emilio Gómez-Déniz, M. E. Ghitany, D. K. Al-Mutairi
The Marshall-Olkin family of probability distributions has been the inspiration of numerous research publications in the field of probability distributions. In this paper, we present several new properties of this family. In particular, we focus on stochastic orders, stress-strength reliability, Lorenz and the Leimkhuler curves, compounding, and integrated tail distribution. Two applications related to Lorenz curves and ruin theory are finally presented.
{"title":"New results for the Marshall-Olkin family of distributions","authors":"Emilio Gómez-Déniz, M. E. Ghitany, D. K. Al-Mutairi","doi":"10.1515/ms-2024-0075","DOIUrl":"https://doi.org/10.1515/ms-2024-0075","url":null,"abstract":"The Marshall-Olkin family of probability distributions has been the inspiration of numerous research publications in the field of probability distributions. In this paper, we present several new properties of this family. In particular, we focus on stochastic orders, stress-strength reliability, Lorenz and the Leimkhuler curves, compounding, and integrated tail distribution. Two applications related to Lorenz curves and ruin theory are finally presented.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221512","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 Euclidean operator radius inequalities of d-tuple operators as well as the sum and the product of d-tuple operators. A power inequality for the Euclidean operator radius of d-tuple operators is also studied. Further, we study the Euclidean operator radius inequalities of 2 × 2 operator matrices whose entries are d-tuple operators.
我们研究了 d 元组算子的欧氏算子半径不等式以及 d 元组算子的和与积。我们还研究了 d 元组算子欧氏算子半径的幂不等式。此外，我们还研究了条目为 d 元组算子的 2 × 2 算子矩阵的欧氏算子半径不等式。
{"title":"Euclidean operator radius inequalities of d-tuple operators and operator matrices","authors":"Suvendu Jana, Pintu Bhunia, Kallol Paul","doi":"10.1515/ms-2024-0070","DOIUrl":"https://doi.org/10.1515/ms-2024-0070","url":null,"abstract":"We study Euclidean operator radius inequalities of <jats:italic>d</jats:italic>-tuple operators as well as the sum and the product of <jats:italic>d</jats:italic>-tuple operators. A power inequality for the Euclidean operator radius of <jats:italic>d</jats:italic>-tuple operators is also studied. Further, we study the Euclidean operator radius inequalities of 2 × 2 operator matrices whose entries are <jats:italic>d</jats:italic>-tuple operators.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221515","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}
Motivated by Bonanzinga and Maesano (2022), we introduce and study the new relative versions of star-Menger property related to some properties studied lately by Kočinac et al. (2022) and Bonanzinga et al. (2023). In this paper, we provide some examples to understand their relationships with other relativizations of star selection principles. Further, we investigate the behaviour of these spaces under various mappings.
{"title":"Relative versions of star-Menger property","authors":"Sumit Mittal, Gaurav Kumar, Brij K. Tyagi","doi":"10.1515/ms-2024-0073","DOIUrl":"https://doi.org/10.1515/ms-2024-0073","url":null,"abstract":"Motivated by Bonanzinga and Maesano (2022), we introduce and study the new relative versions of star-Menger property related to some properties studied lately by Kočinac et al. (2022) and Bonanzinga et al. (2023). In this paper, we provide some examples to understand their relationships with other relativizations of star selection principles. Further, we investigate the behaviour of these spaces under various mappings.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221518","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 a continuation of the study of star-𝓘-Hurewicz and strongly star-𝓘-Hurewicz properties done in [Das et al.:On certain variations of 𝓘-Hurewicz property, Topology Appl. 251 (2018), 363–376]. We primarily consider and study the relative versions of star-𝓘-Hurewicz and strongly star-𝓘-Hurewicz properties. We study their relationships with the star-Hurewicz, strongly star-Hurewicz, star-𝓘-Hurewicz, strongly star-𝓘-Hurewicz and similar other properties. Few related games are also studied.
本文是[Das et al.:On certain variations of 𝓘-Hurewicz property, Topology Appl. 251 (2018), 363-376]中对星型𝓘-Hurewicz和强星型𝓘-Hurewicz性质研究的继续。我们主要考虑和研究星型𝓘-Hurewicz 性质和强星型𝓘-Hurewicz 性质的相对版本。我们研究了它们与星-胡勒维奇、强星-胡勒维奇、星-𝓘-胡勒维奇、强星-𝓘-胡勒维奇及类似其他性质的关系。还研究了一些相关的博弈。
{"title":"On certain star versions of the Hurewicz property using ideals","authors":"Debraj Chandra, Nur Alam","doi":"10.1515/ms-2024-0072","DOIUrl":"https://doi.org/10.1515/ms-2024-0072","url":null,"abstract":"This article is a continuation of the study of star-𝓘-Hurewicz and strongly star-𝓘-Hurewicz properties done in [Das et al.:<jats:italic>On certain variations of</jats:italic> 𝓘-<jats:italic>Hurewicz property</jats:italic>, Topology Appl. 251 (2018), 363–376]. We primarily consider and study the relative versions of star-𝓘-Hurewicz and strongly star-𝓘-Hurewicz properties. We study their relationships with the star-Hurewicz, strongly star-Hurewicz, star-𝓘-Hurewicz, strongly star-𝓘-Hurewicz and similar other properties. Few related games are also studied.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221517","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 prove the existence of small and big Ramsey degrees of classes of finite unary algebras in an arbitrary (not necessarily finite) algebraic language Ω. Our results generalize some Ramsey-type results of M. Sokić concerning finite unary algebras over finite languages. To do so, we develop a completely new strategy that relies on the fact that right adjoints preserve the Ramsey property. We then treat unary algebras as Eilenberg-Moore coalgebras for a functor with comultiplication, and using pre-adjunctions transport the Ramsey properties, we are interested in from the category of finite or countably infinite chains of order type ω. Moreover, we show that finite objects have finite big Ramsey degrees in the corresponding cofree structures over countably many generators.
{"title":"Coalgebraic methods for Ramsey degrees of unary algebras","authors":"Dragan Mašulović","doi":"10.1515/ms-2024-0062","DOIUrl":"https://doi.org/10.1515/ms-2024-0062","url":null,"abstract":"In this paper, we prove the existence of small and big Ramsey degrees of classes of finite unary algebras in an arbitrary (not necessarily finite) algebraic language Ω. Our results generalize some Ramsey-type results of M. Sokić concerning finite unary algebras over finite languages. To do so, we develop a completely new strategy that relies on the fact that right adjoints preserve the Ramsey property. We then treat unary algebras as Eilenberg-Moore coalgebras for a functor with comultiplication, and using pre-adjunctions transport the Ramsey properties, we are interested in from the category of finite or countably infinite chains of order type <jats:italic>ω</jats:italic>. Moreover, we show that finite objects have finite big Ramsey degrees in the corresponding cofree structures over countably many generators.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221525","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}
Saad Ihsan Butt, Josip Pečarić, Sanja Tipurić-Spužević
Grüss inequality is subject of interest for many authors due to its effectiveness in predicting bounds in several quadrature problems. In the present article, we give weighted treatment of the discrete Čebyšev and Grüss type inequalities pertaining two n-tuples of real numbers in which the bounding constants are mobilised with bounding sequences of real numbers. As an application estimations of discrete Ostrowski type inequalities are provided. Finally, by practicing obtained results along with Jensen’s difference, a wide range of estimations are formalised by considering Jensen-Grüss differences.
由于格律斯不等式能有效预测若干正交问题中的界限，因此受到许多学者的关注。在本文中，我们对涉及两个 n 组实数的离散 Čebyšev 和 Grüss 型不等式进行了加权处理，其中界常数是用实数的界序列调动的。作为应用，提供了离散奥斯特洛夫斯基式不等式的估计。最后，通过将所获得的结果与詹森差分相结合，考虑到詹森-格律斯差分，对各种估计进行了形式化。
{"title":"Generalized discrete Grüss and related results with applications","authors":"Saad Ihsan Butt, Josip Pečarić, Sanja Tipurić-Spužević","doi":"10.1515/ms-2024-0065","DOIUrl":"https://doi.org/10.1515/ms-2024-0065","url":null,"abstract":"Grüss inequality is subject of interest for many authors due to its effectiveness in predicting bounds in several quadrature problems. In the present article, we give weighted treatment of the discrete Čebyšev and Grüss type inequalities pertaining two <jats:italic>n</jats:italic>-tuples of real numbers in which the bounding constants are mobilised with bounding sequences of real numbers. As an application estimations of discrete Ostrowski type inequalities are provided. Finally, by practicing obtained results along with Jensen’s difference, a wide range of estimations are formalised by considering Jensen-Grüss differences.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221521","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 propose a method to obtain a new class of copulas using a probability generating function (PGF) of positive-integer valued random variable. Some existing copulas in the literature are sub-families of the proposed copulas. Various dependence measures and invariant property of the tail dependence coefficient under PGF transformation are also discussed. We propose an algorithm for generating random numbers from the PGF copula. The bivariate concavity properties, such as Schur concavity and quasi-concavity, associated with the PGF copula are studied. Two new generalized FGM copulas are introduced using PGFs of geometric and discrete Mittag-Leffler distributions. The proposed two copulas improved the Spearman’s rho of FGM copula by (−0.3333, 0.4751) and (−0.3333, 0.9573). Finally, we analyse a real dataset to illustrate the practical application of the proposed copulas.
{"title":"A new family of copulas based on probability generating functions","authors":"Swaroop Georgy Zachariah, Mohd. Arshad, Ashok Kumar Pathak","doi":"10.1515/ms-2024-0076","DOIUrl":"https://doi.org/10.1515/ms-2024-0076","url":null,"abstract":"We propose a method to obtain a new class of copulas using a probability generating function (PGF) of positive-integer valued random variable. Some existing copulas in the literature are sub-families of the proposed copulas. Various dependence measures and invariant property of the tail dependence coefficient under PGF transformation are also discussed. We propose an algorithm for generating random numbers from the PGF copula. The bivariate concavity properties, such as Schur concavity and quasi-concavity, associated with the PGF copula are studied. Two new generalized FGM copulas are introduced using PGFs of geometric and discrete Mittag-Leffler distributions. The proposed two copulas improved the Spearman’s rho of FGM copula by (−0.3333, 0.4751) and (−0.3333, 0.9573). Finally, we analyse a real dataset to illustrate the practical application of the proposed copulas.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142221416","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 prove general formulae in composition theory. We study the number of restricted compositions of a positive integer n in k parts, where the parts are in very general integer sequences. Note that in compositions the order of the parts is considered.
我们证明了组合理论中的一般公式。我们研究正整数 n 分 k 部分的受限组合数，其中各部分是非常一般的整数序列。需要注意的是，在构成中要考虑各部分的顺序。
{"title":"A general formula in composition theory","authors":"Rafael Jakimczuk","doi":"10.1515/ms-2024-0043","DOIUrl":"https://doi.org/10.1515/ms-2024-0043","url":null,"abstract":"We prove general formulae in composition theory. We study the number of restricted compositions of a positive integer <jats:italic>n</jats:italic> in <jats:italic>k</jats:italic> parts, where the parts are in very general integer sequences. Note that in compositions the order of the parts is considered.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511870","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 obtain some Korovkin type approximation theorems for double sequences of positive linear operators on two-dimensional weighted spaces via statistical type convergence method with respect to power series method. Additionally, we calculate the rate of convergence. As an application, we provide an approximation using the generalization of Gadjiev-Ibragimov operators for Pp-statistical convergence. Our results are meaningful and stronger than those previously given for two-dimensional weighted spaces.
{"title":"Approximation theorems via Pp -statistical convergence on weighted spaces","authors":"Sevda Yıldız, Nilay Şahin Bayram","doi":"10.1515/ms-2024-0050","DOIUrl":"https://doi.org/10.1515/ms-2024-0050","url":null,"abstract":"In this paper, we obtain some Korovkin type approximation theorems for double sequences of positive linear operators on two-dimensional weighted spaces via statistical type convergence method with respect to power series method. Additionally, we calculate the rate of convergence. As an application, we provide an approximation using the generalization of Gadjiev-Ibragimov operators for <jats:italic>P<jats:sub>p</jats:sub> </jats:italic>-statistical convergence. Our results are meaningful and stronger than those previously given for two-dimensional weighted spaces.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511877","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 are concerned with the problem of stabilization of a degenerate parabolic equation with a Dirichlet control, evolving in bounded domain 𝓞 ⊂ ℝd, d ≥ 2. We apply the proportional control design technique based on the spectrum of the linear operator which governs the evolution equation. The stabilizing feedback control, we design here, is linear, of finite-dimensional structure, easily manageable from the computational point of view.
本文关注的是在有界域 𝓞 ⊂ ℝ d , d ≥ 2 中演化的带 Dirichlet 控制的退化抛物方程的稳定问题。我们根据控制演化方程的线性算子的频谱，应用比例控制设计技术。我们在此设计的稳定反馈控制是线性的，具有有限维结构，从计算角度来看易于管理。
{"title":"A note on boundary feedback stabilization for degenerate parabolic equations in multi-dimensional domains","authors":"Ionuţ Munteanu","doi":"10.1515/ms-2024-0060","DOIUrl":"https://doi.org/10.1515/ms-2024-0060","url":null,"abstract":"In this paper, we are concerned with the problem of stabilization of a degenerate parabolic equation with a Dirichlet control, evolving in bounded domain 𝓞 ⊂ ℝ<jats:sup> <jats:italic>d</jats:italic> </jats:sup>, <jats:italic>d</jats:italic> ≥ 2. We apply the proportional control design technique based on the spectrum of the linear operator which governs the evolution equation. The stabilizing feedback control, we design here, is linear, of finite-dimensional structure, easily manageable from the computational point of view.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511871","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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