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Certain Observations on Tightness and Topological Games in Bornology 关于博恩学中严密性和拓扑博弈的若干观察
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-08-17 DOI: 10.1007/s00025-024-02256-7
Debraj Chandra, Pratulananda Das, Subhankar Das
{"title":"Certain Observations on Tightness and Topological Games in Bornology","authors":"Debraj Chandra, Pratulananda Das, Subhankar Das","doi":"10.1007/s00025-024-02256-7","DOIUrl":"https://doi.org/10.1007/s00025-024-02256-7","url":null,"abstract":"<p>This article is a continuation of our investigations in the function space <i>C</i>(<i>X</i>) with respect to the topology <span>(tau ^s_mathfrak {B})</span> of strong uniform convergence on <span>(mathfrak {B})</span> in line of (Chandra et al. in Indag Math 31:43-63, 2020; Das et al. in Topol Appl 310:108005, 2022) using the idea of strong uniform convergence (Beer and Levi in J Math Anal Appl 350:568-589, 2009) on a bornology. First we focus on the notion of the tightness property of <span>((C(X),tau ^s_mathfrak {B}))</span> and some of its variations such as the supertightness, the Id-fan tightness and the <i>T</i>-tightness. Certain situations are discussed when <i>C</i>(<i>X</i>) is a k-space with respect to the topology <span>(tau ^s_mathfrak {B})</span>. Next the notions of strong <span>(mathfrak {B})</span>-open game and <span>(gamma _{mathfrak {B}^s})</span>-open game on <i>X</i> are introduced and some of its consequences are investigated. Finally, we consider discretely selective property and related games. On <span>((C(X),tau ^s_mathfrak {B}))</span> several interactions between topological games related to discretely selective property, the Gruenhage game on <span>((C(X),tau ^s_mathfrak {B}))</span> and certain games on <i>X</i> are presented.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194386","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}
引用次数: 0
A Class of Projectively Flat Finsler Metrics 一类投影平面芬斯勒度量
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-08-17 DOI: 10.1007/s00025-024-02252-x
Huaifu Liu, Xiaohuan Mo, Ling Zhu
{"title":"A Class of Projectively Flat Finsler Metrics","authors":"Huaifu Liu, Xiaohuan Mo, Ling Zhu","doi":"10.1007/s00025-024-02252-x","DOIUrl":"https://doi.org/10.1007/s00025-024-02252-x","url":null,"abstract":"<p>Projectively flat Finlser metrics on a convex domain <i>U</i> in <span>(mathbb {R}^n)</span> are regular solutions to Hilbert’s Fourth Problem. In this paper, we study projectively flat Finlser metrics on <i>U</i>. We find equations that characterize these metrics with weakly orthogonal invariance, refining a theorem due to Sol<span>(acute{o})</span>rzano-Le<span>(acute{o})</span>n. As its application, we obtain infinitely many <i>new</i> projectively flat Finlser metrics on <span>(mathbb {S}^{n+1})</span> and determine their scalar flag curvature. These metrics contain Bryant’s projective spherically symmetric Finsler metric of constant flag curvature 1.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142225008","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}
引用次数: 0
Revisiting Maximum Log-Likelihood Parameter Estimation for Two-Parameter Weibull Distributions: Theory and Applications 重新审视双参数威布尔分布的最大对数似然参数估计：理论与应用
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-08-16 DOI: 10.1007/s00025-024-02258-5
Thomas Kneib, Jan-Christian Schlüter, Benjamin Wacker
{"title":"Revisiting Maximum Log-Likelihood Parameter Estimation for Two-Parameter Weibull Distributions: Theory and Applications","authors":"Thomas Kneib, Jan-Christian Schlüter, Benjamin Wacker","doi":"10.1007/s00025-024-02258-5","DOIUrl":"https://doi.org/10.1007/s00025-024-02258-5","url":null,"abstract":"<p>In this article, we reexamine properties of maximum log-likelihood parameter estimation for two-parameter Weibull distributions which have been applied in many different sciences. Finding reasons for this popularity is a key question. Our main contribution is a thorough existence and uniqueness proof for a global maximizer with respect to the parameter space. We first provide existence and uniqueness of local maximizers by Schauder’s first fixed point theorem, monotony arguments and local concavity of its Hessian matrix. Thus, we can prove our main result of existence and uniqueness of a global maximizer by considering all limiting cases with respect to the parameter space. We finally strengthen our theoretical findings on four data sets. On the one hand, two synthetic data sets underline our need for our data assumptions while, on the other hand, we choose two data sets from wind engineering and reliability engineering to demonstrate usefulness in real-world applications.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142194381","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}
引用次数: 0
On the Trajectories of a Particle in a Translation Invariant Involutive Field 论平移不变卷积场中的粒子轨迹
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-08-09 DOI: 10.1007/s00025-024-02240-1
Cristian Cobeli, Alexandru Zaharescu
{"title":"On the Trajectories of a Particle in a Translation Invariant Involutive Field","authors":"Cristian Cobeli, Alexandru Zaharescu","doi":"10.1007/s00025-024-02240-1","DOIUrl":"https://doi.org/10.1007/s00025-024-02240-1","url":null,"abstract":"<p>We introduce a double-folded operator that, upon iterative application, generates a dynamical system with two types of trajectories: a cyclic one and, another that grows endlessly on parabolas. These trajectories produce two distinct partitions of the set of lattice points in the plane. Our object is to analyze these trajectories and to point out a few special arithmetic properties of the integers they represent. We also introduce and study the parabolic-taxicab distance, which measures the fast traveling on the steps of the stairs defined by points on the parabolic trajectories whose coordinates are based on triangular numbers.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943776","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}
引用次数: 0
Generalized Volterra Operators on Dales–Davie Algebras 戴尔斯-戴维代数上的广义沃尔特拉算子
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-08-06 DOI: 10.1007/s00025-024-02249-6
A. H. Gholizadeh, Z. S. Hosseini, A. H. Sanatpour
{"title":"Generalized Volterra Operators on Dales–Davie Algebras","authors":"A. H. Gholizadeh, Z. S. Hosseini, A. H. Sanatpour","doi":"10.1007/s00025-024-02249-6","DOIUrl":"https://doi.org/10.1007/s00025-024-02249-6","url":null,"abstract":"<p>We investigate the boundedness and compactness properties of integral operators, Volterra operators, and generalized Volterra operators between the Dales–Davie algebras. Additionally, we study the analogous properties of these operators when applied to the Lipschitz versions of Dales–Davie algebras.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969355","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}
引用次数: 0
Reversed Hardy-Littlewood-Sobolev Type Inequality on $${mathbb {R}}^{n-m}times {mathbb {R}}^{n}$$ 关于 $${mathbb {R}}^{n-m}} times {mathbb {R}}^{n}$$ 的反向 Hardy-Littlewood-Sobolev 型不等式
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-08-03 DOI: 10.1007/s00025-024-02227-y
Xiang Li, Minbo Yang
{"title":"Reversed Hardy-Littlewood-Sobolev Type Inequality on $${mathbb {R}}^{n-m}times {mathbb {R}}^{n}$$","authors":"Xiang Li, Minbo Yang","doi":"10.1007/s00025-024-02227-y","DOIUrl":"https://doi.org/10.1007/s00025-024-02227-y","url":null,"abstract":"<p>In this paper, we are going to establish a reversed Hardy–Littlewood–Sobolev inequality on different dimensional space and prove the existence of extremal functions for the best constant. Furthermore, we investigate the regularity of extremal functions and provide a necessary conditions for the existence of solutions of the integral systems. Finally, we classify the extremal functions.\u0000</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886645","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}
引用次数: 0
Strong Consistency of Wavelet Estimator for Biased Nonparametric Regression Function Under Strong Mixing 强混合条件下有偏非参数回归函数的小波估计器的强一致性
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-08-03 DOI: 10.1007/s00025-024-02248-7
Yuncai Yu
{"title":"Strong Consistency of Wavelet Estimator for Biased Nonparametric Regression Function Under Strong Mixing","authors":"Yuncai Yu","doi":"10.1007/s00025-024-02248-7","DOIUrl":"https://doi.org/10.1007/s00025-024-02248-7","url":null,"abstract":"<p>This paper focuses on the function estimation problem in nonparametric regression model based on biased samples under strong mixing. We propose a wavelet estimator by using wavelet kernel and investigate the consistency properties of the wavelet estimator. The mean consistency, strong consistency and convergence rate are obtained and the convergence rate is similar as that of wavelet estimator in the standard nonparametric model even although with the presence of bias and strong mixing dependence.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886640","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}
引用次数: 0
Gevrey Versus q-Gevrey Asymptotic Expansions for Some Linear q-Difference–Differential Cauchy Problem 某些线性 q 差分考奇问题的 Gevrey 与 q-Gevrey 渐近展开
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-08-03 DOI: 10.1007/s00025-024-02250-z
Alberto Lastra, Stéphane Malek
{"title":"Gevrey Versus q-Gevrey Asymptotic Expansions for Some Linear q-Difference–Differential Cauchy Problem","authors":"Alberto Lastra, Stéphane Malek","doi":"10.1007/s00025-024-02250-z","DOIUrl":"https://doi.org/10.1007/s00025-024-02250-z","url":null,"abstract":"<p>The asymptotic behavior of the analytic solutions of a family of singularly perturbed <i>q</i>-difference–differential equations in the complex domain is studied. Different asymptotic expansions with respect to the perturbation parameter and to the time variable are provided: one of Gevrey nature, and another of mixed type Gevrey and <i>q</i>-Gevrey. These asymptotic phenomena are observed due to the modification of the norm established on the space of coefficients of the formal solution. The techniques used are based on the adequate path deformation of the difference of two analytic solutions, and the application of several versions of Ramis–Sibuya theorem.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886636","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}
引用次数: 0
Dual Framelets Transform on Manifolds and Graphs 曲面和图上的双帧小变换
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-08-03 DOI: 10.1007/s00025-024-02247-8
Radhakrushna Sahoo
{"title":"Dual Framelets Transform on Manifolds and Graphs","authors":"Radhakrushna Sahoo","doi":"10.1007/s00025-024-02247-8","DOIUrl":"https://doi.org/10.1007/s00025-024-02247-8","url":null,"abstract":"<p>In this paper, the concept of dual framelets on manifolds and its characterization are introduced. The accuracy of the proposed dual framelets transform is determined by sparse representation on graphs. If any pair of the framelet system is associated with filter-bank transform, then compactly supported refinable functions can have vanishing moments at most one and framelet approximation is the order of at most two. An algorithm of decomposition and reconstruction for the dual framelets transform on graph is presented. A new method called dual framelets filter-bank transform (DFFT) is employed, which is faster than the existing method spectral graph wavelet transform (SGWT). The theoretical results along with algorithms for accurate and efficient computation of the DFFT on discrete data sets are provided. Subsequently, some numerical examples are provided to show the importance of DFFT over SGWT on graphs.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886644","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}
引用次数: 0
Achievement Sets of Series in $$mathbb {R}^2$$ $$mathbb {R}^2$$ 中的数列成就集
IF 2.2 3区 数学
Results in Mathematics Pub Date : 2024-08-03 DOI: 10.1007/s00025-024-02239-8
Mateusz Kula, Piotr Nowakowski
{"title":"Achievement Sets of Series in $$mathbb {R}^2$$","authors":"Mateusz Kula, Piotr Nowakowski","doi":"10.1007/s00025-024-02239-8","DOIUrl":"https://doi.org/10.1007/s00025-024-02239-8","url":null,"abstract":"<p>We examine the properties of achievement sets of series in <span>(mathbb {R}^2)</span>. We show several examples of unusual sets of subsums on the plane. We prove that we can obtain any set of <i>P</i>-sums as a cut of an achievement set in <span>(mathbb {R}^2.)</span> We introduce a notion of the spectre of a set in an Abelian group, which is an algebraic version of the notion of the center of distances. We examine properties of the spectre and we use it, for example, to show that the Sierpiński carpet is not an achievement set of any series.</p>","PeriodicalId":54490,"journal":{"name":"Results in Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886630","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}
引用次数: 0
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