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Some Results on the Free Poisson Distribution 关于自由泊松分布的一些结果
Axioms Pub Date : 2024-07-24 DOI: 10.3390/axioms13080496
Ayed. R. A. Alanzi, Ohud A. Alqasem, M. E. A. Elwahab, Raouf Fakhfakh
{"title":"Some Results on the Free Poisson Distribution","authors":"Ayed. R. A. Alanzi, Ohud A. Alqasem, M. E. A. Elwahab, Raouf Fakhfakh","doi":"10.3390/axioms13080496","DOIUrl":"https://doi.org/10.3390/axioms13080496","url":null,"abstract":"Let K+(μi)={Qsiμi,si∈(m0μi,m+μi)}, i=1,2, be two CSK families generated by the nondegenerate probability measures μ1 and μ2 with support bounded from above. Define the set of measures L=K+(μ1)•K+(μ2)={Qs1μ1•Qs2μ2,s1∈(m0μ1,m+μ1)ands2∈(m0μ2,m+μ2)}, where Qs1μ1•Qs2μ2 denotes the Fermi convolution of Qs1μ1 and Qs2μ2. We prove that if L is still a CSK family (that is, L=K+(σ) for some nondegenerate probability measure ()σ), then the probability measures σ, μ1 and μ2 are of the free Poisson type and follow the free Poisson law up to affinity. The same result, regarding the free Poisson measure, is obtained if we consider the t-deformed free convolution t replacing the Fermi convolution • in the family of measures L.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"21 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141808880","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}
引用次数: 0
On Some Distance Spectral Characteristics of Trees 论树木的一些距离谱特征
Axioms Pub Date : 2024-07-23 DOI: 10.3390/axioms13080494
Sakander Hayat, Asad Khan, Mohammed J. F. Alenazi
{"title":"On Some Distance Spectral Characteristics of Trees","authors":"Sakander Hayat, Asad Khan, Mohammed J. F. Alenazi","doi":"10.3390/axioms13080494","DOIUrl":"https://doi.org/10.3390/axioms13080494","url":null,"abstract":"Graham and Pollack in 1971 presented applications of eigenvalues of the distance matrix in addressing problems in data communication systems. Spectral graph theory employs tools from linear algebra to retrieve the properties of a graph from the spectrum of graph-theoretic matrices. The study of graphs with “few eigenvalues” is a contemporary problem in spectral graph theory. This paper studies graphs with few distinct distance eigenvalues. After mentioning the classification of graphs with one and two distinct distance eigenvalues, we mainly focus on graphs with three distinct distance eigenvalues. Characterizing graphs with three distinct distance eigenvalues is “highly” non-trivial. In this paper, we classify all trees whose distance matrix has precisely three distinct eigenvalues. Our proof is different from earlier existing proof of the result as our proof is extendable to other similar families such as unicyclic and bicyclic graphs. The main tools which we employ include interlacing and equitable partitions. We also list all the connected graphs on ν ≤ 6 vertices and compute their distance spectra. Importantly, all these graphs on ν ≤ 6 vertices are determined from their distance spectra. We deliver a distance cospectral pair of order 7, thus making it a distance cospectral pair of the smallest order. This paper is concluded with some future directions.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"102 25","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141812300","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}
引用次数: 0
Matrix Factorization and Some Fast Discrete Transforms 矩阵因式分解和一些快速离散变换
Axioms Pub Date : 2024-07-23 DOI: 10.3390/axioms13080495
Iliya Bouyukliev, Mariya Dzhumalieva-Stoeva, Paskal Piperkov
{"title":"Matrix Factorization and Some Fast Discrete Transforms","authors":"Iliya Bouyukliev, Mariya Dzhumalieva-Stoeva, Paskal Piperkov","doi":"10.3390/axioms13080495","DOIUrl":"https://doi.org/10.3390/axioms13080495","url":null,"abstract":"In this paper, three discrete transforms related to vector spaces over finite fields are studied. For our purposes, and according to the properties of the finite fields, the most suitable transforms are as follows: for binary fields, this is the Walsh–Hadamard transform; for odd prime fields, the Vilenkin–Chrestenson transform; and for composite fields, the trace transform. A factorization of the transform matrices using Kronecker power is given so that the considered discrete transforms are reduced to the fast discrete transforms. Examples and applications are also presented of the considered transforms in coding theory for calculating the weight distribution of a linear code.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"17 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141810019","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}
引用次数: 0
New Interval-Valued Soft Separation Axioms 新的区间值软分离公理
Axioms Pub Date : 2024-07-22 DOI: 10.3390/axioms13070493
J. I. Baek, T. Al-shami, S. Jafari, M. Cheong, K. Hur
{"title":"New Interval-Valued Soft Separation Axioms","authors":"J. I. Baek, T. Al-shami, S. Jafari, M. Cheong, K. Hur","doi":"10.3390/axioms13070493","DOIUrl":"https://doi.org/10.3390/axioms13070493","url":null,"abstract":"Our research’s main aim is to study two viewpoints: First, we define partial interval-valued soft Ti(j)-spaces (i = 0, 1, 2, 3, 4; j = i, ii), study some of their properties and some of relationships among them, and give some examples. Second, we introduce the notions of partial total interval-valued soft Tj(i)-spaces (i = 0, 1, 2, 3, 4; j = i, ii) and discuss some of their properties. We present some relationships among them and give some examples.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"2 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141815813","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}
引用次数: 0
Locally Convex Spaces with Sequential Dunford–Pettis Type Properties 具有序列邓福德-佩蒂斯类型属性的局部凸空间
Axioms Pub Date : 2024-07-22 DOI: 10.3390/axioms13070491
S. Gabriyelyan
{"title":"Locally Convex Spaces with Sequential Dunford–Pettis Type Properties","authors":"S. Gabriyelyan","doi":"10.3390/axioms13070491","DOIUrl":"https://doi.org/10.3390/axioms13070491","url":null,"abstract":"Let p,q,q′∈[1,∞], q′≤q. Several new characterizations of locally convex spaces with the sequential Dunford–Pettis property of order (p,q) are given. We introduce and thoroughly study the sequential Dunford–Pettis* property of order (p,q) of locally convex spaces (in the realm of Banach spaces, the sequential DP(p,∞)* property coincides with the well-known DPp* property). Being motivated by the coarse p-DP* property and the p-Dunford–Pettis relatively compact property for Banach spaces, we define and study the coarse sequential DP(p,q)* property, the coarse DPp* property and the p-Dunford–Pettis sequentially compact property of order (q′,q) in the class of all locally convex spaces.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"20 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141816477","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}
引用次数: 0
Numerical Computation of 2D Domain Integrals in Boundary Element Method by (α, β) Distance Transformation for Transient Heat Conduction Problems 通过 (α, β) 距离变换计算瞬态热传导问题中边界元法的二维域积分数值计算
Axioms Pub Date : 2024-07-22 DOI: 10.3390/axioms13070490
Yunqiao Dong, Zhengxu Tan, Hengbo Sun
{"title":"Numerical Computation of 2D Domain Integrals in Boundary Element Method by (α, β) Distance Transformation for Transient Heat Conduction Problems","authors":"Yunqiao Dong, Zhengxu Tan, Hengbo Sun","doi":"10.3390/axioms13070490","DOIUrl":"https://doi.org/10.3390/axioms13070490","url":null,"abstract":"When the time-dependent boundary element method, also termed the pseudo-initial condition method, is employed for solving transient heat conduction problems, the numerical evaluation of domain integrals is necessitated. Consequently, the accurate calculation of the domain integrals is of crucial importance for analyzing transient heat conduction. However, as the time step decreases progressively and approaches zero, the integrand of the domain integrals is close to singular, resulting in large errors when employing standard Gaussian quadrature directly. To solve the problem and further improve the calculation accuracy of the domain integrals, an (α, β) distance transformation is presented. Distance transformation is a simple and efficient method for eliminating near-singularity, typically applied to nearly singular integrals. Firstly, the (α, β) coordinate transformation is introduced. Then, a new distance transformation for the domain integrals is constructed by replacing the shortest distance with the time step. With the new method, the integrand of the domain integrals is substantially smoothed, and the singularity arising from small time steps in the domain integrals is effectively eliminated. Thus, more accurate results can be obtained by the (α, β) distance transformation. Different sizes of time steps, positions of source point, and shapes of integration elements are considered in numerical examples. Comparative studies of the numerical results for the domain integrals using various methods demonstrate that higher accuracy and efficiency are achieved by the proposed method.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"29 29","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141814030","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}
引用次数: 0
Probabilistic and Average Gel’fand Widths of Sobolev Space Equipped with Gaussian Measure in the Sq-Norm 索波列夫空间的概率和平均格尔范宽度（配备平方正态高斯量纲
Axioms Pub Date : 2024-07-22 DOI: 10.3390/axioms13070492
Ruihuan Wu, Yuqing Liu, Huan Li
{"title":"Probabilistic and Average Gel’fand Widths of Sobolev Space Equipped with Gaussian Measure in the Sq-Norm","authors":"Ruihuan Wu, Yuqing Liu, Huan Li","doi":"10.3390/axioms13070492","DOIUrl":"https://doi.org/10.3390/axioms13070492","url":null,"abstract":"In this article, we mainly studied the Gel’fand widths of Sobolev space in the probabilistic and average settings. And, we estimated the sharp bounds of the probabilistic Gel’fand (N,δ)-widths of multivariate Sobolev space MW2r(Td) with mixed derivative equipped with the Gaussian measure in the Sq-norm by discretization methods. Later, we estimated the sharp bounds of the p-average Gel’fand N-widths of univariate Sobolev space W2r(T) and multivariate Sobolev space MW2r(Td) with mixed derivative equipped with the Gaussian measure in the Sq-norm.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"35 15","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141816688","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}
引用次数: 0
Consistent Sampling Approximations in Abstract Hilbert Spaces 抽象希尔伯特空间中的一致采样近似法
Axioms Pub Date : 2024-07-21 DOI: 10.3390/axioms13070489
Sinuk Kang, Kil Hyun Kwon, Dae Gwan Lee
{"title":"Consistent Sampling Approximations in Abstract Hilbert Spaces","authors":"Sinuk Kang, Kil Hyun Kwon, Dae Gwan Lee","doi":"10.3390/axioms13070489","DOIUrl":"https://doi.org/10.3390/axioms13070489","url":null,"abstract":"This paper considers generalized consistent sampling and reconstruction processes in an abstract separable Hilbert space. Using an operator-theoretical approach, quasi-consistent and consistent approximations with optimal properties, such as possessing the minimum norm or being closest to the original vector, are derived. The results are illustrated with several examples.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"60 16","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141817883","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}
引用次数: 0
Geometric Inequalities of Slant Submanifolds in Locally Metallic Product Space Forms 局部金属积累空间形式中斜面子曼形体的几何不等式
Axioms Pub Date : 2024-07-19 DOI: 10.3390/axioms13070486
Yanlin Li, Mohd Aquib, Meraj Ali Khan, Ibrahim Al-Dayel, M. Z. Youssef
{"title":"Geometric Inequalities of Slant Submanifolds in Locally Metallic Product Space Forms","authors":"Yanlin Li, Mohd Aquib, Meraj Ali Khan, Ibrahim Al-Dayel, M. Z. Youssef","doi":"10.3390/axioms13070486","DOIUrl":"https://doi.org/10.3390/axioms13070486","url":null,"abstract":"In this particular article, our focus revolves around the establishment of a geometric inequality, commonly referred to as Chen’s inequality. We specifically apply this inequality to assess the square norm of the mean curvature vector and the warping function of warped product slant submanifolds. Our investigation takes place within the context of locally metallic product space forms with quarter-symmetric metric connections. Additionally, we delve into the condition that determines when equality is achieved within the inequality. Furthermore, we explore a number of implications of our findings.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"102 29","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141821588","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}
引用次数: 0
On the Relative Φ-Growth of Hadamard Compositions of Dirichlet Series 论德里赫特数列哈达玛德组合的相对 Φ 增长
Axioms Pub Date : 2024-07-19 DOI: 10.3390/axioms13070487
M. Sheremeta, O. Mulyava
{"title":"On the Relative Φ-Growth of Hadamard Compositions of Dirichlet Series","authors":"M. Sheremeta, O. Mulyava","doi":"10.3390/axioms13070487","DOIUrl":"https://doi.org/10.3390/axioms13070487","url":null,"abstract":"For the Dirichlet series F(s)=∑n=1∞fnexp{sλn}, which is the Hadamard composition of the genus m of similar Dirichlet series Fj(s) with the same exponents, the growth with respect to the function G(s) given as the Dirichlet series is studied in terms of the Φ-type (the upper limit of MG−1(MF(σ))/Φ(σ) as σ↑A) and convergence Φ-class defined by the condition ∫σ0AΦ′(σ)MG−1(MF(σ))Φ2(σ)dσ<+∞, where MF(σ) is the maximum modulus of the function F at an imaginary line and A is the abscissa of the absolute convergence.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"105 18","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141820661","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}
引用次数: 0
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