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On Approximation Operators Involving Tricomi Function 论涉及 Tricomi 函数的近似算子
IF 1.2 3区 数学
Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-08-05 DOI: 10.1007/s40840-024-01750-z
Nusrat Raza, Manoj Kumar, M. Mursaleen
{"title":"On Approximation Operators Involving Tricomi Function","authors":"Nusrat Raza, Manoj Kumar, M. Mursaleen","doi":"10.1007/s40840-024-01750-z","DOIUrl":"https://doi.org/10.1007/s40840-024-01750-z","url":null,"abstract":"<p>The primary objective of this research article is to introduce and study an approximation operator involving the Tricomi function by using Korovkin’s theorem and a conventional method based on the modulus of continuity. In Lipschitz-type spaces, we demonstrate the rate of convergence, and we are also able to determine the convergence properties of our operators. In addition, we illustrate the convergence of our proposed operators using various graphs and error-estimating tables for numerical instances.</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"5 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141969483","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
Angles and Quasimöbius Mappings 角度与夸西莫比乌斯映射
IF 1.2 3区 数学
Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-07-29 DOI: 10.1007/s40840-024-01738-9
Qingshan Zhou, Tiantian Guan, Zhiqiang Yang
{"title":"Angles and Quasimöbius Mappings","authors":"Qingshan Zhou, Tiantian Guan, Zhiqiang Yang","doi":"10.1007/s40840-024-01738-9","DOIUrl":"https://doi.org/10.1007/s40840-024-01738-9","url":null,"abstract":"<p>In this paper we establish an angular characteristic for the class of quasimöbius mappings in metric spaces.</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"48 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141866820","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 Perfect Balanced Rainbow-Free Colorings and Complete Colorings of Projective Spaces 论投影空间的完美平衡无彩虹着色和完全着色
IF 1.2 3区 数学
Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-07-29 DOI: 10.1007/s40840-024-01746-9
Lijun Ma, Zihong Tian
{"title":"On Perfect Balanced Rainbow-Free Colorings and Complete Colorings of Projective Spaces","authors":"Lijun Ma, Zihong Tian","doi":"10.1007/s40840-024-01746-9","DOIUrl":"https://doi.org/10.1007/s40840-024-01746-9","url":null,"abstract":"<p>This paper is motivated by the problem of determining the related chromatic numbers of some hypergraphs. A hypergraph <span>(Pi _{q}(n,k))</span> is defined from a projective space PG<span>((n-1,q))</span>, where the vertices are points and the hyperedges are <span>((k-1))</span>-dimensional subspaces. For the perfect balanced rainbow-free colorings, we show that <span>({overline{chi }}_{p}(Pi _{q}(n,k))=frac{q^n-1}{l(q-1)})</span>, where <span>(kge lceil frac{n+1}{2}rceil )</span> and <i>l</i> is the smallest nontrivial factor of <span>(frac{q^n-1}{q-1})</span>. For the complete colorings, we prove that there is no complete coloring for <span>(Pi _{q}(n,k))</span> with <span>(2le k&lt;n)</span>. We also provide some results on the related chromatic numbers of subhypergraphs of <span>(Pi _{q}(n,k))</span>.</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"56 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141866818","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
Greedy Block Extended Kaczmarz Method for Solving the Least Squares Problems 解决最小二乘法问题的贪心块扩展卡茨马兹法
IF 1.2 3区 数学
Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-07-29 DOI: 10.1007/s40840-024-01739-8
Ni-Hong Ke, Rui Li, Jun-Feng Yin
{"title":"Greedy Block Extended Kaczmarz Method for Solving the Least Squares Problems","authors":"Ni-Hong Ke, Rui Li, Jun-Feng Yin","doi":"10.1007/s40840-024-01739-8","DOIUrl":"https://doi.org/10.1007/s40840-024-01739-8","url":null,"abstract":"<p>A greedy block extended Kaczmarz method is introduced for solving the least squares problem where the greedy rule combines the maximum-distances with relaxation parameters. In order to save the computational cost of Moore–Penrose inverse, an average projection technique is used. The convergence theory of the greedy block extended Kaczmarz method is established and an upper bound for the convergence rate is also derived. Numerical experiments show that the proposed method is efficient and better than the randomized block extended Kaczmarz methods in terms of the number of iteration steps and computational time.</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"10 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141866819","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
Riccati Transformation and Non-Oscillation Criterion for Half-Linear Difference Equations 半线性差分方程的里卡提变换和非振荡准则
IF 1.2 3区 数学
Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-07-18 DOI: 10.1007/s40840-024-01745-w
Kōdai Fujimoto, Petr Hasil, Michal Veselý
{"title":"Riccati Transformation and Non-Oscillation Criterion for Half-Linear Difference Equations","authors":"Kōdai Fujimoto, Petr Hasil, Michal Veselý","doi":"10.1007/s40840-024-01745-w","DOIUrl":"https://doi.org/10.1007/s40840-024-01745-w","url":null,"abstract":"<p>In this paper, we study a general class of half-linear difference equations. Applying a version of the discrete Riccati transformation, we prove a non-oscillation criterion for the analyzed equations. In the formulation of the criterion, we do not use auxiliary sequences, but we consider directly the coefficients of the treated equations. Since the obtained criterion is new in many cases, we also formulate new simple corollaries and mention illustrative examples.</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"35 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141737514","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
Bounds on Zero Forcing Using (Upper) Total Domination and Minimum Degree 使用（上）总支配和最小度数的零强迫界限
IF 1.2 3区 数学
Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-07-15 DOI: 10.1007/s40840-024-01744-x
Boštjan Brešar, María Gracia Cornet, Tanja Dravec, Michael Henning
{"title":"Bounds on Zero Forcing Using (Upper) Total Domination and Minimum Degree","authors":"Boštjan Brešar, María Gracia Cornet, Tanja Dravec, Michael Henning","doi":"10.1007/s40840-024-01744-x","DOIUrl":"https://doi.org/10.1007/s40840-024-01744-x","url":null,"abstract":"<p>While a number of bounds are known on the zero forcing number <i>Z</i>(<i>G</i>) of a graph <i>G</i> expressed in terms of the order of a graph and maximum or minimum degree, we present two bounds that are related to the (upper) total domination number <span>(gamma _t(G))</span> (resp. <span>(Gamma _t(G))</span>) of <i>G</i>. We prove that <span>(Z(G)+gamma _t(G)le n(G))</span> and <span>(Z(G)+frac{Gamma _t(G)}{2}le n(G))</span> holds for any graph <i>G</i> with no isolated vertices of order <i>n</i>(<i>G</i>). Both bounds are sharp as demonstrated by several infinite families of graphs. In particular, we show that every graph <i>H</i> is an induced subgraph of a graph <i>G</i> with <span>(Z(G)+frac{Gamma _t(G)}{2}=n(G))</span>. Furthermore, we prove a characterization of graphs with power domination equal to 1, from which we derive a characterization of the extremal graphs attaining the trivial lower bound <span>(Z(G)ge delta (G))</span>. The class of graphs that appears in the corresponding characterizations is obtained by extending an idea of Row for characterizing the graphs with zero forcing number equal to 2.</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"37 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141717643","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
Finite Groups Whose Maximal Subgroups are 2-Nilpotent or Normal 最大子群为 2 弱或正常的有限群
IF 1.2 3区 数学
Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-07-09 DOI: 10.1007/s40840-024-01743-y
Changguo Shao, Antonio Beltrán
{"title":"Finite Groups Whose Maximal Subgroups are 2-Nilpotent or Normal","authors":"Changguo Shao, Antonio Beltrán","doi":"10.1007/s40840-024-01743-y","DOIUrl":"https://doi.org/10.1007/s40840-024-01743-y","url":null,"abstract":"<p>We describe the structure of those finite groups whose maximal subgroups are either 2-nilpotent or normal. Among other properties, we prove that if such a group <i>G</i> does not have any non-trivial quotient that is a 2-group, then <i>G</i> is solvable. Also, if <i>G</i> is a solvable group satisfying the above conditions, then the 2-length of <i>G</i> is less than or equal to 2. If, on the contrary, <i>G</i> is not solvable, then <i>G</i> has exactly one non-abelian principal factor and the unique simple group involved is one of the groups <span>(textrm{PSL}_2(p^{2^a}))</span>, where <i>p</i> is an odd prime and <span>(age 1)</span>, or <i>p</i> is a prime satisfying <span>(pequiv pm 1)</span> <span>((textrm{mod}~ 8))</span> and <span>(a=0)</span>.</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"23 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574608","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
Some Sharp Bohr-Type Inequalities for Analytic Functions 解析函数的一些尖锐玻尔不等式
IF 1.2 3区 数学
Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-07-08 DOI: 10.1007/s40840-024-01740-1
Xiaojun Hu, Boyong Long
{"title":"Some Sharp Bohr-Type Inequalities for Analytic Functions","authors":"Xiaojun Hu, Boyong Long","doi":"10.1007/s40840-024-01740-1","DOIUrl":"https://doi.org/10.1007/s40840-024-01740-1","url":null,"abstract":"<p>This article focuses on the improvement of the classic Bohr’s inequality for bounded analytic functions on the unit disk. We give some sharp versions of Bohr’s inequality, generalizing the previous results.</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"71 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574610","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
Negative Type and Bi-lipschitz Embeddings into Hilbert Space 希尔伯特空间的负类型和双利普西茨嵌入
IF 1.2 3区 数学
Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-07-08 DOI: 10.1007/s40840-024-01736-x
Gavin Robertson
{"title":"Negative Type and Bi-lipschitz Embeddings into Hilbert Space","authors":"Gavin Robertson","doi":"10.1007/s40840-024-01736-x","DOIUrl":"https://doi.org/10.1007/s40840-024-01736-x","url":null,"abstract":"<p>The usual theory of negative type (and <i>p</i>-negative type) is heavily dependent on an embedding result of Schoenberg, which states that a metric space isometrically embeds in some Hilbert space if and only if it has 2-negative type. A generalisation of this embedding result to the setting of bi-lipschitz embeddings was given by Linial, London and Rabinovich. In this article we use this newer embedding result to define the concept of distorted <i>p</i>-negative type and extend much of the known theory of <i>p</i>-negative type to the setting of bi-lipschitz embeddings. In particular we show that a metric space <span>((X,d_{X}))</span> has <i>p</i>-negative type with distortion <i>C</i> (<span>(0le p&lt;infty )</span>, <span>(1le C&lt;infty )</span>) if and only if <span>((X,d_{X}^{p/2}))</span> admits a bi-lipschitz embedding into some Hilbert space with distortion at most <i>C</i>. Analogues of strict <i>p</i>-negative type and polygonal equalities in this new setting are given and systematically studied. Finally, we provide explicit examples of these concepts in the bi-lipschitz setting for the bipartite graphs <span>(K_{m,n})</span>.</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"13 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574609","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 Generalized Brezis–Lieb Lemma on Graphs and Its Application to Kirchhoff Type Equations 图形上的广义 Brezis-Lieb 定理及其在基尔霍夫式方程中的应用
IF 1.2 3区 数学
Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-07-08 DOI: 10.1007/s40840-024-01741-0
Sheng Cheng, Shuai Yao, Haibo Chen
{"title":"A Generalized Brezis–Lieb Lemma on Graphs and Its Application to Kirchhoff Type Equations","authors":"Sheng Cheng, Shuai Yao, Haibo Chen","doi":"10.1007/s40840-024-01741-0","DOIUrl":"https://doi.org/10.1007/s40840-024-01741-0","url":null,"abstract":"<p>In this paper, with the help of potential function, we extend the classical Brezis–Lieb lemma on Euclidean space to graphs, which can be applied to the following Kirchhoff equation </p><span>$$begin{aligned} left{ begin{array}{l} -left( 1+b int _{mathbb { V}}|nabla u|^2 d mu right) Delta u+ left( lambda V(x) +1 right) u=|u|^{p-2} u text{ in } mathbb { V}, u in W^{1,2}(mathbb {V}), end{array}right. end{aligned}$$</span><p>on a connected locally finite graph <span>(G=(mathbb {V}, mathbb {E}))</span>, where <span>(b, lambda &gt;0)</span>, <span>(p&gt;2)</span> and <i>V</i>(<i>x</i>) is a potential function defined on <span>(mathbb {V})</span>. The purpose of this paper is four-fold. First of all, using the idea of the filtration Nehari manifold technique and a compactness result based on generalized Brezis–Lieb lemma on graphs, we prove that there admits a positive solution <span>(u_{lambda , b} in E_lambda )</span> with positive energy for <span>(b in (0, b^*))</span> when <span>(2&lt;p&lt;4)</span>. In the sequel, when <span>(p geqslant 4)</span>, a positive ground state solution <span>(w_{lambda , b} in E_lambda )</span> is also obtained by using standard variational methods. What’s more, we explore various asymptotic behaviors of <span>(u_{lambda , b}, w_{lambda , b} in E_lambda )</span> by separately controlling the parameters <span>(lambda rightarrow infty )</span> and <span>(b rightarrow 0^{+})</span>, as well as jointly controlling both parameters. Finally, we utilize iteration to obtain the <span>(L^{infty })</span>-norm estimates of the solution.</p>","PeriodicalId":50718,"journal":{"name":"Bulletin of the Malaysian Mathematical Sciences Society","volume":"56 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574611","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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