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Arctangent Series on Pell and Pell-Lucas Polynomials via Cassini-Like Formulae 通过卡西尼公式计算佩尔和佩尔-卢卡斯多项式的反正切数列
Utilitas Mathematica Pub Date : 2024-01-08 DOI: 10.61091/um118-01
Dongwei Guo, Wenchang Chu
{"title":"Arctangent Series on Pell and Pell-Lucas Polynomials via Cassini-Like Formulae","authors":"Dongwei Guo, Wenchang Chu","doi":"10.61091/um118-01","DOIUrl":"https://doi.org/10.61091/um118-01","url":null,"abstract":"By combining the telescoping method with Cassini–like formulae, we evaluate, in closed forms, four classes of sums about products of two arctangent functions with their argument involving Pell and Pell–Lucas polynomials. Several infinite series identities for Fibonacci and Lucas numbers are deduced as consequences.","PeriodicalId":49389,"journal":{"name":"Utilitas Mathematica","volume":"85 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139629328","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
Odd Graceful Labeling of W -Tree W T ( n , k ) and its Disjoint Union W 树 W T ( n , k ) 的奇数优美标签及其二分联盟
Utilitas Mathematica Pub Date : 2024-01-08 DOI: 10.61091/um118-05
Abaid ur Rehman Virk, A. Riasat
{"title":"Odd Graceful Labeling of W -Tree W T ( n , k ) and its Disjoint Union","authors":"Abaid ur Rehman Virk, A. Riasat","doi":"10.61091/um118-05","DOIUrl":"https://doi.org/10.61091/um118-05","url":null,"abstract":"Let G=(V(G),E(G)) be a graph with p vertices and q edges. A graph G of size q is said to be odd graceful if there exists an injection λ:V(G)→0,1,2,…,2q−1 such that assigning each edge xy the label or weight |λ(x)–λ(y)| results in the set of edge labels being 1,3,5,…,2q−1. This concept was introduced in 1991 by Gananajothi. In this paper, we examine the odd graceful labeling of the W-tree, denoted as WT(n,k).","PeriodicalId":49389,"journal":{"name":"Utilitas Mathematica","volume":"231 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139628746","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 S C D F -Modules 关于 S C D F 模块
Utilitas Mathematica Pub Date : 2024-01-08 DOI: 10.61091/um118-06
Mankagna Albert Diompy, Alhousseynou Ba, Andé Souleye Diabang
{"title":"On S C D F -Modules","authors":"Mankagna Albert Diompy, Alhousseynou Ba, Andé Souleye Diabang","doi":"10.61091/um118-06","DOIUrl":"https://doi.org/10.61091/um118-06","url":null,"abstract":"A module M over a commutative ring is termed an SCDF-module if every Dedekind finite object in σ[M] is finitely cogenerated. Utilizing this concept, we explore several properties and characterize various types of SCDF-modules. These include local SCDF-modules, finitely generated $SCDF$-modules, and hollow SCDF-modules with Rad(M)=0≠M. Additionally, we examine QF SCDF-odules in the context of duo-ring.","PeriodicalId":49389,"journal":{"name":"Utilitas Mathematica","volume":"141 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139628874","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
EKFN-Modules EKFN 模块
Utilitas Mathematica Pub Date : 2024-01-08 DOI: 10.61091/um118-03
Mankagna Albert Diompy, Ousseynou Bousso, Remy Diaga Diouf, Oumar Diankha
{"title":"EKFN-Modules","authors":"Mankagna Albert Diompy, Ousseynou Bousso, Remy Diaga Diouf, Oumar Diankha","doi":"10.61091/um118-03","DOIUrl":"https://doi.org/10.61091/um118-03","url":null,"abstract":"In this paper, we utilize the σ category to introduce EKFN-modules, which extend the concept of the EKFN-ring. After presenting some properties, we demonstrate, under certain hypotheses, that if M is an EKFN-module, then the following equivalences hold: the class of uniserial modules coincides with the class of cu-uniserial modules; EKFN-modules correspond to the class of locally noetherian modules; and the class of CD-modules is a subset of the EKFN-modules.","PeriodicalId":49389,"journal":{"name":"Utilitas Mathematica","volume":"116 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139629155","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
Caputo Fractional Derivative Inequalities for Refined Modified ( h , m ) -Convex Functions 细化修正 ( h , m ) -凸函数的卡普托分式衍生不等式
Utilitas Mathematica Pub Date : 2024-01-08 DOI: 10.61091/um118-04
Muhammad Ajmal, Muhammad Rafaqat, Labeeb Ahmad
{"title":"Caputo Fractional Derivative Inequalities for Refined Modified ( h , m ) -Convex Functions","authors":"Muhammad Ajmal, Muhammad Rafaqat, Labeeb Ahmad","doi":"10.61091/um118-04","DOIUrl":"https://doi.org/10.61091/um118-04","url":null,"abstract":"This paper introduces a novel type of convex function known as the refined modified (h,m)-convex function, which is a generalization of the traditional (h,m)-convex function. We establish Hadamard-type inequalities for this new definition by utilizing the Caputo k-fractional derivative. Specifically, we derive two integral identities that involve the nth order derivatives of given functions and use them to prove the estimation of Hadamard-type inequalities for the Caputo k-fractional derivatives of refined modified (h,m)-convex functions. The results obtained in this research demonstrate the versatility of the refined modified (h,m)-convex function and the usefulness of Caputo k-fractional derivatives in establishing important inequalities. Our work contributes to the existing body of knowledge on convex functions and offers insights into the applications of fractional calculus in mathematical analysis. The research findings have the potential to pave the way for future studies in the area of convex functions and fractional calculus, as well as in other areas of mathematical research.","PeriodicalId":49389,"journal":{"name":"Utilitas Mathematica","volume":"113 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139628951","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 Orbital Regular Graph of Finite Solvable Groups 论有限可解群的轨道正则图
Utilitas Mathematica Pub Date : 2024-01-08 DOI: 10.61091/um118-02
Karnika Sharma, Vijay Kumar Bhat, P. Singh
{"title":"On the Orbital Regular Graph of Finite Solvable Groups","authors":"Karnika Sharma, Vijay Kumar Bhat, P. Singh","doi":"10.61091/um118-02","DOIUrl":"https://doi.org/10.61091/um118-02","url":null,"abstract":"Let G be a finite solvable group and Δ be the subset of Υ×Υ, where Υ is the set of all pairs of size two commuting elements in G. If G operates on a transitive G – space by the action (υ1,υ2)g=(υg1,υg2); υ1,υ2∈Υ and g∈G, then orbits of G are called orbitals. The subset Δo={(υ,υ);υ∈Υ,(υ,υ)∈Υ×Υ} represents G′s diagonal orbital.The orbital regular graph is a graph on which G acts regularly on the vertices and the edge set. In this paper, we obtain the orbital regular graphs for some finite solvable groups using a regular action. Furthermore, the number of edges for each of a group’s orbitals is obtained.","PeriodicalId":49389,"journal":{"name":"Utilitas Mathematica","volume":"211 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139628783","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
Detectable colorings of graphs 图的可检测着色
Utilitas Mathematica Pub Date : 2006-03-01 DOI: 10.21136/mb.2005.134214
G. Chartrand, Henry Escuadro, F. Okamoto, Ping Zhang
{"title":"Detectable colorings of graphs","authors":"G. Chartrand, Henry Escuadro, F. Okamoto, Ping Zhang","doi":"10.21136/mb.2005.134214","DOIUrl":"https://doi.org/10.21136/mb.2005.134214","url":null,"abstract":"","PeriodicalId":49389,"journal":{"name":"Utilitas Mathematica","volume":"14 1","pages":"13-32"},"PeriodicalIF":0.0,"publicationDate":"2006-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68443497","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: 21
An optimization theorem with applications in some mathematical programming problems 一个最优化定理及其在若干数学规划问题中的应用
Utilitas Mathematica Pub Date : 1984-11-01 DOI: 10.5555/14033.14048
C. R. Bector, B. L. Bhatia
{"title":"An optimization theorem with applications in some mathematical programming problems","authors":"C. R. Bector, B. L. Bhatia","doi":"10.5555/14033.14048","DOIUrl":"https://doi.org/10.5555/14033.14048","url":null,"abstract":"","PeriodicalId":49389,"journal":{"name":"Utilitas Mathematica","volume":"26 1","pages":"249-258"},"PeriodicalIF":0.0,"publicationDate":"1984-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71115822","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: 1
The development of a time-domain model for transients on lossy, distorting coaxil cables 有损耗、扭曲的同轴电缆瞬态时域模型的建立
Utilitas Mathematica Pub Date : 1984-11-01 DOI: 10.5555/14033.14037
D. Meek
{"title":"The development of a time-domain model for transients on lossy, distorting coaxil cables","authors":"D. Meek","doi":"10.5555/14033.14037","DOIUrl":"https://doi.org/10.5555/14033.14037","url":null,"abstract":"","PeriodicalId":49389,"journal":{"name":"Utilitas Mathematica","volume":"26 1","pages":"33-44"},"PeriodicalIF":0.0,"publicationDate":"1984-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71115705","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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