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Elementary Formulas for Greatest Common Divisors and Semiprime Factors 最大公因数和半公因数的基本公式
arXiv - MATH - General Mathematics Pub Date : 2024-06-22 DOI: arxiv-2407.03357
Joseph M. Shunia
{"title":"Elementary Formulas for Greatest Common Divisors and Semiprime Factors","authors":"Joseph M. Shunia","doi":"arxiv-2407.03357","DOIUrl":"https://doi.org/arxiv-2407.03357","url":null,"abstract":"We present new formulas for computing greatest common divisors (GCDs) and\u0000extracting the prime factors of semiprimes using only elementary arithmetic\u0000operations: addition, subtraction, multiplication, floored division, and\u0000exponentiation. Our GCD formula simplifies a result of Mazzanti, and is derived\u0000using Kronecker substitution techniques from our previous work. We utilize the\u0000GCD formula, along with recent developments on arithmetic terms for square\u0000roots and factorials, to derive explicit expressions for the prime factors of a\u0000semiprime $n=pq$.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"156 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141570924","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
Some Novel Results on (alpha, beta)-Ricci-Yamabe Soliton and its Spacetime 关于（α，β）里奇-山边孤子及其时空的一些新成果
arXiv - MATH - General Mathematics Pub Date : 2024-06-22 DOI: arxiv-2407.05940
Pankaj Pandey, Kamakshi Sharma
{"title":"Some Novel Results on (alpha, beta)-Ricci-Yamabe Soliton and its Spacetime","authors":"Pankaj Pandey, Kamakshi Sharma","doi":"arxiv-2407.05940","DOIUrl":"https://doi.org/arxiv-2407.05940","url":null,"abstract":"This article aims to investigate the characteristics of (alpha, beta) Ricci\u0000Yamabe soliton (briefly (alpha, beta) (RYS)) and its spacetime. The inclusion\u0000of killing vector field and the Lorentzian metrics make the Ricci-Yamabe\u0000soliton richer and interesting. We study the cosmological and dust fluid model\u0000on (RYS) equipped with Lorentzian para Sasakian (LPS) spacetime. The cases of\u0000eta-parallel Ricci tensor and the Poisson structure have been studied on (RYS)\u0000equipped with (LPS) manifold. Gradient (RYS) equipped with (LPS) manifold also\u0000reveal. Finally, we establish an example of four-dimensional LP Sasakian\u0000manifold (LPS) that satisfy (alpha, beta) (RYS) and some results.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141570925","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
Extended Equivalence of Fuzzy Sets 模糊集的扩展等价性
arXiv - MATH - General Mathematics Pub Date : 2024-06-20 DOI: arxiv-2406.16951
Venkat Murali, Sithembele Nkonkobe
{"title":"Extended Equivalence of Fuzzy Sets","authors":"Venkat Murali, Sithembele Nkonkobe","doi":"arxiv-2406.16951","DOIUrl":"https://doi.org/arxiv-2406.16951","url":null,"abstract":"Preferential equality is an equivalence relation on fuzzy subsets of finite\u0000sets and is a generalization of classical equality of subsets. In this paper we\u0000introduce a tightened version of the preferential equality on fuzzy subsets and\u0000derive some important combinatorial formulae for the number of such tight fuzzy\u0000subsets of an n-element set where n is a natural number. We also offer some\u0000asymptotic results","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504907","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
The Chaos Game Versus Uniform Rotation: From Sierpinski Gaskets to Periodic Orbits 混沌游戏与匀速转动：从西尔平斯基垫圈到周期轨道
arXiv - MATH - General Mathematics Pub Date : 2024-06-17 DOI: arxiv-2407.02506
Abdulrahman Abdulaziz
{"title":"The Chaos Game Versus Uniform Rotation: From Sierpinski Gaskets to Periodic Orbits","authors":"Abdulrahman Abdulaziz","doi":"arxiv-2407.02506","DOIUrl":"https://doi.org/arxiv-2407.02506","url":null,"abstract":"In this paper, we introduce a couple of dynamical systems that are related to\u0000the Chaos Game. We begin by discussing different methods of generating the\u0000Sierpinski gasket. Then we show how the transition from random to uniform\u0000selection reduces the Sierpinski gasket to simple periodic orbits. Next, we\u0000provide a simple formula for the attractor of each of the introduced dynamical\u0000systems based only on the contraction ratio and the regular n-gon on which the\u0000game is played. Finally, we show how the basins of attraction of a particular\u0000dynamical system can generate some novel motifs that can tile the plane.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141550838","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
Sandwiching the Riemann hypothesis 夹层黎曼假设
arXiv - MATH - General Mathematics Pub Date : 2024-06-16 DOI: arxiv-2407.00060
R. C. McPhedran
{"title":"Sandwiching the Riemann hypothesis","authors":"R. C. McPhedran","doi":"arxiv-2407.00060","DOIUrl":"https://doi.org/arxiv-2407.00060","url":null,"abstract":"We consider a system of three analytic functions, two of which are known to\u0000have all their zeros on the critical line $Re (s)=sigma=1/2$. We construct\u0000inequalities which constrain the third function, $xi(s)$, on $Im(s)=0$ to lie\u0000between the other two functions, in a sandwich structure. We investigate what\u0000can be said about the location of zeros and radius of convergence of expansions\u0000of $xi(s)$, with promising results.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504908","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
Uniform Stability of Dynamic SICA HIV Transmission Models on Time Scales 动态 SICA 艾滋病毒传播模型在时间尺度上的均匀稳定性
arXiv - MATH - General Mathematics Pub Date : 2024-06-11 DOI: arxiv-2406.18596
Zahra Belarbi, Benaoumeur Bayour, Delfim F. M. Torres
{"title":"Uniform Stability of Dynamic SICA HIV Transmission Models on Time Scales","authors":"Zahra Belarbi, Benaoumeur Bayour, Delfim F. M. Torres","doi":"arxiv-2406.18596","DOIUrl":"https://doi.org/arxiv-2406.18596","url":null,"abstract":"We consider a SICA model for HIV transmission on time scales. We prove\u0000permanence of solutions and we derive sufficient conditions for the existence\u0000and uniform asymptotic stability of a unique positive almost periodic solution\u0000of the system in terms of a Lyapunov function.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"57 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141531663","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
Some Classes of series involving the Riemann zeta function, Fibonacci numbers and the Lucas numbers 涉及黎曼zeta函数、斐波纳契数和卢卡斯数的一些级数
arXiv - MATH - General Mathematics Pub Date : 2024-06-11 DOI: arxiv-2406.16922
Akerele Olofin Segun
{"title":"Some Classes of series involving the Riemann zeta function, Fibonacci numbers and the Lucas numbers","authors":"Akerele Olofin Segun","doi":"arxiv-2406.16922","DOIUrl":"https://doi.org/arxiv-2406.16922","url":null,"abstract":"The objective of this manuscript is to offer explicit expressions for diverse\u0000categories of infinite series incorporating the Fibonacci (Lucas) sequence and\u0000the Riemann zeta function. In demonstrating our findings, we will utilize\u0000conventional methodologies and integrate the Binet formulas pertinent to these\u0000sequences with generating functions that encompass the Riemann zeta function\u0000alongside established evaluations of certain series.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141531664","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
A Primer on Chainmails: Structures for Point-free Connectivity 链甲入门：无点连接结构
arXiv - MATH - General Mathematics Pub Date : 2024-06-11 DOI: arxiv-2406.16923
J. F. Du Plessis, Zurab Janelidze, Bernardus A. Wessels
{"title":"A Primer on Chainmails: Structures for Point-free Connectivity","authors":"J. F. Du Plessis, Zurab Janelidze, Bernardus A. Wessels","doi":"arxiv-2406.16923","DOIUrl":"https://doi.org/arxiv-2406.16923","url":null,"abstract":"In point-free topology, one abstracts the poset of open subsets of a\u0000topological space, by replacing it with a frame (a complete lattice, where meet\u0000distributes over arbitrary join). In this paper we propose a similar\u0000abstraction of the posets of connected subsets in various space-like\u0000structures. The analogue of a frame is called a chainmail, which is defined as\u0000a poset admitting joins of its mails, i.e., subsets having a lower bound. The\u0000main result of the paper is an equivalence between a subcategory of the\u0000category of complete join-semilattices and the category of chainmails.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"133 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521190","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
A rational approximation of the two-term Machin-like formula for $π$ π$的两期马钦式的合理近似值
arXiv - MATH - General Mathematics Pub Date : 2024-06-07 DOI: arxiv-2406.08510
Sanjar M. Abrarov, Rehan Siddiqui, Rajinder Kumar Jagpal, Brendan M. Quine
{"title":"A rational approximation of the two-term Machin-like formula for $π$","authors":"Sanjar M. Abrarov, Rehan Siddiqui, Rajinder Kumar Jagpal, Brendan M. Quine","doi":"arxiv-2406.08510","DOIUrl":"https://doi.org/arxiv-2406.08510","url":null,"abstract":"In this work, we consider the properties of the two-term Machin-like formula\u0000and develop an algorithm for computing digits of $pi$ by using its rational\u0000approximation. In this approximation, both terms are constructed by using a\u0000representation of $1/pi$ in the binary form. This approach provides the\u0000squared convergence in computing digits of $pi$ without any trigonometric\u0000functions and surd numbers. The Mathematica codes showing some examples are\u0000presented.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504912","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 cyclic 3-manifold covers of the type surface x R 在类型曲面 x R 的环状三芒星覆盖层上
arXiv - MATH - General Mathematics Pub Date : 2024-06-07 DOI: arxiv-2406.15457
Jordan A. Sahattchieve
{"title":"On the cyclic 3-manifold covers of the type surface x R","authors":"Jordan A. Sahattchieve","doi":"arxiv-2406.15457","DOIUrl":"https://doi.org/arxiv-2406.15457","url":null,"abstract":"This article contains a proof of the fact that, under certain mild technical\u0000conditions, the action of the automorphism group of a cyclic 3-manifold cover\u0000of the type SxR, where S is a compact surface, yields a compact quotient. This\u0000result is then immediately applied to extend a theorem on the fiberings over\u0000the circle of certain compact 3-manifolds which are torus sums. As a corollary,\u0000I prove the validity of the conditional main theorem in my article titled \"A\u0000fibering theorem for 3-manifolds\", which appeared in the Journal of Groups,\u0000Complexity, Cryptology in 2021 and its subsequent erratum. This paper also\u0000furnishes a proof of the irreducibility of the summands of compact 3-manifolds\u0000which are torus sums and irreducible.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504852","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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