arXiv - MATH - General Mathematics最新文献_第6页

Alternative views on fuzzy numbers and their application to fuzzy differential equations 关于模糊数的其他观点及其在模糊微分方程中的应用

arXiv - MATH - General Mathematics Pub Date : 2024-06-29 DOI: arxiv-2407.07906

Akbar H. Borzabadi, Mohammad Heidari, Delfim F. M. Torres

引用次数: 0

Response Matrix Benchmark for the 1D Transport Equation with Matrix Scaling 带矩阵缩放的一维传输方程的响应矩阵基准

arXiv - MATH - General Mathematics Pub Date : 2024-06-28 DOI: arxiv-2407.07905

B. D. Ganapol, J. K. Patel

引用次数: 0

Euclidean Tours in Fairy Chess 仙女棋中的欧几里得之旅

arXiv - MATH - General Mathematics Pub Date : 2024-06-27 DOI: arxiv-2407.07903

Gabriele Di Pietro, Marco Ripà

引用次数: 0

The correct structures in fuzzy soft set theory 模糊软集合理论中的正确结构

arXiv - MATH - General Mathematics Pub Date : 2024-06-25 DOI: arxiv-2407.06203

Santanu Acharjee, Sidhartha Medhi

{"title":"The correct structures in fuzzy soft set theory","authors":"Santanu Acharjee, Sidhartha Medhi","doi":"arxiv-2407.06203","DOIUrl":"https://doi.org/arxiv-2407.06203","url":null,"abstract":"In 1999, Molodtsov cite{1} developed the idea of soft set theory, proving it\u0000to be a flexible mathematical tool for dealing with uncertainty. Several\u0000researchers have extended the framework by combining it with other theories of\u0000uncertainty, such as fuzzy set theory, intuitionistic fuzzy soft set theory,\u0000rough soft set theory, and so on. These enhancements aim to increase the\u0000applicability and expressiveness of soft set theory, making it a more robust\u0000tool for dealing with complex, real-world problems characterized by uncertainty\u0000and vagueness. The notion of fuzzy soft sets and their associated operations\u0000were introduced by Maji et al. cite{7}. However, Molodtsov cite{3} identified\u0000numerous incorrect results and notions of soft set theory that were introduced\u0000in the paper cite{7}. Therefore, the derived concept of fuzzy soft sets is\u0000equally incorrect since the basic idea of soft sets in cite{7} is flawed.\u0000Consequently, it is essential to address these incorrect notions and provide an\u0000exact and formal definition of the idea of fuzzy soft sets. This reevaluation\u0000is important to guarantee fuzzy soft set theory's theoretical stability and\u0000practical application across a range of domains. In this paper, we propose\u0000fuzzy soft set theory based on Molodtsov's correct notion of soft set theory\u0000and demonstrate a fuzzy soft set in matrix form. Additionally, we derive\u0000several significant findings on fuzzy soft sets.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141570926","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

Cryptanalysis of RSA Cryptosystem: Prime Factorization using Genetic Algorithm RSA 密码系统的密码分析：利用遗传算法进行质因数分解

arXiv - MATH - General Mathematics Pub Date : 2024-06-24 DOI: arxiv-2407.05944

Mahadee Al Mobin, Md Kamrujjaman

{"title":"Cryptanalysis of RSA Cryptosystem: Prime Factorization using Genetic Algorithm","authors":"Mahadee Al Mobin, Md Kamrujjaman","doi":"arxiv-2407.05944","DOIUrl":"https://doi.org/arxiv-2407.05944","url":null,"abstract":"Prime factorization has been a buzzing topic in the field of number theory\u0000since time unknown. However, in recent years, alternative avenues to tackle\u0000this problem are being explored by researchers because of its direct\u0000application in the arena of cryptography. One of such applications is the\u0000cryptanalysis of RSA numbers, which requires prime factorization of large\u0000semiprimes. Based on numerical experiments, this paper proposes a conjecture on\u0000the distribution of digits on prime of infinite length. This paper infuses the\u0000theoretical understanding of primes to optimize the search space of prime\u0000factors by shrinking it upto 98.15%, which, in terms of application, has shown\u000026.50% increase in the success rate and 41.91% decrease of the maximum number\u0000of generations required by the genetic algorithm used traditionally in the\u0000literature. This paper also introduces a variation of the genetic algorithm\u0000named Sieve Method that is fine-tuned for factorization of big semi-primes,\u0000which was able to factor numbers up to 23 decimal digits with 84% success rate.\u0000Our findings shows that sieve methods on average has achieved 321.89% increase\u0000in success rate and 64.06% decrement in the maximum number of generations\u0000required for the algorithm to converge compared to the existing literatures.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141570923","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

Numerically Computed Double and Triple Bubbles in $R^3$ for Density $r^p$ 密度为 $r^p$ 的 $R^3$ 数值计算双气泡和三气泡

arXiv - MATH - General Mathematics Pub Date : 2024-06-24 DOI: arxiv-2407.07122

Eve Parrott

引用次数: 0

Ax, 3 polyominoes for tiling the plane non-periodically Ax，3 个用于非周期性平铺平面的多面体

arXiv - MATH - General Mathematics Pub Date : 2024-06-24 DOI: arxiv-2407.06202

Vincent Van Dongen, Pierre Gradit

引用次数: 0

Fibonacci--Theodorus Spiral and its properties 斐波那契--狄奥多罗斯螺旋及其特性

arXiv - MATH - General Mathematics Pub Date : 2024-06-24 DOI: arxiv-2407.07109

Michael R. Bacon, Charles K. Cook, Rigoberto Flórez, Robinson A. Higuita, José L. Ramírez

{"title":"Fibonacci--Theodorus Spiral and its properties","authors":"Michael R. Bacon, Charles K. Cook, Rigoberto Flórez, Robinson A. Higuita, José L. Ramírez","doi":"arxiv-2407.07109","DOIUrl":"https://doi.org/arxiv-2407.07109","url":null,"abstract":"Inspired by the ancient spiral constructed by the greek philosopher Theodorus\u0000which is based on concatenated right triangles, we have created a spiral. In\u0000this spiral, called emph{Fibonacci--Theodorus}, the sides of the triangles\u0000have lengths corresponding to Fibonacci numbers. Towards the end of the paper,\u0000we present a generalized method applicable to second-order recurrence\u0000relations. Our exploration of the Fibonacci--Theodorus spiral aims to address a variety\u0000of questions, showcasing its unique properties and behaviors. For example, we\u0000study topics such as area, perimeter, and angles. Notably, we establish a\u0000relationship between the ratio of two consecutive areas and the golden ratio, a\u0000pattern that extends to angles sharing a common vertex. Furthermore, we present\u0000some asymptotic results. For instance, we demonstrate that the sum of the first\u0000$n$ areas comprising the spiral approaches a multiple of the sum of the initial\u0000$n$ Fibonacci numbers. Moreover, we provide a sequence of open problems related\u0000to all spiral worked in this paper. Finally, in his work Hahn, Hahn observed a potential connection between the\u0000golden ratio and the ratio of areas between spines of lengths $sqrt{F_{n+1}}$\u0000and $sqrt{F_{n+2}-1}$ and the areas between spines of lengths $sqrt{F_{n}}$\u0000and $sqrt{F_{n+1}-1}$ in the Theodorus spiral. However, no formal proof has\u0000been provided in his work. In this paper, we provide a proof for Hahn's\u0000conjecture.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141584701","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 New Method For Solving Fractional And Classical Differential Equations Based On a New Generalized Fractional Power Series 基于新广义分式幂级数的分式和经典微分方程求解新方法

arXiv - MATH - General Mathematics Pub Date : 2024-06-23 DOI: arxiv-2406.16980

Youness Assebbane, Mohamed Echchehira, Mohamed Bouaouid, Mustapha Atraoui

引用次数: 0

The p-adic valuation of the general degree-2 and degree-3 polynomial in 2 variables 2 变量中一般 2 级和 3 级多项式的 p-adic 估值

arXiv - MATH - General Mathematics Pub Date : 2024-06-23 DOI: arxiv-2407.07103

Shubham

引用次数: 0