Two farmers decide to divide a triangle farm between them. The problem is modeled as a simple application of game theory in geometry. The game is defined and is solved, theoretically, in independent case. Simulation results are proposed using the copula function, in the dependent cases. Finally, concluding remarks are proposed.
{"title":"Dividing a Farm: A Simple Application of Game Theory in Geometry","authors":"Reza Habibi","doi":"10.31559/glm2024.14.2.2","DOIUrl":"https://doi.org/10.31559/glm2024.14.2.2","url":null,"abstract":"Two farmers decide to divide a triangle farm between them. The problem is modeled as a simple application of game theory in geometry. The game is defined and is solved, theoretically, in independent case. Simulation results are proposed using the copula function, in the dependent cases. Finally, concluding remarks are proposed.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"115 14","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141390643","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}
The concept of the reversible ring property concerning nilpotent elements was introduced by A.M. Abdul-Jabbar and C. A. Ahmed, who introduced the concept of commutativity of nilpotent elements at zero, termed as a CNZ ring, as an extension of reversible rings. In this paper, we extend the CNZ property through the influence of a central ring endomorphism alpha , introducing a new type of ring called a right alpha -skew central CNZ ring. This concept not only expands upon CNZ rings but also serves as a generalization of right alpha -skew central reversible rings. We explore various properties of these rings and delve into extensions of right alpha -skew central CNZ rings, along with examining several established results, which emerge as corollaries of our findings.
A.M. Abdul-Jabbar 和 C. A. Ahmed 提出了关于零元素的可逆环性质的概念，并将零点零元素的换元性概念称为 CNZ 环，作为可逆环的扩展。在本文中，我们通过中心环内态 alpha 的影响扩展了 CNZ 特性，引入了一种新的环，称为右 alpha 斜中心 CNZ 环。这一概念不仅是对 CNZ 环的扩展，也是对α-斜中心可逆环的概括。我们探讨了这些环的各种性质，并深入研究了右α-斜中心 CNZ 环的扩展，同时还研究了几个既定结果，这些结果是我们的发现的必然结果。
{"title":"Right Central CNZ Property Skewed by Ring Endomorphisms","authors":"Saman Shafiq Othman, C. A. K. Ahmed","doi":"10.31559/glm2024.14.2.1","DOIUrl":"https://doi.org/10.31559/glm2024.14.2.1","url":null,"abstract":"The concept of the reversible ring property concerning nilpotent elements was introduced by A.M. Abdul-Jabbar and C. A. Ahmed, who introduced the concept of commutativity of nilpotent elements at zero, termed as a CNZ ring, as an extension of reversible rings. In this paper, we extend the CNZ property through the influence of a central ring endomorphism alpha , introducing a new type of ring called a right alpha -skew central CNZ ring. This concept not only expands upon CNZ rings but also serves as a generalization of right alpha -skew central reversible rings. We explore various properties of these rings and delve into extensions of right alpha -skew central CNZ rings, along with examining several established results, which emerge as corollaries of our findings.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141392396","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}
In our analysis, we approximate the sine and cosine trigonometric functions within the interval (cid:2) 0, π 2 (cid:3) . This examination yields two distinct formulas for approximating sine and cosine. Initially, we endeavor to derive the formula that involves a square root, and then we develop an alternative formula that does not require any use of a square root. However, even after establishing the square root-free procedure, we seek to enhance its accuracy and subsequently derive yet another formula for more precise approximations of trigonometric functions within the interval (cid:2) 0, π 2 (cid:3) . Thus, our analysis presents two primary procedures. One is utilizing square roots, and the other abstaining from them. Our focus extends to ensuring the accuracy of these trigonometric functions specifically within the interval (cid:2) 0, π 2 (cid:3) . This precision assessment is visually represented through graphs, illustrating the disparity between the values generated by the formulated functions and the exact values of these functions. Consequently, these graphs serve as indicators of the error within the interval (cid:2) 0, π 2 (cid:3) . Finally, we conduct a comparative analysis between our approximation and the 7th-century Indian mathematician Bhaskara I’s approximation formula.
{"title":"A series of new formulas to approximate the Sine and Cosine functions","authors":"Mashrur Azim, Asma Akter Akhi, Md. Kamrujjaman","doi":"10.31559/glm2023.13.3.2","DOIUrl":"https://doi.org/10.31559/glm2023.13.3.2","url":null,"abstract":"In our analysis, we approximate the sine and cosine trigonometric functions within the interval (cid:2) 0, π 2 (cid:3) . This examination yields two distinct formulas for approximating sine and cosine. Initially, we endeavor to derive the formula that involves a square root, and then we develop an alternative formula that does not require any use of a square root. However, even after establishing the square root-free procedure, we seek to enhance its accuracy and subsequently derive yet another formula for more precise approximations of trigonometric functions within the interval (cid:2) 0, π 2 (cid:3) . Thus, our analysis presents two primary procedures. One is utilizing square roots, and the other abstaining from them. Our focus extends to ensuring the accuracy of these trigonometric functions specifically within the interval (cid:2) 0, π 2 (cid:3) . This precision assessment is visually represented through graphs, illustrating the disparity between the values generated by the formulated functions and the exact values of these functions. Consequently, these graphs serve as indicators of the error within the interval (cid:2) 0, π 2 (cid:3) . Finally, we conduct a comparative analysis between our approximation and the 7th-century Indian mathematician Bhaskara I’s approximation formula.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"83 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139347054","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}
Fortune's conjecture (named after the social anthropologist Reo Franklin Fortune) is an extremely elegant mathematical conjecture that always remains an open problem in number theory. It is a conjecture about prime numbers, which leads to the so-called "fortunate numbers" (not to be confused with "lucky numbers"): Reo F. Fortune predicted that no fortunate number is composite. This conjecture impresses us all as mathematicians, that's why we decided that it will be the subject of this paper, which has many objectives and very interesting findings, among them: - Highlighting numerous properties of the fortunate numbers. - Giving a proof of Fortune's conjecture in a particular case, by two different methods one of which is original. - Presenting many counterexamples that reinforce the previous point, when the satisfied hypothesis in that particular case, is not met. - Proving a new remarkable inequality that all the 3000 first (known until now) fortunate numbers perfectly fulfill. Despite our continuous research (quite recently) on the subject of Fortune’s conjecture, we have never found a mathematical reference with a variety of ideas dealing with this conjecture, so we hope that this paper will be the first scientific work containing multiple ideas, comments, results and goals, and contributing significantly to find a definitive solution of Fortune's conjecture, therefore this paper may advance the field.
{"title":"New explorations and remarkable inequalities related to Fortune’s conjecture and fortunate numbers","authors":"Hayat Rezgui","doi":"10.31559/glm2023.13.3.1","DOIUrl":"https://doi.org/10.31559/glm2023.13.3.1","url":null,"abstract":"Fortune's conjecture (named after the social anthropologist Reo Franklin Fortune) is an extremely elegant mathematical conjecture that always remains an open problem in number theory. It is a conjecture about prime numbers, which leads to the so-called \"fortunate numbers\" (not to be confused with \"lucky numbers\"): Reo F. Fortune predicted that no fortunate number is composite. This conjecture impresses us all as mathematicians, that's why we decided that it will be the subject of this paper, which has many objectives and very interesting findings, among them: - Highlighting numerous properties of the fortunate numbers. - Giving a proof of Fortune's conjecture in a particular case, by two different methods one of which is original. - Presenting many counterexamples that reinforce the previous point, when the satisfied hypothesis in that particular case, is not met. - Proving a new remarkable inequality that all the 3000 first (known until now) fortunate numbers perfectly fulfill. Despite our continuous research (quite recently) on the subject of Fortune’s conjecture, we have never found a mathematical reference with a variety of ideas dealing with this conjecture, so we hope that this paper will be the first scientific work containing multiple ideas, comments, results and goals, and contributing significantly to find a definitive solution of Fortune's conjecture, therefore this paper may advance the field.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139344836","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}
The aim of this paper is to establish an efficient of a new transform called double SEJI integral transform to solve integral differential equations. Some important properties are proved by this suggested transform with theorem for the partial fractional Caputo derivatives. Finally, we use them to solve applications of some kinds of integral equations by transforming them to algebraic equations and solve by using the giving properties.
{"title":"Double SEJI Integral Transform and its Applications of Solution Integral Differential Equations","authors":"Jinan A. Jasim, Sadiq A. Mehdi, Emad A. Kuffi","doi":"10.31559/glm2023.13.3.4","DOIUrl":"https://doi.org/10.31559/glm2023.13.3.4","url":null,"abstract":"The aim of this paper is to establish an efficient of a new transform called double SEJI integral transform to solve integral differential equations. Some important properties are proved by this suggested transform with theorem for the partial fractional Caputo derivatives. Finally, we use them to solve applications of some kinds of integral equations by transforming them to algebraic equations and solve by using the giving properties.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139346716","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}
{"title":"Detection of Outlier in Time Series with Application to Dohuk Dam Using the SCA Statistical System","authors":"Shelan Saied Ismaeel, K. M. Omar, S. A. Othman","doi":"10.31559/glm2023.13.2.2","DOIUrl":"https://doi.org/10.31559/glm2023.13.2.2","url":null,"abstract":"","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44921095","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}
{"title":"A Novel View of Regular and Normal Spaces via Nano Sβ-Open Sets in Nano Topological Spaces","authors":"Nehmat K. Ahmed, Osama T. Pirbal","doi":"10.31559/glm2023.13.2.1","DOIUrl":"https://doi.org/10.31559/glm2023.13.2.1","url":null,"abstract":"","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47926164","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}
In this paper, we introduce F( R p ) , the collection of all finite sets of fuzzy subsets in F bc ( R p ) , which is the class of the upper semicontinuous fuzzy subsets of R p with bounded convex compact closure of the supports. Then we define set-fuzzy-set multifunctions and discuss various kinds of them such as monotone, fuzzy measure, subadditive, null-additive, null-null-additive, multisubmeasure and null-continuous. We introduce the set-fuzzy-set-norm variation of a set-fuzzy-set multifunction and present some properties between a set-fuzzy-set multifunction and its variations such as fuzzyness, continuity from below, null-additivity, and null-null-additivity.
本文引入F(R p)， F(R bc (R p))中所有模糊子集的有限集合的集合，它是R p的上半连续模糊子集的一类，具有有界凸紧闭的支撑。然后定义了集模糊集多函数，并讨论了集模糊集多函数的单调、模糊测度、次加性、零加性、零-零加性、多子测度和零连续等类型。引入了集模糊集多函数的集模糊-集范数变分，给出了集模糊集多函数及其变分之间的一些性质，如模糊性、自下连续性、零可加性和零可加性。
{"title":"Set-fuzzy-set-norm Variation of Set-fuzzy-set Multifunctions","authors":"Marzieh Mostafavi","doi":"10.31559/glm2023.13.1.3","DOIUrl":"https://doi.org/10.31559/glm2023.13.1.3","url":null,"abstract":"In this paper, we introduce F( R p ) , the collection of all finite sets of fuzzy subsets in F bc ( R p ) , which is the class of the upper semicontinuous fuzzy subsets of R p with bounded convex compact closure of the supports. Then we define set-fuzzy-set multifunctions and discuss various kinds of them such as monotone, fuzzy measure, subadditive, null-additive, null-null-additive, multisubmeasure and null-continuous. We introduce the set-fuzzy-set-norm variation of a set-fuzzy-set multifunction and present some properties between a set-fuzzy-set multifunction and its variations such as fuzzyness, continuity from below, null-additivity, and null-null-additivity.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46924314","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}
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