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The characterizations of monotone functions which generate associative functions 生成关联函数的单调函数的特征
arXiv - MATH - General Mathematics Pub Date : 2024-08-24 DOI: arxiv-2409.02941
Chen Meng, Yun-Mao Zhang, Xue-ping Wang
{"title":"The characterizations of monotone functions which generate associative functions","authors":"Chen Meng, Yun-Mao Zhang, Xue-ping Wang","doi":"arxiv-2409.02941","DOIUrl":"https://doi.org/arxiv-2409.02941","url":null,"abstract":"Associativity of a two-place function $T: [0,1]^2rightarrow [0,1]$ defined\u0000by $T(x,y)=f^{(-1)}(F(f(x),f(y)))$ where $F:[0,infty]^2rightarrow[0,infty]$\u0000is an associative function, $f: [0,1]rightarrow [0,infty]$ is a monotone\u0000function which satisfies either $f(x)=f(x^{+})$ when $f(x^{+})in\u0000mbox{Ran}(f)$ or $f(x)neq f(y)$ for any $yneq x$ when $f(x^{+})notin\u0000mbox{Ran}(f)$ for all $xin[0,1]$ and $f^{(-1)}:[0,infty]rightarrow[0,1]$ is\u0000a pseudo-inverse of $f$ depends only on properties of the range of $f$. The\u0000necessary and sufficient conditions for the $T$ to be associative are presented\u0000by applying the properties of the monotone function $f$.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203933","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
Associativity of a class of two-place functions and its consequences for classes of triangular norms 双位函数类的关联性及其对三角准则类的影响
arXiv - MATH - General Mathematics Pub Date : 2024-08-24 DOI: arxiv-2409.09037
Yun-Mao Zhang, Xue-ping Wang
{"title":"Associativity of a class of two-place functions and its consequences for classes of triangular norms","authors":"Yun-Mao Zhang, Xue-ping Wang","doi":"arxiv-2409.09037","DOIUrl":"https://doi.org/arxiv-2409.09037","url":null,"abstract":"This article characterizes the associativity of two-place functions $T:\u0000[0,1]^2rightarrow [0,1]$ defined by $T(x,y)=f^{(-1)}(F(f(x),f(y)))$ where\u0000$F:[0,1]^2rightarrow[0,1]$ is a triangular norm (even a triangular subnorm),\u0000$f: [0,1]rightarrow [0,1]$ is a strictly increasing function and\u0000$f^{(-1)}:[0,1]rightarrow[0,1]$ is the pseudo-inverse of $f$. We prove that\u0000the associativity of functions $T$ only depends on the range of $f$, which is\u0000used to give a sufficient and necessary condition for the function $T$ being\u0000associative when the triangular norm $F$ is an ordinal sum of triangular norms\u0000and an ordinal sum of triangular subnorms in the sense of A. H. Clifford,\u0000respectively. These results finally are applied for describing classes of\u0000triangular norms generated by strictly increasing functions.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142252876","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
Graphical sequences are determined by the majorization order 图形序列由主次顺序决定
arXiv - MATH - General Mathematics Pub Date : 2024-08-23 DOI: arxiv-2409.02937
Leo Egghe
{"title":"Graphical sequences are determined by the majorization order","authors":"Leo Egghe","doi":"arxiv-2409.02937","DOIUrl":"https://doi.org/arxiv-2409.02937","url":null,"abstract":"This paper studies the relation between the Lorenz majorization order and the\u0000realizability of degree sequences X of a network in the sense of being\u0000graphical or connected graphical c-graphical or not. We prove the main result\u0000that, if X is dominated (in the Lorenz majorization sense) by Y and Y is c-\u0000graphical, then X is also (c-) graphical. From this, a classical result of\u0000Hakimi on trees follows but also a new generalization of it to general\u0000connected networks. Moreover, a characterization of c-graphical sequences in\u0000terms of the Lorenz majorization order is given.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203934","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 Problem of Knot 结的问题
arXiv - MATH - General Mathematics Pub Date : 2024-08-21 DOI: arxiv-2409.02932
Ryohei Miyadera, Hikaru Manabe, Aoi Murakami, Shoma Morimoto
{"title":"A Problem of Knot","authors":"Ryohei Miyadera, Hikaru Manabe, Aoi Murakami, Shoma Morimoto","doi":"arxiv-2409.02932","DOIUrl":"https://doi.org/arxiv-2409.02932","url":null,"abstract":"In this article, the authors give the correct answer to the following\u0000problem, which is presented in the well-known problem book \"CHALLENGING\u0000MATHEMATICAL PROBLEMS WITH ELEMENTARY SOLUTIONS\"? by A. M. Yaglom and L. M.\u0000Yaglom. There are six long blades of grass with the ends protruding above and below,\u0000and you will tie together the six upper ends in pairs and then tie together the\u0000six lower ends in pairs. What is the probability that a ring will be formed\u0000when the blades of grass are tied at random in this fashion? The solution in the above book needs to be corrected, and we will present a\u0000correct answer in this article. Therefore, we are the first persons to present\u0000a correct?answer to a problem in a book published in the USSR? in 1954. By\u0000following the original idea of this problem book, we present the correct answer\u0000without using knowledge of higher knowledge, although we used a very basic\u0000knowledge of the Knot theory.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"172 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203935","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
Exploring criteria for designing novel waterbomb tessellations using triangular convex polygons 探索利用三角形凸多边形设计新型水弹方格网的标准
arXiv - MATH - General Mathematics Pub Date : 2024-08-21 DOI: arxiv-2409.02931
Sukanya Deshmukh, Michael Assis
{"title":"Exploring criteria for designing novel waterbomb tessellations using triangular convex polygons","authors":"Sukanya Deshmukh, Michael Assis","doi":"arxiv-2409.02931","DOIUrl":"https://doi.org/arxiv-2409.02931","url":null,"abstract":"Waterbomb style tessellations have been explored in the past by artists such\u0000as Ronald D. Resch, Benjamin Parker and Mitya Miller. Generalised waterbomb\u0000tessellations are still underexplored in origami design. We have explored\u0000various sets of criteria for generalising waterbomb tessellations in order to\u0000enumerate valid patterns. We only consider triangular waterbomb tessellations,\u0000other polygons will be explored in future papers. In our search we have\u0000uncovered some new waterbomb tessellations, which could offer new uses in\u0000representational and geometric origami design. We conclude by discussing\u0000foldability properties and possible generalisations.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203936","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 note on exact results for Burgers-like equations involving Laguerre derivatives 关于涉及拉盖尔导数的伯格斯方程精确结果的说明
arXiv - MATH - General Mathematics Pub Date : 2024-08-19 DOI: arxiv-2409.02928
Giuseppe Dattoli, Riccardo Droghei, Roberto Garra
{"title":"A note on exact results for Burgers-like equations involving Laguerre derivatives","authors":"Giuseppe Dattoli, Riccardo Droghei, Roberto Garra","doi":"arxiv-2409.02928","DOIUrl":"https://doi.org/arxiv-2409.02928","url":null,"abstract":"In this note, we consider some Burgers-like equations involving Laguerre\u0000derivatives and demonstrate that it is possible to construct specific exact\u0000solutions using separation of variables. We prove that a general scheme exists\u0000for constructing exact solutions for these Burgers-like equations, extending to\u0000more general cases, including nonlinear time-fractional equations. Exact\u0000solutions can also be obtained for KdV-like equations involving Laguerre\u0000derivatives. We finally consider a particular class of Burgers equations with\u0000variable coefficients whose solution can be obtained similarly.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203938","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
Generalization of some of Ramanujan's formulae 拉马努扬公式的推广
arXiv - MATH - General Mathematics Pub Date : 2024-08-17 DOI: arxiv-2408.09077
Aung Phone Maw
{"title":"Generalization of some of Ramanujan's formulae","authors":"Aung Phone Maw","doi":"arxiv-2408.09077","DOIUrl":"https://doi.org/arxiv-2408.09077","url":null,"abstract":"We will make use of the method of partial fractions to generalize some of\u0000Ramanujan's infinite series identities, including Ramanujan's famous formula\u0000for $zeta(2n+1)$. It is shown here that the method of partial fractions can be\u0000used to obtain many similar identities of this kind.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203941","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
Love Dynamical Model with persepectives of Piecewise Differential Operators 带片断微分算子的爱的动力学模型
arXiv - MATH - General Mathematics Pub Date : 2024-08-15 DOI: arxiv-2409.02927
Atul Kumar
{"title":"Love Dynamical Model with persepectives of Piecewise Differential Operators","authors":"Atul Kumar","doi":"arxiv-2409.02927","DOIUrl":"https://doi.org/arxiv-2409.02927","url":null,"abstract":"For love dynamical models, a new idea combining piecewise concept for\u0000integer-order, stochastic, and fractional derivatives is presented in order to\u0000capture the chaos and several crossover emotional scenerios. Under the\u0000assumptions of linear growth and Lipschitz condition, the fixed-point theorem\u0000explain the uniqueness and existence to the models under the investigation. The\u0000piecewise derivatives were approximated utilising the Lagrange interpolation\u0000method, and the computer results were demonstrated numerically for several\u0000values of order $alpha$. It was observed that the recently presented new idea\u0000in love dynamical models can represent disordered emotional patterns in\u0000passionate loving partnerships.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203937","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
Artistic Aspects of the Wigner Caustic and the Centre Symmetry Set 维格纳苛集和中心对称集的艺术方面
arXiv - MATH - General Mathematics Pub Date : 2024-08-14 DOI: arxiv-2409.04443
Iza Danielewska, Dawid Poławski, Dominika Sterczewska, Michał Zwierzyński
{"title":"Artistic Aspects of the Wigner Caustic and the Centre Symmetry Set","authors":"Iza Danielewska, Dawid Poławski, Dominika Sterczewska, Michał Zwierzyński","doi":"arxiv-2409.04443","DOIUrl":"https://doi.org/arxiv-2409.04443","url":null,"abstract":"The Wigner caustic and the Centre Symmetry Set of a closed smooth planar\u0000curve are known singular sets which generically admit only cusp singularities.\u0000Applications of these objects in semi-classical quantum physics, in chaos\u0000theory, in singularity theory, in convex geometry, have been studied since the\u00001970s until today. These sets can be viewed as envelopes of special families of\u0000lines and thanks to that they have many geometric artistic values.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203939","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
Modified Lotka Volterra Model with Perspectives of the Piecewise Derivative 修正的 Lotka Volterra 模型与片断衍生的视角
arXiv - MATH - General Mathematics Pub Date : 2024-08-13 DOI: arxiv-2409.02925
Atul Kumar
{"title":"Modified Lotka Volterra Model with Perspectives of the Piecewise Derivative","authors":"Atul Kumar","doi":"arxiv-2409.02925","DOIUrl":"https://doi.org/arxiv-2409.02925","url":null,"abstract":"This study uses the Lotka Volterra Predator-Prey model to offer a notion of\u0000piecewise patterns for the various piecewise derivatives. Using the piecewise\u0000derivatives, we produced numerical solutions that are referred to as the\u0000Adams-Bashforth method. The computer results show piecewise patterns in the\u0000Lotka Volterra Predator-Prey model's real-world behaviours. The Lotka-Volterra\u0000model looks into the relationships between competition and abundance between\u0000two competing species. Changes in the abundance of one species are modelled as\u0000a function of the abundance of its competitors, but the competitive mechanism\u0000is given and evaluated. This notion led some scholars to label certain\u0000mathematical expressions as \"phenomenological\" and to propose a different\u0000theoretical framework that gives resources special consideration. The\u0000Lotka-Volterra model, often called the predator-prey model or the\u0000Lotka-Volterra model, is a nonlinear mathematical expression that is frequently\u0000used to analyse the dynamical behaviours of biological systems in which two\u0000species interact, one as a predator and the other as prey. The variation in the\u0000populations over time is illustrated by the mathematical statement.","PeriodicalId":501502,"journal":{"name":"arXiv - MATH - General Mathematics","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142203942","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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