University of IsfahanMathematics and Society2345-64933220180823A geometric solution of a Cubic by Omar Khayyam in which coloured diagrams are used instead of letters for the greater ease of learnersA geometric solution of a Cubic by Omar Khayyam in which coloured diagrams are used instead of letters for the greater ease of learners1102245610.22108/msci.2018.78166.1194FAAkbarTayebiUniversity of QomSayyed AhmadFaghihiUniversity of QomJournal Article20161004This paper is a translation of the the following paper into Persian:
D. A. Kent and D. J. Muraki, A Geometric solution of a Cubic by Omar Khayyam in which Coloured Diagrams are used<br />instead of letters for the greater ease of learners, The American Mathematical Monthly, 123 (2016) 149–160.This paper is a translation of the the following paper into Persian:
D. A. Kent and D. J. Muraki, A Geometric solution of a Cubic by Omar Khayyam in which Coloured Diagrams are used<br />instead of letters for the greater ease of learners, The American Mathematical Monthly, 123 (2016) 149–160.https://math-sci.ui.ac.ir/article_22456_3a757142729865d32165445795baf269.pdfUniversity of IsfahanMathematics and Society2345-64933220180823How google works?How google works?11192270810.22108/msci.2018.110135.1270FAMaryamLotfipourDepartment of Mathematics and Applications - Fasa University - Fars - IranJournal Article20180313This paper is a translation of the the following paper into Persian:<br />C. Roussau, How Google works? klein vignette (www.kleinproject.org)<br />In this writing, the Google ranking algorithm is examined and the mathematical methods used in it are explained. Here, an important application of the Banach fixed-point theorem is presented and by using the proof technique of this theorem, the required fixed point in the Google ranking algorithm is obtained.This paper is a translation of the the following paper into Persian:<br />C. Roussau, How Google works? klein vignette (www.kleinproject.org)<br />In this writing, the Google ranking algorithm is examined and the mathematical methods used in it are explained. Here, an important application of the Banach fixed-point theorem is presented and by using the proof technique of this theorem, the required fixed point in the Google ranking algorithm is obtained.https://math-sci.ui.ac.ir/article_22708_322592b2cb5c1f6d05da22f809405a62.pdfUniversity of IsfahanMathematics and Society2345-64933220180823A historical overview in the fields of Euclidean geometryA historical overview in the fields of Euclidean geometry21352286110.22108/msci.2018.106491.1248FAAmirMafiUniversity of KurdistanShahabArkianUniversity of KurdistanJournal Article20170917This article aims to provide an overview of the history of work conducted in the fields of Euclidean Domains and Euclidean number fields. The goal is to create a foundation for those interested in these mathematical topics.This article aims to provide an overview of the history of work conducted in the fields of Euclidean Domains and Euclidean number fields. The goal is to create a foundation for those interested in these mathematical topics.https://math-sci.ui.ac.ir/article_22861_ba2ffe5b432cf8204bd59ffa491a0d51.pdfUniversity of IsfahanMathematics and Society2345-64933220180823Flexibility and facilitation of frames compared to bases in signal processingFlexibility and facilitation of frames compared to bases in signal processing37442288010.22108/msci.2018.33449.1148FAMohsenEsmaeilbeigiMalayer UniversityOmidChatrabgounMalayer UniversityJournal Article20150806Bases are fundamental tools in applied mathematics, and from the past to the present, from polynomial bases to wavelet bases, they have always played an indispensable role in expanding the frontiers of knowledge. However, the conditions that a basis must satisfy are highly restrictive. In fact, the elements of a basis must be linearly independent and ideally orthogonal to each other. Such a requirement makes accessing bases with suitable flexibility difficult or even impossible. Frames, on the other hand, are a suitable option for accessing bases with fewer restrictive characteristics and more flexibility. In order to better understand the advantages of using frames in various practical fields, we will briefly review the role of frames in reducing the effects of random disturbances in signal processing.Bases are fundamental tools in applied mathematics, and from the past to the present, from polynomial bases to wavelet bases, they have always played an indispensable role in expanding the frontiers of knowledge. However, the conditions that a basis must satisfy are highly restrictive. In fact, the elements of a basis must be linearly independent and ideally orthogonal to each other. Such a requirement makes accessing bases with suitable flexibility difficult or even impossible. Frames, on the other hand, are a suitable option for accessing bases with fewer restrictive characteristics and more flexibility. In order to better understand the advantages of using frames in various practical fields, we will briefly review the role of frames in reducing the effects of random disturbances in signal processing.https://math-sci.ui.ac.ir/article_22880_d31a4e2b22d60b7ccf1ffd7c2f92c4d0.pdfUniversity of IsfahanMathematics and Society2345-64933220180823Bernoulli family and the solution of the Bernoulli differential equationBernoulli family and the solution of the Bernoulli differential equation45582289410.22108/msci.2018.103951.1225FASeyyed Ali MohammadMohseni Al-HusseiniYazd UniversityHengamehSenemarYazd UniversityJournal Article20170908The Bernoulli differential equation is a fascinating topic with significant applications in mathematics, engineering, and physics. In this article, we explore the history of the emergence and expansion of the Bernoulli differential equation. We also delve into the role of scholars who have attempted to solve this equation, notably the Bernoulli family, which, over three generations, contributed eight mathematicians to the community. Jacob, Daniel, and Johann Bernoulli played a prominent role in solving this equation. Finally, we examine the applications of the Bernoulli differential equation.The Bernoulli differential equation is a fascinating topic with significant applications in mathematics, engineering, and physics. In this article, we explore the history of the emergence and expansion of the Bernoulli differential equation. We also delve into the role of scholars who have attempted to solve this equation, notably the Bernoulli family, which, over three generations, contributed eight mathematicians to the community. Jacob, Daniel, and Johann Bernoulli played a prominent role in solving this equation. Finally, we examine the applications of the Bernoulli differential equation.https://math-sci.ui.ac.ir/article_22894_d9644ef6a07f15d29e4d29e43f8da3da.pdfUniversity of IsfahanMathematics and Society2345-64933220180823A Graphical method for generating fractalsA Graphical method for generating fractals59682290210.22108/msci.2018.47307.1160FAPedramJafariAmirkabir University of TechnologyJournal Article20160126This research focuses on introducing the theory of L-systems (Lindenmayer systems), initially designed to model the behavior of multicellular plants. However, it has evolved into a successful tool for simulating the growth processes of plants and trees with the design of graphical interpreters. Beginning with the introduction of various types of grammars, the study explores the structure and position of L-systems in formal language theory. By introducing a turtle graphics interpreter, one can convert the output strings from L-system grammars into concise commands for generating fractal curves and nearly natural images of plants and trees. In general, a key feature of L-system theory is the parallel and simultaneous execution of rules on variables, leading to broad applications in evolutionary biology and various areas of theoretical computer science.This research focuses on introducing the theory of L-systems (Lindenmayer systems), initially designed to model the behavior of multicellular plants. However, it has evolved into a successful tool for simulating the growth processes of plants and trees with the design of graphical interpreters. Beginning with the introduction of various types of grammars, the study explores the structure and position of L-systems in formal language theory. By introducing a turtle graphics interpreter, one can convert the output strings from L-system grammars into concise commands for generating fractal curves and nearly natural images of plants and trees. In general, a key feature of L-system theory is the parallel and simultaneous execution of rules on variables, leading to broad applications in evolutionary biology and various areas of theoretical computer science.https://math-sci.ui.ac.ir/article_22902_9a62308c602557cb8eeff86eb6707806.pdf