University of Isfahan Mathematics and Society 2345-6493 3 3 2018 11 22 Research touring persia with a guide named hermann weyl Research touring persia with a guide named hermann weyl 1 28 22992 10.22108/msci.2018.106318.1244 FA Hojat Rostami Mulla Sadra Institute of Education and Training, Zanjan Journal Article 2017 09 06 This paper is a translation of the the following paper into Persian: [Alain Juhel, Research touring persia with a guide named hermann weyl, Nexus Netw J. , 14 No. 2 (2012) 203-226.] A journey across the lands that were part of Persia long ago offers a friendly introduction to symmetry and symmetry groups, as presented in Hermann Weyl’s seminal and popular book, Symmetry (1952). Weyl’s intent was to show how geometrical transformations first, then mathematical structures, could be better understood from a cultural point of view through art and architecture. Our intent is to provide a complementary set of selected pictures of Persian monuments to illustrate Weyl’s ideas. Following the master, we have focused on different kinds of symmetries, starting from the simplest and oldest to those that are more complex, disregarding chronology or geography within the lands of Persia. This paper is a translation of the the following paper into Persian: [Alain Juhel, Research touring persia with a guide named hermann weyl, Nexus Netw J. , 14 No. 2 (2012) 203-226.] A journey across the lands that were part of Persia long ago offers a friendly introduction to symmetry and symmetry groups, as presented in Hermann Weyl’s seminal and popular book, Symmetry (1952). Weyl’s intent was to show how geometrical transformations first, then mathematical structures, could be better understood from a cultural point of view through art and architecture. Our intent is to provide a complementary set of selected pictures of Persian monuments to illustrate Weyl’s ideas. Following the master, we have focused on different kinds of symmetries, starting from the simplest and oldest to those that are more complex, disregarding chronology or geography within the lands of Persia.

https://math-sci.ui.ac.ir/article_22992_f1340871d8483ec6c59e249bc03f5304.pdf

University of Isfahan Mathematics and Society 2345-6493 3 3 2018 11 22 Mathematical methods and algorithms in image compression Mathematical methods and algorithms in image compression 29 36 23029 10.22108/msci.2018.107568.1257 FA Ali Tavakoli Mathematics Department, Islamic Azad University, Shahr Majlesi Branch, Isfahan Journal Article 2017 10 29 In this article, we have examined image compression methods, especially the fractal method. The primary goal is to familiarize and expand the knowledge of the mathematical community and telecommunications experts. The fractal method cannot be used for every image; for example, in satellite image compression, Wavelet and Contourlet methods are more commonly used. The fractal method is more suitable for images with a small depth parameter, allowing them to be non-uniformly compressed by block segmentation using their repeatable function system. In this article, we have examined image compression methods, especially the fractal method. The primary goal is to familiarize and expand the knowledge of the mathematical community and telecommunications experts. The fractal method cannot be used for every image; for example, in satellite image compression, Wavelet and Contourlet methods are more commonly used. The fractal method is more suitable for images with a small depth parameter, allowing them to be non-uniformly compressed by block segmentation using their repeatable function system.

https://math-sci.ui.ac.ir/article_23029_b507ebe64c0bd44acec585254cb02dcf.pdf

University of Isfahan Mathematics and Society 2345-6493 3 3 2018 11 22 Les mosaïques de Thiele Les mosaïques de Thiele 37 46 23129 10.22108/msci.2018.109316.1266 FA Hamid Ghorbani Faculty of Mathematics Department:Statistics and Applications, University of Kashan Journal Article 2018 01 27 This paper is a translation of the the following paper into Persian: [C. Genest, S. L. Lauritzen, Les mosaïques de Thiele, Accromath, 11 No. 2 (2016) 24–29.] L’astronome, statisticien et actuaire danois Thorvald Thiele a trouvé une façon de générer automatiquement de très beaux motifs de mosaïques au moyen du concept de résidu quadratique dans l’ensemble des entiers de Gauss. This paper is a translation of the the following paper into Persian: [C. Genest, S. L. Lauritzen, Les mosaïques de Thiele, Accromath, 11 No. 2 (2016) 24–29.] L’astronome, statisticien et actuaire danois Thorvald Thiele a trouvé une façon de générer automatiquement de très beaux motifs de mosaïques au moyen du concept de résidu quadratique dans l’ensemble des entiers de Gauss. https://math-sci.ui.ac.ir/article_23129_83d9e525fe54892a779b80e666b889ba.pdf

University of Isfahan Mathematics and Society 2345-6493 3 3 2025 01 20 Common writing mistakes in mathematical articles in english Common writing mistakes in mathematical articles in english 47 66 23159 10.22108/msci.2018.114036.1300 FA Zohreh Vasagh Ferdowsi University of Mashhad Mohammad Sal Moslehian Ferdowsi University of Mashhad Journal Article 1397 08 25 In this writing, an attempt is made to outline common writing mistakes in mathematical articles based on the authors' experience in editing English articles. The errors are categorized into three groups: grammatical mistakes, punctuation and formatting errors, and formula writing. Additionally, the proper and conventional structure of a mathematical article is discussed. In this writing, an attempt is made to outline common writing mistakes in mathematical articles based on the authors' experience in editing English articles. The errors are categorized into three groups: grammatical mistakes, punctuation and formatting errors, and formula writing. Additionally, the proper and conventional structure of a mathematical article is discussed.

https://math-sci.ui.ac.ir/article_23159_e4cee358f91968cd45be52c213394d24.pdf

University of Isfahan Mathematics and Society 2345-6493 3 3 2018 11 22 Pfister algebras with involution Pfister algebras with involution 67 78 23233 10.22108/msci.2018.106405.1253 FA Amirhosein Nokhodkar University of Kashan Journal Article 2017 10 15 This article provides a review of bilinear forms on fields and involution algebras on central simple algebras. It discusses important conjectures in this context, the efforts made to prove them, and the remaining open problems in the opposite characteristic. Finally, attempts to generalize these conjectures to characteristic two and the differences in results obtained in this characteristic compared to others are reviewed. This article provides a review of bilinear forms on fields and involution algebras on central simple algebras. It discusses important conjectures in this context, the efforts made to prove them, and the remaining open problems in the opposite characteristic. Finally, attempts to generalize these conjectures to characteristic two and the differences in results obtained in this characteristic compared to others are reviewed.

https://math-sci.ui.ac.ir/article_23233_2dad3d4aad0c788630d5a1d4d2bd0226.pdf

University of Isfahan Mathematics and Society 2345-6493 3 3 2018 11 22 Constructive analysis of bishop and its comparison with classical analysis Constructive analysis of bishop and its comparison with classical analysis 79 89 23235 10.22108/msci.2018.110442.1274 FA Reza Sotoudeh Yasouj University Hamid Reza Goudarzi Yasouj University Journal Article 2018 04 15 In this article, the intuitionistic logic of Brouwer in mathematics and the constructive analysis of Bishop is introduced based on this logic, and the differences with classical mathematical logic and analysis are explained. The fundamental difference in constructive analysis compared to classical analysis is that in constructive analysis, a solution and algorithm for finding desirable elements in existential theorems are always provided. Therefore, this type of mathematical analysis can be considered a very high-level programming language. To become familiar with the constructive reasoning methods, we first construct the system of real numbers using a constructive method and explain the fundamental differences of constructive analysis compared to classical analysis, which has its roots in the recognized properties of real numbers. Next, we present some existential theorems in classical analysis and their constructive equivalents. It will be seen that in most cases, exact existential theorems in classical analysis are transformed into approximate existential theorems in constructive analysis. In this article, the intuitionistic logic of Brouwer in mathematics and the constructive analysis of Bishop is introduced based on this logic, and the differences with classical mathematical logic and analysis are explained. The fundamental difference in constructive analysis compared to classical analysis is that in constructive analysis, a solution and algorithm for finding desirable elements in existential theorems are always provided. Therefore, this type of mathematical analysis can be considered a very high-level programming language. To become familiar with the constructive reasoning methods, we first construct the system of real numbers using a constructive method and explain the fundamental differences of constructive analysis compared to classical analysis, which has its roots in the recognized properties of real numbers. Next, we present some existential theorems in classical analysis and their constructive equivalents. It will be seen that in most cases, exact existential theorems in classical analysis are transformed into approximate existential theorems in constructive analysis.

https://math-sci.ui.ac.ir/article_23235_dffed39a671c61015a5658661af5f414.pdf