University of IsfahanMathematics and Society2345-649311120250927Some symmetric polynomial and related identitiesSome symmetric polynomial and related identities1242916810.22108/msci.2025.142987.1703FANargesGhareghaniSchool of Mathematics, Department of Mathematics, statistics and Computer Science, College of Science, University of TehranMortezaMohammad-NooriSchool of Computer Science, Department of Mathematics, Statistics and Coputer Science, College of Science, University of TehranJournal Article20241014In this paper, we study some symmetric polynomials and their properties. In addition to the elementary and complete symmetric polynomials, we consider the accumulative versions of these polynomials and using common combinatorial tools, particularly generating functions, we study related identities. In order to precise how these identities generalize and extend binomial-type identities, the notation is developed through the paper.In this paper, we study some symmetric polynomials and their properties. In addition to the elementary and complete symmetric polynomials, we consider the accumulative versions of these polynomials and using common combinatorial tools, particularly generating functions, we study related identities. In order to precise how these identities generalize and extend binomial-type identities, the notation is developed through the paper.https://math-sci.ui.ac.ir/article_29168_d3bffe75ceb471cdac55f2ba0bc63db4.pdfUniversity of IsfahanMathematics and Society2345-649311120250707Application of anthropological theory of didactic in teaching of mathematicsApplication of anthropological theory of didactic in teaching of mathematics25412934110.22108/msci.2025.143082.1718FASajjadZamanabadiDepartment of Mathematics Education,
Faculty of Mathematics and Computer,
Shahid Bahonar University of Kerman,
Kerman, Iran. Mahani Math Center, Afzalipour Research Institute, Shahid Bahonar University of Kerman, Kerman, IranAbolfazlRafiepourDepartment of Mathematics Education, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
Mahani Math Center, Afzalipour Research Institute, Shahid Bahonar University of Kerman, Kerman, IranJournal Article20241228The anthropological theory of didactic is a new theory in the field of mathematics education, which was presented by a French mathematician named Chevellard in 1991. The main focus of the anthropological theory of didactic is on human interactions in the teaching-learning process. According to the framework of the Anthropological Theory of the Didactic (ATD), the goal of education is to elucidate the mechanism through which knowledge within an institution $ I $ is transmitted to individuals $ x $ in society $ \widehat{S} $. Chevellard identified two aspects of human mathematical activity, which includes a practical part (Praxis) and a knowledge part (Logos). The Anthropological Theory of the Didactic (ATD) introduces praxeology as a tool for analyzing mathematical activities by considering their constituent components and the conditions present within educational institutions. Praxeology is a central concept and a key instrument in ATD. The aim of ATD is to provide a theory about human actions, and praxeology<br />serves as the core concept for describing these actions. The practical part and the knowledge part are the components of praxeology (behavioral science). The practical part includes tasks and techniques. The knowledge part includes technology that explains the practical part. Also, the knowledge section contains a theory that justifies the technology used. The four elements of the anthropological theory of didactic (tasks, techniques, technology, and theory) are interconnected. In this article, after introducing the anthropological theory of didactic, the relationship between this theory and the theory of didactical situations (TDS) is stated. Then, the application of this theory in two mathematical examples from the school mathematics curriculum has been examined in detail. The article ends with the idea that the application of the anthropological theory of didactic can lead to a paradigm shift in the process of teaching and learning mathematics at school.The anthropological theory of didactic is a new theory in the field of mathematics education, which was presented by a French mathematician named Chevellard in 1991. The main focus of the anthropological theory of didactic is on human interactions in the teaching-learning process. According to the framework of the Anthropological Theory of the Didactic (ATD), the goal of education is to elucidate the mechanism through which knowledge within an institution $ I $ is transmitted to individuals $ x $ in society $ \widehat{S} $. Chevellard identified two aspects of human mathematical activity, which includes a practical part (Praxis) and a knowledge part (Logos). The Anthropological Theory of the Didactic (ATD) introduces praxeology as a tool for analyzing mathematical activities by considering their constituent components and the conditions present within educational institutions. Praxeology is a central concept and a key instrument in ATD. The aim of ATD is to provide a theory about human actions, and praxeology<br />serves as the core concept for describing these actions. The practical part and the knowledge part are the components of praxeology (behavioral science). The practical part includes tasks and techniques. The knowledge part includes technology that explains the practical part. Also, the knowledge section contains a theory that justifies the technology used. The four elements of the anthropological theory of didactic (tasks, techniques, technology, and theory) are interconnected. In this article, after introducing the anthropological theory of didactic, the relationship between this theory and the theory of didactical situations (TDS) is stated. Then, the application of this theory in two mathematical examples from the school mathematics curriculum has been examined in detail. The article ends with the idea that the application of the anthropological theory of didactic can lead to a paradigm shift in the process of teaching and learning mathematics at school.https://math-sci.ui.ac.ir/article_29341_633f2aac8e786cc97520d9ae7a251ba4.pdfUniversity of IsfahanMathematics and Society2345-649311120250930Thoughts on jun otsuka’s thinking about statistics– the philosphical foundationsThoughts on jun otsuka’s thinking about statistics– the philosphical foundations43562934210.22108/msci.2025.144347.1726FAMohammad GhasemVahidi AslFaculty of Mathematical Sciences, Shahid Beheshti University, Tehran, IranJournal Article20250212Jun Otsuka’s excellent book, Thinking about Statistics - the Philosophical Foundations (Otsuka 2023) is mostly organized around the idea that diferent statistical approaches can be illuminated by linking them to diferent ideas in general epistemology. Otsuka connects Bayesianism to internalism and foundationalism, frequentism to reliabilism, and the Akaike Information Criterion in model selection theory to instrumentalism. This useful mapping doesn’t cover all the interesting ideas he presents. His discussions of causal inference and machine learning are philosophically insightful, as is his idea that statisticians embrace an assumption that is similar to Hume’s Principle of the Uniformity of Nature. I discuss these topics in what follows, sometimes disagreeing with details while at other times adding ideas that complement those presented in the book.Jun Otsuka’s excellent book, Thinking about Statistics - the Philosophical Foundations (Otsuka 2023) is mostly organized around the idea that diferent statistical approaches can be illuminated by linking them to diferent ideas in general epistemology. Otsuka connects Bayesianism to internalism and foundationalism, frequentism to reliabilism, and the Akaike Information Criterion in model selection theory to instrumentalism. This useful mapping doesn’t cover all the interesting ideas he presents. His discussions of causal inference and machine learning are philosophically insightful, as is his idea that statisticians embrace an assumption that is similar to Hume’s Principle of the Uniformity of Nature. I discuss these topics in what follows, sometimes disagreeing with details while at other times adding ideas that complement those presented in the book.https://math-sci.ui.ac.ir/article_29342_d3dc8ef5d46460e3de72e96cbd946802.pdfUniversity of IsfahanMathematics and Society2345-649311120251028Harnack inequalities for nonlinear parabolic equations under integral ricci curvature boundsHarnack inequalities for nonlinear parabolic equations under integral ricci curvature bounds57802948310.22108/msci.2025.143102.1705FAShahroudAzamiDepartment of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, IranMehdiJafariDepartment of Mathematics, Payame Noor University, PO BOX 19395-4697, Tehran, IranJournal Article20241018This work is devoted to the study of gradient estimates and Harnack inequalities for positive solutions to a class of nonlinear parabolic equations on compact Riemannian manifolds under integral Ricci curvature bounds. More precisely, we consider equations of the form:<br />\[<br />\partial_t v = \Delta v + a v (\ln v)^b + q(x,t) A(v),<br />\]<br />where $a,b \in \mathbb{R}$ and $A(v)$ is a smooth function. These equations naturally generalize the classical heat equation and arise in various geometric and physical contexts. We establish Li-Yau, Hamilton, and Souplet-Zhang type gradient estimates, and deduce corresponding Harnack inequalities. Our results extend previous works by relaxing the curvature conditions to integral lower bounds on the Ricci tensor, thereby allowing for more general geometric settings.<br /> This work is devoted to the study of gradient estimates and Harnack inequalities for positive solutions to a class of nonlinear parabolic equations on compact Riemannian manifolds under integral Ricci curvature bounds. More precisely, we consider equations of the form:<br />\[<br />\partial_t v = \Delta v + a v (\ln v)^b + q(x,t) A(v),<br />\]<br />where $a,b \in \mathbb{R}$ and $A(v)$ is a smooth function. These equations naturally generalize the classical heat equation and arise in various geometric and physical contexts. We establish Li-Yau, Hamilton, and Souplet-Zhang type gradient estimates, and deduce corresponding Harnack inequalities. Our results extend previous works by relaxing the curvature conditions to integral lower bounds on the Ricci tensor, thereby allowing for more general geometric settings.<br /> https://math-sci.ui.ac.ir/article_29483_6596c69d5981d05f7758cae1290c2dea.pdfUniversity of IsfahanMathematics and Society2345-649311120251021Equivariant T-harmonic Maps between Compact Riemannian Manifolds of
Cohomogeneity OneEquivariant T-harmonic Maps between Compact Riemannian Manifolds of
Cohomogeneity One811082948510.22108/msci.2025.143572.1714FAMehranAminianDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, IranMehranNamjooDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran0000-0001-5949-6766Journal Article20241204The aim of this paper is to develop works of Urakawa [H. Urakawa, Equivariant harmonic maps between compact Riemannian manifolds of cohomogeneity $1$, <em>Michigan Math. J.</em>, <strong>40</strong> no. 1 (1993) 27--51. ] on equivariant harmonic maps between compact Riemannian manifolds of cohomogeneityone, to equivariant $ T $-harmonic maps between them and also his reduction of the Euler-Lagrange equation on harmonicity of these maps to $ T $-harmonicity of them.The aim of this paper is to develop works of Urakawa [H. Urakawa, Equivariant harmonic maps between compact Riemannian manifolds of cohomogeneity $1$, <em>Michigan Math. J.</em>, <strong>40</strong> no. 1 (1993) 27--51. ] on equivariant harmonic maps between compact Riemannian manifolds of cohomogeneityone, to equivariant $ T $-harmonic maps between them and also his reduction of the Euler-Lagrange equation on harmonicity of these maps to $ T $-harmonicity of them.https://math-sci.ui.ac.ir/article_29485_aaa7782b62dcd56f0f1cc6559a46e0d2.pdfUniversity of IsfahanMathematics and Society2345-649311120250629Evaluation of the measurement error of Iranian labor force indicators due to changing data gathering mode based on the Markov latent class modelEvaluation of the measurement error of Iranian labor force indicators due to changing data gathering mode based on the Markov latent class model1091312953110.22108/msci.2025.142988.1700FALidaKalhori NadrabadiTechnical Designs and Statistical Methods Department, Statistical Research and Training Center, Tehran, IranPariaTorabi KahlanTechnical Designs and Statistical Methods Department. Statistical Research and Training Center. Tehran,Iran.Journal Article20241009One of the most important non-sampling errors is measurement error, which causes the measured value of the target variable to be different from its true value. The markov latent class model allows for the estimation of measurement error for categorical variables in panel surveys that have at least three repetition periods, with the advantage that it does not require re-interviews. In the Iranian labor force survey, which is conducted with rotational sampling panel with a 2-2-2 pattern, this model can be applied. In this article, the challenges of changing the survey mode in times of crisis and the advantages of telephone interviews compared to face-to-face interviews are reviewed. Also, in order to evaluate the results of the labor force survey in the context of the COVID-19 pandemic, when the survey mode was suddenly changed from face-to-face to telephone interviews, the markov latent class model was used to evaluate the measurement error using data from four survey periods from spring 2018 to summer 2021. The results indicate that the measurement error increased in the first period of changing the interview mode, but decreased in subsequent periods. Overall, it can be stated that telephone interviews can be a suitable method for collecting labor force survey data.One of the most important non-sampling errors is measurement error, which causes the measured value of the target variable to be different from its true value. The markov latent class model allows for the estimation of measurement error for categorical variables in panel surveys that have at least three repetition periods, with the advantage that it does not require re-interviews. In the Iranian labor force survey, which is conducted with rotational sampling panel with a 2-2-2 pattern, this model can be applied. In this article, the challenges of changing the survey mode in times of crisis and the advantages of telephone interviews compared to face-to-face interviews are reviewed. Also, in order to evaluate the results of the labor force survey in the context of the COVID-19 pandemic, when the survey mode was suddenly changed from face-to-face to telephone interviews, the markov latent class model was used to evaluate the measurement error using data from four survey periods from spring 2018 to summer 2021. The results indicate that the measurement error increased in the first period of changing the interview mode, but decreased in subsequent periods. Overall, it can be stated that telephone interviews can be a suitable method for collecting labor force survey data.https://math-sci.ui.ac.ir/article_29531_a735c1c177da64a577e03f260bf80cd6.pdf