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Publications related to Mathematics (10,000)
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Article
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Many fields of mathematics rely on convexity and nonconvexity, especially when stud-16 ying optimization issues, where it stands out for a variety of practical aspects. Due to the behaviour 17 of its definition, the idea of convexity also contributes significantly to the discussion of inequalities. 18 The concepts of symmetry and convexity are rela...
Article
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In recent years, fractional calculus has witnessed tremendous progress in variousareas of sciences and mathematics [...]
Research
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https://www.mdpi.com/journal/mathematics/special_issues/3RN0F4V760
Conference Paper
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This study aimed to assess the performance of Calculus students for some mathematical tasks, the procedures they follow in Composition Functions and finding an inverse function, and to determine the interpretation of these procedures. The study used the mixed methodology and the sample consisted of three students from Sohar University at Sultanate...
Article
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Research literature on the role of mathematics teachers during the COVID-19 crisis shows that teacher preparation for emergency situations is required. In reporting on this exploratory study, we present and analyse lesson plans created by seven future teachers for mathematics classes during the pandemic. Data were collected between April and Octobe...
Article
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In this work, we introduce and theoretically analyze a relatively simple numerical algorithm to solve a double-fractional condensate model. The mathematical system is a generalization of the famous Gross--Pitaevskii equations, which is a model consisting of two nonlinear complex-valued diffusive differential equations. The continuous model studied...
Article
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Based on computer search, Furtula characterized the connected graphs with maximal ABCGG index. In this paper we give a mathematical proof of the established hypothesizes.
Article
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This research aims to understand how prospective teachers develop their knowledge about whole-class discussions during a lesson study. Following a qualitative approach, we focus on the work of three prospective mathematics teachers preparing, leading, and reflecting on whole-class discussions. Data was collected through participant observation with...
Article
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While much is known about assessment, a study examining the conceptions that teachers hold and its relation with their practices in mathematics classrooms is crucial for educators and needs further investigation. This cross-sectional survey study examined teachers’ conceptions and practices of classroom assessment and the relationships between them...
Article
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Following publication of this article1, it is noticed that some brackets are missing in the mathematical expressions in Fig. 1. Updated Fig. 1 is provided in this Correction.
Article
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We provide general sets of functionals for which parabolic phase space Feynman path integrals on the torus Td≡(R/2πZ)d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\...
Article
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We consider a fixed point problem $\mathcal {S}u=u$ S u = u where ${\mathcal {S}:C(\mathbb{R}_{+};X)\to C(\mathbb{R}_{+};X)}$ S : C ( R + ; X ) → C ( R + ; X ) is an almost history-dependent operator. First, we recall the unique solvability of the problem. Then, we introduce the concept of Tykhonov triple, provide several relevant examples, and pro...
Article
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Strengthening of RC columns using GFRP is the solution to enhance the load carrying capacity of columns. GFRP wrap glued with epoxy resin provides lateral confinement, which enhances the capacity of column. The lateral confinement pressure provided by the GFRP on circular column is uniform. But in the case of rectangular sections, the lateral confi...
Article
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Capacitor allocation is one of the most important topics in distribution network operation. In this paper, reactive power based on capacitors allocation is presented in electrical distribution network using mathematical Remora Optimization Algorithm (ROA) as a powerful optimization method to identify the optimal location and size of the capacitors...
Article
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The surface tension of a molten sample can be evaluated based on its resonant frequency with various levitation techniques. Under a 1-G condition, the use of levitation forces to counteract gravity will cause the levitated sample’s resonant frequency to differ from that under microgravity. A mathematical relationship to correct for this deviation i...
Conference Paper
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This Working Group was occasioned by a convergence of concerns over the widespread de facto acceptance of notions of objectivity in the field of mathematics education. Because the ideologies of the field continue to be based largely in elements of scientism, we propose that the mathematics education arena familiar to researchers must shift and take...
Article
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The classical Kuramoto model consists of finitely many pairwisely coupled oscillators on the circle. In many applications a simple pairwise coupling is not sufficient to describe real-world phenomena as higher-order (or group) interactions take place. Hence, we replace the classical coupling law with a very general coupling function involving highe...
Book
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L’ouvrage est organisé en douze chapitres qui développent les différents thèmes du programme de mathématiques. Chaque chapitre est divisé en trois parties : un rappel des définitions et des principaux résultats du cours qui s’appuient sur des exemples ; un ensemble d’exercices d’application et de problèmes de synthèse et de concours ; et enfin, l’e...
Article
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In this paper, a flexible version of the Fréchet distribution called the extended Weibull– Fréchet (EWFr) distribution is proposed. Its failure rate has a decreasing shape, an increasing shape, and an upside-down bathtub shape. Its density function can be a symmetric shape, an asymmetric shape, a reversed-J shape and J shape. Some mathematical prop...
Article
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Compartmental models are popular in the mathematics of epidemiology for their simplicity and wide range of applications. Although they are typically solved as initial value problems for a system of ordinary differential equations, the observed data are typically akin to a boundary value-type problem: we observe some of the dependent variables at gi...
Preprint
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Although many well-intentioned organizations and institutions emphasize the importance of antiracism and social justice in mathematics education, there remains a lack of practitioner-oriented curricular materials exhibiting how these long-overdue shifts can and do manifest in classrooms. This article describes how modifying a project on absolute va...
Article
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In a decision-making problem, there is often some uncertainty regarding the user preferences. We assume a parameterised utility model, where in each scenario we have a utility function over alternatives, and where each scenario represents a possible user preference model consistent with the input preference information. With a set $$A$$ A of altern...
Article
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Renormalization and Renormalization Group (RG) have proven to be very powerful tools in contemporary physics, with a decisive influence on how to conceive of key physical aspects, including theories themselves. While they can be tackled from a variety of standpoints, this paper focuses on a specific philosophical issue, that is, which kind of expla...
Article
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Color comparison is a key aspect in many areas of application, including industrial applications, and different metrics have been proposed. In many applications, this comparison is required to be closely related to human perception of color differences, thus adding complexity to the process. To tackle this, different approaches were proposed throug...
Article
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Mathematics cannot be separated from human life. However, mathematics is often taught directly through formulas and abstract mathematical forms at school and is less associated with students' daily lives. Hence, it makes it difficult for students to understand mathematics and often find it difficult to understand how mathematics can be useful in de...
Article
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This paper considers the normalized lengths of the factors of the Lyndon decomposition of finite random words with $n$ independent letters drawn from a finite or infinite totally ordered alphabet according to a general probability distribution. We prove, firstly, that the limit law of the lengths of the smallest Lyndon factors is a variant of the s...
Preprint
The paper is concerned with a generalization of Dirichlet's Theorem on arithmetic progresions.of positive natural numbers. Let t(x) be a arbitrary unary non-constant term of the language of the elementary Peano arithmetic. The interpretation t N of t in the standard model N of arithmetic is a strictly increasing function from N to N. It is proved t...
Conference Paper
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Pendidikan STEM merupakan antara agenda yang diberikan penekanan dalam Pelan Pembangunan Pendidikan Malaysia (PPPM) 2013–2025 yang merupakan antara usaha Kementerian Pendidikan Malaysia (KPM) untuk meningkatkan sumber tenaga mahir dan pakar dalam bidang penyelidikan dan industri. Pendidikan STEM adalah pendidikan yang berasaskan kepada konsep mendi...
Preprint
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This is a tribute to the visionary work of Ed Dubinsky, who passed away in May 2022. It concentrates his work on the establishment of the Special Interest Group of the Mathematical Association of America for Research in Undergraduate Mathematics Education (SIGMAA on RUME) and on his preparatory work towards a journal for research in undergraduate m...
Article
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A mathematical compounding of bokoharamism problem at a rate percent over a periodic simple time increment constrain 100 for T is + 100 , where =
Book
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Eğitim Yayınevinin bir ürünü olarak ilk ders kitabımı “Genel Matematik-1” i siz değerli okuyucularıma sunmuş bulunuyorum. Oldukça güç bir işi üstlendim, fakat bir o kadar da öğrencilere yardımcı ve yararlı olabileceğini umduğum bu eseri hazırladığım için de çok mutluyum. Burada matematiğin önemini savunmanın bir yararı olduğunu düşünmüyorum. Çünkü,...
Conference Paper
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Qualitative methods have been the basis for the study of nonlinear systems since the beginning of the 20th century, highlighting their key concepts allows a better understanding of the evolution of these methods and their role in mathematics. To fulfill this task, specific features inherent in nonlinear systems were identified and the corresponding...
Preprint
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Can a principal still offer optimal dynamic contracts that are linear in end-of-period outcomes when the agent controls a process that exhibits memory? We provide a positive answer by considering a general Gaussian setting where the output dynamics are not necessarily semi-martingales or Markov processes. We introduce a rich class of principal-agen...
Conference Paper
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The paper presents the sTeX3 format for representing informal mathematics. sTeX3 acts as a surface language for two systems: the (presentation-oriented) LaTeX system to produce PDF and the semantics-aware MMT system for advanced knowledge management services. We discuss how the sTeX3 markup facilities allow in situ flexiformalization (and the neces...
Poster
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AIMS Mathematics - Article Review Acknowledgement - 21 September 2022
Article
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In epidemiology, the rule of association is used to determine the factors at the origin of diseases; implicative statistical analysis is thus a necessary tool in epidemiology too. Epidemiologists have more often chosen the so-called odds ratio measure in their studies of the quantification of the implicit link between an exposure and disease. In or...
Article
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The study aims at examining middle school mathematics teachers' conceptions of open-ended questions. A questionnaire consisting of open-ended items was applied to 40 mathematics teachers. The teachers were asked to define the open-ended question in general and the mathematical open-ended question in particular and provide examples to exemplify thei...
Article
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This manuscript contributes to research on how algebraic thinking about operations and properties can develop, and relevant forms of curricular activity. The key question asked is: how can students’ early algebraic activity be fostered through focusing on relations involving operations and properties? We adopt Radford’s three aspects of algebraic t...
Article
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Resumen La investigación sobre formas de pensamiento algebraico no evade la discusión de las formas de pensamiento aritmético. Resultados de investigación muestran que la ausencia de indicios espaciales en el estudio de secuencias numéricas hace que los estudiantes limiten el proceso de generalización al trabajo sobre relaciones entre números. En e...
Article
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This article proposes an alternative strain energy density function to describe the hyperelastic behavior of rubber-like materials under various deformations. This proposed strain energy function fulfilled all the necessary characteristics of a hyperelastic material model. This function consists of four material parameters and represents an invaria...
Article
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Fractional derivative and integral operators are often employed to present new general- izations of mathematical inequalities. The introduction of new fractional operators has prompted another direction in different branches of mathematics and applied sciences. First, we investigate and prove new fractional equality. Considering this equality as th...
Article
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En este artículo abordo la cuestión de lo que significa el aprendizaje colectivo y de cómo poder propiciarlo en el aula de matemáticas. Sugiero que la cercanía espacial (real o virtual) no es un criterio suficiente para caracterizar el aprendizaje colectivo. Los estudiantes pueden estar encerrados en las cuatro paredes de un aula (real o virtual) s...
Article
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In this research work, we introduce generalized geometric expressions of a certain product combination via Salagean and Ruchewehy differential operators denoted as B n γ (β) andB n γ (α, β), and obtain the conditions for univalence of the resulting product combinations, differential subordinations of the class and our result completely unify earlie...
Conference Paper
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Bugungi kunda har bir mamlakat ta’lim tizimiga aloxida e’tibor qaratmoqda. Xususan, sharq va g’arb mamlakatlarining o’qitish tizimlari o’tgan 50 yil davomida tubdan takomillashtirildi. 2018-yilda nufuzli “Iqtisodiy hamkorlik va taraqqiyot tashkiloti tomonidan uch yilda bir o‘tkaziluvchi xalqaro tadqiqotlarga ko‘ra, finlyandiyalik maktab o‘quvchilar...
Preprint
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We propose a probabilistic setting in which we study the probability law of the Rajaraman and Ullman \textit{RU} algorithm and a modified version of it denoted by \textit{RUM}. These algorithms aim at estimating the similarity index between huge texts in the context of the web. We give a foundation of this method by showing, in the ideal case of ca...
Preprint
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Cactus groups Jn are currently attracting considerable interest from diverse mathematical communities. This work explores their relations to right-angled Coxeter groups, and in particular twin groups Twn and Mostovoy's Gauss diagram groups Dn, which are better understood. Concretely, we construct an injective group 1-cocycle from Jn to Dn, and show...
Preprint
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We develop a sharp boundary trace theory in arbitrary bounded Lipschitz domains which, in contrast to classical results, allows "forbidden" endpoints and permits the consideration of functions exhibiting very limited regularity. This is done at the (necessary) expense of stipulating an additional regularity condition involving the action of the Lap...
Conference Paper
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Various numerical methods have been proposed to find the funicular shell forms that are in equilibrium state only with membrane force without bending moment against its own weight, for example the dynamic relaxation method, the force density method, shape optimizations and the thrust network analysis. These methods are not easy, as they require adv...
Article
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The author wishes to make the following corrections to this paper [1]:In Abstract, (1) “It depicts how data analytics has been used in IR for a better understanding system effectiveness” should be “It depicts how data analytics has been used in IR to gain a better understanding of system effectiveness”; (2) “This review concludes lack of full under...
Preprint
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In this paper, we develop upon the emerging topic of loss function learning, which aims to learn loss functions that significantly improve the performance of the models trained under them. Specifically, we propose a new meta-learning framework for learning model-agnostic loss functions via a hybrid neuro-symbolic search approach. The framework firs...
Research
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ViscoWave is a dynamic Finite Layer Method (FLM) which is capable of modeling the dynamics (i.e., transient stress wave propagation) of a variety of flexible pavement structures with elastic/viscoelastic layers, with/without bedrock. This documentation provides the mathematical formulation of the updates that were made to original ViscoWave (Chapte...
Article
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Zusammenfassung Der Handlungsplanung als Teil professioneller Kompetenz kommt eine wesentliche Bedeutung bei der Überführung von Wissen in spontane Handlungen in pädagogischen Situationen zu. Obwohl Forschung die Bedeutung der Handlungsplanung für professionelles Handeln im Bereich früher mathematischer Bildung kontinuierlich betont, ist sowohl emp...
Article
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In this paper, we study the number of limit cycles of polynomial differential systems of the form   ẋ = ẏ y = −x − ε(h1 (x) y 2α + g1 (x) y 2α+1 + f1 (x) y 2α+2) − ε 2 (h2 (x) y 2α + g2 (x) y 2α+1 + f2 (x) y 2α+2) where m, n, k and α are positive integers, hi, gi and fi have degree n, m and k, respectively for each i = 1, 2, and ε is a small par...
Article
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This study was conducted to determine the predictor variables of job satisfaction of mathematics teachers as either achievement, power, or affiliation. The one hundred (100) randomly selected secondary mathematics teachers teaching in the First District of Iloilo for the school year 2019-2020 served as the respondents of the study. The data were ob...
Preprint
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As David Gale noted in his 1960 book The Theory of Linear Economic Models, it is striking that two fundamental mathematical tools in linear economic theory, linear programming and game theory, developed simultaneously, and independently, in the years following the Second World War. More remarkable still was the realization that these two areas are...
Article
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Chemical graph theory is a branch of mathematics which combines graph theory and chemistry. A numerical quantity that gives information related to be topology of graph. our objective is to compute the degree based topological indices foe the molecular structure of aztec diamond. In the degree based topological indices, we compute first K-banhatti i...
Article
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Learning mathematics is associated with the assumption as a killer subject that are struggled by many students. This subject is not strictly for one particular field but learners are coming from different disciplines as well. Differences between the disciplines in education may results in difference motivation towards learning mathematics. Thus, th...
Article
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This paper investigates the coverage path planning problem for a fixed-wing UAV in convex polygon regions with several practical task requirements in photogrammetry considered. A typical camera model pointing forward-down for photogrammetric application is developed. In addition, the coordinates of the region vertices are converted from the WGS-84...
Chapter
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We report on – a complete redesign and reimplementation (using ) from the ground up of the ecosystem for semantic markup of mathematical documents. Specifically, we present: i) The package that allows declaring semantic macros and provides a module system for organizing and importing semantic macros using logical identifiers. is a (now) standard pa...
Poster
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Reviewer Certificate MDPI Journal Mathematics, 16 September 2022
Preprint
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Strings on AdS 3 ×S 3 ×S 3 ×S 1 with mixed flux exhibit exact integrability. We wish to construct an integrable Neumann-Rosochatius (NR) model of strings starting with the type IIB supergravity action in AdS 3 ×S 3 ×S 3 ×S 1 with pure NSNS flux. We observe that the forms of the Lagrangian and the Uhlenbeck integrals of motion of the considered syst...
Poster
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This poster presents quantitative analyses of the mathematical experiences of Queer high school students from a significant Midwest state in the US.
Conference Paper
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This paper reports from a study that investigates the quality of advanced mathematics lectures, in particular regarding the presentation of definitions. We compare the presentation of definitions given in two real analysis courses by two different lecturers using a structured observation protocol. The results show, that both lecturers present forma...
Article
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This study examines mathematics education doctoral students’ perspectives of statistics. Several studies have been conducted regarding undergraduate students’ attitudes toward statistics during their experiences in introductory statistics courses (e.g, Gal, Ginsburg, & Schau, 1997; Wise, 1985). Far fewer studies have been conducted regarding teache...
Article
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At the National Institute of Metrological Research (INRIM) an evaluation of a commercial dual source high resistance bridge has been performed. Its two main measurement modes (single measurements and multiple measurements) have been investigated. The best settle time of a 10:1 measurement of high resistance ratio has been estimated to be about thre...
Preprint
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Mathematical proof that light has mass
Article
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Modeling dynamic networks has attracted much interest in recent years, which helps understand networks’ behavior. Many works have been dedicated to modeling discrete-time networks, but less work is done for continuous-time networks. Point processes as powerful tools for modeling discrete events in continuous time have been widely used for modeling...
Article
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Since the 2000s, early co-constructive mathematical learning in kindergarten has been the focus of political discussion and mathematics didactic research. This is based on the fact that kindergarten is the first place for subject-specific mathematical learning, alongside socialization in the family. The focus of research on this first institutional...
Poster
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In Fächern mit mathematischen Inhalten werden häufig Mathematikvorkurse angeboten. Das Verhältnis aus Aufwand und Ertrag gilt jedoch als umstritten (z.B. Austerschmidt et al. 2021, S. 129). Als alternativen Ansatz wird für Physik-Lehramtsstudierende an der PH Ludwigsburg ein Online-Brückenkurs angeboten. Dabei wird auf Basis einer Diagnostik zu mat...
Book
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Although there is much literature on multimodal interaction, multimodal synchrony analysis, and related behavioural adaptivity, mathematical formalisation and computational simulation of it is a nontrivial topic. Moreover, the subjective, agent-oriented perspective on synchrony analysis has not yet received much attention in the literature. This bo...
Article
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This paper is a review of all recent and most relevant research in the field of dynamics in micro-milling processes. It associates the recent research works, future trends, and thoughts in the field of dynamics and revises the dynamics in machining definition, the mathematical notions applied for micro-milling with the consideration of the size eff...
Article
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We compare two well-known set-theoretical statements, namely the axiom of choice and the continuum hypothesis, with regard to their historical development and formulation, as well as their consequences in mathematics. It is known that both statements are independent from the other axioms of set theory (if they are consistent). The axiom of choice –...
Chapter
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In part III "Functions in the school course of mathematics" of the methodical guide for students of the specialty 014.04 Secondary education (Mathematics) of the mechanical and mathematical faculty, the main concepts and theorems of the theory of functions are considered in the order of their study in the school course of mathematics according to t...
Article
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Truth pluralists say that truth-bearers in different “discourses”, “domains”, “domains of discourse”, or “domains of inquiry” are apt to be true in different ways – for instance, that mathematical discourse or ethical discourse is apt to be true in a different way to ordinary descriptive or scientific discourse. Moreover, the notion of a “domain” i...
Conference Paper
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We study linear ordinary differential equations with generic inhomogeneous boundary conditions in Sobolev spaces. Necessary and sufficient conditions for continuity with respect to a parameter of the solutions to such problems have been found. They are of a constructive character and can be used in: \begin{enumerate} \item [1)] finding approximate...
Preprint
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Strings on $AdS_3 \times S^3\times S^3\times S^1$ with mixed flux exhibit exact integrability. We wish to construct an integrable Neumann-Rosochatius (NR) model of strings starting with the type IIB supergravity action in $AdS_3 \times S^3\times S^3\times S^1$ with pure NSNS flux. We observe that the forms of the Lagrangian and the Uhlenbeck integr...
Article
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The first person to introduce possibility theory was Lotfi A. Zadeh, in 1977. It was, of course, of no coincidence that he directly combined it with the theory of fuzzy sets. Later, several researchers dealt with the mathematical foundations of the theory of possibilities. They introduced possibility distribution as a concept, and they directly com...
Article
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This article proposes an analytical model to understand the rod growth of eutectic in the bulk undercooled melt. Based on the previous derivations of the lamellar eutectic growth models, relaxing the assumptions of small Péclet numbers, the model is derived by considering melt kinetic and thermal undercoolings. The intent of this model is to predic...
Article
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We prove the continuous dependence, with respect to the initial datum of solutions of the “quenching parabolic problem” $$\partial _{t}u-\Delta u+\chi _{\{u>0\}}u^{-\beta }=\lambda u^{p}$$ ∂ t u - Δ u + χ { u > 0 } u - β = λ u p , with zero Dirichlet boundary conditions, when $$\beta \in (0,1),p\in (0,1],\lambda \ge 0$$ β ∈ ( 0 , 1 ) , p ∈ ( 0 , 1...
Article
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The Dirac-Dolbeault operator for a compact oriented Kähler manifold is a special case of a Dirac operator. The Green function for the Dirac Laplacian over a manifold with boundary allows to express the values of the sections of the Dirac bundle in terms of the values on the boundary, extending the mean value theorem of harmonic analysis. Utilizing...