Finite mathematics models and applications

CERN Document Server

Morris, Carla C

2015-01-01

Features step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences.

The 24-Hour Mathematical Modeling Challenge

Science.gov (United States)

Galluzzo, Benjamin J.; Wendt, Theodore J.

2015-01-01

Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…

Mathematical problems in meteorological modelling

CERN Document Server

Csomós, Petra; Faragó, István; Horányi, András; Szépszó, Gabriella

2016-01-01

This book deals with mathematical problems arising in the context of meteorological modelling. It gathers and presents some of the most interesting and important issues from the interaction of mathematics and meteorology. It is unique in that it features contributions on topics like data assimilation, ensemble prediction, numerical methods, and transport modelling, from both mathematical and meteorological perspectives. The derivation and solution of all kinds of numerical prediction models require the application of results from various mathematical fields. The present volume is divided into three parts, moving from mathematical and numerical problems through air quality modelling, to advanced applications in data assimilation and probabilistic forecasting. The book arose from the workshop “Mathematical Problems in Meteorological Modelling” held in Budapest in May 2014 and organized by the ECMI Special Interest Group on Numerical Weather Prediction. Its main objective is to highlight the beauty of the de...

A Primer for Mathematical Modeling

Science.gov (United States)

Sole, Marla

2013-01-01

With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…

Applied impulsive mathematical models

CERN Document Server

Stamova, Ivanka

2016-01-01

Using the theory of impulsive differential equations, this book focuses on mathematical models which reflect current research in biology, population dynamics, neural networks and economics. The authors provide the basic background from the fundamental theory and give a systematic exposition of recent results related to the qualitative analysis of impulsive mathematical models. Consisting of six chapters, the book presents many applicable techniques, making them available in a single source easily accessible to researchers interested in mathematical models and their applications. Serving as a valuable reference, this text is addressed to a wide audience of professionals, including mathematicians, applied researchers and practitioners.

Mathematical Modeling in the Undergraduate Curriculum

Science.gov (United States)

Toews, Carl

2012-01-01

Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…

Teachers' Conceptions of Mathematical Modeling

Science.gov (United States)

Gould, Heather

2013-01-01

The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…

Mathematical modeling with multidisciplinary applications

CERN Document Server

Yang, Xin-She

2013-01-01

Features mathematical modeling techniques and real-world processes with applications in diverse fields Mathematical Modeling with Multidisciplinary Applications details the interdisciplinary nature of mathematical modeling and numerical algorithms. The book combines a variety of applications from diverse fields to illustrate how the methods can be used to model physical processes, design new products, find solutions to challenging problems, and increase competitiveness in international markets. Written by leading scholars and international experts in the field, the

Mathematical modelling of membrane separation

DEFF Research Database (Denmark)

Vinther, Frank

This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate mathemat......This thesis concerns mathematical modelling of membrane separation. The thesis consists of introductory theory on membrane separation, equations of motion, and properties of dextran, which will be the solute species throughout the thesis. Furthermore, the thesis consist of three separate...... mathematical models, each with a different approach to membrane separation. The first model is a statistical model investigating the interplay between solute shape and the probability of entering the membrane. More specific the transition of solute particles from being spherical to becoming more elongated...

Introducing Modeling Transition Diagrams as a Tool to Connect Mathematical Modeling to Mathematical Thinking

Science.gov (United States)

Czocher, Jennifer A.

2016-01-01

This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…

Understanding Prospective Teachers' Mathematical Modeling Processes in the Context of a Mathematical Modeling Course

Science.gov (United States)

Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat

2017-01-01

This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…

Opinions of Secondary School Mathematics Teachers on Mathematical Modelling

Science.gov (United States)

Tutak, Tayfun; Güder, Yunus

2013-01-01

The aim of this study is to identify the opinions of secondary school mathematics teachers about mathematical modelling. Qualitative research was used. The participants of the study were 40 secondary school teachers working in the Bingöl Province in Turkey during 2012-2013 education year. Semi-structured interview form prepared by the researcher…

An introduction to mathematical modeling

CERN Document Server

Bender, Edward A

2000-01-01

Employing a practical, ""learn by doing"" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields - including science, engineering, and operations research - to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The

The Relationship between Students' Performance on Conventional Standardized Mathematics Assessments and Complex Mathematical Modeling Problems

Science.gov (United States)

Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.

2016-01-01

Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

Mathematical Modeling: A Bridge to STEM Education

Science.gov (United States)

Kertil, Mahmut; Gurel, Cem

2016-01-01

The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…

Beyond Motivation: Exploring Mathematical Modeling as a Context for Deepening Students' Understandings of Curricular Mathematics

Science.gov (United States)

Zbiek, Rose Mary; Conner, Annamarie

2006-01-01

Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical…

Causal Bayes Model of Mathematical Competence in Kindergarten

Directory of Open Access Journals (Sweden)

Božidar Tepeš

2016-06-01

Full Text Available In this paper authors define mathematical competences in the kindergarten. The basic objective was to measure the mathematical competences or mathematical knowledge, skills and abilities in mathematical education. Mathematical competences were grouped in the following areas: Arithmetic and Geometry. Statistical set consisted of 59 children, 65 to 85 months of age, from the Kindergarten Milan Sachs from Zagreb. The authors describe 13 variables for measuring mathematical competences. Five measuring variables were described for the geometry, and eight measuring variables for the arithmetic. Measuring variables are tasks which children solved with the evaluated results. By measuring mathematical competences the authors make causal Bayes model using free software Tetrad 5.2.1-3. Software makes many causal Bayes models and authors as experts chose the model of the mathematical competences in the kindergarten. Causal Bayes model describes five levels for mathematical competences. At the end of the modeling authors use Bayes estimator. In the results, authors describe by causal Bayes model of mathematical competences, causal effect mathematical competences or how intervention on some competences cause other competences. Authors measure mathematical competences with their expectation as random variables. When expectation of competences was greater, competences improved. Mathematical competences can be improved with intervention on causal competences. Levels of mathematical competences and the result of intervention on mathematical competences can help mathematical teachers.

Strategies to Support Students' Mathematical Modeling

Science.gov (United States)

Jung, Hyunyi

2015-01-01

An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…

The influence of mathematics learning using SAVI approach on junior high school students’ mathematical modelling ability

Science.gov (United States)

Khusna, H.; Heryaningsih, N. Y.

2018-01-01

The aim of this research was to examine mathematical modeling ability who learn mathematics by using SAVI approach. This research was a quasi-experimental research with non-equivalent control group designed by using purposive sampling technique. The population of this research was the state junior high school students in Lembang while the sample consisted of two class at 8th grade. The instrument used in this research was mathematical modeling ability. Data analysis of this research was conducted by using SPSS 20 by Windows. The result showed that students’ ability of mathematical modeling who learn mathematics by using SAVI approach was better than students’ ability of mathematical modeling who learn mathematics using conventional learning.

Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-efficacy Beliefs towards Mathematics and Mathematics Teaching

OpenAIRE

Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

2017-01-01

The purpose of the research is to investigate the relationships betweenself-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacybeliefs toward mathematics teaching, mathematics teaching anxiety variables andtesting the relationships between these variables with structural equationmodel. The sample of the research, which was conducted in accordance withrelational survey model, consists of 380 university students, who studied atthe department of Elementary Mathematics Educ...

Mathematical models for plant-herbivore interactions

Science.gov (United States)

Feng, Zhilan; DeAngelis, Donald L.

2017-01-01

Mathematical Models of Plant-Herbivore Interactions addresses mathematical models in the study of practical questions in ecology, particularly factors that affect herbivory, including plant defense, herbivore natural enemies, and adaptive herbivory, as well as the effects of these on plant community dynamics. The result of extensive research on the use of mathematical modeling to investigate the effects of plant defenses on plant-herbivore dynamics, this book describes a toxin-determined functional response model (TDFRM) that helps explains field observations of these interactions. This book is intended for graduate students and researchers interested in mathematical biology and ecology.

Mathematical Modelling of Predatory Prokaryotes

NARCIS (Netherlands)

Wilkinson, Michael H.F.

2006-01-01

Predator–prey models have a long history in mathematical modelling of ecosystem dynamics and evolution. In this chapter an introduction to the methodology of mathematical modelling is given, with emphasis on microbial predator–prey systems, followed by a description of variants of the basic

Predicting Relationships between Mathematics Anxiety, Mathematics Teaching Anxiety, Self-Efficacy Beliefs towards Mathematics and Mathematics Teaching

Science.gov (United States)

Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

2017-01-01

The purpose of the research is to investigate the relationships between self-efficacy beliefs toward mathematics, mathematics anxiety and self-efficacy beliefs toward mathematics teaching, mathematics teaching anxiety variables and testing the relationships between these variables with structural equation model. The sample of the research, which…

Using Covariation Reasoning to Support Mathematical Modeling

Science.gov (United States)

Jacobson, Erik

2014-01-01

For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…

Engaging Elementary Students in the Creative Process of Mathematizing Their World through Mathematical Modeling

Directory of Open Access Journals (Sweden)

Jennifer M. Suh

2017-06-01

Full Text Available This paper examines the experiences of two elementary teachers’ implementation of mathematical modeling in their classrooms and how the enactment by the teachers and the engagement by students exhibited their creativity, critical thinking, collaboration and communication skills. In particular, we explore the questions: (1 How can phases of mathematical modeling as a process serve as a venue for exhibiting students’ critical 21st century skills? (2 What were some effective pedagogical practices teachers used as they implemented mathematical modeling with elementary students and how did these promote students’ 21st century skills? We propose that mathematical modeling provides space for teachers and students to have a collective experience through the iterative process of making sense of and building knowledge of important mathematical ideas while engaging in the critical 21st century skills necessary in our complex modern world.

Summer Camp of Mathematical Modeling in China

Science.gov (United States)

Tian, Xiaoxi; Xie, Jinxing

2013-01-01

The Summer Camp of Mathematical Modeling in China is a recently created experience designed to further Chinese students' academic pursuits in mathematical modeling. Students are given more than three months to research on a mathematical modeling project. Researchers and teams with outstanding projects are invited to the Summer Camp to present…

Mathematical Modeling and Computational Thinking

Science.gov (United States)

Sanford, John F.; Naidu, Jaideep T.

2017-01-01

The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…

PENGEMBANGAN MODEL COMPREHENSIVE MATHEMATICS INSTRUCTION (CMI DALAM MEMBANGUN KEMAMPUAN MATHEMATICAL THINKING SISWA

Directory of Open Access Journals (Sweden)

Nita Delima

2017-03-01

Full Text Available Kesetaraan dalam pendidikan merupakan elemen penting dari beberapa standar visi NCTM dalam pendidikan matematika. Kesetaraan yang dimaksud, tidak berarti bahwa setiap siswa harus menerima pembelajaran yang identik dari guru; sebaliknya, menuntut sebuah pembelajaran yang mengakomodasi sebuah akses dalam mencapai kemampuan setiap siswa. Selain itu, NCTM juga mengemukakan bahwa dalam pembelajaran matematika terdapat lima standar proses yang harus terpenuhi, yakni problem solving, reasoning and proof, connections, communication, dan representation. Sementara itu, kemampuan problem solving yang dimiliki oleh seseorang akan mempengaruhi pada fleksibilitas proses berpikir mereka. Proses berpikir yang dimaksud dapat berupa proses dinamik yang memuat kompleksitas ide–ide matematik yang dimiliki serta dapat mengekspansi pemahaman tentang matematika yang disebut sebagai mathematical thinking. Dengan demikian, diperlukan sebuah model pembelajaran yang dapat berfungsi sebagai alat pedagogis guru, baik sebelum, selama dan setelah pembelajaran, terutama dalam membangun mathematical thinking siswa. Kerangka Comprehensive Mathematics Instruction (CMI merupakan sebuah kerangka prinsip – prinsip praktek pembelajaran yang bertujuan untuk menciptakan pengalaman matematika yang seimbang, sehingga siswa dapat memiliki pemikiran dan pemahaman matematika secara mendalam, kerangka CMI memiliki semua kriteria sebuah model pembelajaran. Adapun syntax untuk model CMI terdiri dari develop, solidify dan practice. Dalam penerapannya, setiap syntax tersebut meliputi tiga tahapan, yakni tujuan (purpose, peran guru (teacher role dan peran siswa (student role. Berdasarkan hasil analisis eksploratif yang telah dilakukan, dapat disimpulkan bahwa model pembelajaran CMI ini dapat menjadi sebuah alat pedagogis yang baru bagi guru yang dapat digunakan, baik sebelum, selama dan setelah pembelajaran dalam membangun kemampuan mathematical thinking siswa.    Kata Kunci: Comprehensive

An introduction to mathematical modeling of infectious diseases

CERN Document Server

Li, Michael Y

2018-01-01

This text provides essential modeling skills and methodology for the study of infectious diseases through a one-semester modeling course or directed individual studies.  The book includes mathematical descriptions of epidemiological concepts, and uses classic epidemic models to introduce different mathematical methods in model analysis.  Matlab codes are also included for numerical implementations. It is primarily written for upper undergraduate and beginning graduate students in mathematical sciences who have an interest in mathematical modeling of infectious diseases.  Although written in a rigorous mathematical manner, the style is not unfriendly to non-mathematicians.

Authenticity of Mathematical Modeling

Science.gov (United States)

Tran, Dung; Dougherty, Barbara J.

2014-01-01

Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…

Mathematical models in medicine: Diseases and epidemics

International Nuclear Information System (INIS)

Witten, M.

1987-01-01

This volume presents the numerous applications of mathematics in the life sciences and medicine, and demonstrates how mathematics and computers have taken root in these fields. The work covers a variety of techniques and applications including mathematical and modelling methodology, modelling/simulation technology, and philosophical issues in model formulation, leading to speciality medical modelling, artificial intelligence, psychiatric models, medical decision making, and molecular modelling

Mathematical Modeling in the High School Curriculum

Science.gov (United States)

Hernández, Maria L.; Levy, Rachel; Felton-Koestler, Mathew D.; Zbiek, Rose Mary

2016-01-01

In 2015, mathematics leaders and instructors from the Society for Industrial and Applied Mathematics (SIAM) and the Consortium for Mathematics and Its Applications (COMAP), with input from NCTM, came together to write the "Guidelines for Assessment and Instruction in Mathematical Modeling Education" (GAIMME) report as a resource for…

Explorations in Elementary Mathematical Modeling

Science.gov (United States)

Shahin, Mazen

2010-01-01

In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and…

Principles of mathematical modeling

CERN Document Server

Dym, Clive

2004-01-01

Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...

Modelling Mathematical Reasoning in Physics Education

Science.gov (United States)

Uhden, Olaf; Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche

2012-04-01

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

Mathematical Problem Solving Ability of Junior High School Students through Ang’s Framework for Mathematical Modelling Instruction

Science.gov (United States)

Fasni, N.; Turmudi, T.; Kusnandi, K.

2017-09-01

This research background of this research is the importance of student problem solving abilities. The purpose of this study is to find out whether there are differences in the ability to solve mathematical problems between students who have learned mathematics using Ang’s Framework for Mathematical Modelling Instruction (AFFMMI) and students who have learned using scientific approach (SA). The method used in this research is a quasi-experimental method with pretest-postest control group design. Data analysis of mathematical problem solving ability using Indepent Sample Test. The results showed that there was a difference in the ability to solve mathematical problems between students who received learning with Ang’s Framework for Mathematical Modelling Instruction and students who received learning with a scientific approach. AFFMMI focuses on mathematical modeling. This modeling allows students to solve problems. The use of AFFMMI is able to improve the solving ability.

Concepts of mathematical modeling

CERN Document Server

Meyer, Walter J

2004-01-01

Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each sec

Teaching mathematical modelling through project work

DEFF Research Database (Denmark)

Blomhøj, Morten; Kjeldsen, Tinne Hoff

2006-01-01

are reported in manners suitable for internet publication for colleagues. The reports and the related discussions reveal interesting dilemmas concerning the teaching of mathematical modelling and how to cope with these through “setting the scene” for the students modelling projects and through dialogues......The paper presents and analyses experiences from developing and running an in-service course in project work and mathematical modelling for mathematics teachers in the Danish gymnasium, e.g. upper secondary level, grade 10-12. The course objective is to support the teachers to develop, try out...... in their own classes, evaluate and report a project based problem oriented course in mathematical modelling. The in-service course runs over one semester and includes three seminars of 3, 1 and 2 days. Experiences show that the course objectives in general are fulfilled and that the course projects...

Mathematical modelling of scour: A review

DEFF Research Database (Denmark)

Sumer, B. Mutlu

2007-01-01

A review is presented of mathematical modelling of scour around hydraulic and marine structures. Principal ideas, general features and procedures are given. The paper is organized in three sections: the first two sections deal with the mathematical modelling of scour around piers....../piles and pipelines, respectively, the two benchmark cases, while the third section deals with the mathematical modelling of scour around other structures such as groins, breakwaters and sea walls. A section is also added to discuss potential future research areas. Over one hundred references are included...

Mathematical modeling a chemical engineer's perspective

CERN Document Server

Rutherford, Aris

1999-01-01

Mathematical modeling is the art and craft of building a system of equations that is both sufficiently complex to do justice to physical reality and sufficiently simple to give real insight into the situation. Mathematical Modeling: A Chemical Engineer's Perspective provides an elementary introduction to the craft by one of the century's most distinguished practitioners.Though the book is written from a chemical engineering viewpoint, the principles and pitfalls are common to all mathematical modeling of physical systems. Seventeen of the author's frequently cited papers are reprinted to illus

Exploring Yellowstone National Park with Mathematical Modeling

Science.gov (United States)

Wickstrom, Megan H.; Carr, Ruth; Lackey, Dacia

2017-01-01

Mathematical modeling, a practice standard in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), is a process by which students develop and use mathematics as a tool to make sense of the world around them. Students investigate a real-world situation by asking mathematical questions; along the way, they need to decide how to use…

Mathematical Modeling of Diverse Phenomena

Science.gov (United States)

Howard, J. C.

1979-01-01

Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.

Wind tunnel modeling of roadways: Comparison with mathematical models

International Nuclear Information System (INIS)

Heidorn, K.; Davies, A.E.; Murphy, M.C.

1991-01-01

The assessment of air quality impacts from roadways is a major concern to urban planners. In order to assess future road and building configurations, a number of techniques have been developed including mathematical models, which simulate traffic emissions and atmospheric dispersion through a series of mathematical relationships and physical models. The latter models simulate emissions and dispersion through scaling of these processes in a wind tunnel. Two roadway mathematical models, HIWAY-2 and CALINE-4, were applied to a proposed development in a large urban area. Physical modeling procedures developed by Rowan Williams Davies and Irwin Inc. (RWDI) in the form of line source simulators were also applied, and the resulting carbon monoxide concentrations were compared. The results indicated a factor of two agreement between the mathematical and physical models. The physical model, however, reacted to change in building massing and configuration. The mathematical models did not, since no provision for such changes was included in the mathematical models. In general, the RWDI model resulted in higher concentrations than either HIWAY-2 or CALINE-4. Where there was underprediction, it was often due to shielding of the receptor by surrounding buildings. Comparison of these three models with the CALTRANS Tracer Dispersion Experiment showed good results although concentrations were consistently underpredicted

Continuum mechanics the birthplace of mathematical models

CERN Document Server

Allen, Myron B

2015-01-01

Continuum mechanics is a standard course in many graduate programs in engineering and applied mathematics as it provides the foundations for the various differential equations and mathematical models that are encountered in fluid mechanics, solid mechanics, and heat transfer.  This book successfully makes the topic more accessible to advanced undergraduate mathematics majors by aligning the mathematical notation and language with related courses in multivariable calculus, linear algebra, and differential equations; making connections with other areas of applied mathematics where parial differe

Specific Type of Knowledge Map: Mathematical Model

OpenAIRE

Milan, Houška; Martina, Beránková

2005-01-01

The article deals with relationships between mathematical models and knowledge maps. The goal of the article is to suggest how to use the mathematical model as a knowledge map and/or as a part (esp. the inference mechanism) of the knowledge system. The results are demonstrated on the case study, when the knowledge from a story is expressed by mathematical model. The model is used for both knowledge warehousing and inferencing new artificially derived knowledge.

Mathematical modeling courses for Media technology students

DEFF Research Database (Denmark)

Timcenko, Olga

2009-01-01

This paper addresses curriculum development for Mathematical Modeling course at Medialogy education. Medialogy as a study line was established in 2002 at Faculty for Engineering and Natural Sciences at Aalborg University, and mathematics curriculum has already been revised three times, Mathematic...

The many faces of the mathematical modeling cycle

NARCIS (Netherlands)

Perrenet, J.C.; Zwaneveld, B.

2012-01-01

In literature about mathematical modeling a diversity can be seen in ways of presenting the modeling cycle. Every year, students in the Bachelor’s program Applied Mathematics of the Eindhoven University of Technology, after having completed a series of mathematical modeling projects, have been

Mathematical Modelling as a Professional Task

Science.gov (United States)

Frejd, Peter; Bergsten, Christer

2016-01-01

Educational research literature on mathematical modelling is extensive. However, not much attention has been paid to empirical investigations of its scholarly knowledge from the perspective of didactic transposition processes. This paper reports from an interview study of mathematical modelling activities involving nine professional model…

Mathematics Underground

Science.gov (United States)

Luther, Kenneth H.

2012-01-01

Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…

Mathematical Modeling Approaches in Plant Metabolomics.

Science.gov (United States)

Fürtauer, Lisa; Weiszmann, Jakob; Weckwerth, Wolfram; Nägele, Thomas

2018-01-01

The experimental analysis of a plant metabolome typically results in a comprehensive and multidimensional data set. To interpret metabolomics data in the context of biochemical regulation and environmental fluctuation, various approaches of mathematical modeling have been developed and have proven useful. In this chapter, a general introduction to mathematical modeling is presented and discussed in context of plant metabolism. A particular focus is laid on the suitability of mathematical approaches to functionally integrate plant metabolomics data in a metabolic network and combine it with other biochemical or physiological parameters.

Exploring Differential Effects of Mathematics Courses on Mathematics Achievement

Science.gov (United States)

Ma, Xin; McIntyre, Laureen J.

2005-01-01

Using data from the Longitudinal Study of Mathematics Participation (N = 1,518 students from 34 schools), we investigated the effects of pure and applied mathematics courses on mathematics achievement, controlling for prior mathematics achievement. Results of multilevel modelling showed that the effects of pure mathematics were significant after…

Mathematical models in radiogeochronology

International Nuclear Information System (INIS)

Abril, J.M.; Garcia Leon, M.

1991-01-01

The study of activity vs. depth profiles in sediment cores of some man-made and natural ocurring radionuclides have shown to be a poweful tool for dating purposes. Nevertheless, in most cases, an adecuate interpretation of such profiles requires mathematical models. In this paper, by considering the sediment as a continuum, a general equation for diffusion of radionuclides through it is obtained. Consequentely, some previously published dating models are found to be particular solutions of such general advenction-diffusion problem. Special emphasis is given to the mathematical treatment of compactation effect and time dependent problems. (author)

Teaching Mathematical Modelling for Earth Sciences via Case Studies

Science.gov (United States)

Yang, Xin-She

2010-05-01

Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).

Qualitative mathematics for the social sciences mathematical models for research on cultural dynamics

CERN Document Server

Rudolph, Lee

2012-01-01

In this book Lee Rudolph brings together international contributors who combine psychological and mathematical perspectives to analyse how qualitative mathematics can be used to create models of social and psychological processes. Bridging the gap between the fields with an imaginative and stimulating collection of contributed chapters, the volume updates the current research on the subject, which until now has been rather limited, focussing largely on the use of statistics. Qualitative Mathematics for the Social Sciences contains a variety of useful illustrative figures, in

Mathematical modelling a case studies approach

CERN Document Server

Illner, Reinhard; McCollum, Samantha; Roode, Thea van

2004-01-01

Mathematical modelling is a subject without boundaries. It is the means by which mathematics becomes useful to virtually any subject. Moreover, modelling has been and continues to be a driving force for the development of mathematics itself. This book explains the process of modelling real situations to obtain mathematical problems that can be analyzed, thus solving the original problem. The presentation is in the form of case studies, which are developed much as they would be in true applications. In many cases, an initial model is created, then modified along the way. Some cases are familiar, such as the evaluation of an annuity. Others are unique, such as the fascinating situation in which an engineer, armed only with a slide rule, had 24 hours to compute whether a valve would hold when a temporary rock plug was removed from a water tunnel. Each chapter ends with a set of exercises and some suggestions for class projects. Some projects are extensive, as with the explorations of the predator-prey model; oth...

Mathematical manipulative models: in defense of "beanbag biology".

Science.gov (United States)

Jungck, John R; Gaff, Holly; Weisstein, Anton E

2010-01-01

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.

Pre-Service Teachers' Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

Science.gov (United States)

Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc

2016-01-01

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…

Mathematical modelling of metabolism

DEFF Research Database (Denmark)

Gombert, Andreas Karoly; Nielsen, Jens

2000-01-01

Mathematical models of the cellular metabolism have a special interest within biotechnology. Many different kinds of commercially important products are derived from the cell factory, and metabolic engineering can be applied to improve existing production processes, as well as to make new processes...... availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology....... available. Both stoichiometric and kinetic models have been used to investigate the metabolism, which has resulted in defining the optimal fermentation conditions, as well as in directing the genetic changes to be introduced in order to obtain a good producer strain or cell line. With the increasing...

Mathematical models in biology bringing mathematics to life

CERN Document Server

Ferraro, Maria; Guarracino, Mario

2015-01-01

This book presents an exciting collection of contributions based on the workshop “Bringing Maths to Life” held October 27-29, 2014 in Naples, Italy.  The state-of-the art research in biology and the statistical and analytical challenges facing huge masses of data collection are treated in this Work. Specific topics explored in depth surround the sessions and special invited sessions of the workshop and include genetic variability via differential expression, molecular dynamics and modeling, complex biological systems viewed from quantitative models, and microscopy images processing, to name several. In depth discussions of the mathematical analysis required to extract insights from complex bodies of biological datasets, to aid development in the field novel algorithms, methods and software tools for genetic variability, molecular dynamics, and complex biological systems are presented in this book. Researchers and graduate students in biology, life science, and mathematics/statistics will find the content...

Assessment of Primary 5 Students' Mathematical Modelling Competencies

Science.gov (United States)

Chan, Chun Ming Eric; Ng, Kit Ee Dawn; Widjaja, Wanty; Seto, Cynthia

2012-01-01

Mathematical modelling is increasingly becoming part of an instructional approach deemed to develop students with competencies to function as 21st century learners and problem solvers. As mathematical modelling is a relatively new domain in the Singapore primary school mathematics curriculum, many teachers may not be aware of the learning outcomes…

Mathematical modeling and computational intelligence in engineering applications

CERN Document Server

Silva Neto, Antônio José da; Silva, Geraldo Nunes

2016-01-01

This book brings together a rich selection of studies in mathematical modeling and computational intelligence, with application in several fields of engineering, like automation, biomedical, chemical, civil, electrical, electronic, geophysical and mechanical engineering, on a multidisciplinary approach. Authors from five countries and 16 different research centers contribute with their expertise in both the fundamentals and real problems applications based upon their strong background on modeling and computational intelligence. The reader will find a wide variety of applications, mathematical and computational tools and original results, all presented with rigorous mathematical procedures. This work is intended for use in graduate courses of engineering, applied mathematics and applied computation where tools as mathematical and computational modeling, numerical methods and computational intelligence are applied to the solution of real problems.

Mathematical models of hysteresis

International Nuclear Information System (INIS)

1998-01-01

The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above

Mathematical models of hysteresis

Energy Technology Data Exchange (ETDEWEB)

NONE

1998-08-01

The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above.

Prospective Mathematics Teachers' Opinions about Mathematical Modeling Method and Applicability of This Method

Science.gov (United States)

Akgün, Levent

2015-01-01

The aim of this study is to identify prospective secondary mathematics teachers' opinions about the mathematical modeling method and the applicability of this method in high schools. The case study design, which is among the qualitative research methods, was used in the study. The study was conducted with six prospective secondary mathematics…

Structural Equation Model to Validate: Mathematics-Computer Interaction, Computer Confidence, Mathematics Commitment, Mathematics Motivation and Mathematics Confidence

Science.gov (United States)

Garcia-Santillán, Arturo; Moreno-Garcia, Elena; Escalera-Chávez, Milka E.; Rojas-Kramer, Carlos A.; Pozos-Texon, Felipe

2016-01-01

Most mathematics students show a definite tendency toward an attitudinal deficiency, which can be primarily understood as intolerance to the matter, affecting their scholar performance adversely. In addition, information and communication technologies have been gradually included within the process of teaching mathematics. Such adoption of…

An introduction to mathematical modeling a course in mechanics

CERN Document Server

Oden, Tinsley J

2011-01-01

A modern approach to mathematical modeling, featuring unique applications from the field of mechanics An Introduction to Mathematical Modeling: A Course in Mechanics is designed to survey the mathematical models that form the foundations of modern science and incorporates examples that illustrate how the most successful models arise from basic principles in modern and classical mathematical physics. Written by a world authority on mathematical theory and computational mechanics, the book presents an account of continuum mechanics, electromagnetic field theory, quantum mechanics, and statistical mechanics for readers with varied backgrounds in engineering, computer science, mathematics, and physics. The author streamlines a comprehensive understanding of the topic in three clearly organized sections: Nonlinear Continuum Mechanics introduces kinematics as well as force and stress in deformable bodies; mass and momentum; balance of linear and angular momentum; conservation of energy; and constitutive equation...

Students’ mathematical learning in modelling activities

DEFF Research Database (Denmark)

Kjeldsen, Tinne Hoff; Blomhøj, Morten

2013-01-01

Ten years of experience with analyses of students’ learning in a modelling course for first year university students, led us to see modelling as a didactical activity with the dual goal of developing students’ modelling competency and enhancing their conceptual learning of mathematical concepts i...... create and help overcome hidden cognitive conflicts in students’ understanding; that reflections within modelling can play an important role for the students’ learning of mathematics. These findings are illustrated with a modelling project concerning the world population....

Mathematics Models in Chemistry--An Innovation for Non-Mathematics and Non-Science Majors

Science.gov (United States)

Rash, Agnes M.; Zurbach, E. Peter

2004-01-01

The intention of this article is to present a year-long interdisciplinary course, Mathematical Models in Chemistry. The course is comprised of eleven units, each of which has both a mathematical and a chemical component. A syllabus of the course is given and the format of the class is explained. The interaction of the professors and the content is…

The Comparison of Think Talk Write and Think Pair Share Model with Realistic Mathematics Education Approach Viewed from Mathematical-Logical Intelligence

Directory of Open Access Journals (Sweden)

Himmatul Afthina

2017-12-01

Full Text Available The aims of this research to determine the effect of Think Talk Write (TTW and Think Pair Share (TPS model with Realistic Mathematics Education (RME approach viewed from mathematical-logical intelligence. This research employed the quasi experimental research. The population of research was all students of the eight graders of junior high school in Karangamyar Regency in academic year 2016/2017. The result of this research shows that (1 TTW with RME approach gave better mathematics achievement than TPS with RME approach, (2 Students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low, whereas students with average mathematical-logical intelligence can reach a better achievement than those with low one, (3 In TTW model with RME approach, students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low, whereas students with average and low mathematical-logical intelligence gave same mathematics achievement, and  in TPS model with RME approach students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low, whereas students with average mathematical-logical intelligence can reach a better achievement than those with low one (4 In each category of  mathematical-logical intelligence, TTW with RME approach and TPS with RME approach gave same mathematics achievement.

Modelling and Optimizing Mathematics Learning in Children

Science.gov (United States)

Käser, Tanja; Busetto, Alberto Giovanni; Solenthaler, Barbara; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; von Aster, Michael; Gross, Markus

2013-01-01

This study introduces a student model and control algorithm, optimizing mathematics learning in children. The adaptive system is integrated into a computer-based training system for enhancing numerical cognition aimed at children with developmental dyscalculia or difficulties in learning mathematics. The student model consists of a dynamic…

Development of a Multidisciplinary Middle School Mathematics Infusion Model

Science.gov (United States)

Russo, Maria; Hecht, Deborah; Burghardt, M. David; Hacker, Michael; Saxman, Laura

2011-01-01

The National Science Foundation (NSF) funded project "Mathematics, Science, and Technology Partnership" (MSTP) developed a multidisciplinary instructional model for connecting mathematics to science, technology and engineering content areas at the middle school level. Specifically, the model infused mathematics into middle school curriculum…

The effect of Missouri mathematics project learning model on students’ mathematical problem solving ability

Science.gov (United States)

Handayani, I.; Januar, R. L.; Purwanto, S. E.

2018-01-01

This research aims to know the influence of Missouri Mathematics Project Learning Model to Mathematical Problem-solving Ability of Students at Junior High School. This research is a quantitative research and uses experimental research method of Quasi Experimental Design. The research population includes all student of grade VII of Junior High School who are enrolled in the even semester of the academic year 2016/2017. The Sample studied are 76 students from experimental and control groups. The sampling technique being used is cluster sampling method. The instrument is consisted of 7 essay questions whose validity, reliability, difficulty level and discriminating power have been tested. Before analyzing the data by using t-test, the data has fulfilled the requirement for normality and homogeneity. The result of data shows that there is the influence of Missouri mathematics project learning model to mathematical problem-solving ability of students at junior high school with medium effect.

Mathematical Footprints Discovering Mathematics Everywhere

CERN Document Server

Pappas, Theoni

1999-01-01

MATHEMATICAL FOOTPRINTS takes a creative look at the role mathematics has played since prehistoric times, and will play in the future, and uncovers mathematics where you least expect to find it from its many uses in medicine, the sciences, and its appearance in art to its patterns in nature and its central role in the development of computers. Pappas presents mathematical ideas in a readable non-threatening manner. MATHEMATICAL FOOTPRINTS is another gem by the creator of THE MATHEMATICS CALENDAR and author of THE JOY OF MATHEMATICS. "Pappas's books have been gold mines of mathematical ent

Mathematical biology

CERN Document Server

Murray, James D

1993-01-01

The book is a textbook (with many exercises) giving an in-depth account of the practical use of mathematical modelling in the biomedical sciences. The mathematical level required is generally not high and the emphasis is on what is required to solve the real biological problem. The subject matter is drawn, e.g. from population biology, reaction kinetics, biological oscillators and switches, Belousov-Zhabotinskii reaction, reaction-diffusion theory, biological wave phenomena, central pattern generators, neural models, spread of epidemics, mechanochemical theory of biological pattern formation and importance in evolution. Most of the models are based on real biological problems and the predictions and explanations offered as a direct result of mathematical analysis of the models are important aspects of the book. The aim is to provide a thorough training in practical mathematical biology and to show how exciting and novel mathematical challenges arise from a genuine interdisciplinary involvement with the biosci...

Mathematical modeling of laser lipolysis

Directory of Open Access Journals (Sweden)

Reynaud Jean

2008-02-01

Full Text Available Abstract Background and Objectives Liposuction continues to be one of the most popular procedures performed in cosmetic surgery. As the public's demand for body contouring continues, laser lipolysis has been proposed to improve results, minimize risk, optimize patient comfort, and reduce the recovery period. Mathematical modeling of laser lipolysis could provide a better understanding of the laser lipolysis process and could determine the optimal dosage as a function of fat volume to be removed. Study design/Materials and Methods An Optical-Thermal-Damage Model was formulated using finite-element modeling software (Femlab 3.1, Comsol Inc. The general model simulated light distribution using the diffusion approximation of the transport theory, temperature rise using the bioheat equation and laser-induced injury using the Arrhenius damage model. Biological tissue was represented by two homogenous regions (dermis and fat layer with a nonlinear air-tissue boundary condition including free convection. Video recordings were used to gain a better understanding of the back and forth movement of the cannula during laser lipolysis in order to consider them in our mathematical model. Infrared video recordings were also performed in order to compare the actual surface temperatures to our calculations. The reduction in fat volume was determined as a function of the total applied energy and subsequently compared to clinical data reported in the literature. Results In patients, when using cooled tumescent anesthesia, 1064 nm Nd:YAG laser or 980 nm diode laser: (6 W, back and forth motion: 100 mm/s give similar skin surface temperature (max: 41°C. These measurements are in accordance with those obtained by mathematical modeling performed with a 1 mm cannula inserted inside the hypodermis layer at 0.8 cm below the surface. Similarly, the fat volume reduction observed in patients at 6-month follow up can be determined by mathematical modeling. This fat reduction

Mathematical psychology.

Science.gov (United States)

Batchelder, William H

2010-09-01

Mathematical psychology is a sub-field of psychology that started in the 1950s and has continued to grow as an important contributor to formal psychological theory, especially in the cognitive areas of psychology such as learning, memory, classification, choice response time, decision making, attention, and problem solving. In addition, there are several scientific sub-areas that were originated by mathematical psychologists such as the foundations of measurement, stochastic memory models, and psychologically motivated reformulations of expected utility theory. Mathematical psychology does not include all uses of mathematics and statistics in psychology, and indeed there is a long history of such uses especially in the areas of perception and psychometrics. What is most unique about mathematical psychology is its approach to theory construction. While accepting the behaviorist dictum that the data in psychology must be observable and replicable, mathematical models are specified in terms of unobservable formal constructs that can predict detailed aspects of data across multiple experimental and natural settings. By now almost all the substantive areas of cognitive and experimental psychology have formal mathematical models and theories, and many of these are due to researchers that identify with mathematical psychology. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.

Mathematical modeling of a process the rolling delivery

Science.gov (United States)

Stepanov, Mikhail A.; Korolev, Andrey A.

2018-03-01

An adduced analysis of the scientific researches in a domain of the rolling equipments, also research of properties the working material. A one of perspective direction of scientific research this is mathematical modeling. That is broadly used in many scientific disciplines and especially at the technical, applied sciences. With the aid of mathematical modeling it can be study of physical properties of the researching objects and systems. A research of the rolling delivery and transporting devices realized with the aid of a construction of mathematical model of appropriate process. To be described the basic principles and conditions of a construction of mathematical models of the real objects. For example to be consider a construction of mathematical model the rolling delivery device. For a construction that is model used system of the equations, which consist of: Lagrange’s equation of a motion, describing of the law conservation of energy of a mechanical system, and the Navier - Stokes equations, which characterize of the flow of a continuous non-compressed fluid. A construction of mathematical model the rolling deliver to let determined of a total energy of device, and therefore to got the dependence upon the power of drive to a gap between of rolls. A corroborate the hypothesis about laminar the flow of a material into the rolling gap of deliver.

mathematical models for estimating radio channels utilization

African Journals Online (AJOL)

2017-08-08

Aug 8, 2017 ... Mathematical models for radio channels utilization assessment by real-time flows transfer in ... data transmission networks application having dynamic topology ..... Journal of Applied Mathematics and Statistics, 56(2): 85–90.

Rival approaches to mathematical modelling in immunology

Science.gov (United States)

Andrew, Sarah M.; Baker, Christopher T. H.; Bocharov, Gennady A.

2007-08-01

In order to formulate quantitatively correct mathematical models of the immune system, one requires an understanding of immune processes and familiarity with a range of mathematical techniques. Selection of an appropriate model requires a number of decisions to be made, including a choice of the modelling objectives, strategies and techniques and the types of model considered as candidate models. The authors adopt a multidisciplinary perspective.

The Relationship between Big Data and Mathematical Modeling: A Discussion in a Mathematical Education Scenario

Science.gov (United States)

Dalla Vecchia, Rodrigo

2015-01-01

This study discusses aspects of the association between Mathematical Modeling (MM) and Big Data in the scope of mathematical education. We present an example of an activity to discuss two ontological factors that involve MM. The first is linked to the modeling stages. The second involves the idea of pedagogical objectives. The main findings…

Developing Teaching Material Based on Realistic Mathematics Andoriented to the Mathematical Reasoning and Mathematical Communication

OpenAIRE

Habsah, Fitria

2017-01-01

This research aims to produce mathematics textbook for grade VII junior high school students based on realistic mathematics and oriented to the mathematical reasoning and mathematical communication. The quality is determined based on Nieveen criteria, including validity, practicality, and effectiveness.This study was a research and development and used Borg & Gall model. The subject of this research were the students of SMPN 2 Pujon-Kabupaten Malang, that is 30 students in an experimental cla...

Leading Undergraduate Research Projects in Mathematical Modeling

Science.gov (United States)

Seshaiyer, Padmanabhan

2017-01-01

In this article, we provide some useful perspectives and experiences in mentoring students in undergraduate research (UR) in mathematical modeling using differential equations. To engage students in this topic, we present a systematic approach to the creation of rich problems from real-world phenomena; present mathematical models that are derived…

Scaffolding Mathematical Modelling with a Solution Plan

Science.gov (United States)

Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner

2015-01-01

In the study presented in this paper, we examined the possibility to scaffold mathematical modelling with strategies. The strategies were prompted using an instrument called "solution plan" as a scaffold. The effects of this step by step instrument on mathematical modelling competency and on self-reported strategies were tested using…

Mathematical modelling of fracture hydrology

International Nuclear Information System (INIS)

Herbert, A.W.; Hodgkindon, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.

1985-01-01

This report reviews work carried out between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology' which forms part of the CEC Mirage project (CEC 1984. Come 1985. Bourke et. al. 1983). It describes the development and use of a variety of mathematical models for the flow of water and transport of radionuclides in flowing groundwater. These models have an important role to play in assessing the long-term safety of radioactive waste burial, and in the planning and interpretation of associated experiments. The work is reported under five headings, namely 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments, 5) Analysis of field experiments

Mathematical modeling of biological processes

CERN Document Server

Friedman, Avner

2014-01-01

This book on mathematical modeling of biological processes includes a wide selection of biological topics that demonstrate the power of mathematics and computational codes in setting up biological processes with a rigorous and predictive framework. Topics include: enzyme dynamics, spread of disease, harvesting bacteria, competition among live species, neuronal oscillations, transport of neurofilaments in axon, cancer and cancer therapy, and granulomas. Complete with a description of the biological background and biological question that requires the use of mathematics, this book is developed for graduate students and advanced undergraduate students with only basic knowledge of ordinary differential equations and partial differential equations; background in biology is not required. Students will gain knowledge on how to program with MATLAB without previous programming experience and how to use codes in order to test biological hypothesis.

Mathematical Modeling with Middle School Students: The Robot Art Model-Eliciting Activity

Science.gov (United States)

Stohlmann, Micah S.

2017-01-01

Internationally mathematical modeling is garnering more attention for the benefits associated with it. Mathematical modeling can develop students' communication skills and the ability to demonstrate understanding through different representations. With the increased attention on mathematical modeling, there is a need for more curricula to be…

Mathematical models in marketing a collection of abstracts

CERN Document Server

Funke, Ursula H

1976-01-01

Mathematical models can be classified in a number of ways, e.g., static and dynamic; deterministic and stochastic; linear and nonlinear; individual and aggregate; descriptive, predictive, and normative; according to the mathematical technique applied or according to the problem area in which they are used. In marketing, the level of sophistication of the mathe­ matical models varies considerably, so that a nurnber of models will be meaningful to a marketing specialist without an extensive mathematical background. To make it easier for the nontechnical user we have chosen to classify the models included in this collection according to the major marketing problem areas in which they are applied. Since the emphasis lies on mathematical models, we shall not as a rule present statistical models, flow chart models, computer models, or the empirical testing aspects of these theories. We have also excluded competitive bidding, inventory and transportation models since these areas do not form the core of ·the market...

Mathematical models for therapeutic approaches to control HIV disease transmission

CERN Document Server

Roy, Priti Kumar

2015-01-01

The book discusses different therapeutic approaches based on different mathematical models to control the HIV/AIDS disease transmission. It uses clinical data, collected from different cited sources, to formulate the deterministic as well as stochastic mathematical models of HIV/AIDS. It provides complementary approaches, from deterministic and stochastic points of view, to optimal control strategy with perfect drug adherence and also tries to seek viewpoints of the same issue from different angles with various mathematical models to computer simulations. The book presents essential methods and techniques for students who are interested in designing epidemiological models on HIV/AIDS. It also guides research scientists, working in the periphery of mathematical modeling, and helps them to explore a hypothetical method by examining its consequences in the form of a mathematical modelling and making some scientific predictions. The model equations, mathematical analysis and several numerical simulations that are...

Mathematical Modelling of Surfactant Self-assembly at Interfaces

KAUST Repository

Morgan, C. E.; Breward, C. J. W.; Griffiths, I. M.; Howell, P. D.

2015-01-01

© 2015 Society for Industrial and Applied Mathematics. We present a mathematical model to describe the distribution of surfactant pairs in a multilayer structure beneath an adsorbed monolayer. A mesoscopic model comprising a set of ordinary

Ocular hemodynamics and glaucoma: the role of mathematical modeling.

Science.gov (United States)

Harris, Alon; Guidoboni, Giovanna; Arciero, Julia C; Amireskandari, Annahita; Tobe, Leslie A; Siesky, Brent A

2013-01-01

To discuss the role of mathematical modeling in studying ocular hemodynamics, with a focus on glaucoma. We reviewed recent literature on glaucoma, ocular blood flow, autoregulation, the optic nerve head, and the use of mathematical modeling in ocular circulation. Many studies suggest that alterations in ocular hemodynamics play a significant role in the development, progression, and incidence of glaucoma. Although there is currently a limited number of studies involving mathematical modeling of ocular blood flow, regulation, and diseases (such as glaucoma), preliminary modeling work shows the potential of mathematical models to elucidate the mechanisms that contribute most significantly to glaucoma progression. Mathematical modeling is a useful tool when used synergistically with clinical and laboratory data in the study of ocular blood flow and glaucoma. The development of models to investigate the relationship between ocular hemodynamic alterations and glaucoma progression will provide a unique and useful method for studying the pathophysiology of glaucoma.

Mathematical modelling of two-phase flows

International Nuclear Information System (INIS)

Komen, E.M.J.; Stoop, P.M.

1992-11-01

A gradual shift from methods based on experimental correlations to methods based on mathematical models to study 2-phase flows can be observed. The latter can be used to predict dynamical behaviour of 2-phase flows. This report discusses various mathematical models for the description of 2-phase flows. An important application of these models can be found in thermal-hydraulic computer codes used for analysis of the thermal-hydraulic behaviour of water cooled nuclear power plants. (author). 17 refs., 7 figs., 6 tabs

The possibilities of a modelling perspective for school mathematics

Directory of Open Access Journals (Sweden)

Dirk Wessels

2009-09-01

complex teaching methodology requires in-depth thinking about the role of the teacher, the role of the learner, the nature of the classroom culture, the nature of the negotiation of meaning between the teacher and individuals or groups, the nature of selected problems and material, as well as the kind of integrative assessment used in the mathematics classroom. Modelling is closely related to the problem-centred teaching approach, but it also smoothly relates to bigger and longer mathematical tasks. This article gives a theoretical exposition of the scope and depth of mathematical modelling. It is possible to introduce modelling at every school phase in our educational sytem. Modelling in school mathematics seems to make the learning of mathematics more effective. The mastering of problem solving and modelling strategies has definitely changed the orientation, the competencies and performances of learners at each school level. It would appear from research that learners like the application side of mathematics and that they want to see it in action. Genuine real life problems should be selected, which is why a modelling perspective is so important for the teaching and mastering of mathematics. Modelling should be integrated into the present curriculum because learners will then get full access to involvement in the classroom, to mathematisation, to doing problems, to criticising arguments, to finding proofs, to recognising concepts and to obtaining the ability to abstract these from the realistic situation. Modelling should be given a full opportunity in mathematics teacher education so that our learners can get the full benefit of it. This will put the mathematical performances of learners in our country on a more solid base, which will make our learners more competitive at all levels in the future. 

Exploring the Relationship between Mathematical Modelling and Classroom Discourse

Science.gov (United States)

Redmond, Trevor; Sheehy, Joanne; Brown, Raymond

2010-01-01

This paper explores the notion that the discourse of the mathematics classroom impacts on the practices that students engage when modelling mathematics. Using excerpts of a Year 12 student's report on modelling Newton's law of cooling, this paper argues that when students engage with the discourse of their mathematics classroom in a manner that…

Predicting Success in College Mathematics from High School Mathematics Preparation

OpenAIRE

Shepley, Richard A.

1983-01-01

The purpose of this study was to develop a model to predict the college mathematics courses a freshman could expect to pass by considering their high school mathematics preparation. The high school information that was used consisted of the student's sex, the student's grade point average in mathematics, the highest level of high school mathematics courses taken, and the number of mathematics courses taken in high school. The high school sample was drawn from graduated Seniors in the State...

Changing Pre-Service Mathematics Teachers' Beliefs about Using Computers for Teaching and Learning Mathematics: The Effect of Three Different Models

Science.gov (United States)

Karatas, Ilhan

2014-01-01

This study examines the effect of three different computer integration models on pre-service mathematics teachers' beliefs about using computers in mathematics education. Participants included 104 pre-service mathematics teachers (36 second-year students in the Computer Oriented Model group, 35 fourth-year students in the Integrated Model (IM)…

Mathematical models and accuracy of radioisotope gauges

International Nuclear Information System (INIS)

Urbanski, P.

1989-01-01

Mathematical expressions relating the variance and mean value of the intrinsic error with the parameters of one and multi-dimensional mathematical models of radioisotope gauges are given. Variance of the intrinsic error at the model's output is considered as a sum of the variances of the random error which is created in the first stages of the measuring chain and the random error of calibration procedure. The mean value of the intrinsic error (systematic error) appears always for nonlinear models. It was found that the optimal model of calibration procedure not always corresponds to the minimal value of the intrinsic error. The derived expressions are applied for the assessment of the mathematical models of some of the existing gauges (radioisotope belt weigher, XRF analyzer and coating thickness gauge). 7 refs., 5 figs., 1 tab. (author)

a Discrete Mathematical Model to Simulate Malware Spreading

Science.gov (United States)

Del Rey, A. Martin; Sánchez, G. Rodriguez

2012-10-01

With the advent and worldwide development of Internet, the study and control of malware spreading has become very important. In this sense, some mathematical models to simulate malware propagation have been proposed in the scientific literature, and usually they are based on differential equations exploiting the similarities with mathematical epidemiology. The great majority of these models study the behavior of a particular type of malware called computer worms; indeed, to the best of our knowledge, no model has been proposed to simulate the spreading of a computer virus (the traditional type of malware which differs from computer worms in several aspects). In this sense, the purpose of this work is to introduce a new mathematical model not based on continuous mathematics tools but on discrete ones, to analyze and study the epidemic behavior of computer virus. Specifically, cellular automata are used in order to design such model.

A mathematical approach to research problems of science and technology theoretical basis and developments in mathematical modeling

CERN Document Server

Ei, Shin-ichiro; Koiso, Miyuki; Ochiai, Hiroyuki; Okada, Kanzo; Saito, Shingo; Shirai, Tomoyuki

2014-01-01

This book deals with one of the most novel advances in mathematical modeling for applied scientific technology, including computer graphics, public-key encryption, data visualization, statistical data analysis, symbolic calculation, encryption, error correcting codes, and risk management. It also shows that mathematics can be used to solve problems from nature, e.g., slime mold algorithms. One of the unique features of this book is that it shows readers how to use pure and applied mathematics, especially those mathematical theory/techniques developed in the twentieth century, and developing now, to solve applied problems in several fields of industry. Each chapter includes clues on how to use "mathematics" to solve concrete problems faced in industry as well as practical applications. The target audience is not limited to researchers working in applied mathematics and includes those in engineering, material sciences, economics, and life sciences.

Mathematical model in economic environmental problems

Energy Technology Data Exchange (ETDEWEB)

Nahorski, Z. [Polish Academy of Sciences, Systems Research Inst. (Poland); Ravn, H.F. [Risoe National Lab. (Denmark)

1996-12-31

The report contains a review of basic models and mathematical tools used in economic regulation problems. It starts with presentation of basic models of capital accumulation, resource depletion, pollution accumulation, and population growth, as well as construction of utility functions. Then the one-state variable model is discussed in details. The basic mathematical methods used consist of application of the maximum principle and phase plane analysis of the differential equations obtained as the necessary conditions of optimality. A summary of basic results connected with these methods is given in appendices. (au) 13 ills.; 17 refs.

The (Mathematical) Modeling Process in Biosciences.

Science.gov (United States)

Torres, Nestor V; Santos, Guido

2015-01-01

In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology.

Mathematical modeling and applications in nonlinear dynamics

CERN Document Server

Merdan, Hüseyin

2016-01-01

The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...

Mathematical physiology

CERN Document Server

Sneyd, James

2009-01-01

There has been a long history of interaction between mathematics and physiology. This book looks in detail at a wide selection of mathematical models in physiology, showing how physiological problems can be formulated and studied mathematically, and how such models give rise to interesting and challenging mathematical questions. With its coverage of many recent models it gives an overview of the field, while many older models are also discussed, to put the modern work in context. In this second edition the coverage of basic principles has been expanded to include such topics as stochastic differential equations, Markov models and Gibbs free energy, and the selection of models has also been expanded to include some of the basic models of fluid transport, respiration/perfusion, blood diseases, molecular motors, smooth muscle, neuroendrocine cells, the baroreceptor loop, turboglomerular oscillations, blood clotting and the retina. Owing to this extensive coverage, the second edition is published in two volumes. ...

Improving ability mathematic literacy, self-efficacy and reducing mathematical anxiety with learning Treffinger model at senior high school students

Directory of Open Access Journals (Sweden)

Hafizh Nizham

2017-12-01

Full Text Available This study is a Quasi Experimental study with the design of The Pretest-Post-Test Non-Equivalent Group Design. Population in this research is all student of class X SHS in South Jakarta. Sampling is done by purposive sampling, to obtain an experimental class and control class. In the experimental class, students learn with Treffinger learning model and control, class learning with conventional learning. This study is also to examine the differences of self-efficacy improvement and students literacy skills, and decreased students' mathematical anxiety. Also, this study also examines the relevance of early mathematical abilities (high, medium, low with improving students' math literacy skills. The instrument used in this research is literacy skill test, self-efficacy scale, mathematical anxiety scale, observation sheet, and student interview. Data were analyzed by t-test, one-way ANOVA, and two lines. From the results of the data, it is found that: (1 The improvement of literacy ability of students who are learned with Treffinger model learning is not significantly higher than students who learn with conventional. (2 The self-efficacy of students who learning with the Treffinger model learning  is better than the student that is learning by conventional. (3 The mathematical anxiety of students learning with Treffinger model learning reduces better than students learning with conventional. (4 There is a difference in the improvement of students' mathematical literacy skills learning by learning the Treffinger model and students learning with conventional learning based on early mathematical abilities. (5 Student response to Treffinger model learning is better than students learning with conventional learning. Therefore, learning model Treffinger can be an alternative model of learning to improve students' mathematical literacy skills, and self-efficacy students, and able to reduce mathematical anxiety.

Use of mathematical modeling in nuclear measurements projects

International Nuclear Information System (INIS)

Toubon, H.; Menaa, N.; Mirolo, L.; Ducoux, X.; Khalil, R. A.; Chany, P.; Devita, A.

2011-01-01

Mathematical modeling of nuclear measurement systems is not a new concept. The response of the measurement system is described using a pre-defined mathematical model that depends on a set of parameters. These parameters are determined using a limited set of experimental measurement points e.g. efficiency curve, dose rates... etc. The model that agrees with the few experimental points is called an experimentally validated model. Once these models have been validated, we use mathematical interpolation to find the parameters of interest. Sometimes, when measurements are not practical or are impossible extrapolation is implemented but with care. CANBERRA has been extensively using mathematical modeling for the design and calibration of large and sophisticated systems to create and optimize designs that would be prohibitively expensive with only experimental tools. The case studies that will be presented here are primarily performed with MCNP, CANBERRA's MERCURAD/PASCALYS and ISOCS (In Situ Object Counting Software). For benchmarking purposes, both Monte Carlo and ray-tracing based codes are inter-compared to show models consistency and add a degree of reliability to modeling results. (authors)

Mathematics in Nature Modeling Patterns in the Natural World

CERN Document Server

Adam, John A

2011-01-01

From rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature.Generously illustrated, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathem

Modeling interdisciplinary activities involving Mathematics

DEFF Research Database (Denmark)

Iversen, Steffen Møllegaard

2006-01-01

In this paper a didactical model is presented. The goal of the model is to work as a didactical tool, or conceptual frame, for developing, carrying through and evaluating interdisciplinary activities involving the subject of mathematics and philosophy in the high schools. Through the terms...... of Horizontal Intertwining, Vertical Structuring and Horizontal Propagation the model consists of three phases, each considering different aspects of the nature of interdisciplinary activities. The theoretical modelling is inspired by work which focuses on the students abilities to concept formation in expanded...... domains (Michelsen, 2001, 2005a, 2005b). Furthermore the theoretical description rest on a series of qualitative interviews with teachers from the Danish high school (grades 9-11) conducted recently. The special case of concrete interdisciplinary activities between mathematics and philosophy is also...

Parental modelling of mathematical affect: self-efficacy and emotional arousal

Science.gov (United States)

Bartley, Sarah R.; Ingram, Naomi

2017-12-01

This study explored the relationship between parents' mathematics self-efficacy and emotional arousal to mathematics and their 12- and 13-year-old children's mathematics self-efficacy and emotional arousal to mathematics. Parental modelling of affective relationships during homework was a focus. Eighty-four parent and child pairings from seven schools in New Zealand were examined using embedded design methodology. No significant correlations were found when the parents' mathematics self-efficacy and emotional arousal to mathematics were compared with the children's mathematics self-efficacy and emotional arousal to mathematics. However, the parents' level of emotional arousal to mathematics was found to have affected their willingness to assist with mathematics homework. For those parents who assisted, a significant positive correlation was found between their mathematics self-efficacy and their children's emotional arousal to mathematics. Parents who did assist were generally reported as being calm, and used techniques associated with positive engagement. Fathers were calmer and more likely to express readiness to assist with mathematics homework than mothers. A further significant positive correlation was found between fathers' emotional arousal to mathematics and children's mathematics self-efficacy. Implications from the study suggest directions for future research.

FEMME, a flexible environment for mathematically modelling the environment

NARCIS (Netherlands)

Soetaert, K.E.R.; DeClippele, V.; Herman, P.M.J.

2002-01-01

A new, FORTRAN-based, simulation environment called FEMME (Flexible Environment for Mathematically Modelling the Environment), designed for implementing, solving and analysing mathematical models in ecology is presented. Three separate phases in ecological modelling are distinguished: (1) the model

Interfacial Fluid Mechanics A Mathematical Modeling Approach

CERN Document Server

Ajaev, Vladimir S

2012-01-01

Interfacial Fluid Mechanics: A Mathematical Modeling Approach provides an introduction to mathematical models of viscous flow used in rapidly developing fields of microfluidics and microscale heat transfer. The basic physical effects are first introduced in the context of simple configurations and their relative importance in typical microscale applications is discussed. Then,several configurations of importance to microfluidics, most notably thin films/droplets on substrates and confined bubbles, are discussed in detail.  Topics from current research on electrokinetic phenomena, liquid flow near structured solid surfaces, evaporation/condensation, and surfactant phenomena are discussed in the later chapters. This book also:  Discusses mathematical models in the context of actual applications such as electrowetting Includes unique material on fluid flow near structured surfaces and phase change phenomena Shows readers how to solve modeling problems related to microscale multiphase flows Interfacial Fluid Me...

Mathematical Models of Tuberculosis Reactivation and Relapse

Directory of Open Access Journals (Sweden)

Robert Steven Wallis

2016-05-01

Full Text Available The natural history of human infection with Mycobacterium tuberculosis (Mtb is highly variable, as is the response to treatment of active tuberculosis. There is presently no direct means to identify individuals in whom Mtb infection has been eradicated, whether by a bactericidal immune response or sterilizing antimicrobial chemotherapy. Mathematical models can assist in such circumstances by measuring or predicting events that cannot be directly observed. The 3 models discussed in this review illustrate instances in which mathematical models were used to identify individuals with innate resistance to Mtb infection, determine the etiology of tuberculosis in patients treated with tumor necrosis factor antagonists, and predict the risk of relapse in persons undergoing tuberculosis treatment. These examples illustrate the power of various types of mathematic models to increase knowledge and thereby inform interventions in the present global tuberculosis epidemic.

Applied Mathematics, Modelling and Computational Science

CERN Document Server

Kotsireas, Ilias; Makarov, Roman; Melnik, Roderick; Shodiev, Hasan

2015-01-01

The Applied Mathematics, Modelling, and Computational Science (AMMCS) conference aims to promote interdisciplinary research and collaboration. The contributions in this volume cover the latest research in mathematical and computational sciences, modeling, and simulation as well as their applications in natural and social sciences, engineering and technology, industry, and finance. The 2013 conference, the second in a series of AMMCS meetings, was held August 26–30 and organized in cooperation with AIMS and SIAM, with support from the Fields Institute in Toronto, and Wilfrid Laurier University. There were many young scientists at AMMCS-2013, both as presenters and as organizers. This proceedings contains refereed papers contributed by the participants of the AMMCS-2013 after the conference. This volume is suitable for researchers and graduate students, mathematicians and engineers, industrialists, and anyone who would like to delve into the interdisciplinary research of applied and computational mathematics ...

International Conference on Applied Mathematics, Modeling and Computational Science & Annual meeting of the Canadian Applied and Industrial Mathematics

CERN Document Server

Bélair, Jacques; Kunze, Herb; Makarov, Roman; Melnik, Roderick; Spiteri, Raymond J

2016-01-01

Focusing on five main groups of interdisciplinary problems, this book covers a wide range of topics in mathematical modeling, computational science and applied mathematics. It presents a wealth of new results in the development of modeling theories and methods, advancing diverse areas of applications and promoting interdisciplinary interactions between mathematicians, scientists, engineers and representatives from other disciplines. The book offers a valuable source of methods, ideas, and tools developed for a variety of disciplines, including the natural and social sciences, medicine, engineering, and technology. Original results are presented on both the fundamental and applied level, accompanied by an ample number of real-world problems and examples emphasizing the interdisciplinary nature and universality of mathematical modeling, and providing an excellent outline of today’s challenges. Mathematical modeling, with applied and computational methods and tools, plays a fundamental role in modern science a...

Simple mathematical models of symmetry breaking. Application to particle physics

International Nuclear Information System (INIS)

Michel, L.

1976-01-01

Some mathematical facts relevant to symmetry breaking are presented. A first mathematical model deals with the smooth action of compact Lie groups on real manifolds, a second model considers linear action of any group on real or complex finite dimensional vector spaces. Application of the mathematical models to particle physics is considered. (B.R.H.)

International note: Are Emirati parents' attitudes toward mathematics linked to their adolescent children's attitudes toward mathematics and mathematics achievement?

Science.gov (United States)

Areepattamannil, Shaljan; Khine, Myint Swe; Melkonian, Michael; Welch, Anita G; Al Nuaimi, Samira Ahmed; Rashad, Fatimah F

2015-10-01

Drawing on data from the 2012 Program for International Student Assessment (PISA) and employing multilevel modeling as an analytic strategy, this study examined the relations of adolescent children's perceptions of their parents' attitudes towards mathematics to their own attitudes towards mathematics and mathematics achievement among a sample of 5116 adolescents from 384 schools in the United Arab Emirates. The results of this cross-sectional study revealed that adolescents who perceived that their parents liked mathematics and considered mathematics was important for their children not only to study but also for their career tended to report higher levels of intrinsic and instrumental motivation to learn mathematics, mathematics self-concept and self-efficacy, and mathematics work ethic. Moreover, adolescents who perceived that their parents liked mathematics and considered mathematics was important for their children's career tended to report positive intentions and behaviors toward mathematics. However, adolescents who perceived that their parents considered mathematics was important for their children's career tended to report higher levels of mathematics anxiety. Finally, adolescents who perceived that their parents considered mathematics was important for their children to study performed significantly better on the mathematics assessment than did their peers whose parents disregarded the importance of learning mathematics. Copyright © 2015 The Foundation for Professionals in Services for Adolescents. Published by Elsevier Ltd. All rights reserved.

Mathematical Properties Relevant to Geomagnetic Field Modeling

DEFF Research Database (Denmark)

Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils

2010-01-01

be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focussed. Time can be dealt with as an independent variable and is not explicitly considered......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations.The set of numerical coefficients defining this linear combination is then what one refers.......The relevant elementary mathematical functions are introduced, their properties are reviewed, and how they can be used to describe the magnetic field in a source-free (such as the Earth’s neutral atmosphere) or source-dense (such as the ionosphere) environment is explained. Completeness and uniqueness...

Mathematical Properties Relevant to Geomagnetic Field Modeling

DEFF Research Database (Denmark)

Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils

2014-01-01

be directly measured. In this chapter, the mathematical foundation of global (as opposed to regional) geomagnetic field modeling is reviewed, and the spatial modeling of the field in spherical coordinates is focused. Time can be dealt with as an independent variable and is not explicitly considered......Geomagnetic field modeling consists in converting large numbers of magnetic observations into a linear combination of elementary mathematical functions that best describes those observations. The set of numerical coefficients defining this linear combination is then what one refers....... The relevant elementary mathematical functions are introduced, their properties are reviewed, and how they can be used to describe the magnetic field in a source-free (such as the Earth’s neutral atmosphere) or source-dense (such as the ionosphere) environment is explained. Completeness and uniqueness...

Building Mathematical Models of Simple Harmonic and Damped Motion.

Science.gov (United States)

Edwards, Thomas

1995-01-01

By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)

On the mathematical modeling of memristors

KAUST Repository

Radwan, Ahmed G.

2012-10-06

Since the fourth fundamental element (Memristor) became a reality by HP labs, and due to its huge potential, its mathematical models became a necessity. In this paper, we provide a simple mathematical model of Memristors characterized by linear dopant drift for sinusoidal input voltage, showing a high matching with the nonlinear SPICE simulations. The frequency response of the Memristor\\'s resistance and its bounding conditions are derived. The fundamentals of the pinched i-v hysteresis, such as the critical resistances, the hysteresis power and the maximum operating current, are derived for the first time.

Mathematical modeling of dissolved oxygen in fish ponds ...

African Journals Online (AJOL)

Mathematical modeling of dissolved oxygen in fish ponds. WJS Mwegoha, ME Kaseva, SMM Sabai. Abstract. A mathematical model was developed to predict the effects of wind speed, light, pH, Temperature, dissolved carbon dioxide and chemical oxygen demand (COD) on Dissolved Oxygen (DO) in fish ponds. The effects ...

Perspectives on instructor modeling in mathematics teacher education

OpenAIRE

Brown, Cassondra

2009-01-01

Teachers' instructional practices are greatly shaped by their own learning experiences as students in K-12 and college classrooms, which for most teachers was traditional, teacher-centered instruction. One of the challenges facing mathematics education reform is that, traditional teaching is in contrast to reform student- centered instruction. If teachers learn from their experiences as mathematics students, mathematics teacher educators are encouraged to model practices they would like teach...

Applied mathematics

CERN Document Server

Logan, J David

2013-01-01

Praise for the Third Edition"Future mathematicians, scientists, and engineers should find the book to be an excellent introductory text for coursework or self-study as well as worth its shelf space for reference." -MAA Reviews Applied Mathematics, Fourth Edition is a thoroughly updated and revised edition on the applications of modeling and analyzing natural, social, and technological processes. The book covers a wide range of key topics in mathematical methods and modeling and highlights the connections between mathematics and the applied and nat

Mathematical models and methods for planet Earth

CERN Document Server

Locatelli, Ugo; Ruggeri, Tommaso; Strickland, Elisabetta

2014-01-01

In 2013 several scientific activities have been devoted to mathematical researches for the study of planet Earth. The current volume presents a selection of the highly topical issues presented at the workshop “Mathematical Models and Methods for Planet Earth”, held in Roma (Italy), in May 2013. The fields of interest span from impacts of dangerous asteroids to the safeguard from space debris, from climatic changes to monitoring geological events, from the study of tumor growth to sociological problems. In all these fields the mathematical studies play a relevant role as a tool for the analysis of specific topics and as an ingredient of multidisciplinary problems. To investigate these problems we will see many different mathematical tools at work: just to mention some, stochastic processes, PDE, normal forms, chaos theory.

Mathematical Modelling Plant Signalling Networks

KAUST Repository

Muraro, D.; Byrne, H.M.; King, J.R.; Bennett, M.J.

2013-01-01

methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more

Mathematical Modelling of Involute Spur Gears Manufactured by Rack Cutter

Directory of Open Access Journals (Sweden)

Tufan Gürkan YILMAZ

2016-05-01

Full Text Available In this study, mathematical modelling of asymmetric involute spur gears was situated in by Litvin approach. In this context, firstly, mathematical expressions of rack cutter which manufacture asymmetric involute spur gear, then mathematical expression of asymmetric involute spur gear were obtained by using differential geometry, coordinate transformation and gear theory. Mathematical expressions were modelled in MATLAB and output files including points of involute spur gear’s teeth were designed automatically thanks to macros.

Mathematical modelling in solid mechanics

CERN Document Server

Sofonea, Mircea; Steigmann, David

2017-01-01

This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling a...

Mathematical Modelling of Unmanned Aerial Vehicles with Four Rotors

Directory of Open Access Journals (Sweden)

Zoran Benić

2016-01-01

Full Text Available Mathematical model of an unmanned aerial vehicle with four propulsors (quadcopter is indispensable in quadcopter movement simulation and later modelling of the control algorithm. Mathematical model is, at the same time, the first step in comprehending the mathematical principles and physical laws which are applied to the quadcopter system. The objective is to define the mathematical model which will describe the quadcopter behavior with satisfactory accuracy and which can be, with certain modifications, applicable for the similar configurations of multirotor aerial vehicles. At the beginning of mathematical model derivation, coordinate systems are defined and explained. By using those coordinate systems, relations between parameters defined in the earth coordinate system and in the body coordinate system are defined. Further, the quadcopter kinematic is described which enables setting those relations. Also, quadcopter dynamics is used to introduce forces and torques to the model through usage of Newton-Euler method. Final derived equation is Newton’s second law in the matrix notation. For the sake of model simplification, hybrid coordinate system is defined, and quadcopter dynamic equations derived with the respect to it. Those equations are implemented in the simulation. Results of behavior of quadcopter mathematical model are graphically shown for four cases. For each of the cases the propellers revolutions per minute (RPM are set in a way that results in the occurrence of the controllable variables which causes one of four basic quadcopter movements in space.

iSTEM: Promoting Fifth Graders' Mathematical Modeling

Science.gov (United States)

Yanik, H. Bahadir; Karabas, Celil

2014-01-01

Modeling requires that people develop representations or procedures to address particular problem situations (Lesh et al. 2000). Mathematical modeling is used to describe essential characteristics of a phenomenon or a situation that one intends to study in the real world through building mathematical objects. This article describes how fifth-grade…

Developing teaching material based on realistic mathematics andoriented to the mathematical reasoning and mathematical communication

Directory of Open Access Journals (Sweden)

Fitria Habsah

2017-05-01

Full Text Available This research aims to produce mathematics textbook for grade VII junior high school students based on realistic mathematics and oriented to the mathematical reasoning and mathematical communication. The quality is determined based on Nieveen criteria, including validity, practicality, and effectiveness.This study was a research and development and used Borg & Gall model. The subject of this research were the students of SMPN 2 Pujon-Kabupaten Malang, that is 30 students in an experimental class (using the developed textbook and 29 students in a control class (using BSE book from the government. The teaching material was categorized valid if the expert's judgment at least is categorized as “good”. The teaching material was categorized practical if both of teachers and students assessment at least categorized as “good”. The teaching material was categorized effectively if minimum 75% of student scores at least is categorized as “good” for the mathematical reasoning test and mathematical communication test. This research resulted in a valid, practical, and effective teaching material. The resulted of the validation show that material teaching is valid. The resulted of teachers and students assessment show that the product is practical. The tests scores show that the product is effective. Percentage of students who categorized at least as “good” is 83,33% for the mathematical reasoning and 86,67% for the mathematical communication. The resulted of statistic test shows that the product more effective than the BSE book from the government in terms of mathematical reasoning and mathematical communication.

Mathematical modeling and optimization of complex structures

CERN Document Server

Repin, Sergey; Tuovinen, Tero

2016-01-01

This volume contains selected papers in three closely related areas: mathematical modeling in mechanics, numerical analysis, and optimization methods. The papers are based upon talks presented  on the International Conference for Mathematical Modeling and Optimization in Mechanics, held in Jyväskylä, Finland, March 6-7, 2014 dedicated to Prof. N. Banichuk on the occasion of his 70th birthday. The articles are written by well-known scientists working in computational mechanics and in optimization of complicated technical models. Also, the volume contains papers discussing the historical development, the state of the art, new ideas, and open problems arising in  modern continuum mechanics and applied optimization problems. Several papers are concerned with mathematical problems in numerical analysis, which are also closely related to important mechanical models. The main topics treated include:  * Computer simulation methods in mechanics, physics, and biology;  * Variational problems and methods; minimiz...

Vibratory gyroscopes : identification of mathematical model from test data

CSIR Research Space (South Africa)

Shatalov, MY

2007-05-01

Full Text Available Simple mathematical model of vibratory gyroscopes imperfections is formulated, which includes anisotropic damping and variation of mass-stiffness parameters and their harmonics. The method of identification of parameters of the mathematical model...

Сontrol systems using mathematical models of technological objects ...

African Journals Online (AJOL)

Сontrol systems using mathematical models of technological objects in the control loop. ... Journal of Fundamental and Applied Sciences ... Such mathematical models make it possible to specify the optimal operating modes of the considered ...

Modelling and applications in mathematics education the 14th ICMI study

CERN Document Server

Galbraith, Peter L; Niss, Mogens

2007-01-01

The book aims at showing the state-of-the-art in the field of modeling and applications in mathematics education. This is the first volume to do this. The book deals with the question of how key competencies of applications and modeling at the heart of mathematical literacy may be developed; with the roles that applications and modeling may play in mathematics teaching, making mathematics more relevant for students.

The role of mathematics in politics as an issue for mathematics teaching

DEFF Research Database (Denmark)

Sánchez, Mario; Blomhøj, Morten

2010-01-01

This paper presents analyses of some examples of mathematical models used in the Mexican society of today. We seek to justify why and illustrate how such examples can be included in mathematics teaching and in teacher education.......This paper presents analyses of some examples of mathematical models used in the Mexican society of today. We seek to justify why and illustrate how such examples can be included in mathematics teaching and in teacher education....

Application of mathematical modeling in sustained release delivery systems.

Science.gov (United States)

Grassi, Mario; Grassi, Gabriele

2014-08-01

This review, presenting as starting point the concept of the mathematical modeling, is aimed at the physical and mathematical description of the most important mechanisms regulating drug delivery from matrix systems. The precise knowledge of the delivery mechanisms allows us to set up powerful mathematical models which, in turn, are essential for the design and optimization of appropriate drug delivery systems. The fundamental mechanisms for drug delivery from matrices are represented by drug diffusion, matrix swelling, matrix erosion, drug dissolution with possible recrystallization (e.g., as in the case of amorphous and nanocrystalline drugs), initial drug distribution inside the matrix, matrix geometry, matrix size distribution (in the case of spherical matrices of different diameter) and osmotic pressure. Depending on matrix characteristics, the above-reported variables may play a different role in drug delivery; thus the mathematical model needs to be built solely on the most relevant mechanisms of the particular matrix considered. Despite the somewhat diffident behavior of the industrial world, in the light of the most recent findings, we believe that mathematical modeling may have a tremendous potential impact in the pharmaceutical field. We do believe that mathematical modeling will be more and more important in the future especially in the light of the rapid advent of personalized medicine, a novel therapeutic approach intended to treat each single patient instead of the 'average' patient.

Modellus: Learning Physics with Mathematical Modelling

Science.gov (United States)

Teodoro, Vitor

Computers are now a major tool in research and development in almost all scientific and technological fields. Despite recent developments, this is far from true for learning environments in schools and most undergraduate studies. This thesis proposes a framework for designing curricula where computers, and computer modelling in particular, are a major tool for learning. The framework, based on research on learning science and mathematics and on computer user interface, assumes that: 1) learning is an active process of creating meaning from representations; 2) learning takes place in a community of practice where students learn both from their own effort and from external guidance; 3) learning is a process of becoming familiar with concepts, with links between concepts, and with representations; 4) direct manipulation user interfaces allow students to explore concrete-abstract objects such as those of physics and can be used by students with minimal computer knowledge. Physics is the science of constructing models and explanations about the physical world. And mathematical models are an important type of models that are difficult for many students. These difficulties can be rooted in the fact that most students do not have an environment where they can explore functions, differential equations and iterations as primary objects that model physical phenomena--as objects-to-think-with, reifying the formal objects of physics. The framework proposes that students should be introduced to modelling in a very early stage of learning physics and mathematics, two scientific areas that must be taught in very closely related way, as they were developed since Galileo and Newton until the beginning of our century, before the rise of overspecialisation in science. At an early stage, functions are the main type of objects used to model real phenomena, such as motions. At a later stage, rates of change and equations with rates of change play an important role. This type of equations

Mathematics and engineering in real life through mathematical competitions

Science.gov (United States)

More, M.

2018-02-01

We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build curiosity and give an understanding of mathematical applications in real life. Participation in the competition has been classified under four broad categories. Student can showcase their findings in various forms of expression like model, poster, soft presentation, animation, live performance, art and poetry. The basic focus of the competition is on using open source computation tools and modern technology, to emphasize the relationship of mathematical concepts with engineering applications in real life.

The Spectrum of Mathematical Models.

Science.gov (United States)

Karplus, Walter J.

1983-01-01

Mathematical modeling problems encountered in many disciplines are discussed in terms of the modeling process and applications of models. The models are classified according to three types of abstraction: continuous-space-continuous-time, discrete-space-continuous-time, and discrete-space-discrete-time. Limitations in different kinds of modeling…

Ethnophysics, Mathematical Modeling, Geometry... All in the same Manzuá

Directory of Open Access Journals (Sweden)

Ednilson Sergio Ramalho de Souza

2013-06-01

Full Text Available The objective this is paper is to show partial results of research for project of doctorate whose intention is to analyze the Ethnophysics of the amazon fisherman end to develop innovative didactic resources for the conceptual approach in Physics and Mathematics in the classroom of the high school and higher education in environment of Mathematical Modeling. The research question was: How the build the Manzuá can contextualize lessons of Physics and Mathematics in high school? The methodology used was ethnographicresearch. The theoretical foundations were Ethnomathematics (D’AMBROSIO, 2008, Mental Models (JONHSON-LAIRD, 1983, Mathematical Modeling (CHAVES e ESPÍRITO SANTO, 2008 end Conceptual Field ((VERGNAUD, 2007. The initial results suggest which the traditional physical knowledge is strongly related to mental models formed in function long years practice in the construction of the Manzuá end the operational invariants take part in the mental models. The situations lived during the construction of the Manzuá can base situations-problem in the classes of Physics and Mathematics in environment of Mathematical Modeling. We can, therefore, develop didactics resources that relate the traditional knowledge to the school knowledge

Mathematical modelling of the process of quality control of construction products

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Pogorelov Vadim

2017-01-01

Full Text Available The study presents the results of years of research in the field of quality management of industrial production construction production, based on mathematical modelling techniques, process and results of implementing the developed programme of monitoring and quality control in the production process of the enterprise. The aim of this work is the presentation of scientific community of the practical results of mathematical modelling in application programs. In the course of the research addressed the description of the applied mathematical models, views, practical results of its application in the applied field to assess quality control. The authors used this mathematical model in practice. The article presents the results of applying this model. The authors developed the experimental software management and quality assessment by using mathematical modeling methods. The authors continue research in this direction to improve the diagnostic systems and quality management systems based on mathematical modeling methods prognostic and diagnostic processes.

Mathematical modeling of rainwater runoff over catchment surface ...

African Journals Online (AJOL)

The subject of an article is the mathematical modeling of the rainwater runoff along the surface catchment taking account the transport of pollution which permeates into the water flow from a porous media of soil at the certain areas of this surface. The developed mathematical model consists of two types of equations: the ...

The use of mathematical models in teaching wastewater treatment engineering

DEFF Research Database (Denmark)

Morgenroth, Eberhard Friedrich; Arvin, Erik; Vanrolleghem, P.

2002-01-01

Mathematical modeling of wastewater treatment processes has become increasingly popular in recent years. To prepare students for their future careers, environmental engineering education should provide students with sufficient background and experiences to understand and apply mathematical models...... efficiently and responsibly. Approaches for introducing mathematical modeling into courses on wastewater treatment engineering are discussed depending on the learning objectives, level of the course and the time available....

Elementary Preservice Teachers' and Elementary Inservice Teachers' Knowledge of Mathematical Modeling

Science.gov (United States)

Schwerdtfeger, Sara

2017-01-01

This study examined the differences in knowledge of mathematical modeling between a group of elementary preservice teachers and a group of elementary inservice teachers. Mathematical modeling has recently come to the forefront of elementary mathematics classrooms because of the call to add mathematical modeling tasks in mathematics classes through…

Mathematical modeling for novel cancer drug discovery and development.

Science.gov (United States)

Zhang, Ping; Brusic, Vladimir

2014-10-01

Mathematical modeling enables: the in silico classification of cancers, the prediction of disease outcomes, optimization of therapy, identification of promising drug targets and prediction of resistance to anticancer drugs. In silico pre-screened drug targets can be validated by a small number of carefully selected experiments. This review discusses the basics of mathematical modeling in cancer drug discovery and development. The topics include in silico discovery of novel molecular drug targets, optimization of immunotherapies, personalized medicine and guiding preclinical and clinical trials. Breast cancer has been used to demonstrate the applications of mathematical modeling in cancer diagnostics, the identification of high-risk population, cancer screening strategies, prediction of tumor growth and guiding cancer treatment. Mathematical models are the key components of the toolkit used in the fight against cancer. The combinatorial complexity of new drugs discovery is enormous, making systematic drug discovery, by experimentation, alone difficult if not impossible. The biggest challenges include seamless integration of growing data, information and knowledge, and making them available for a multiplicity of analyses. Mathematical models are essential for bringing cancer drug discovery into the era of Omics, Big Data and personalized medicine.

Mathematics Teaching Today

Science.gov (United States)

Martin, Tami S.; Speer, William R.

2009-01-01

This article describes features, consistent messages, and new components of "Mathematics Teaching Today: Improving Practice, Improving Student Learning" (NCTM 2007), an updated edition of "Professional Standards for Teaching Mathematics" (NCTM 1991). The new book describes aspects of high-quality mathematics teaching; offers a model for observing,…

Structural Modeling for Influence of Mathematics Self-Concept, Motivation to Learn Mathematics and Self-Regulation Learning on Mathematics Academic Achievement

OpenAIRE

Hamideh Jafari Koshkouei; Ahmad Shahvarani; Mohammad Hassan Behzadi; Mohsen Rostamy-Malkhalifeh

2016-01-01

The present study was carried out to investigate the influence of mathematics self-concept (MSC), motivation to learn mathematics (SMOT) and self-regulation learning (SRL) on students' mathematics academic achievement. This study is of a descriptive survey type. 300 female students at the first grade of high school (the second period) in City Qods, were selected by multiple step cluster sampling method and completed MSC, SMOT and SRL questionnaires. Mathematics academic achievement was measur...

Mathematics related anxiety: Mathematics bogeyman or not?

Directory of Open Access Journals (Sweden)

Videnović Marina

2011-01-01

Full Text Available Data of the PISA 2003 survey indicate high levels of mathematics anxiety of students in Serbia. More than half of our students worry whether they will have difficulties in mathematics class or whether they will earn poor marks. Aims of this study therefore are: examining relationship between math anxiety and achievement at mathematics literacy scale; establishing possible predictors of math anxiety and identification of students' groups in relations to their relationship towards mathematics as a subject. Mathematics anxiety is statistically negatively correlated with school achievement and achievement at mathematics literacy scale. Socio-demographic factors, motivational and cognitive aspects related to learning mathematics, perception of school and classroom climate explain 40% variance of mathematics anxiety. Based on students' relationship towards mathematics they cam be divided into three groups; while dimensions that apart them are uninterested-interested in mathematics and presence-absence of anxiety. The group displaying anxiety scores lowest among the three. Applying qualitative analysis students' and teachers' attitudes on specific issues related to teaching and learning mathematics was examined.

Technological geological and mathematical models of petroleum stratum

International Nuclear Information System (INIS)

Zhumagulov, B.T.; Monakhov, V.N.

1997-01-01

The comparative analysis of different mathematical methods of petroleum stratum, the limit of their applicability and hydrodynamical analysis of numerical calculation's results is carried out. The problem of adaptation of the mathematical models and the identification of petroleum stratum parameters are considered. (author)

Teachers' Mathematics as Mathematics-at-Work

Science.gov (United States)

Bednarz, Nadine; Proulx, Jérôme

2017-01-01

Through recognising mathematics teachers as professionals who use mathematics in their workplace, this article traces a parallel between the mathematics enacted by teachers in their practice and the mathematics used in workplaces found in studies of professionals (e.g. nurses, engineers, bankers). This parallel is developed through the five…

Mathematical modelling of fracture hydrology

International Nuclear Information System (INIS)

Herbert, A.W.; Hodgkinson, D.P.; Lever, D.A.; Robinson, P.C.; Rae, J.

1985-06-01

This report summarises the work performed between January 1983 and December 1984 for the CEC/DOE contract 'Mathematical Modelling of Fracture Hydrology', under the following headings: 1) Statistical fracture network modelling, 2) Continuum models of flow and transport, 3) Simplified models, 4) Analysis of laboratory experiments and 5) Analysis of field experiments. (author)

Mathematics for energy

International Nuclear Information System (INIS)

Snow, D.R.

1975-01-01

This paper provides mathematicians and other persons interested in energy problems with some ideas of the kinds of mathematics being applied and a few ideas for further investigation both in the relevant mathematics and in mathematical modeling. This paper is not meant to be an extensive bibliography on the subject, but references are provided. The Conference emphasized large scale and economic considerations related to energy rather than specific technologies, but additional mathematical problems arising in current and future technologies are suggested. Several of the papers dealt with linear programming models of large scale systems related to energy. These included economic models, policy models, energy sector models for supply and demand and environmental concerns. One of the economic models utilized variational techniques including such things as the Hamiltonian, the Euler-Lagrange differential equation, transversality and natural boundary conditions

Mathematical Modelling at Secondary School: The MACSI-Clongowes Wood College Experience

Science.gov (United States)

Charpin, J. P. F.; O'Hara, S.; Mackey, D.

2013-01-01

In Ireland, to encourage the study of STEM (science, technology, engineering and mathematics) subjects and particularly mathematics, the Mathematics Applications Consortium for Science and Industry (MACSI) and Clongowes Wood College (County Kildare, Ireland) organized a mathematical modelling workshop for senior cycle secondary school students.…

Hybrid modelling framework by using mathematics-based and information-based methods

International Nuclear Information System (INIS)

Ghaboussi, J; Kim, J; Elnashai, A

2010-01-01

Mathematics-based computational mechanics involves idealization in going from the observed behaviour of a system into mathematical equations representing the underlying mechanics of that behaviour. Idealization may lead mathematical models that exclude certain aspects of the complex behaviour that may be significant. An alternative approach is data-centric modelling that constitutes a fundamental shift from mathematical equations to data that contain the required information about the underlying mechanics. However, purely data-centric methods often fail for infrequent events and large state changes. In this article, a new hybrid modelling framework is proposed to improve accuracy in simulation of real-world systems. In the hybrid framework, a mathematical model is complemented by information-based components. The role of informational components is to model aspects which the mathematical model leaves out. The missing aspects are extracted and identified through Autoprogressive Algorithms. The proposed hybrid modelling framework has a wide range of potential applications for natural and engineered systems. The potential of the hybrid methodology is illustrated through modelling highly pinched hysteretic behaviour of beam-to-column connections in steel frames.

Molecular modeling: An open invitation for applied mathematics

Science.gov (United States)

Mezey, Paul G.

2013-10-01

Molecular modeling methods provide a very wide range of challenges for innovative mathematical and computational techniques, where often high dimensionality, large sets of data, and complicated interrelations imply a multitude of iterative approximations. The physical and chemical basis of these methodologies involves quantum mechanics with several non-intuitive aspects, where classical interpretation and classical analogies are often misleading or outright wrong. Hence, instead of the everyday, common sense approaches which work so well in engineering, in molecular modeling one often needs to rely on rather abstract mathematical constraints and conditions, again emphasizing the high level of reliance on applied mathematics. Yet, the interdisciplinary aspects of the field of molecular modeling also generates some inertia and perhaps too conservative reliance on tried and tested methodologies, that is at least partially caused by the less than up-to-date involvement in the newest developments in applied mathematics. It is expected that as more applied mathematicians take up the challenge of employing the latest advances of their field in molecular modeling, important breakthroughs may follow. In this presentation some of the current challenges of molecular modeling are discussed.

Achilles and the tortoise: Some caveats to mathematical modeling in biology.

Science.gov (United States)

Gilbert, Scott F

2018-01-31

Mathematical modeling has recently become a much-lauded enterprise, and many funding agencies seek to prioritize this endeavor. However, there are certain dangers associated with mathematical modeling, and knowledge of these pitfalls should also be part of a biologist's training in this set of techniques. (1) Mathematical models are limited by known science; (2) Mathematical models can tell what can happen, but not what did happen; (3) A model does not have to conform to reality, even if it is logically consistent; (4) Models abstract from reality, and sometimes what they eliminate is critically important; (5) Mathematics can present a Platonic ideal to which biologically organized matter strives, rather than a trial-and-error bumbling through evolutionary processes. This "Unity of Science" approach, which sees biology as the lowest physical science and mathematics as the highest science, is part of a Western belief system, often called the Great Chain of Being (or Scala Natura), that sees knowledge emerge as one passes from biology to chemistry to physics to mathematics, in an ascending progression of reason being purification from matter. This is also an informal model for the emergence of new life. There are now other informal models for integrating development and evolution, but each has its limitations. Copyright © 2018 Elsevier Ltd. All rights reserved.

Developing Understanding of Mathematical Modeling in Secondary Teacher Preparation

Science.gov (United States)

Anhalt, Cynthia Oropesa; Cortez, Ricardo

2016-01-01

This study examines the evolution of 11 prospective teachers' understanding of mathematical modeling through the implementation of a modeling module within a curriculum course in a secondary teacher preparation program. While the prospective teachers had not previously taken a course on mathematical modeling, they will be expected to include…

Modelling as a foundation for academic forming in mathematics education

NARCIS (Netherlands)

Perrenet, J.C.; Morsche, ter H.G.

2004-01-01

The Bachelor curriculum of Applied Mathematics in Eindhoven includes a series of modelling projects where pairs of students solve mathematical problems posed in non-mathematical language. Communication skills training is integrated with this track. Recently a new course has been added. The students

Mathematical and numerical foundations of turbulence models and applications

CERN Document Server

Chacón Rebollo, Tomás

2014-01-01

With applications to climate, technology, and industry, the modeling and numerical simulation of turbulent flows are rich with history and modern relevance. The complexity of the problems that arise in the study of turbulence requires tools from various scientific disciplines, including mathematics, physics, engineering, and computer science. Authored by two experts in the area with a long history of collaboration, this monograph provides a current, detailed look at several turbulence models from both the theoretical and numerical perspectives. The k-epsilon, large-eddy simulation, and other models are rigorously derived and their performance is analyzed using benchmark simulations for real-world turbulent flows. Mathematical and Numerical Foundations of Turbulence Models and Applications is an ideal reference for students in applied mathematics and engineering, as well as researchers in mathematical and numerical fluid dynamics. It is also a valuable resource for advanced graduate students in fluid dynamics,...

Mathematical model of compact type evaporator

Science.gov (United States)

Borovička, Martin; Hyhlík, Tomáš

2018-06-01

In this paper, development of the mathematical model for evaporator used in heat pump circuits is covered, with focus on air dehumidification application. Main target of this ad-hoc numerical model is to simulate heat and mass transfer in evaporator for prescribed inlet conditions and different geometrical parameters. Simplified 2D mathematical model is developed in MATLAB SW. Solvers for multiple heat and mass transfer problems - plate surface temperature, condensate film temperature, local heat and mass transfer coefficients, refrigerant temperature distribution, humid air enthalpy change are included as subprocedures of this model. An automatic procedure of data transfer is developed in order to use results of MATLAB model in more complex simulation within commercial CFD code. In the end, Proper Orthogonal Decomposition (POD) method is introduced and implemented into MATLAB model.

Structured Mathematical Modeling of Industrial Boiler

Directory of Open Access Journals (Sweden)

Abdullah Nur Aziz

2014-04-01

Full Text Available As a major utility system in industry, boilers consume a large portion of the total energy and costs. Significant reduction of boiler cost operation can be gained through improvements in efficiency. In accomplishing such a goal, an adequate dynamic model that comprehensively reflects boiler characteristics is required. This paper outlines the idea of developing a mathematical model of a water-tube industrial boiler based on first principles guided by the bond graph method in its derivation. The model describes the temperature dynamics of the boiler subsystems such as economizer, steam drum, desuperheater, and superheater. The mathematical model was examined using industrial boiler performance test data.It can be used to build a boiler simulator or help operators run a boiler effectively.

Investigating and Developing Engineering Students' Mathematical Modelling and Problem-Solving Skills

Science.gov (United States)

Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven

2015-01-01

How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced…

Examining Fourth-Grade Mathematics Writing: Features of Organization, Mathematics Vocabulary, and Mathematical Representations

Science.gov (United States)

Hebert, Michael A.; Powell, Sarah R.

2016-01-01

Increasingly, students are expected to write about mathematics. Mathematics writing may be informal (e.g., journals, exit slips) or formal (e.g., writing prompts on high-stakes mathematics assessments). In order to develop an effective mathematics-writing intervention, research needs to be conducted on how students organize mathematics writing and…

Application of computer mathematical modeling in nuclear well-logging industry

International Nuclear Information System (INIS)

Cai Shaohui

1994-01-01

Nuclear well logging techniques have made rapid progress since the first well log calibration facility (the API pits) was dedicated in 1959. Then came the first computer mathematical model in the late 70's. Mathematical modeling can now minimize design and experiment time, as well as provide new information and idea on tool design, environmental effects and result interpretation. The author gives a brief review on the achievements of mathematical modeling on nuclear logging problems

mathematical modelling of atmospheric dispersion of pollutants

International Nuclear Information System (INIS)

Mohamed, M.E.

2002-01-01

the main objectives of this thesis are dealing with environmental problems adopting mathematical techniques. in this respect, atmospheric dispersion processes have been investigated by improving the analytical models to realize the realistic physical phenomena. to achieve these aims, the skeleton of this work contained both mathematical and environmental topics,performed in six chapters. in chapter one we presented a comprehensive review study of most important informations related to our work such as thermal stability , plume rise, inversion, advection , dispersion of pollutants, gaussian plume models dealing with both radioactive and industrial contaminants. chapter two deals with estimating the decay distance as well as the decay time of either industrial or radioactive airborne pollutant. further, highly turbulent atmosphere has been investigated as a special case in the three main thermal stability classes namely, neutral, stable, and unstable atmosphere. chapter three is concerned with obtaining maximum ground level concentration of air pollutant. the variable effective height of pollutants has been considered throughout the mathematical treatment. as a special case the constancy of effective height has been derived mathematically and the maximum ground level concentration as well as its location have been established

Mathematical modeling in wound healing, bone regeneration and tissue engineering.

Science.gov (United States)

Geris, Liesbet; Gerisch, Alf; Schugart, Richard C

2010-12-01

The processes of wound healing and bone regeneration and problems in tissue engineering have been an active area for mathematical modeling in the last decade. Here we review a selection of recent models which aim at deriving strategies for improved healing. In wound healing, the models have particularly focused on the inflammatory response in order to improve the healing of chronic wound. For bone regeneration, the mathematical models have been applied to design optimal and new treatment strategies for normal and specific cases of impaired fracture healing. For the field of tissue engineering, we focus on mathematical models that analyze the interplay between cells and their biochemical cues within the scaffold to ensure optimal nutrient transport and maximal tissue production. Finally, we briefly comment on numerical issues arising from simulations of these mathematical models.

A practical course in differential equations and mathematical modeling

CERN Document Server

Ibragimov , Nail H

2009-01-01

A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book which aims to present new mathematical curricula based on symmetry and invariance principles is tailored to develop analytic skills and working knowledge in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundame

Mathematical Modelling Plant Signalling Networks

KAUST Repository

Muraro, D.

2013-01-01

During the last two decades, molecular genetic studies and the completion of the sequencing of the Arabidopsis thaliana genome have increased knowledge of hormonal regulation in plants. These signal transduction pathways act in concert through gene regulatory and signalling networks whose main components have begun to be elucidated. Our understanding of the resulting cellular processes is hindered by the complex, and sometimes counter-intuitive, dynamics of the networks, which may be interconnected through feedback controls and cross-regulation. Mathematical modelling provides a valuable tool to investigate such dynamics and to perform in silico experiments that may not be easily carried out in a laboratory. In this article, we firstly review general methods for modelling gene and signalling networks and their application in plants. We then describe specific models of hormonal perception and cross-talk in plants. This mathematical analysis of sub-cellular molecular mechanisms paves the way for more comprehensive modelling studies of hormonal transport and signalling in a multi-scale setting. © EDP Sciences, 2013.

How to Introduce Mathematic Modeling in Industrial Design Education

NARCIS (Netherlands)

Langereis, G.R.; Hu, J.; Feijs, L.M.G.; Stillmann, G.A.; Kaiser, G.; Blum, W.B.; Brown, J.P.

2013-01-01

With competency based learning in a project driven environment, we are facing a different perspective of how students perceive mathematical modelling. In this chapter, a model is proposed where conventional education is seen as a process from mathematics to design, while competency driven approaches

Aspects of Mathematical Modelling Applications in Science, Medicine, Economics and Management

CERN Document Server

Hosking, Roger J

2008-01-01

The construction of mathematical models is an essential scientific activity. Mathematics has long been associated with developments in the exact sciences and engineering, but more recently mathematical modelling has been used to investigate complex systems that arise in many other fields. The contributors to this book demonstrate the application of mathematics to modern research topics in ecology and environmental science, health and medicine, phylogenetics and neural networks, theoretical chemistry, economics and management.

A Mathematical Model Development for the Lateral Collapse of Octagonal Tubes

Science.gov (United States)

Ghazali Kamardan, M.; Sufahani, Suliadi; Othman, M. Z. M.; Che-Him, Norziha; Khalid, Kamil; Roslan, Rozaini; Ali, Maselan; Zaidi, A. M. A.

2018-04-01

Many researches has been done on the lateral collapse of tube. However, the previous researches only focus on cylindrical and square tubes. Then a research has been done discovering the collapse behaviour of hexagonal tube and the mathematic model of the deformation behaviour had been developed [8]. The purpose of this research is to study the lateral collapse behaviour of symmetric octagonal tubes and hence to develop a mathematical model of the collapse behaviour of these tubes. For that, a predictive mathematical model was developed and a finite element analysis procedure was conducted for the lateral collapse behaviour of symmetric octagonal tubes. Lastly, the mathematical model was verified by using the finite element analysis simulation results. It was discovered that these tubes performed different deformation behaviour than the cylindrical tube. Symmetric octagonal tubes perform 2 phases of elastic - plastic deformation behaviour patterns. The mathematical model had managed to show the fundamental of the deformation behaviour of octagonal tubes. However, further studies need to be conducted in order to further improve on the proposed mathematical model.

Mathematical Modeling of Loop Heat Pipes

Science.gov (United States)

Kaya, Tarik; Ku, Jentung; Hoang, Triem T.; Cheung, Mark L.

1998-01-01

The primary focus of this study is to model steady-state performance of a Loop Heat Pipe (LHP). The mathematical model is based on the steady-state energy balance equations at each component of the LHP. The heat exchange between each LHP component and the surrounding is taken into account. Both convection and radiation environments are modeled. The loop operating temperature is calculated as a function of the applied power at a given loop condition. Experimental validation of the model is attempted by using two different LHP designs. The mathematical model is tested at different sink temperatures and at different elevations of the loop. Tbc comparison of the calculations and experimental results showed very good agreement (within 3%). This method proved to be a useful tool in studying steady-state LHP performance characteristics.

An Interdisciplinary Approach to Designing Online Learning: Fostering Pre-Service Mathematics Teachers' Capabilities in Mathematical Modelling

Science.gov (United States)

Geiger, Vince; Mulligan, Joanne; Date-Huxtable, Liz; Ahlip, Rehez; Jones, D. Heath; May, E. Julian; Rylands, Leanne; Wright, Ian

2018-01-01

In this article we describe and evaluate processes utilized to develop an online learning module on mathematical modelling for pre-service teachers. The module development process involved a range of professionals working within the STEM disciplines including mathematics and science educators, mathematicians, scientists, in-service and pre-service…

Dealing with dissatisfaction in mathematical modelling to integrate QFD and Kano’s model

Science.gov (United States)

Retno Sari Dewi, Dian; Debora, Joana; Edy Sianto, Martinus

2017-12-01

The purpose of the study is to implement the integration of Quality Function Deployment (QFD) and Kano’s Model into mathematical model. Voice of customer data in QFD was collected using questionnaire and the questionnaire was developed based on Kano’s model. Then the operational research methodology was applied to build the objective function and constraints in the mathematical model. The relationship between voice of customer and engineering characteristics was modelled using linier regression model. Output of the mathematical model would be detail of engineering characteristics. The objective function of this model is to maximize satisfaction and minimize dissatisfaction as well. Result of this model is 62% .The major contribution of this research is to implement the existing mathematical model to integrate QFD and Kano’s Model in the case study of shoe cabinet.

2nd Tbilisi-Salerno Workshop on Modeling in Mathematics

CERN Document Server

Ricci, Paolo; Tavkhelidze, Ilia

2017-01-01

This book contains a collection of papers presented at the 2nd Tbilisi Salerno Workshop on Mathematical Modeling in March 2015. The focus is on applications of mathematics in physics, electromagnetics, biochemistry and botany, and covers such topics as multimodal logic, fractional calculus, special functions, Fourier-like solutions for PDE’s, Rvachev-functions and linear dynamical systems. Special chapters focus on recent uniform analytic descriptions of natural and abstract shapes using the Gielis Formula. The book is intended for a wide audience with interest in application of mathematics to modeling in the natural sciences.

A Mathematical Approach to Establishing Constitutive Models for Geomaterials

Directory of Open Access Journals (Sweden)

Guang-hua Yang

2013-01-01

Full Text Available The mathematical foundation of the traditional elastoplastic constitutive theory for geomaterials is presented from the mathematical point of view, that is, the expression of stress-strain relationship in principal stress/strain space being transformed to the expression in six-dimensional space. A new framework is then established according to the mathematical theory of vectors and tensors, which is applicable to establishing elastoplastic models both in strain space and in stress space. Traditional constitutive theories can be considered as its special cases. The framework also enables modification of traditional constitutive models.

Mathematics of epidemics on networks from exact to approximate models

CERN Document Server

Kiss, István Z; Simon, Péter L

2017-01-01

This textbook provides an exciting new addition to the area of network science featuring a stronger and more methodical link of models to their mathematical origin and explains how these relate to each other with special focus on epidemic spread on networks. The content of the book is at the interface of graph theory, stochastic processes and dynamical systems. The authors set out to make a significant contribution to closing the gap between model development and the supporting mathematics. This is done by: Summarising and presenting the state-of-the-art in modeling epidemics on networks with results and readily usable models signposted throughout the book; Presenting different mathematical approaches to formulate exact and solvable models; Identifying the concrete links between approximate models and their rigorous mathematical representation; Presenting a model hierarchy and clearly highlighting the links between model assumptions and model complexity; Providing a reference source for advanced undergraduate...

Linking Preservice Teachers' Mathematics Self-Efficacy and Mathematics Teaching Efficacy to Their Mathematical Performance

Science.gov (United States)

Bates, Alan B.; Latham, Nancy; Kim, Jin-ah

2011-01-01

This study examined preservice teachers' mathematics self-efficacy and mathematics teaching efficacy and compared them to their mathematical performance. Participants included 89 early childhood preservice teachers at a Midwestern university. Instruments included the Mathematics Self-Efficacy Scale (MSES), Mathematics Teaching Efficacy Beliefs…

Mathematical models of natural gas consumption

International Nuclear Information System (INIS)

Sabo, Kristian; Scitovski, Rudolf; Vazler, Ivan; Zekic-Susac, Marijana

2011-01-01

In this paper we consider the problem of natural gas consumption hourly forecast on the basis of hourly movement of temperature and natural gas consumption in the preceding period. There are various methods and approaches for solving this problem in the literature. Some mathematical models with linear and nonlinear model functions relating to natural gas consumption forecast with the past natural gas consumption data, temperature data and temperature forecast data are mentioned. The methods are tested on concrete examples referring to temperature and natural gas consumption for the area of the city of Osijek (Croatia) from the beginning of the year 2008. The results show that most acceptable forecast is provided by mathematical models in which natural gas consumption and temperature are related explicitly.

An Integrated Approach to Mathematical Modeling: A Classroom Study.

Science.gov (United States)

Doerr, Helen M.

Modeling, simulation, and discrete mathematics have all been identified by professional mathematics education organizations as important areas for secondary school study. This classroom study focused on the components and tools for modeling and how students use these tools to construct their understanding of contextual problems in the content area…

Mathematical Models of Breast and Ovarian Cancers

Science.gov (United States)

Botesteanu, Dana-Adriana; Lipkowitz, Stanley; Lee, Jung-Min; Levy, Doron

2016-01-01

Women constitute the majority of the aging United States (US) population, and this has substantial implications on cancer population patterns and management practices. Breast cancer is the most common women's malignancy, while ovarian cancer is the most fatal gynecological malignancy in the US. In this review we focus on these subsets of women's cancers, seen more commonly in postmenopausal and elderly women. In order to systematically investigate the complexity of cancer progression and response to treatment in breast and ovarian malignancies, we assert that integrated mathematical modeling frameworks viewed from a systems biology perspective are needed. Such integrated frameworks could offer innovative contributions to the clinical women's cancers community, since answers to clinical questions cannot always be reached with contemporary clinical and experimental tools. Here, we recapitulate clinically known data regarding the progression and treatment of the breast and ovarian cancers. We compare and contrast the two malignancies whenever possible, in order to emphasize areas where substantial contributions could be made by clinically inspired and validated mathematical modeling. We show how current paradigms in the mathematical oncology community focusing on the two malignancies do not make comprehensive use of, nor substantially reflect existing clinical data, and we highlight the modeling areas in most critical need of clinical data integration. We emphasize that the primary goal of any mathematical study of women's cancers should be to address clinically relevant questions. PMID:27259061

Contrasts in Mathematical Challenges in A-Level Mathematics and Further Mathematics, and Undergraduate Mathematics Examinations

Science.gov (United States)

Darlington, Ellie

2014-01-01

This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics…

Mathematical model for temperature change of a journal bearing

Directory of Open Access Journals (Sweden)

Antunović Ranko

2018-01-01

Full Text Available In this work, a representative mathematical model has been developed, which reliably describes the heating and cooling of a journal bearing as a result of its malfunctioning, and the model has been further confirmed on a test bench. The bearing model was validated by using analytical modeling methods, i. e. the experimental results were compared to the data obtained by analytical calculations. The regression and variance analysis techniques were applied to process the recorded data, to test the mathematical model and to define mathematical functions for the heating/cooling of the journal bearing. This investigation shows that a representative model may reliably indicate the change in the thermal field, which may be a consequence of journal bearing damage.

A mathematical model for iodine kinetics

International Nuclear Information System (INIS)

Silva, E.A.T. da.

1976-01-01

A mathematical model for the iodine kinetics in thyroid is presented followed by its analytical solution. An eletroanalogical model is also developed for a simplified stage and another is proposed for the main case [pt

Mathematical modeling of swirled flows in industrial applications

Science.gov (United States)

Dekterev, A. A.; Gavrilov, A. A.; Sentyabov, A. V.

2018-03-01

Swirled flows are widely used in technological devices. Swirling flows are characterized by a wide range of flow regimes. 3D mathematical modeling of flows is widely used in research and design. For correct mathematical modeling of such a flow, it is necessary to use turbulence models, which take into account important features of the flow. Based on the experience of computational modeling of a wide class of problems with swirling flows, recommendations on the use of turbulence models for calculating the applied problems are proposed.

Missing the Promise of Mathematical Modeling

Science.gov (United States)

Meyer, Dan

2015-01-01

The Common Core State Standards for Mathematics (CCSSM) have exerted enormous pressure on every participant in a child's education. Students are struggling to meet new standards for mathematics learning, and parents are struggling to understand how to help them. Teachers are growing in their capacity to develop new mathematical competencies, and…

Methods of mathematical modelling continuous systems and differential equations

CERN Document Server

Witelski, Thomas

2015-01-01

This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.

PROBLEMS OF MATHEMATICAL MODELING OF THE ENTERPRISES ORGANIZATIONAL STRUCTURE

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N. V. Andrianov

2006-01-01

Full Text Available The analysis of the mathematical models which can be used at optimization of the control system of the enterprise organizational structure is presented. The new approach to the mathematical modeling of the enterprise organizational structure, based on using of temporary characteristics of the control blocks working, is formulated

Mathematical models of information and stochastic systems

CERN Document Server

Kornreich, Philipp

2008-01-01

From ancient soothsayers and astrologists to today's pollsters and economists, probability theory has long been used to predict the future on the basis of past and present knowledge. Mathematical Models of Information and Stochastic Systems shows that the amount of knowledge about a system plays an important role in the mathematical models used to foretell the future of the system. It explains how this known quantity of information is used to derive a system's probabilistic properties. After an introduction, the book presents several basic principles that are employed in the remainder of the t

MATHEMATICAL MODEL OF TRIAXIAL MULTIMODE ATTITUDE AND HEADING REFERENCE SYSTEM

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Olha Sushchenko

2017-07-01

Full Text Available Purpose: The paper deals with the mathematical description of the gimballed attitude and heading reference systems, which can be applied in design of strategic precision navigation systems. The main goal is to created mathematical description taking into consideration the necessity to use different navigations operating modes of this class of navigation systems. To provide the high accuracy the indirect control is used when the position of the gimballed platform is controlled by signals of gyroscopic devices, which are corrected using accelerometer’s signals. Methods: To solve the given problem the methods of the classical theoretical mechanics, gyro theory, and inertial navigation are used. Results: The full mathematical model of the gimballed attitude and heading reference system is derived including descriptions of different operating modes. The mathematical models of the system Expressions for control and correction moments in the different modes are represented. The simulation results are given. Conclusions: The represented results prove efficiency of the proposed models. Developed mathematical models can be useful for design of navigation systems of the wide class of moving vehicles.

Mathematical Modeling in Population Dynamics: The Case of Single ...

African Journals Online (AJOL)

kofimereku

Department of Mathematics, Kwame Nkrumah University of Science and Technology,. Kumasi, Ghana ... The trust of this paper is the application of mathematical models in helping to ..... Statistics and Computing, New York: Wiley. Cox, C.B and ...

Mathematics Instructional Model Based on Realistic Mathematics Education to Promote Problem Solving Ability at Junior High School Padang

OpenAIRE

Edwin Musdi

2016-01-01

This research aims to develop a mathematics instructional model based realistic mathematics education (RME) to promote students' problem-solving abilities. The design research used Plomp models, which consists of preliminary phase, development or proto-typing phase and assessment phase.  At this study, only the first two phases conducted. The first phase, a preliminary investigation, carried out with a literature study to examine the theory-based instructional learning RME model, characterist...

Using Mathematics Literature with Prospective Secondary Mathematics Teachers

Science.gov (United States)

Jett, Christopher C.

2014-01-01

Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…

Mathematical Modeling of Biofilm Structures Using COMSTAT Data

DEFF Research Database (Denmark)

Verotta, Davide; Haagensen, Janus Anders Juul; Spormann, Alfred M.

2017-01-01

Mathematical modeling holds great potential for quantitatively describing biofilm growth in presence or absence of chemical agents used to limit or promote biofilm growth. In this paper, we describe a general mathematical/statistical framework that allows for the characterization of complex data...... in terms of few parameters and the capability to (i) compare different experiments and exposures to different agents, (ii) test different hypotheses regarding biofilm growth and interaction with different agents, and (iii) simulate arbitrary administrations of agents. The mathematical framework is divided...... to submodels characterizing biofilm, including new models characterizing live biofilm growth and dead cell accumulation; the interaction with agents inhibiting or stimulating growth; the kinetics of the agents. The statistical framework can take into account measurement and interexperiment variation. We...

Mathematical Modelling Research in Turkey: A Content Analysis Study

Science.gov (United States)

Çelik, H. Coskun

2017-01-01

The aim of the present study was to examine the mathematical modelling studies done between 2004 and 2015 in Turkey and to reveal their tendencies. Forty-nine studies were selected using purposeful sampling based on the term, "mathematical modelling" with Higher Education Academic Search Engine. They were analyzed with content analysis.…

Turbofan engine mathematic model for its static and dynamic characteristics research

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О.Є. Карпов

2004-01-01

Full Text Available  Demands to mathematical model of the turbofan engine are determined in the article. The mathematical model is used for calculations static and dynamic parameters, which are required for estimation of engine technical state in operation. There are the mathematical model of the turbofan engine AИ-25 and the results of calculations static and dynamic parameters at initial condition in the article.

The mathematics of models for climatology and environment. Proceedings

Energy Technology Data Exchange (ETDEWEB)

Ildefonso Diaz, J. [ed.] [Universidad Complutense de Madrid (Spain). Facultad de Ciencas Matematicas

1997-12-31

This book presents a coherent survey of modelling in climatology and the environment and the mathematical treatment of those problems. It is divided into 4 parts containing a total of 16 chapters. Parts I, II and III are devoted to general models and part IV to models related to some local problems. Most of the mathematical models considered here involve systems of nonlinear partial differential equations.

A mathematical look at a physical power prediction model

DEFF Research Database (Denmark)

Landberg, L.

1998-01-01

This article takes a mathematical look at a physical model used to predict the power produced from wind farms. The reason is to see whether simple mathematical expressions can replace the original equations and to give guidelines as to where simplifications can be made and where they cannot....... The article shows that there is a linear dependence between the geostrophic wind and the local wind at the surface, but also that great care must be taken in the selection of the simple mathematical models, since physical dependences play a very important role, e.g. through the dependence of the turning...

Comparison of learning models based on mathematics logical intelligence in affective domain

Science.gov (United States)

Widayanto, Arif; Pratiwi, Hasih; Mardiyana

2018-04-01

The purpose of this study was to examine the presence or absence of different effects of multiple treatments (used learning models and logical-mathematical intelligence) on the dependent variable (affective domain of mathematics). This research was quasi experimental using 3x3 of factorial design. The population of this research was VIII grade students of junior high school in Karanganyar under the academic year 2017/2018. Data collected in this research was analyzed by two ways analysis of variance with unequal cells using 5% of significance level. The result of the research were as follows: (1) Teaching and learning with model TS lead to better achievement in affective domain than QSH, teaching and learning with model QSH lead to better achievement in affective domain than using DI; (2) Students with high mathematics logical intelligence have better achievement in affective domain than students with low mathematics logical intelligence have; (3) In teaching and learning mathematics using learning model TS, students with moderate mathematics logical intelligence have better achievement in affective domain than using DI; and (4) In teaching and learning mathematics using learning model TS, students with low mathematics logical intelligence have better achievement in affective domain than using QSH and DI.

Doing Mathematics with Purpose: Mathematical Text Types

Science.gov (United States)

Dostal, Hannah M.; Robinson, Richard

2018-01-01

Mathematical literacy includes learning to read and write different types of mathematical texts as part of purposeful mathematical meaning making. Thus in this article, we describe how learning to read and write mathematical texts (proof text, algorithmic text, algebraic/symbolic text, and visual text) supports the development of students'…

Mathematical modeling of reciprocating pump

International Nuclear Information System (INIS)

Lee, Jong Kyeom; Jung, Jun Ki; Chai, Jang Bom; Lee, Jin Woo

2015-01-01

A new mathematical model is presented for the analysis and diagnosis of a high-pressure reciprocating pump system with three cylinders. The kinematic and hydrodynamic behaviors of the pump system are represented by the piston displacements, volume flow rates and pressures in its components, which are expressed as functions of the crankshaft angle. The flow interaction among the three cylinders, which was overlooked in the previous models, is considered in this model and its effect on the cylinder pressure profiles is investigated. The tuning parameters in the mathematical model are selected, and their values are adjusted to match the simulated and measured cylinder pressure profiles in each cylinder in a normal state. The damage parameter is selected in an abnormal state, and its value is adjusted to match the simulated and ensured pressure profiles under the condition of leakage in a valve. The value of the damage parameter over 300 cycles is calculated, and its probability density function is obtained for diagnosis and prognosis on the basis of the probabilistic feature of valve leakage.

Explorations in Elementary Mathematical Modeling

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Mazen Shahin

2010-06-01

Full Text Available In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and cooperative learning into this inquiry-based learning course where students work in small groups on carefully designed activities and utilize available software to support problem solving and understanding of real life situations. We emphasize the use of graphical and numerical techniques, rather than theoretical techniques, to investigate and analyze the behavior of the solutions of the difference equations.As an illustration of our approach, we will show a nontraditional and efficient way of introducing models from finance and economics. We will also present an interesting model of supply and demand with a lag time, which is called the cobweb theorem in economics. We introduce a sample of a research project on a technique of removing chaotic behavior from a chaotic system.

Mathematical models of ABE fermentation: review and analysis.

Science.gov (United States)

Mayank, Rahul; Ranjan, Amrita; Moholkar, Vijayanand S

2013-12-01

Among different liquid biofuels that have emerged in the recent past, biobutanol produced via fermentation processes is of special interest due to very similar properties to that of gasoline. For an effective design, scale-up, and optimization of the acetone-butanol-ethanol (ABE) fermentation process, it is necessary to have insight into the micro- and macro-mechanisms of the process. The mathematical models for ABE fermentation are efficient tools for this purpose, which have evolved from simple stoichiometric fermentation equations in the 1980s to the recent sophisticated and elaborate kinetic models based on metabolic pathways. In this article, we have reviewed the literature published in the area of mathematical modeling of the ABE fermentation. We have tried to present an analysis of these models in terms of their potency in describing the overall physiology of the process, design features, mode of operation along with comparison and validation with experimental results. In addition, we have also highlighted important facets of these models such as metabolic pathways, basic kinetics of different metabolites, biomass growth, inhibition modeling and other additional features such as cell retention and immobilized cultures. Our review also covers the mathematical modeling of the downstream processing of ABE fermentation, i.e. recovery and purification of solvents through flash distillation, liquid-liquid extraction, and pervaporation. We believe that this review will be a useful source of information and analysis on mathematical models for ABE fermentation for both the appropriate scientific and engineering communities.

Mathematical modeling of physiological systems: an essential tool for discovery.

Science.gov (United States)

Glynn, Patric; Unudurthi, Sathya D; Hund, Thomas J

2014-08-28

Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: "What is the value of a model?" Copyright © 2014 Elsevier Inc. All rights reserved.

Mathematical models to predict rheological parameters of lateritic hydromixtures

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Gabriel Hernández-Ramírez

2017-10-01

Full Text Available The present work had as objective to establish mathematical models that allow the prognosis of the rheological parameters of the lateritic pulp at concentrations of solids from 35% to 48%, temperature of the preheated hydromixture superior to 82 ° C and number of mineral between 3 and 16. Four samples of lateritic pulp were used in the study at different process locations. The results allowed defining that the plastic properties of the lateritic pulp in the conditions of this study conform to the Herschel-Bulkley model for real plastics. In addition, they show that for current operating conditions, even for new situations, UPD mathematical models have a greater ability to predict rheological parameters than least squares mathematical models.

Mathematical modeling of efficient protocols to control glioma growth.

Science.gov (United States)

Branco, J R; Ferreira, J A; de Oliveira, Paula

2014-09-01

In this paper we propose a mathematical model to describe the evolution of glioma cells taking into account the viscoelastic properties of brain tissue. The mathematical model is established considering that the glioma cells are of two phenotypes: migratory and proliferative. The evolution of the migratory cells is described by a diffusion-reaction equation of non Fickian type deduced considering a mass conservation law with a non Fickian migratory mass flux. The evolution of the proliferative cells is described by a reaction equation. A stability analysis that leads to the design of efficient protocols is presented. Numerical simulations that illustrate the behavior of the mathematical model are included. Copyright © 2014 Elsevier Inc. All rights reserved.

Science modelling in pre-calculus: how to make mathematics problems contextually meaningful

Science.gov (United States)

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-04-01

'Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum' (National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000). Commonly used pre-calculus textbooks provide a wide range of application problems. However, these problems focus students' attention on evaluating or solving pre-arranged formulas for given values. The role of scientific content is reduced to provide a background for these problems instead of being sources of data gathering for inducing mathematical tools. Students are neither required to construct mathematical models based on the contexts nor are they asked to validate or discuss the limitations of applied formulas. Using these contexts, the instructor may think that he/she is teaching problem solving, where in reality he/she is teaching algorithms of the mathematical operations (G. Kulm (ed.), New directions for mathematics assessment, in Assessing Higher Order Thinking in Mathematics, Erlbaum, Hillsdale, NJ, 1994, pp. 221-240). Without a thorough representation of the physical phenomena and the mathematical modelling processes undertaken, problem solving unintentionally appears as simple algorithmic operations. In this article, we deconstruct the representations of mathematics problems from selected pre-calculus textbooks and explicate their limitations. We argue that the structure and content of those problems limits students' coherent understanding of mathematical modelling, and this could result in weak student problem-solving skills. Simultaneously, we explore the ways to enhance representations of those mathematical problems, which we have characterized as lacking a meaningful physical context and limiting coherent student understanding. In light of our discussion, we recommend an alternative to strengthen the process of teaching mathematical modelling - utilization

Modeling eBook acceptance: A study on mathematics teachers

Science.gov (United States)

Jalal, Azlin Abd; Ayub, Ahmad Fauzi Mohd; Tarmizi, Rohani Ahmad

2014-12-01

The integration and effectiveness of eBook utilization in Mathematics teaching and learning greatly relied upon the teachers, hence the need to understand their perceptions and beliefs. The eBook, an individual laptop completed with digitized textbook sofwares, were provided for each students in line with the concept of 1 student:1 laptop. This study focuses on predicting a model on the acceptance of the eBook among Mathematics teachers. Data was collected from 304 mathematics teachers in selected schools using a survey questionnaire. The selection were based on the proportionate stratified sampling. Structural Equation Modeling (SEM) were employed where the model was tested and evaluated and was found to have a good fit. The variance explained for the teachers' attitude towards eBook is approximately 69.1% where perceived usefulness appeared to be a stronger determinant compared to perceived ease of use. This study concluded that the attitude of mathematics teachers towards eBook depends largely on the perception of how useful the eBook is on improving their teaching performance, implying that teachers should be kept updated with the latest mathematical application and sofwares to use with the eBook to ensure positive attitude towards using it in class.

Mathematics Literacy on Problem Based Learning with Indonesian Realistic Mathematics Education Approach Assisted E-Learning Edmodo

Science.gov (United States)

Wardono; Waluya, S. B.; Mariani, Scolastika; Candra D, S.

2016-02-01

This study aims to find out that there are differences in mathematical literacy ability in content Change and Relationship class VII Junior High School 19, Semarang by Problem Based Learning (PBL) model with an Indonesian Realistic Mathematics Education (called Pendidikan Matematika Realistik Indonesia or PMRI in Indonesia) approach assisted Elearning Edmodo, PBL with a PMRI approach, and expository; to know whether the group of students with learning PBL models with PMRI approach and assisted E-learning Edmodo can improve mathematics literacy; to know that the quality of learning PBL models with a PMRI approach assisted E-learning Edmodo has a good category; to describe the difficulties of students in working the problems of mathematical literacy ability oriented PISA. This research is a mixed methods study. The population was seventh grade students of Junior High School 19, Semarang Indonesia. Sample selection is done by random sampling so that the selected experimental class 1, class 2 and the control experiment. Data collected by the methods of documentation, tests and interviews. From the results of this study showed average mathematics literacy ability of students in the group PBL models with a PMRI approach assisted E-learning Edmodo better than average mathematics literacy ability of students in the group PBL models with a PMRI approach and better than average mathematics literacy ability of students in the expository models; Mathematics literacy ability in the class using the PBL model with a PMRI approach assisted E-learning Edmodo have increased and the improvement of mathematics literacy ability is higher than the improvement of mathematics literacy ability of class that uses the model of PBL learning with PMRI approach and is higher than the improvement of mathematics literacy ability of class that uses the expository models; The quality of learning using PBL models with a PMRI approach assisted E-learning Edmodo have very good category.

Methods and models in mathematical biology deterministic and stochastic approaches

CERN Document Server

Müller, Johannes

2015-01-01

This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models, and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks, and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and  branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.

A mathematical model for postirradiation immunity

International Nuclear Information System (INIS)

Smirnova, O.A.

1988-01-01

A mathematical model of autoimmune processes in exposed mammals was developed. In terms of this model a study was made of the dependence of the autoimmunity kinetics on radiation dose and radiosensitivity of autologous tissues. The model simulates the experimentally observed dynamics of autoimmune diseases

Mathematical modelling in economic processes.

Directory of Open Access Journals (Sweden)

L.V. Kravtsova

2008-06-01

Full Text Available In article are considered a number of methods of mathematical modelling of economic processes and opportunities of use of spreadsheets Excel for reception of the optimum decision of tasks or calculation of financial operations with the help of the built-in functions.

Design based Investigation on Construction of Mathematical Modelling Problems: Example of Financial Content

Directory of Open Access Journals (Sweden)

Melike TURAL SÖNMEZ

2017-12-01

Full Text Available The purpose of this study is to examine the construction of mathematical modelling problems process in the content of financial literacy. It is also aimed to create design proposals for construction of mathematical modelling problems. A design based research method was used in this study. The participants were three seventh grade students, six finance experts and nine mathematics education experts. Data collection tools were transcription of video and tapes group discussions, presentations and worksheets during mathematical modelling activities, and participant experts’ feedback form about mathematical modelling problems. There were three stages in this study. First stage was application of preliminary study. This stage gave information about convenience of problems to grade level, students’ timing for solution of problems, clarity of problems and students’ background about content. In second stage, finance experts commented on convenience of mathematical modelling problems to financial literacy standards. In third stage, mathematics education experts commented on convenience of problems to students’ grade level, mathematical modelling principles and seventh grade mathematics lesson objectives. They also gave suggestion on progress. The frequency value of theme in feedback forms was calculated and experts’ expressions were given as citation. It was given suggestion about stages and application of the design guide

Mathematical and numerical models for eddy currents and magnetostatics with selected applications

CERN Document Server

Rappaz, Jacques

2013-01-01

This monograph addresses fundamental aspects of mathematical modeling and numerical solution methods of electromagnetic problems involving low frequencies, i.e. magnetostatic and eddy current problems which are rarely presented in the applied mathematics literature. In the first part, the authors introduce the mathematical models in a realistic context in view of their use for industrial applications. Several geometric configurations of electric conductors leading to different mathematical models are carefully derived and analyzed, and numerical methods for the solution of the obtained problem

Mathematical Modeling of Circadian/Performance Countermeasures

Data.gov (United States)

National Aeronautics and Space Administration — We developed and refined our current mathematical model of circadian rhythms to incorporate melatonin as a marker rhythm. We used an existing physiologically based...

Mathematical Modelling of Unmanned Aerial Vehicles

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Saeed Sarwar

2013-04-01

Full Text Available UAVs (Unmanned Arial Vehicleis UAVs are emerging as requirement of time and it is expected that in next five to ten years, complete air space will be flooded with UAVs, committed in varied assignments ranging from military, scientific and commercial usage. Non availability of human pilot inside UAV necessitates the requirement of an onboard autopilot in order to maintain desired flight profile against any unexpected disturbance and/or parameter variations. Design of such an autopilot requires an accurate mathematical model of UAV. The aim of this paper is to present a consolidated picture of UAV model. This paper first consolidates complete 6 DOF Degree of Freedom equations of motion into a nonlinear mathematical model and its simulation using model parameters of a real UAV. Model is then linearized into longitudinal and lateral modes. State space models of linearized modes are simulated and analyzed for stability parameters. The developed model can be used to design autopilot for UAV

Mathematical modelling of unmanned aerial vehicles

International Nuclear Information System (INIS)

Sarwar, S.; Rehman, S.U.

2013-01-01

UAVs (Unmanned Aerial Vehicles) UAVs are emerging as requirement of time and it is expected that in next five to ten years, complete air space will be flooded with UAVs, committed in varied assignments ranging from military, scientific and commercial usage. Non availability of human pilot inside UAV necessitates the requirement of an onboard auto pilot in order to maintain desired flight profile against any unexpected disturbance and/or parameter variations. Design of such an auto pilot requires an accurate mathematical model of UAV. The aim of this paper is to present a consolidated picture of UAV model. This paper first consolidates complete 6 DOF Degree of Freedom) equations of motion into a nonlinear mathematical model and its simulation using model parameters of a real UAV. Model is then linearized into longitudinal and lateral modes. State space models of linearized modes are simulated and analyzed for stability parameters. The developed model can be used to design auto pilot for UAV. (author)

Mathematical modelling of flooding at Magela Creek

International Nuclear Information System (INIS)

Vardavas, I.

1989-01-01

The extent and frequency of the flooding at Magela Creek can be predicted from a mathematical/computer model describing the hydrological phases of surface runoff. Surface runoff involves complex water transfer processes over very inhomogeneous terrain. A simple mathematical model of these has been developed which includes the interception of rainfall by the plant canopy, evapotranspiration, infiltration of surface water into the soil, the storage of water in surface depressions, and overland and subsurface water flow. The rainfall-runoff model has then been incorporated into a more complex computer model to predict the amount of water that enters and leaves the Magela Creek flood plain, downstream of the mine. 2 figs., ills

Mathematical Modeling Applied to Maritime Security

OpenAIRE

Center for Homeland Defense and Security

2010-01-01

Center for Homeland Defense and Security, OUT OF THE CLASSROOM Download the paper: Layered Defense: Modeling Terrorist Transfer Threat Networks and Optimizing Network Risk Reduction” Students in Ted Lewis’ Critical Infrastructure Protection course are taught how mathematic modeling can provide...

Local Stability Analysis of an Infection-Age Mathematical Model for ...

African Journals Online (AJOL)

Timothy

1Department of Mathematics/Statistics/Computer Science, Federal University of Agriculture, Makurdi, ... ABSTRACT: An infection age structured mathematical model for tuberculosis disease ...... its applications to optimal vaccination strategies.

A mathematical framework for agent based models of complex biological networks.

Science.gov (United States)

Hinkelmann, Franziska; Murrugarra, David; Jarrah, Abdul Salam; Laubenbacher, Reinhard

2011-07-01

Agent-based modeling and simulation is a useful method to study biological phenomena in a wide range of fields, from molecular biology to ecology. Since there is currently no agreed-upon standard way to specify such models, it is not always easy to use published models. Also, since model descriptions are not usually given in mathematical terms, it is difficult to bring mathematical analysis tools to bear, so that models are typically studied through simulation. In order to address this issue, Grimm et al. proposed a protocol for model specification, the so-called ODD protocol, which provides a standard way to describe models. This paper proposes an addition to the ODD protocol which allows the description of an agent-based model as a dynamical system, which provides access to computational and theoretical tools for its analysis. The mathematical framework is that of algebraic models, that is, time-discrete dynamical systems with algebraic structure. It is shown by way of several examples how this mathematical specification can help with model analysis. This mathematical framework can also accommodate other model types such as Boolean networks and the more general logical models, as well as Petri nets.

What Is Mathematical Modelling? Exploring Prospective Teachers' Use of Experiments to Connect Mathematics to the Study of Motion

Science.gov (United States)

Carrejo, David J.; Marshall, Jill

2007-01-01

This paper focuses on the construction, development, and use of mathematical models by prospective science and mathematics teachers enrolled in a university physics course. By studying their involvement in an inquiry-based, experimental approach to learning kinematics, we address a fundamental question about the meaning and role of abstraction in…

Research Methods in Healthcare Epidemiology and Antimicrobial Stewardship-Mathematical Modeling.

Science.gov (United States)

Barnes, Sean L; Kasaie, Parastu; Anderson, Deverick J; Rubin, Michael

2016-11-01

Mathematical modeling is a valuable methodology used to study healthcare epidemiology and antimicrobial stewardship, particularly when more traditional study approaches are infeasible, unethical, costly, or time consuming. We focus on 2 of the most common types of mathematical modeling, namely compartmental modeling and agent-based modeling, which provide important advantages-such as shorter developmental timelines and opportunities for extensive experimentation-over observational and experimental approaches. We summarize these advantages and disadvantages via specific examples and highlight recent advances in the methodology. A checklist is provided to serve as a guideline in the development of mathematical models in healthcare epidemiology and antimicrobial stewardship. Infect Control Hosp Epidemiol 2016;1-7.

Reorganizing Freshman Business Mathematics II: Authentic Assessment in Mathematics through Professional Memos

Science.gov (United States)

Green, Kris; Emerson, Allen

2008-01-01

The first part of this two-part paper [see EJ787497] described the development of a new freshman business mathematics (FBM) course at our college. In this paper, we discuss our assessment tool, the business memo, as a venue for students to apply mathematical skills, via mathematical modelling, to realistic business problems. These memos have…

Mathematical modelling and numerical simulation of oil pollution problems

CERN Document Server

2015-01-01

Written by outstanding experts in the fields of marine engineering, atmospheric physics and chemistry, fluid dynamics and applied mathematics, the contributions in this book cover a wide range of subjects, from pure mathematics to real-world applications in the oil spill engineering business. Offering a truly interdisciplinary approach, the authors present both mathematical models and state-of-the-art numerical methods for adequately solving the partial differential equations involved, as well as highly practical experiments involving actual cases of ocean oil pollution. It is indispensable that different disciplines of mathematics, like analysis and numerics,  together with physics, biology, fluid dynamics, environmental engineering and marine science, join forces to solve today’s oil pollution problems.   The book will be of great interest to researchers and graduate students in the environmental sciences, mathematics and physics, showing the broad range of techniques needed in order to solve these poll...

Mathematical biophysics

CERN Document Server

Rubin, Andrew

2014-01-01

This book presents concise descriptions and analysis of the classical and modern models used in mathematical biophysics. The authors ask the question "what new information can be provided by the models that cannot be obtained directly from experimental data?" Actively developing fields such as regulatory mechanisms in cells and subcellular systems and electron transport and energy transport in membranes are addressed together with more classical topics such as metabolic processes, nerve conduction and heart activity, chemical kinetics, population dynamics, and photosynthesis. The main approach is to describe biological processes using different mathematical approaches necessary to reveal characteristic features and properties of simulated systems. With the emergence of powerful mathematics software packages such as MAPLE, Mathematica, Mathcad, and MatLab, these methodologies are now accessible to a wide audience. Provides succinct but authoritative coverage of a broad array of biophysical topics and models Wr...

Two Project-Based Strategies in an Interdisciplinary Mathematical Modeling in Biology Course

Science.gov (United States)

Ludwig, Patrice; Tongen, Anthony; Walton, Brian

2018-01-01

James Madison University faculty team-teach an interdisciplinary mathematical modeling course for mathematics and biology students. We have used two different project-based approaches to emphasize the mathematical concepts taught in class, while also exposing students to new areas of mathematics not formally covered in class. The first method…

Mathematical model of polyethylene pipe bending stress state

Science.gov (United States)

Serebrennikov, Anatoly; Serebrennikov, Daniil

2018-03-01

Introduction of new machines and new technologies of polyethylene pipeline installation is usually based on the polyethylene pipe flexibility. It is necessary that existing bending stresses do not lead to an irreversible polyethylene pipe deformation and to violation of its strength characteristics. Derivation of the mathematical model which allows calculating analytically the bending stress level of polyethylene pipes with consideration of nonlinear characteristics is presented below. All analytical calculations made with the mathematical model are experimentally proved and confirmed.

Ordinary Mathematical Models in Calculating the Aviation GTE Parameters

Directory of Open Access Journals (Sweden)

E. A. Khoreva

2017-01-01

Full Text Available The paper presents the analytical review results of the ordinary mathematical models of the operating process used to study aviation GTE parameters and characteristics at all stages of its creation and operation. Considers the mathematical models of the zero and the first level, which are mostly used when solving typical problems in calculating parameters and characteristics of engines.Presents a number of practical problems arising in designing aviation GTE for various applications.The application of mathematical models of the zero-level engine can be quite appropriate when the engine is considered as a component in the aircraft system to estimate its calculated individual flight performance or when modeling the flight cycle of the aircrafts of different purpose.The paper demonstrates that introduction of correction functions into the first-level mathematical models in solving typical problems (influence of the Reynolds number, characteristics deterioration of the units during the overhaul period of engine, as well as influence of the flow inhomogeneity at the inlet because of manufacturing tolerance, etc. enables providing a sufficient engineering estimate accuracy to reflect a realistic operating process in the engine and its elements.

A mathematical medley fifty easy pieces on mathematics

CERN Document Server

Szpiro, George G

2010-01-01

Szpiro's book provides a delightful, well-written, eclectic selection of mathematical tidbits that makes excellent airplane reading for anyone with an interest in mathematics, regardless of their mathematical background. Excellent gift material. -Keith Devlin, Stanford University, author of The Unfinished Game and The Language of Mathematics It is great to have collected in one volume the many varied, insightful and often surprising mathematical stories that George Szpiro has written in his mathematical columns for the newspapers through the years. -Marcus du Sautoy, Oxford University, author

Mathematical Modeling of Biofilm Structures Using COMSTAT Data

Directory of Open Access Journals (Sweden)

Davide Verotta

2017-01-01

Full Text Available Mathematical modeling holds great potential for quantitatively describing biofilm growth in presence or absence of chemical agents used to limit or promote biofilm growth. In this paper, we describe a general mathematical/statistical framework that allows for the characterization of complex data in terms of few parameters and the capability to (i compare different experiments and exposures to different agents, (ii test different hypotheses regarding biofilm growth and interaction with different agents, and (iii simulate arbitrary administrations of agents. The mathematical framework is divided to submodels characterizing biofilm, including new models characterizing live biofilm growth and dead cell accumulation; the interaction with agents inhibiting or stimulating growth; the kinetics of the agents. The statistical framework can take into account measurement and interexperiment variation. We demonstrate the application of (some of the models using confocal microscopy data obtained using the computer program COMSTAT.

The Relationship among Elementary Teachers’ Mathematics Anxiety, Mathematics Instructional Practices, and Student Mathematics Achievement

OpenAIRE

Hadley, Kristin M.; Dorward, Jim

2011-01-01

Many elementary teachers have been found to have high levels of mathematics anxiety but the impact on student achievement was unknown. Elementary teachers (N = 692) completed the modified Mathematics Anxiety Rating Scale-Revised (Hopko, 2003) along with a questionnaire probing anxiety about teaching mathematics and current mathematics instructional practices. Student mathematics achievement data were collected for the classrooms taught by the teachers. A positive relationship was found betwee...

Mathematical Model for the Control of measles 1*PETER, OJ ...

African Journals Online (AJOL)

PROF HORSFALL

2018-04-16

Apr 16, 2018 ... 5Department of Mathematics/Statistics, Federal University of Technology, Minna, Nigeria ... ABSTRACT: We proposed a mathematical model of measles disease dynamics with vaccination by ...... Equation with application.

Measuring Developmental Students' Mathematics Anxiety

Science.gov (United States)

Ding, Yanqing

2016-01-01

This study conducted an item-level analysis of mathematics anxiety and examined the dimensionality of mathematics anxiety in a sample of developmental mathematics students (N = 162) by Multi-dimensional Random Coefficients Multinominal Logit Model (MRCMLM). The results indicate a moderately correlated factor structure of mathematics anxiety (r =…

Mathematical models in biological discovery

CERN Document Server

Walter, Charles

1977-01-01

When I was asked to help organize an American Association for the Advancement of Science symposium about how mathematical models have con­ tributed to biology, I agreed immediately. The subject is of immense importance and wide-spread interest. However, too often it is discussed in biologically sterile environments by "mutual admiration society" groups of "theoreticians", many of whom have never seen, and most of whom have never done, an original scientific experiment with the biolog­ ical materials they attempt to describe in abstract (and often prejudiced) terms. The opportunity to address the topic during an annual meeting of the AAAS was irresistable. In order to try to maintain the integrity ;,f the original intent of the symposium, it was entitled, "Contributions of Mathematical Models to Biological Discovery". This symposium was organized by Daniel Solomon and myself, held during the 141st annual meeting of the AAAS in New York during January, 1975, sponsored by sections G and N (Biological and Medic...

The language of mathematics telling mathematical tales

CERN Document Server

Barton, Bill

2008-01-01

Everyday mathematical ideas are expressed differently in different languages. This book probes those differences and explores their implications for mathematics education, arguing for alternatives to how we teach and learn mathematics.

Mathematical model of two-phase flow in accelerator channel

Directory of Open Access Journals (Sweden)

О.Ф. Нікулін

2010-01-01

Full Text Available  The problem of  two-phase flow composed of energy-carrier phase (Newtonian liquid and solid fine-dispersed phase (particles in counter jet mill accelerator channel is considered. The mathematical model bases goes on the supposition that the phases interact with each other like independent substances by means of aerodynamics’ forces in conditions of adiabatic flow. The mathematical model in the form of system of differential equations of order 11 is represented. Derivations of equations by base physical principles for cross-section-averaged quantity are produced. The mathematical model can be used for estimation of any kinematic and thermodynamic flow characteristics for purposely parameters optimization problem solving and transfer functions determination, that take place in  counter jet mill accelerator channel design.

ABOUT THE RELEVANCE AND METHODOLOGY ASPECTS OF TEACHING THE MATHEMATICAL MODELING TO PEDAGOGICAL STUDENTS

Directory of Open Access Journals (Sweden)

Y. A. Perminov

2014-01-01

Full Text Available The paper substantiates the need for profile training in mathematical modeling for pedagogical students, caused by the total penetration of mathematics into different sciences, including the humanities; fast development of the information communications technologies; and growing importance of mathematical modeling, combining the informal scientific and formal mathematical languages with the unique opportunities of computer programming. The author singles out the reasons for mastering and using the mathematical apparatus by teaches in every discipline. Indeed, among all the modern mathematical methods and ideas, mathematical modeling retains its priority in all professional spheres. Therefore, the discipline of “Mathematical Modeling” can play an important role in integrating different components of specialists training in various profiles. By mastering the basics of mathematical modeling, students acquire skills of methodological thinking; learn the principles of analysis, synthesis, generalization of ideas and methods in different disciplines and scientific spheres; and achieve general culture competences. In conclusion, the author recommends incorporating the “Methods of Profile Training in Mathematical Modeling” into the pedagogical magistracy curricula. 

Striking a Balance: Students' Tendencies to Oversimplify or Overcomplicate in Mathematical Modeling

Science.gov (United States)

Gould, Heather; Wasserman, Nicholas H.

2014-01-01

With the adoption of the "Common Core State Standards for Mathematics" (CCSSM), the process of mathematical modeling has been given increased attention in mathematics education. This article reports on a study intended to inform the implementation of modeling in classroom contexts by examining students' interactions with the process of…

Attitudes of Pre-Service Mathematics Teachers towards Modelling: A South African Inquiry

Science.gov (United States)

Jacobs, Gerrie J.; Durandt, Rina

2017-01-01

This study explores the attitudes of mathematics pre-service teachers, based on their initial exposure to a model-eliciting challenge. The new Curriculum and Assessment Policy Statement determines that mathematics students should be able to identify, investigate and solve problems via modelling. The unpreparedness of mathematics teachers in…

The Real and the Mathematical in Quantum Modeling: From Principles to Models and from Models to Principles

Science.gov (United States)

Plotnitsky, Arkady

2017-06-01

The history of mathematical modeling outside physics has been dominated by the use of classical mathematical models, C-models, primarily those of a probabilistic or statistical nature. More recently, however, quantum mathematical models, Q-models, based in the mathematical formalism of quantum theory have become more prominent in psychology, economics, and decision science. The use of Q-models in these fields remains controversial, in part because it is not entirely clear whether Q-models are necessary for dealing with the phenomena in question or whether C-models would still suffice. My aim, however, is not to assess the necessity of Q-models in these fields, but instead to reflect on what the possible applicability of Q-models may tell us about the corresponding phenomena there, vis-à-vis quantum phenomena in physics. In order to do so, I shall first discuss the key reasons for the use of Q-models in physics. In particular, I shall examine the fundamental principles that led to the development of quantum mechanics. Then I shall consider a possible role of similar principles in using Q-models outside physics. Psychology, economics, and decision science borrow already available Q-models from quantum theory, rather than derive them from their own internal principles, while quantum mechanics was derived from such principles, because there was no readily available mathematical model to handle quantum phenomena, although the mathematics ultimately used in quantum did in fact exist then. I shall argue, however, that the principle perspective on mathematical modeling outside physics might help us to understand better the role of Q-models in these fields and possibly to envision new models, conceptually analogous to but mathematically different from those of quantum theory, helpful or even necessary there or in physics itself. I shall suggest one possible type of such models, singularized probabilistic, SP, models, some of which are time-dependent, TDSP-models. The

Mathematical Modelling for Micropiles Embedded in Salt Rock

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Rădan (Toader Georgiana

2016-03-01

Full Text Available This study presents the results of the mathematical modelling for the micropiles foundation of an investement objective located in Slanic, Prahova county. Three computing models were created and analyzed with software, based on Finite Element Method. With Plaxis 2D model was analyzed the isolated micropile and the three-dimensional analysis was made with Plaxis 3D model, for group of micropiles. For the micropiles foundation was used Midas GTS-NX model. The mathematical models were calibrated based with the in-situ tests results for axially loaded micropiles, embedded in salt rock. The paper presents the results obtained with the three software, the calibration and validation models.

Mathematical modeling of flow-injection techniques and their applications for environmental monitoring

International Nuclear Information System (INIS)

Begum, N.N.; Ahmed, J.

2006-01-01

A classification of the existing mathematical models of flow-injection (FI) manifolds based on the main principles on which they are built, have been proposed. Numerous mathematical models of FI systems employing ideas from different scientific areas (e.g. mathematical statistics, chemical engineering, chromatography) have been developed so far. The models have been compared with respect to their predictive power, the complexity of their mathematical treatment, and the requirements for computation time when applied to single-line, multi-channel and conjugated two-line FI systems. It is concluded that the axially dispersed plug flow model deserves special attention because it offers an acceptable compromise between the conflicting requirements for maximal possible mathematical simplicity and maximal possible precision. Applicability of these existing flow-injection models to single-line, multi-channel and conjugated two-line systems for environmental monitoring have been discussed. (author)

Mathematical bridges

CERN Document Server

Andreescu, Titu; Tetiva, Marian

2017-01-01

Building bridges between classical results and contemporary nonstandard problems, Mathematical Bridges embraces important topics in analysis and algebra from a problem-solving perspective. Blending old and new techniques, tactics and strategies used in solving challenging mathematical problems, readers will discover numerous genuine mathematical gems throughout that will heighten their appreciation of the inherent beauty of mathematics. Most of the problems are original to the authors and are intertwined in a well-motivated exposition driven by representative examples. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and educators teaching problem-solving courses or organizing mathematics clubs, as well as motivated mathematics students from high school juniors to college seniors, will find Mathematical Bri...

Exploring mathematics anxiety and attitude: Mathematics students' experiences

Science.gov (United States)

Sahri, Nurul Ashikin; Kamaruzaman, Wan Nur Farahdalila Wan; Jamil, Jastini Mohd.; Shaharanee, Izwan Nizal Mohd.

2017-11-01

A quantitative and correlational, survey methods were used to investigate the relationships among mathematical anxiety and attitude toward student's mathematics performance. Participants were 100 students volunteer to enroll in undergraduate Industrial Statistics, Decision Sciences and Business Mathematics at one of northern university in Malaysia. Survey data consisted of demographic items and Likert scale items. The collected data was analyzed by using the idea of correlation and regression analysis. The results indicated that there was a significant positive relationship between students' attitude and mathematics anxiety. Results also indicated that a substantial positive effect of students' attitude and mathematics anxiety in students' achievement. Further study can be conducted on how mathematical anxiety and attitude toward mathematics affects can be used to predict the students' performance in the class.

Mathematical modeling of the mixing zone for getting bimetallic compound

Energy Technology Data Exchange (ETDEWEB)

Kim, Stanislav L. [Institute of Applied Mechanics, Ural Branch, Izhevsk (Russian Federation)

2011-07-01

A mathematical model of the formation of atomic bonds in metals and alloys, based on the electrostatic interaction between the outer electron shells of atoms of chemical elements. Key words: mathematical model, the interatomic bonds, the electron shell of atoms, the potential, the electron density, bimetallic compound.

A Capstone Mathematics Course for Prospective Secondary Mathematics Teachers

Science.gov (United States)

Artzt, Alice F.; Sultan, Alan; Curcio, Frances R.; Gurl, Theresa

2012-01-01

This article describes an innovative capstone mathematics course that links college mathematics with school mathematics and pedagogy. It describes how college juniors in a secondary mathematics teacher preparation program engage in leadership experiences that enable them to learn mathematics for teaching while developing student-centered…

Mathematical supply-chain modelling: Product analysis of cost and time

International Nuclear Information System (INIS)

Easters, D J

2014-01-01

Establishing a mathematical supply-chain model is a proposition that has received attention due to its inherent benefits of evolving global supply-chain efficiencies. This paper discusses the prevailing relationships found within apparel supply-chain environments, and contemplates the complex issues indicated for constituting a mathematical model. Principal results identified within the data suggest, that the multifarious nature of global supply-chain activities require a degree of simplification in order to fully dilate the necessary factors which affect, each sub-section of the chain. Subsequently, the research findings allowed the division of supply-chain components into sub-sections, which amassed a coherent method of product development activity. Concurrently, the supply-chain model was found to allow systematic mathematical formulae analysis, of cost and time, within the multiple contexts of each subsection encountered. The paper indicates the supply-chain model structure, the mathematics, and considers how product analysis of cost and time can improve the comprehension of product lifecycle management

Mathematical supply-chain modelling: Product analysis of cost and time

Science.gov (United States)

Easters, D. J.

2014-03-01

Establishing a mathematical supply-chain model is a proposition that has received attention due to its inherent benefits of evolving global supply-chain efficiencies. This paper discusses the prevailing relationships found within apparel supply-chain environments, and contemplates the complex issues indicated for constituting a mathematical model. Principal results identified within the data suggest, that the multifarious nature of global supply-chain activities require a degree of simplification in order to fully dilate the necessary factors which affect, each sub-section of the chain. Subsequently, the research findings allowed the division of supply-chain components into sub-sections, which amassed a coherent method of product development activity. Concurrently, the supply-chain model was found to allow systematic mathematical formulae analysis, of cost and time, within the multiple contexts of each subsection encountered. The paper indicates the supply-chain model structure, the mathematics, and considers how product analysis of cost and time can improve the comprehension of product lifecycle management.

A mathematical model

International Nuclear Information System (INIS)

Castillo M, J.A.; Pimentel P, A.E.

2000-01-01

This work presents the results to define the adult egg viability behavior (VHA) of two species, Drosophila melanogaster and D. simulans obtained with the mathematical model proposed, as well as the respective curves. The data are the VHA result of both species coming from the vicinity of the Laguna Verde Nuclear Power plant (CNLV) comprise a 10 years collect period starting from 1987 until 1997. Each collect includes four series of data which are the VHA result obtained after treatment with 0, 4, 6 and 8 Gy of gamma rays. (Author)

The role of mathematical models in the optimization of radiopharmaceutical therapy

International Nuclear Information System (INIS)

Divgi, C.

2001-01-01

Mathematical models have been used in radiopharmaceutical therapy for over five decades. These have served to determine the amount of radioactivity required to treat disease, as in the therapy of hyperthyroidism with iodine-131, or, more frequently, to determine the largest amount of radioactivity that can be safely administered. Mathematical models are especially useful in the determination of fractionated radiopharmaceutical therapy. This review will briefly outline the historical development and current utility of mathematical models in radiopharmaceutical therapy, including thyroid disorders and radioimmunotherapy; and describe the potential of modeling in fractionated therapy. The extended application of such models to currently used radiopharmaceutical therapy based on indices of body mass or surface area, to alleviate toxicity and increase radiation dose to tumour, will be proposed. Finally, future applications of mathematical models in radiopharmaceutical therapy will be outlined. (author)

Mathematical modelling with case studies using Maple and Matlab

CERN Document Server

Barnes, B

2014-01-01

Introduction to Mathematical ModelingMathematical models An overview of the book Some modeling approaches Modeling for decision makingCompartmental Models Introduction Exponential decay and radioactivity Case study: detecting art forgeries Case study: Pacific rats colonize New Zealand Lake pollution models Case study: Lake Burley Griffin Drug assimilation into the blood Case study: dull, dizzy, or dead? Cascades of compartments First-order linear DEs Equilibrium points and stability Case study: money, money, money makes the world go aroundModels of Single PopulationsExponential growth Density-

Identification of Chemical Reactor Plant’s Mathematical Model

OpenAIRE

Pyakullya, Boris Ivanovich; Kladiev, Sergey Nikolaevich

2015-01-01

This work presents a solution of the identification problem of chemical reactor plant’s mathematical model. The main goal is to obtain a mathematical description of a chemical reactor plant from experimental data, which based on plant’s time response measurements. This data consists sequence of measurements for water jacket temperature and information about control input signal, which is used to govern plant’s behavior.

On Mathematical Understanding: Perspectives of Experienced Chinese Mathematics Teachers

Science.gov (United States)

Cai, Jinfa; Ding, Meixia

2017-01-01

Researchers have long debated the meaning of mathematical understanding and ways to achieve mathematical understanding. This study investigated experienced Chinese mathematics teachers' views about mathematical understanding. It was found that these mathematics teachers embrace the view that understanding is a web of connections, which is a result…

Hands-On Mathematics: Two Cases from Ancient Chinese Mathematics

Science.gov (United States)

Wang, Youjun

2009-01-01

In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in…

Optimization and mathematical modeling in computer architecture

CERN Document Server

Sankaralingam, Karu; Nowatzki, Tony

2013-01-01

In this book we give an overview of modeling techniques used to describe computer systems to mathematical optimization tools. We give a brief introduction to various classes of mathematical optimization frameworks with special focus on mixed integer linear programming which provides a good balance between solver time and expressiveness. We present four detailed case studies -- instruction set customization, data center resource management, spatial architecture scheduling, and resource allocation in tiled architectures -- showing how MILP can be used and quantifying by how much it outperforms t

Theoretical Mathematics

Science.gov (United States)

Stöltzner, Michael

Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.

IMPROVEMENT OF MATHEMATICAL MODELS FOR ESTIMATION OF TRAIN DYNAMICS

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L. V. Ursulyak

2017-12-01

Full Text Available Purpose. Using scientific publications the paper analyzes the mathematical models developed in Ukraine, CIS countries and abroad for theoretical studies of train dynamics and also shows the urgency of their further improvement. Methodology. Information base of the research was official full-text and abstract databases, scientific works of domestic and foreign scientists, professional periodicals, materials of scientific and practical conferences, methodological materials of ministries and departments. Analysis of publications on existing mathematical models used to solve a wide range of problems associated with the train dynamics study shows the expediency of their application. Findings. The results of these studies were used in: 1 design of new types of draft gears and air distributors; 2 development of methods for controlling the movement of conventional and connected trains; 3 creation of appropriate process flow diagrams; 4 development of energy-saving methods of train driving; 5 revision of the Construction Codes and Regulations (SNiP ΙΙ-39.76; 6 when selecting the parameters of the autonomous automatic control system, created in DNURT, for an auxiliary locomotive that is part of a connected train; 7 when creating computer simulators for the training of locomotive drivers; 8 assessment of the vehicle dynamic indices characterizing traffic safety. Scientists around the world conduct numerical experiments related to estimation of train dynamics using mathematical models that need to be constantly improved. Originality. The authors presented the main theoretical postulates that allowed them to develop the existing mathematical models for solving problems related to the train dynamics. The analysis of scientific articles published in Ukraine, CIS countries and abroad allows us to determine the most relevant areas of application of mathematical models. Practicalvalue. The practical value of the results obtained lies in the scientific validity

Mathematics Curriculum, the Philosophy of Mathematics and its ...

African Journals Online (AJOL)

It is my observation that the current school mathematics curriculum in Ethiopia is not producing competent mathematics students. Many mathematicians in Ethiopia and other part of the world have often expressed grief that the majority of students do not understand mathematical concepts, or do not see why mathematical ...

Mathematization in introductory physics

Science.gov (United States)

Brahmia, Suzanne M.

Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in

Parallel Boltzmann machines : a mathematical model

NARCIS (Netherlands)

Zwietering, P.J.; Aarts, E.H.L.

1991-01-01

A mathematical model is presented for the description of parallel Boltzmann machines. The framework is based on the theory of Markov chains and combines a number of previously known results into one generic model. It is argued that parallel Boltzmann machines maximize a function consisting of a

Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics

Science.gov (United States)

Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955

Mathematical biology modules based on modern molecular biology and modern discrete mathematics.

Science.gov (United States)

Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.

Mathematics, the Computer, and the Impact on Mathematics Education.

Science.gov (United States)

Tooke, D. James

2001-01-01

Discusses the connection between mathematics and the computer; mathematics curriculum; mathematics instruction, including teachers learning to use computers; and the impact of the computer on learning mathematics. (LRW)

Finite Mathematics and Discrete Mathematics: Is There a Difference?

Science.gov (United States)

Johnson, Marvin L.

Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…

Constraint theory multidimensional mathematical model management

CERN Document Server

Friedman, George J

2017-01-01

Packed with new material and research, this second edition of George Friedman’s bestselling Constraint Theory remains an invaluable reference for all engineers, mathematicians, and managers concerned with modeling. As in the first edition, this text analyzes the way Constraint Theory employs bipartite graphs and presents the process of locating the “kernel of constraint” trillions of times faster than brute-force approaches, determining model consistency and computational allowability. Unique in its abundance of topological pictures of the material, this book balances left- and right-brain perceptions to provide a thorough explanation of multidimensional mathematical models. Much of the extended material in this new edition also comes from Phan Phan’s PhD dissertation in 2011, titled “Expanding Constraint Theory to Determine Well-Posedness of Large Mathematical Models.” Praise for the first edition: "Dr. George Friedman is indisputably the father of the very powerful methods of constraint theory...

Electrorheological fluids modeling and mathematical theory

CERN Document Server

Růžička, Michael

2000-01-01

This is the first book to present a model, based on rational mechanics of electrorheological fluids, that takes into account the complex interactions between the electromagnetic fields and the moving liquid. Several constitutive relations for the Cauchy stress tensor are discussed. The main part of the book is devoted to a mathematical investigation of a model possessing shear-dependent viscosities, proving the existence and uniqueness of weak and strong solutions for the steady and the unsteady case. The PDS systems investigated possess so-called non-standard growth conditions. Existence results for elliptic systems with non-standard growth conditions and with a nontrivial nonlinear r.h.s. and the first ever results for parabolic systems with a non-standard growth conditions are given for the first time. Written for advanced graduate students, as well as for researchers in the field, the discussion of both the modeling and the mathematics is self-contained.

Mathematical Intelligence and Mathematical Creativity: A Causal Relationship

Science.gov (United States)

Tyagi, Tarun Kumar

2017-01-01

This study investigated the causal relationship between mathematical creativity and mathematical intelligence. Four hundred thirty-nine 8th-grade students, age ranged from 11 to 14 years, were included in the sample of this study by random cluster technique on which mathematical creativity and Hindi adaptation of mathematical intelligence test…

short communication mathematical modelling for magnetite

African Journals Online (AJOL)

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The present research focuses to develop mathematical model for the ..... Staler, M.J. The Principle of Ion Exchange Technology, Butterworth-Heinemann: Boston; ... Don, W.G. Perry's Chemical Engineering Hand Book, 7th ed., McGraw-Hill:.

Teaching Writing and Communication in a Mathematical Modeling Course

Science.gov (United States)

Linhart, Jean Marie

2014-01-01

Writing and communication are essential skills for success in the workplace or in graduate school, yet writing and communication are often the last thing that instructors think about incorporating into a mathematics course. A mathematical modeling course provides a natural environment for writing assignments. This article is an analysis of the…

Mathematical model comparing of the multi-level economics systems

Science.gov (United States)

Brykalov, S. M.; Kryanev, A. V.

2017-12-01

The mathematical model (scheme) of a multi-level comparison of the economic system, characterized by the system of indices, is worked out. In the mathematical model of the multi-level comparison of the economic systems, the indicators of peer review and forecasting of the economic system under consideration can be used. The model can take into account the uncertainty in the estimated values of the parameters or expert estimations. The model uses the multi-criteria approach based on the Pareto solutions.

Mathematics a minimal introduction

CERN Document Server

Buium, Alexandru

2013-01-01

Pre-Mathematical Logic Languages Metalanguage Syntax Semantics Tautologies Witnesses Theories Proofs Argot Strategies Examples Mathematics ZFC Sets Maps Relations Operations Integers Induction Rationals Combinatorics Sequences Reals Topology Imaginaries Residues p-adics Groups Orders Vectors Matrices Determinants Polynomials Congruences Lines Conics Cubics Limits Series Trigonometry Integrality Reciprocity Calculus Metamodels Categories Functors Objectives Mathematical Logic Models Incompleteness Bibliography Index

Antioxidant Capacity: Experimental Determination by EPR Spectroscopy and Mathematical Modeling.

Science.gov (United States)

Polak, Justyna; Bartoszek, Mariola; Chorążewski, Mirosław

2015-07-22

A new method of determining antioxidant capacity based on a mathematical model is presented in this paper. The model was fitted to 1000 data points of electron paramagnetic resonance (EPR) spectroscopy measurements of various food product samples such as tea, wine, juice, and herbs with Trolox equivalent antioxidant capacity (TEAC) values from 20 to 2000 μmol TE/100 mL. The proposed mathematical equation allows for a determination of TEAC of food products based on a single EPR spectroscopy measurement. The model was tested on the basis of 80 EPR spectroscopy measurements of herbs, tea, coffee, and juice samples. The proposed model works for both strong and weak antioxidants (TEAC values from 21 to 2347 μmol TE/100 mL). The determination coefficient between TEAC values obtained experimentally and TEAC values calculated with proposed mathematical equation was found to be R(2) = 0.98. Therefore, the proposed new method of TEAC determination based on a mathematical model is a good alternative to the standard EPR method due to its being fast, accurate, inexpensive, and simple to perform.

Advanced engineering mathematics

CERN Document Server

Jeffrey, Alan

2001-01-01

Advanced Engineering Mathematics provides comprehensive and contemporary coverage of key mathematical ideas, techniques, and their widespread applications, for students majoring in engineering, computer science, mathematics and physics. Using a wide range of examples throughout the book, Jeffrey illustrates how to construct simple mathematical models, how to apply mathematical reasoning to select a particular solution from a range of possible alternatives, and how to determine which solution has physical significance. Jeffrey includes material that is not found in works of a similar nature, such as the use of the matrix exponential when solving systems of ordinary differential equations. The text provides many detailed, worked examples following the introduction of each new idea, and large problem sets provide both routine practice, and, in many cases, greater challenge and insight for students. Most chapters end with a set of computer projects that require the use of any CAS (such as Maple or Mathematica) th...

The Effect of Teacher Beliefs on Student Competence in Mathematical Modeling--An Intervention Study

Science.gov (United States)

Mischo, Christoph; Maaß, Katja

2013-01-01

This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and…

Integrating Dynamic Mathematics Software into Cooperative Learning Environments in Mathematics

Science.gov (United States)

Zengin, Yilmaz; Tatar, Enver

2017-01-01

The aim of this study was to evaluate the implementation of the cooperative learning model supported with dynamic mathematics software (DMS), that is a reflection of constructivist learning theory in the classroom environment, in the teaching of mathematics. For this purpose, a workshop was conducted with the volunteer teachers on the…

Analysis of creative mathematical thinking ability by using model eliciting activities (MEAs)

Science.gov (United States)

Winda, A.; Sufyani, P.; Elah, N.

2018-05-01

Lack of creative mathematical thinking ability can lead to not accustomed with open ended problem. Students’ creative mathematical thinking ability in the first grade at one of junior high school in Tangerang City is not fully developed. The reason of students’ creative mathematical thinking ability is not optimally developed is so related with learning process which has done by the mathematics teacher, maybe the learning design that teacher use is unsuitable for increasing students’ activity in the learning process. This research objective is to see the differences in students’ ways of answering the problems in terms of students’ creative mathematical thinking ability during the implementation of Model Eliciting Activities (MEAs). This research use post-test experimental class design. The indicators for creative mathematical thinking ability in this research arranged in three parts, as follow: (1) Fluency to answer the problems; (2) Flexibility to solve the problems; (3) Originality of answers. The result of this research found that by using the same learning model and same instrument from Model Eliciting Activities (MEAs) there are some differences in the way students answer the problems and Model Eliciting Activities (MEAs) can be one of approach used to increase students’ creative mathematical thinking ability.

Identification of Chemical Reactor Plant’s Mathematical Model

Directory of Open Access Journals (Sweden)

Pyakillya Boris

2015-01-01

Full Text Available This work presents a solution of the identification problem of chemical reactor plant’s mathematical model. The main goal is to obtain a mathematical description of a chemical reactor plant from experimental data, which based on plant’s time response measurements. This data consists sequence of measurements for water jacket temperature and information about control input signal, which is used to govern plant’s behavior.

Mathematics Pedagogical Standards: A Suggested Model of Instruction in Enhancing the Mathematics Teacher’s Quality of Instruction

Science.gov (United States)

Saad, N. S.; Jemali, M.; Zakaria, Z. Hj; Yusof, Q.

2018-01-01

The paper aims at identifying the standards for teaching and learning of mathematics based on National Council of Teacher of Mathematics (NCTM, 2000), The Australian Association of Mathematics Teachers (AAMT, 2006) and Training and Development Agency for School (TDA, 2007). These known standards were used as a guide in identifying the constructs of the mathematics teacher’s instruction in the classroom. The survey method used in which a questionnaire instrument encompassed on the four identified constructs on the standards for teaching and learning of mathematics, namely professional practices, professional attributes, professional knowledge, and professional instructional processes. The instrument was tested during a pilot study and a Cronbach’s Alpha reliability index of greater than 0.85 was obtained. The actual research was carried out in Peninsular Malaysia involving 224 secondary schools with 1.120 mathematics teachers and 108 primary schools with 540 mathematics teachers. From the selected schools, only 820 secondary mathematics teachers (73.2%) and 361 primary teachers (66.9%) gave a response to the mailed questionnaires. The findings of the study revealed that the secondary and primary mathematics teachers strongly agreed on three constructs; professional practices, professional attributes and professional instructional processes.

Mathematical model of gluconic acid fermentation by Aspergillus niger

Energy Technology Data Exchange (ETDEWEB)

Takamatsu, T.; Shioya, S.; Furuya, T.

1981-11-01

A mathematical model for the study of gluconic acid fermentation by Aspergillus niger has been developed. The model has been deduced from the basic biological concept of multicellular filamentous microorganisms, i.e. cell population balance. It can be used to explain the behaviour of both batch and continuous cultures, even when in a lag phase. A new characteristic, involving the existence of dual equilibrium stages during fermentation, has been predicted using this mathematical model. (Refs. 6).

A mathematical model of embodied consciousness

NARCIS (Netherlands)

Rudrauf, D.; Bennequin, D.; Granic, I.; Landini, G.; Friston, K.; Williford, K.

2017-01-01

We introduce a mathematical model of embodied consciousness, the Projective Consciousness Model (PCM), which is based on the hypothesis that the spatial field of consciousness (FoC) is structured by a projective geometry and under the control of a process of active inference. The FoC in the PCM

A mathematical model for camera calibration based on straight lines

Directory of Open Access Journals (Sweden)

Antonio M. G. Tommaselli

2005-12-01

Full Text Available In other to facilitate the automation of camera calibration process, a mathematical model using straight lines was developed, which is based on the equivalent planes mathematical model. Parameter estimation of the developed model is achieved by the Least Squares Method with Conditions and Observations. The same method of adjustment was used to implement camera calibration with bundles, which is based on points. Experiments using simulated and real data have shown that the developed model based on straight lines gives results comparable to the conventional method with points. Details concerning the mathematical development of the model and experiments with simulated and real data will be presented and the results with both methods of camera calibration, with straight lines and with points, will be compared.

The Chicken or the Egg? The Direction of the Relationship Between Mathematics Anxiety and Mathematics Performance.

Science.gov (United States)

Carey, Emma; Hill, Francesca; Devine, Amy; Szücs, Dénes

2015-01-01

This review considers the two possible causal directions between mathematics anxiety (MA) and poor mathematics performance. Either poor maths performance may elicit MA (referred to as the Deficit Theory), or MA may reduce future maths performance (referred to as the Debilitating Anxiety Model). The evidence is in conflict: the Deficit Theory is supported by longitudinal studies and studies of children with mathematical learning disabilities, but the Debilitating Anxiety Model is supported by research which manipulates anxiety levels and observes a change in mathematics performance. It is suggested that this mixture of evidence might indicate a bidirectional relationship between MA and mathematics performance (the Reciprocal Theory), in which MA and mathematics performance can influence one another in a vicious cycle.

Modeling life the mathematics of biological systems

CERN Document Server

Garfinkel, Alan; Guo, Yina

2017-01-01

From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. This book develops the mathematical tools essential for students in the life sciences to describe these interacting systems and to understand and predict their behavior. Complex feedback relations and counter-intuitive responses are common in dynamical systems in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models ...

Mathematics Teacher Education: A Model from Crimea.

Science.gov (United States)

Ferrucci, Beverly J.; Evans, Richard C.

1993-01-01

Reports on the mathematics teacher preparation program at Simferopol State University, the largest institution of higher education in the Crimea. The article notes the value of investigating what other countries consider essential in mathematics teacher education to improve the mathematical competence of students in the United States. (SM)

Theoretical Basics of Teaching Discrete Mathematics

Directory of Open Access Journals (Sweden)

Y. A. Perminov

2012-01-01

Full Text Available  The paper deals with the research findings concerning the process of mastering the theoretical basics of discrete mathematics by the students of vocational pedagogic profile. The methodological analysis is based on the subject and functions of the modern discrete mathematics and its role in mathematical modeling and computing. The modern discrete mathematics (i.e. mathematics of the finite type structures plays the important role in modernization of vocational training. It is especially rele- vant to training students for vocational pedagogic qualifications, as in the future they will be responsible for training the middle and the senior level specialists in engineer- ing and technical spheres. Nowadays in different industries, there arise the problems which require for their solving both continual – based on the classical mathematical methods – and discrete modeling. The teaching course of discrete mathematics for the future vocational teachers should be relevant to the target qualification and aimed at mastering the mathematical modeling, systems of computer mathematics and computer technologies. The author emphasizes the fundamental role of mastering the language of algebraic and serial structures, as well as the logical, algorithmic, combinatory schemes dominating in dis- crete mathematics. The guidelines for selecting the content of the course in discrete mathematics are specified. The theoretical findings of the research can be put into practice whilst developing curricula and working programs for bachelors and masters’ training. 

MATHEMATICS EDUCATION FOR LOGISTICS ENGINEERING

OpenAIRE

BÉLA ILLÉS; GABRIELLA BOGNÁR

2012-01-01

Mathematics is a crucial language in all engineering courses and researches where mathematical modeling, simulation and manipulation are commonly used. Engineering Mathematics courses are considered difficult courses in engineering curricula. This is reflected in engineering students’ performance at the end of each semester for these courses. Our goal is to overview a few questions on mathematics as a core subject of engineering.

Mathematical structures for computer graphics

CERN Document Server

Janke, Steven J

2014-01-01

A comprehensive exploration of the mathematics behind the modeling and rendering of computer graphics scenes Mathematical Structures for Computer Graphics presents an accessible and intuitive approach to the mathematical ideas and techniques necessary for two- and three-dimensional computer graphics. Focusing on the significant mathematical results, the book establishes key algorithms used to build complex graphics scenes. Written for readers with various levels of mathematical background, the book develops a solid foundation for graphics techniques and fills in relevant grap

Mathematical modeling of the flash converting process

Energy Technology Data Exchange (ETDEWEB)

Sohn, H.Y.; Perez-Tello, M.; Riihilahti, K.M. [Utah Univ., Salt Lake City, UT (United States)

1996-12-31

An axisymmetric mathematical model for the Kennecott-Outokumpu flash converting process for converting solid copper matte to copper is presented. The model is an adaptation of the comprehensive mathematical model formerly developed at the University of Utah for the flash smelting of copper concentrates. The model incorporates the transport of momentum, heat, mass, and reaction kinetics between gas and particles in a particle-laden turbulent gas jet. The standard k-{epsilon} model is used to describe gas-phase turbulence in an Eulerian framework. The particle-phase is treated from a Lagrangian viewpoint which is coupled to the gas-phase via the source terms in the Eulerian gas-phase governing equations. Matte particles were represented as Cu{sub 2}S yFeS, and assumed to undergo homogeneous oxidation to Cu{sub 2}O, Fe{sub 3}O{sub 4}, and SO{sub 2}. A reaction kinetics mechanism involving both external mass transfer of oxygen gas to the particle surface and diffusion of oxygen through the porous oxide layer is proposed to estimate the particle oxidation rate Predictions of the mathematical model were compared with the experimental data collected in a bench-scale flash converting facility. Good agreement between the model predictions and the measurements was obtained. The model was used to study the effect of different gas-injection configurations on the overall fluid dynamics in a commercial size flash converting shaft. (author)

Mathematical modeling of the flash converting process

Energy Technology Data Exchange (ETDEWEB)

Sohn, H Y; Perez-Tello, M; Riihilahti, K M [Utah Univ., Salt Lake City, UT (United States)

1997-12-31

An axisymmetric mathematical model for the Kennecott-Outokumpu flash converting process for converting solid copper matte to copper is presented. The model is an adaptation of the comprehensive mathematical model formerly developed at the University of Utah for the flash smelting of copper concentrates. The model incorporates the transport of momentum, heat, mass, and reaction kinetics between gas and particles in a particle-laden turbulent gas jet. The standard k-{epsilon} model is used to describe gas-phase turbulence in an Eulerian framework. The particle-phase is treated from a Lagrangian viewpoint which is coupled to the gas-phase via the source terms in the Eulerian gas-phase governing equations. Matte particles were represented as Cu{sub 2}S yFeS, and assumed to undergo homogeneous oxidation to Cu{sub 2}O, Fe{sub 3}O{sub 4}, and SO{sub 2}. A reaction kinetics mechanism involving both external mass transfer of oxygen gas to the particle surface and diffusion of oxygen through the porous oxide layer is proposed to estimate the particle oxidation rate Predictions of the mathematical model were compared with the experimental data collected in a bench-scale flash converting facility. Good agreement between the model predictions and the measurements was obtained. The model was used to study the effect of different gas-injection configurations on the overall fluid dynamics in a commercial size flash converting shaft. (author)

A model of professional competences in mathematics to update mathematical and didactic knowledge of teachers

Science.gov (United States)

Díaz, Verónica; Poblete, Alvaro

2017-07-01

This paper describes part of a research and development project carried out in public elementary schools. Its objective was to update the mathematical and didactic knowledge of teachers in two consecutive levels in urban and rural public schools of Region de Los Lagos and Region de Los Rios of southern Chile. To that effect, and by means of an advanced training project based on a professional competences model, didactic interventions based on types of problems and types of mathematical competences with analysis of contents and learning assessment were designed. The teachers' competence regarding the didactic strategy used and its results, as well as the students' learning achievements are specified. The project made possible to validate a strategy of lifelong improvement in mathematics, based on the professional competences of teachers and their didactic transposition in the classroom, as an alternative to consolidate learning in areas considered vulnerable in two regions of the country.

Learning Mathematics for Teaching Mathematics: Non-Specialist Teachers' Mathematics Teacher Identity

Science.gov (United States)

Crisan, Cosette; Rodd, Melissa

2017-01-01

A non-specialist teacher of mathematics is a school teacher who qualified to teach in a subject other than mathematics yet teaches mathematics to students in secondary school. There is an emerging interest internationally in this population, a brief report of which is given in the paper. Because of concerns about the quality of non-specialists'…

Effectiveness of discovery learning model on mathematical problem solving

Science.gov (United States)

Herdiana, Yunita; Wahyudin, Sispiyati, Ririn

2017-08-01

This research is aimed to describe the effectiveness of discovery learning model on mathematical problem solving. This research investigate the students' problem solving competency before and after learned by using discovery learning model. The population used in this research was student in grade VII in one of junior high school in West Bandung Regency. From nine classes, class VII B were randomly selected as the sample of experiment class, and class VII C as control class, which consist of 35 students every class. The method in this research was quasi experiment. The instrument in this research is pre-test, worksheet and post-test about problem solving of mathematics. Based on the research, it can be conclude that the qualification of problem solving competency of students who gets discovery learning model on level 80%, including in medium category and it show that discovery learning model effective to improve mathematical problem solving.

Mathematical model for solid fuel combustion in fluidized bed

International Nuclear Information System (INIS)

Kostikj, Zvonimir; Noshpal, Aleksandar

1994-01-01

A mathematical model for computation of the combustion process of solid fuel in fluidized bed is presented in this work. Only the combustor part of the plant (the fluidized bed and the free board) is treated with this model. In that manner, all principal, physical presumption and improvements (upon which this model is based) are given. Finally, the results of the numerical realisation of the mathematical model for combustion of minced straw as well as the results of the experimental investigation of a concrete physical model are presented. (author)

Cooking Potatoes: Experimentation and Mathematical Modeling.

Science.gov (United States)

Chen, Xiao Dong

2002-01-01

Describes a laboratory activity involving a mathematical model of cooking potatoes that can be solved analytically. Highlights the microstructure aspects of the experiment. Provides the key aspects of the results, detailed background readings, laboratory procedures and data analyses. (MM)

Introductory mathematics for earth scientists

CERN Document Server

Yang, Xin-She

2009-01-01

Any quantitative work in earth sciences requires mathematical analysis and mathematical methods are essential to the modelling and analysis of the geological, geophysical and environmental processes involved. This book provides an introduction to the fundamental mathematics that all earth scientists need.

Mathematical models of viscous friction

CERN Document Server

Buttà, Paolo; Marchioro, Carlo

2015-01-01

In this monograph we present a review of a number of recent results on the motion of a classical body immersed in an infinitely extended medium and subjected to the action of an external force. We investigate this topic in the framework of mathematical physics by focusing mainly on the class of purely Hamiltonian systems, for which very few results are available. We discuss two cases: when the medium is a gas and when it is a fluid. In the first case, the aim is to obtain microscopic models of viscous friction. In the second, we seek to underline some non-trivial features of the motion. Far from giving a general survey on the subject, which is very rich and complex from both a phenomenological and theoretical point of view, we focus on some fairly simple models that can be studied rigorously, thus providing a first step towards a mathematical description of viscous friction. In some cases, we restrict ourselves to studying the problem at a heuristic level, or we present the main ideas, discussing only some as...

Crossroads in the History of Mathematics and Mathematics Education. The Montana Mathematics Enthusiast: Monograph Series in Mathematics Education

Science.gov (United States)

Sriraman, Bharath, Ed.

2012-01-01

The interaction of the history of mathematics and mathematics education has long been construed as an esoteric area of inquiry. Much of the research done in this realm has been under the auspices of the history and pedagogy of mathematics group. However there is little systematization or consolidation of the existing literature aimed at…

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...

Mathematical methods for cancer evolution

CERN Document Server

Suzuki, Takashi

2017-01-01

The purpose of this monograph is to describe recent developments in mathematical modeling and mathematical analysis of certain problems arising from cell biology. Cancer cells and their growth via several stages are of particular interest. To describe these events, multi-scale models are applied, involving continuously distributed environment variables and several components related to particles. Hybrid simulations are also carried out, using discretization of environment variables and the Monte Carlo method for the principal particle variables. Rigorous mathematical foundations are the bases of these tools. The monograph is composed of four chapters. The first three chapters are concerned with modeling, while the last one is devoted to mathematical analysis. The first chapter deals with molecular dynamics occurring at the early stage of cancer invasion. A pathway network model based on a biological scenario is constructed, and then its mathematical structures are determined. In the second chapter mathematica...

Mathematical Literacy: A new literacy or a new mathematics?

Directory of Open Access Journals (Sweden)

Renuka Vithal

2006-10-01

Full Text Available Mathematical Literacy is a ‘hot’ topic at present in most countries, whether it is referred to by that name, or in some cases as Numeracy, or Quantitative Literacy, or Matheracy, or as some part of Ethnomathematics, or related to Mathematics in Society. Questions continue to be asked about what is meant by mathematics in any concept of Mathematical Literacy and the use of the very word ‘Literacy’ in its association with Mathematics has been challenged. Its importance, however, lies in changing our perspective on mathematics teaching, away from the elitism so often associated with much mathematics education, and towards a more equitable, accessible and genuinely educational ideal.

Modeling Clinic for Industrial Mathematics: A Collaborative Project Under Erasmus+ Program

DEFF Research Database (Denmark)

Jurlewicz, Agnieszka; Nunes, Claudia; Russo, Giovanni

2018-01-01

Modeling Clinic for Industrial Mathematics (MODCLIM) is a Strategic Partnership for the Development of Training Workshops and Modeling Clinic for Industrial Mathematics, funded through the European Commission under the Erasmus Plus Program, Key Action 2: Cooperation for innovation and the exchang...

Handbook of mathematics

CERN Document Server

Bronshtein, I N; Musiol, Gerhard; Mühlig, Heiner

2015-01-01

This guide book to mathematics contains in handbook form the fundamental working knowledge of mathematics which is needed as an everyday guide for working scientists and engineers, as well as for students. Easy to understand, and convenient to use, this guide book gives concisely the information necessary to evaluate most problems which occur in concrete applications. In the newer editions emphasis was laid on those fields of mathematics that became more important for the formulation and modeling of technical and natural processes, namely Numerical Mathematics, Probability Theory and Statistics, as well as Information Processing. Besides many enhancements and  new paragraphs,  new sections on Geometric and Coordinate Transformations, Quaternions and Applications, and Lie Groups and Lie Algebras were added for the sixth edition.

Mathematical modeling of infectious disease dynamics

Science.gov (United States)

Siettos, Constantinos I.; Russo, Lucia

2013-01-01

Over the last years, an intensive worldwide effort is speeding up the developments in the establishment of a global surveillance network for combating pandemics of emergent and re-emergent infectious diseases. Scientists from different fields extending from medicine and molecular biology to computer science and applied mathematics have teamed up for rapid assessment of potentially urgent situations. Toward this aim mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. To better understand and model the contagious dynamics the impact of numerous variables ranging from the micro host–pathogen level to host-to-host interactions, as well as prevailing ecological, social, economic, and demographic factors across the globe have to be analyzed and thoroughly studied. Here, we present and discuss the main approaches that are used for the surveillance and modeling of infectious disease dynamics. We present the basic concepts underpinning their implementation and practice and for each category we give an annotated list of representative works. PMID:23552814

The Relationship of Mathematics Anxiety and Mathematical Knowledge to the Learning of Mathematical Pedagogy by Preservice Elementary Teachers.

Science.gov (United States)

Battista, Michael T.

1986-01-01

Examined how preservice elementary teachers' (N=38) mathematical knowledge and mathematics anxiety affect their success in a mathematics methods course. Also examined the hypothesis that a mathematics methods course can reduce the mathematics anxiety of these teachers. One finding is that mathematics anxiety does not inhibit their learning of…

The Relationships among Mathematics Teaching Efficacy, Mathematics Self-Efficacy, and Mathematical Beliefs for Elementary Pre-Service Teachers

Science.gov (United States)

Briley, Jason S.

2012-01-01

Ninety-five elementary pre-service teachers enrolled in a mathematics content course for elementary school teachers completed 3 surveys to measure mathematics teaching efficacy, mathematics self-efficacy, and mathematical beliefs. The pre-service teachers who reported stronger beliefs in their capabilities to teach mathematics effectively were…

Mathematical model of glucose-insulin homeostasis in healthy rats.

Science.gov (United States)

Lombarte, Mercedes; Lupo, Maela; Campetelli, German; Basualdo, Marta; Rigalli, Alfredo

2013-10-01

According to the World Health Organization there are over 220 million people in the world with diabetes and 3.4 million people died in 2004 as a consequence of this pathology. Development of an artificial pancreas would allow to restore control of blood glucose by coupling an infusion pump to a continuous glucose sensor in the blood. The design of such a device requires the development and application of mathematical models which represent the gluco-regulatory system. Models developed by other research groups describe very well the gluco-regulatory system but have a large number of mathematical equations and require complex methodologies for the estimation of its parameters. In this work we propose a mathematical model to study the homeostasis of glucose and insulin in healthy rats. The proposed model consists of three differential equations and 8 parameters that describe the variation of: blood glucose concentration, blood insulin concentration and amount of glucose in the intestine. All parameters were obtained by setting functions to the values of glucose and insulin in blood obtained after oral glucose administration. In vivo and in silico validations were performed. Additionally, a qualitative analysis has been done to verify the aforementioned model. We have shown that this model has a single, biologically consistent equilibrium point. This model is a first step in the development of a mathematical model for the type I diabetic rat. Copyright © 2013 Elsevier Inc. All rights reserved.

The chicken or the egg? The direction of the relationship between mathematics anxiety and mathematics performance

Directory of Open Access Journals (Sweden)

Emma eCarey

2016-01-01

Full Text Available This review considers the two possible causal directions between mathematics anxiety (MA and poor mathematics performance. Either poor maths performance may elicit MA (referred to as the Deficit Theory, or MA may reduce future maths performance (referred to as the Debilitating Anxiety Model. The evidence is in conflict: the Deficit Theory is supported by longitudinal studies and studies of children with mathematical learning disabilities, but the Debilitating Anxiety Model is supported by research which manipulates anxiety levels and observes a change in mathematics performance. It is suggested that this mixture of evidence might indicate a bidirectional relationship between MA and mathematics performance (the Reciprocal Theory, in which MA and mathematics performance can influence one another in a vicious cycle.

A Mathematical Model, Implementation and Study of a Swarm System

OpenAIRE

Varghese, Blesson; McKee, Gerard

2013-01-01

The work reported in this paper is motivated towards the development of a mathematical model for swarm systems based on macroscopic primitives. A pattern formation and transformation model is proposed. The pattern transformation model comprises two general methods for pattern transformation, namely a macroscopic transformation and mathematical transformation method. The problem of transformation is formally expressed and four special cases of transformation are considered. Simulations to conf...

Potential of mathematical modeling in fruit quality

African Journals Online (AJOL)

ONOS

2010-01-18

Jan 18, 2010 ... successful mathematical model, the modeler needs to chose what .... equations. In the SUCROS models, the rate of CO2 assimilation is .... insect ecology. ... García y García A, Ingram KT, Hatch U, Hoogenboom G, Jones JW,.

The academic merits of modelling in higher mathematics education: A case study

NARCIS (Netherlands)

Perrenet, J.; Adan, I.

2010-01-01

Modelling is an important subject in the Bachelor curriculum of Applied Mathematics at Eindhoven University of Technology in the Netherlands. Students not only learn how to apply their knowledge to solve mathematical problems posed in non-mathematical language, but also they learn to look actively

The academic merits of modelling in higher mathematics education : a case study

NARCIS (Netherlands)

Perrenet, J.C.; Adan, I.J.B.F.

2010-01-01

Modelling is an important subject in the Bachelor curriculum of Applied Mathematics at Eindhoven University of Technology in the Netherlands. Students not only learn how to apply their knowledge to solve mathematical problems posed in non-mathematical language, but also they learn to look actively

Mathematical Modeling: Are Prior Experiences Important?

Science.gov (United States)

Czocher, Jennifer A.; Moss, Diana L.

2017-01-01

Why are math modeling problems the source of such frustration for students and teachers? The conceptual understanding that students have when engaging with a math modeling problem varies greatly. They need opportunities to make their own assumptions and design the mathematics to fit these assumptions (CCSSI 2010). Making these assumptions is part…

Mathematical Modelling of Intraretinal Oxygen Partial Pressure

African Journals Online (AJOL)

Erah

The system of non-linear differential equations was solved numerically using Runge-kutta. Nystroms method. ... artery occlusion. Keywords: Mathematical modeling, Intraretinal oxygen pressure, Retinal capillaries, Oxygen ..... Mass transfer,.

Outlooks for mathematical modelling of the glass melting process

Energy Technology Data Exchange (ETDEWEB)

Waal, H. de [TNO Institute of Applied Physics, Delft (Netherlands)

1997-12-31

Mathematical modelling is nowadays a standard tool for major producers of float glass, T.V. glass and fiberglass. Also for container glass furnaces, glass tank modelling proves to be a valuable method to optimize process conditions. Mathematical modelling is no longer just a way to visualize the flow patterns and to provide data on heat transfer. It can also predict glass quality in relation to process parameters, because all chemical and physical phenomena are included in the latest generation of models, based on experimental and theoretical research on these phenomena.

Learning Mathematics through Programming

DEFF Research Database (Denmark)

Misfeldt, Morten; Ejsing-Duun, Stine

2015-01-01

In this paper we explore the potentials for learning mathematics through programming by a combination of theoretically derived potentials and cases of practical pedagogical work. We propose a model with three interdependent learning potentials as programming which can: (1) help reframe the students...... to mathematics is paramount. Analyzing two cases, we suggest a number of ways in which didactical attention to epistemic mediation can support learning mathematics....

Mathematical Representation of VoIP Connection Delay

Directory of Open Access Journals (Sweden)

M. Halas

2007-09-01

Full Text Available The main topic of this article is to define mathematical formulation of VoIP connection delay model. It handles about all partial delay components, the mechanism of their generation, facilities and their mathematical formulation. Thereafter based on mathematical formulation of all partial delay components, the final mathematical model of whole VoIP call delay is created. In conclusion of this article the results of the designed mathematical model are compared with the experimentally gained results.

Discrete Mathematics and the Secondary Mathematics Curriculum.

Science.gov (United States)

Dossey, John

Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…

Mathematical Perspectives

Energy Technology Data Exchange (ETDEWEB)

Glimm, J.

2009-10-14

Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.

Tracer kinetic modelling of receptor data with mathematical metabolite correction

International Nuclear Information System (INIS)

Burger, C.; Buck, A.

1996-01-01

Quantitation of metabolic processes with dynamic positron emission tomography (PET) and tracer kinetic modelling relies on the time course of authentic ligand in plasma, i.e. the input curve. The determination of the latter often requires the measurement of labelled metabilites, a laborious procedure. In this study we examined the possibility of mathematical metabolite correction, which might obviate the need for actual metabolite measurements. Mathematical metabilite correction was implemented by estimating the input curve together with kinetic tissue parameters. The general feasibility of the approach was evaluated in a Monte Carlo simulation using a two tissue compartment model. The method was then applied to a series of five human carbon-11 iomazenil PET studies. The measured cerebral tissue time-activity curves were fitted with a single tissue compartment model. For mathematical metabolite correction the input curve following the peak was approximated by a sum of three decaying exponentials, the amplitudes and characteristic half-times of which were then estimated by the fitting routine. In the simulation study the parameters used to generate synthetic tissue time-activity curves (K 1 -k 4 ) were refitted with reasonable identifiability when using mathematical metabolite correciton. Absolute quantitation of distribution volumes was found to be possible provided that the metabolite and the kinetic models are adequate. If the kinetic model is oversimplified, the linearity of the correlation between true and estimated distribution volumes is still maintained, although the linear regression becomes dependent on the input curve. These simulation results were confirmed when applying mathematical metabolite correction to the 11 C iomazenil study. Estimates of the distribution volume calculated with a measured input curve were linearly related to the estimates calculated using mathematical metabolite correction with correlation coefficients >0.990. (orig./MG)

Mathematical modeling of optical glazing performance

NARCIS (Netherlands)

Nijnatten, van P.A.; Wittwer, V.; Granqvist, C.G.; Lampert, C.M.

1994-01-01

Mathematical modelling can be a powerful tool in the design and optimalization of glazing. By calculation, the specifications of a glazing design and the optimal design parameters can be predicted without building costly prototypes first. Furthermore, properties which are difficult to measure, like

Introduction to mathematical models and methods

Energy Technology Data Exchange (ETDEWEB)

Siddiqi, A. H.; Manchanda, P. [Gautam Budha University, Gautam Budh Nagar-201310 (India); Department of Mathematics, Guru Nanak Dev University, Amritsar (India)

2012-07-17

Some well known mathematical models in the form of partial differential equations representing real world systems are introduced along with fundamental concepts of Image Processing. Notions such as seismic texture, seismic attributes, core data, well logging, seismic tomography and reservoirs simulation are discussed.

Current problems in applied mathematics and mathematical physics

Science.gov (United States)

Samarskii, A. A.

Papers are presented on such topics as mathematical models in immunology, mathematical problems of medical computer tomography, classical orthogonal polynomials depending on a discrete variable, and boundary layer methods for singular perturbation problems in partial derivatives. Consideration is also given to the computer simulation of supernova explosion, nonstationary internal waves in a stratified fluid, the description of turbulent flows by unsteady solutions of the Navier-Stokes equations, and the reduced Galerkin method for external diffraction problems using the spline approximation of fields.

Mathematical Modelling in Engineering: A Proposal to Introduce Linear Algebra Concepts

Science.gov (United States)

Cárcamo Bahamonde, Andrea; Gómez Urgelles, Joan; Fortuny Aymemí, Josep

2016-01-01

The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasise the development of mathematical abilities primarily associated with modelling and interpreting, which are not exclusively calculus abilities. Considering this, an instructional design was created based on mathematical modelling and…

Mathematical modeling of a V-stack piezoelectric aileron actuation

Directory of Open Access Journals (Sweden)

Ioan URSU

2016-12-01

Full Text Available The article presents a mathematical modeling of aileron actuation that uses piezo V-shaped stacks. The aim of the actuation is the increasing of flutter speed in the context of a control law, in order to widen the flight envelope. In this way the main advantage of such a piezo actuator, the bandwidth is exploited. The mathematical model is obtained based on free body diagrams, and the numerical simulations allow a preliminary sizing of the actuator.

Meeting in mathematics

DEFF Research Database (Denmark)

Mogensen, Arne; Georgiev, Vladimir; Ulovec, Andreas

To encourage many more young people to appreciate the real nature and spirit of mathematics and possibly to be enrolled in mathematics study it is important to involve them in doing mathematics (not just learning about mathematics). This goal could be achieved if mathematics teachers are prepared...... to identify and work with mathematically gifted students (without loosing the rest). The book offers chapters on gifted students, mathematical competences and other issues....

Mathematical modelling and numerical simulation of forces in milling process

Science.gov (United States)

Turai, Bhanu Murthy; Satish, Cherukuvada; Prakash Marimuthu, K.

2018-04-01

Machining of the material by milling induces forces, which act on the work piece material, tool and which in turn act on the machining tool. The forces involved in milling process can be quantified, mathematical models help to predict these forces. A lot of research has been carried out in this area in the past few decades. The current research aims at developing a mathematical model to predict forces at different levels which arise machining of Aluminium6061 alloy. Finite element analysis was used to develop a FE model to predict the cutting forces. Simulation was done for varying cutting conditions. Different experiments was designed using Taguchi method. A L9 orthogonal array was designed and the output was measure for the different experiments. The same was used to develop the mathematical model.

Science Modelling in Pre-Calculus: How to Make Mathematics Problems Contextually Meaningful

Science.gov (United States)

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-01-01

"Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum" [National Council of Teachers of Mathematics (NCTM), "Principles and Standards for School Mathematics", NCTM, Reston, VA, 2000]. Commonly used pre-calculus textbooks provide a…

Influence of mathematical models in design of PV-Diesel systems

International Nuclear Information System (INIS)

Dufo-Lopez, Rodolfo; Bernal-Agustin, Jose L.

2008-01-01

This paper presents a study of the influence of mathematical models in the optimal design of PV-Diesel systems. For this purpose, a design tool developed by the authors, which allows obtaining the most cost effective design of a PV-Diesel system through the genetic algorithm technique, has been used. The mathematical models of some elements of the hybrid system have been improved in comparison to those usually employed in hybrid systems design programs. Furthermore, a more complete general control strategy has been developed, one that also takes into account more characteristics than those usually considered in this kind of design. Several designs have been made, evaluating the effect on the results of the different mathematical models and the novel strategy that can be considered

The prediction of epidemics through mathematical modeling.

Science.gov (United States)

Schaus, Catherine

2014-01-01

Mathematical models may be resorted to in an endeavor to predict the development of epidemics. The SIR model is one of the applications. Still too approximate, the use of statistics awaits more data in order to come closer to reality.

Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties

Science.gov (United States)

Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

2015-01-01

Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil’s Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children’s LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions. PMID:26090806

Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties.

Directory of Open Access Journals (Sweden)

Yinghui Lai

Full Text Available Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA and mathematical metacognition on word problem solving (WPS. We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56 with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA, typical achieving (TA, low achieving (LA, and mathematical learning difficulty (MLD. Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA than the TA and HA children, but not in mathematical evaluation anxiety (MEA. MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.

Effects of Mathematics Anxiety and Mathematical Metacognition on Word Problem Solving in Children with and without Mathematical Learning Difficulties.

Science.gov (United States)

Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun

2015-01-01

Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.

The Relationships among Pre-Service Mathematics Teachers' Beliefs about Mathematics, Mathematics Teaching, and Use of Technology in China

Science.gov (United States)

Yang, Xinrong; Leung, Frederick K. S.

2015-01-01

This paper investigated pre-service mathematics teachers' mathematics beliefs, beliefs about information and communication technology (ICT), and their relationships. 787 pre-service mathematics teachers in China completed a survey questionnaire measuring their beliefs about the nature of mathematics, beliefs about mathematics learning and…

Modularizing Remedial Mathematics

Science.gov (United States)

Wong, Aaron

2013-01-01

As remedial mathematics education has become an increasingly important topic of conversation in higher education. Mathematics departments have been put under increased pressure to change their programs to increase the student success rate. A number of models have been introduced over the last decade that represent a wide range of new ideas and…

Mathematical modeling of cancer metabolism.

Science.gov (United States)

Medina, Miguel Ángel

2018-04-01

Systemic approaches are needed and useful for the study of the very complex issue of cancer. Modeling has a central position in these systemic approaches. Metabolic reprogramming is nowadays acknowledged as an essential hallmark of cancer. Mathematical modeling could contribute to a better understanding of cancer metabolic reprogramming and to identify new potential ways of therapeutic intervention. Herein, I review several alternative approaches to metabolic modeling and their current and future impact in oncology. Copyright © 2018 Elsevier B.V. All rights reserved.

Mathematical Sciences Institute Workshop

CERN Document Server

Scott, Philip

1990-01-01

A so-called "effective" algorithm may require arbitrarily large finite amounts of time and space resources, and hence may not be practical in the real world. A "feasible" algorithm is one which only requires a limited amount of space and/or time for execution; the general idea is that a feasible algorithm is one which may be practical on today's or at least tomorrow's computers. There is no definitive analogue of Church's thesis giving a mathematical definition of feasibility; however, the most widely studied mathematical model of feasible computability is polynomial-time computability. Feasible Mathematics includes both the study of feasible computation from a mathematical and logical point of view and the reworking of traditional mathematics from the point of view of feasible computation. The diversity of Feasible Mathematics is illustrated by the. contents of this volume which includes papers on weak fragments of arithmetic, on higher type functionals, on bounded linear logic, on sub recursive definitions ...

Mathematics without boundaries surveys in pure mathematics

CERN Document Server

Pardalos, Panos

2014-01-01

The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the  latest information.

Pre-Service Teachers' Mathematics Self-Efficacy and Mathematics Teaching Self-Efficacy

Science.gov (United States)

Zuya, Habila Elisha; Kwalat, Simon Kevin; Attah, Bala Galle

2016-01-01

Pre-service mathematics teachers' mathematics self-efficacy and mathematics teaching self-efficacy were investigated in this study. The purpose was to determine the confidence levels of their self-efficacy in mathematics and mathematics teaching. Also, the study was aimed at finding whether their mathematics self-efficacy and teaching…

Mathematics Teachers' Perceptions of Their Students' Mathematical Competence: Relations to Mathematics Achievement, Affect, and Engagement in Singapore and Australia

Science.gov (United States)

Areepattamannil, Shaljan; Kaur, Berinderjeet

2013-01-01

This study, drawing on data from the Trends in International Mathematics and Science Study (TIMSS) 2011, examined whether mathematics teachers' perceptions of their students' mathematical competence were related to mathematics achievement, affect toward mathematics, and engagement in mathematics lessons among Grade 8 students in Singapore and…

Description of a comprehensive mathematical model

DEFF Research Database (Denmark)

Li, Xiyan; Yin, Chungen

2017-01-01

Biomass gasification is still a promising technology after over 30 years’ research and development and has success only in a few niche markets. In this paper, a comprehensive mathematical model for biomass particle gasification is developed within a generic particle framework, assuming the feed...

Mathematics education a spectrum of work in mathematical sciences departments

CERN Document Server

Hsu, Pao-sheng; Pollatsek, Harriet

2016-01-01

Many in the mathematics community in the U.S. are involved in mathematics education in various capacities. This book highlights the breadth of the work in K-16 mathematics education done by members of US departments of mathematical sciences. It contains contributions by mathematicians and mathematics educators who do work in areas such as teacher education, quantitative literacy, informal education, writing and communication, social justice, outreach and mentoring, tactile learning, art and mathematics, ethnomathematics, scholarship of teaching and learning, and mathematics education research. Contributors describe their work, its impact, and how it is perceived and valued. In addition, there is a chapter, co-authored by two mathematicians who have become administrators, on the challenges of supporting, evaluating, and rewarding work in mathematics education in departments of mathematical sciences. This book is intended to inform the readership of the breadth of the work and to encourage discussion of its val...

How Ordinary Meaning Underpins the Meaning of Mathematics.

Science.gov (United States)

Ormell, Christopher

1991-01-01

Discusses the meaning of mathematics by looking at its uses in the real world. Offers mathematical modeling as a way to represent mathematical applications in real or potential situations. Presents levels of applicability, modus operandi, relationship to "pure mathematics," and consequences for education for mathematical modeling. (MDH)

Solutions manual to accompany finite mathematics models and applications

CERN Document Server

Morris, Carla C

2015-01-01

A solutions manual to accompany Finite Mathematics: Models and Applications In order to emphasize the main concepts of each chapter, Finite Mathematics: Models and Applications features plentiful pedagogical elements throughout such as special exercises, end notes, hints, select solutions, biographies of key mathematicians, boxed key principles, a glossary of important terms and topics, and an overview of use of technology. The book encourages the modeling of linear programs and their solutions and uses common computer software programs such as LINDO. In addition to extensive chapters on pr

Improving Primary School Prospective Teachers' Understanding of the Mathematics Modeling Process

Science.gov (United States)

Bal, Aytgen Pinar; Doganay, Ahmet

2014-01-01

The development of mathematical thinking plays an important role on the solution of problems faced in daily life. Determining the relevant variables and necessary procedural steps in order to solve problems constitutes the essence of mathematical thinking. Mathematical modeling provides an opportunity for explaining thoughts in real life by making…

How to Build a Course in Mathematical-Biological Modeling: Content and Processes for Knowledge and Skill

Science.gov (United States)

Hoskinson, Anne-Marie

2010-01-01

Biological problems in the twenty-first century are complex and require mathematical insight, often resulting in mathematical models of biological systems. Building mathematical-biological models requires cooperation among biologists and mathematicians, and mastery of building models. A new course in mathematical modeling presented the opportunity…

Applying an alternative mathematics pedagogy for students with weak mathematics: meta-analysis of alternative pedagogies

Science.gov (United States)

Lake, Warren; Wallin, Margie; Woolcott, Geoff; Boyd, Wendy; Foster, Alan; Markopoulos, Christos; Boyd, William

2017-02-01

Student mathematics performance and the need for work-ready graduates to be mathematics-competent is a core issue for many universities. While both student and teacher are responsible for learning outcomes, there is a need to explicitly acknowledge the weak mathematics foundation of many university students. A systematic literature review was undertaken of identified innovations and/or interventions that may lead to improvement in student outcomes for university mathematics-based units of study. The review revealed the importance of understanding the foundations of student performance in higher education mathematics learning, especially in first year. Pre-university mathematics skills were identified as significant in student retention and mathematics success at university, and a specific focus on student pre-university mathematics skill level was found to be more effective in providing help, rather than simply focusing on a particular at-risk group. Diagnostics tools were found to be important in identifying (1) student background and (2) appropriate intervention. The studies highlighted the importance of appropriate and validated interventions in mathematics teaching and learning, and the need to improve the learning model for mathematics-based subjects, communication and technology innovations.

The role of mathematical models in understanding pattern formation in developmental biology.

Science.gov (United States)

Umulis, David M; Othmer, Hans G

2015-05-01

In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics-whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: "It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations." This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, "The laws of Nature are written in the language of mathematics[Formula: see text] the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word." Mathematics has moved beyond the geometry-based model of Galileo's time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837-838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades-that of how organisms can scale in size. Mathematical analysis alone cannot "solve" these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology.

Using Mathematics in Science: Working with Your Mathematics Department

Science.gov (United States)

Lyon, Steve

2014-01-01

Changes to the mathematics and science curriculums are designed to increase rigour in mathematics, and place greater emphasis on mathematical content in science subjects at key stages 3, 4 and 5 (ages 11-18). One way to meet the growing challenge of providing increased emphasis on mathematics in the science curriculum is greater collaboration…

Investigating and developing engineering students' mathematical modelling and problem-solving skills

Science.gov (United States)

Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven

2015-09-01

How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced problem solvers, unaware of the importance of understanding the problem and exploring alternatives, and impeded by inappropriate beliefs, attitudes and expectations. Important impacts of the course belong to the metacognitive domain. The nature of the problems, the supervision and the follow-up lectures were emphasised as contributing to the impacts of the course, where students show major development. We discuss these empirical results in relation to a framework for mathematical thinking and the notion of cognitive apprenticeship. Based on the results, we argue that this kind of teaching should be considered in the education of all engineers.

Mathematics and Measurement.

Science.gov (United States)

Boisvert, R F; Donahue, M J; Lozier, D W; McMichael, R; Rust, B W

2001-01-01

In this paper we describe the role that mathematics plays in measurement science at NIST. We first survey the history behind NIST's current work in this area, starting with the NBS Math Tables project of the 1930s. We then provide examples of more recent efforts in the application of mathematics to measurement science, including the solution of ill-posed inverse problems, characterization of the accuracy of software for micromagnetic modeling, and in the development and dissemination of mathematical reference data. Finally, we comment on emerging issues in measurement science to which mathematicians will devote their energies in coming years.

Mathematical human body modelling for impact loading

NARCIS (Netherlands)

Happee, R.; Morsink, P.L.J.; Wismans, J.S.H.M.

1999-01-01

Mathematical modelling of the human body is widely used for automotive crash safety research and design. Simulations have contributed to a reduction of injury numbers by optimisation of vehicle structures and restraint systems. Currently such simulations are largely performed using occupant models

Pneumatic Adaptive Absorber: Mathematical Modelling with Experimental Verification

Directory of Open Access Journals (Sweden)

Grzegorz Mikułowski

2016-01-01

Full Text Available Many of mechanical energy absorbers utilized in engineering structures are hydraulic dampers, since they are simple and highly efficient and have favourable volume to load capacity ratio. However, there exist fields of applications where a threat of toxic contamination with the hydraulic fluid contents must be avoided, for example, food or pharmacy industries. A solution here can be a Pneumatic Adaptive Absorber (PAA, which is characterized by a high dissipation efficiency and an inactive medium. In order to properly analyse the characteristics of a PAA, an adequate mathematical model is required. This paper proposes a concept for mathematical modelling of a PAA with experimental verification. The PAA is considered as a piston-cylinder device with a controllable valve incorporated inside the piston. The objective of this paper is to describe a thermodynamic model of a double chamber cylinder with gas migration between the inner volumes of the device. The specific situation considered here is that the process cannot be defined as polytropic, characterized by constant in time thermodynamic coefficients. Instead, the coefficients of the proposed model are updated during the analysis. The results of the experimental research reveal that the proposed mathematical model is able to accurately reflect the physical behaviour of the fabricated demonstrator of the shock absorber.

Mathematical modelling of tissue formation in chondrocyte filter cultures.

Science.gov (United States)

Catt, C J; Schuurman, W; Sengers, B G; van Weeren, P R; Dhert, W J A; Please, C P; Malda, J

2011-12-17

In the field of cartilage tissue engineering, filter cultures are a frequently used three-dimensional differentiation model. However, understanding of the governing processes of in vitro growth and development of tissue in these models is limited. Therefore, this study aimed to further characterise these processes by means of an approach combining both experimental and applied mathematical methods. A mathematical model was constructed, consisting of partial differential equations predicting the distribution of cells and glycosaminoglycans (GAGs), as well as the overall thickness of the tissue. Experimental data was collected to allow comparison with the predictions of the simulation and refinement of the initial models. Healthy mature equine chondrocytes were expanded and subsequently seeded on collagen-coated filters and cultured for up to 7 weeks. Resulting samples were characterised biochemically, as well as histologically. The simulations showed a good representation of the experimentally obtained cell and matrix distribution within the cultures. The mathematical results indicate that the experimental GAG and cell distribution is critically dependent on the rate at which the cell differentiation process takes place, which has important implications for interpreting experimental results. This study demonstrates that large regions of the tissue are inactive in terms of proliferation and growth of the layer. In particular, this would imply that higher seeding densities will not significantly affect the growth rate. A simple mathematical model was developed to predict the observed experimental data and enable interpretation of the principal underlying mechanisms controlling growth-related changes in tissue composition.

Workshop on Advanced Modelling in Mathematical Finance : in Honour of Ernst Eberlein

CERN Document Server

Papapantoleon, Antonis

2016-01-01

This Festschrift resulted from a workshop on “Advanced Modelling in Mathematical Finance” held in honour of Ernst Eberlein’s 70th birthday, from 20 to 22 May 2015 in Kiel, Germany. It includes contributions by several invited speakers at the workshop, including several of Ernst Eberlein’s long-standing collaborators and former students. Advanced mathematical techniques play an ever-increasing role in modern quantitative finance. Written by leading experts from academia and financial practice, this book offers state-of-the-art papers on the application of jump processes in mathematical finance, on term-structure modelling, and on statistical aspects of financial modelling. It is aimed at graduate students and researchers interested in mathematical finance, as well as practitioners wishing to learn about the latest developments.

ECONOMIC AND MATHEMATICAL MODELING INNOVATION SYSTEMS

Directory of Open Access Journals (Sweden)

D.V. Makarov

2014-06-01

Full Text Available The paper presents one of the mathematical tools for modeling innovation processes. With the help of Kondratieff long waves can define innovation cycles. However, complexity of the innovation system implies a qualitative description. The article describes the problems of this area of research.

Proposal of a pedagogical model for mathematics teacher education

Directory of Open Access Journals (Sweden)

Alfonso Jiménez Espinosa

2011-01-01

Full Text Available This research-based article reflects on mathematics teacher education, and proposes a pedagogical model for this purpose, called Gradual Research Pedagogical Model (MPGI. This model considers the central curricular elements of any academic education process: student, teacher and contents, with evaluation as transversal element for analysis and feedback. The training of future teachers is constituted by three moments, each with its specific emphasis: the first is “contextualization”, which aims at having the student understand his or her new academic role, and identify and overcome his or her academic weak points, the second is “knowledge foundation”, which offers basic education in the fields of mathematics and pedagogy, as well as sensibilization towards social issues, opening up the student’s possibilities as leader and agent of change, and lastly, “knowledge immersion”, which is centered on research and the identification and study of topics and problems of the mathematical discipline as well as the pedagogical field.

Computational mathematics and mathematical computer software. Vychislitel'naia matematika i matematicheskoe obespechenie EVM

Energy Technology Data Exchange (ETDEWEB)

Tikhonov, A.N.; Samarskii, A.A.

1985-01-01

Various aspects of mathematical modeling and problem-oriented computer software are examined with reference to numerical methods in mathematical physics, methods for solving inverse problems, development of automatic systems for experimental data processing, and mathematical modeling in plasma physics. Papers are presented on some properties of difference schemes in one-dimensional gas dynamics, an algorithm for processing signals reflected from multipoint targets, and the application of simplified Navier-Stokes equations for calculating flow of a viscous gas past long bodies.

Thermoregulation in premature infants: A mathematical model.

Science.gov (United States)

Pereira, Carina Barbosa; Heimann, Konrad; Czaplik, Michael; Blazek, Vladimir; Venema, Boudewijn; Leonhardt, Steffen

2016-12-01

In 2010, approximately 14.9 million babies (11.1%) were born preterm. Because preterm infants suffer from an immature thermoregulatory system they have difficulty maintaining their core body temperature at a constant level. Therefore, it is essential to maintain their temperature at, ideally, around 37°C. For this, mathematical models can provide detailed insight into heat transfer processes and body-environment interactions for clinical applications. A new multi-node mathematical model of the thermoregulatory system of newborn infants is presented. It comprises seven compartments, one spherical and six cylindrical, which represent the head, thorax, abdomen, arms and legs, respectively. The model is customizable, i.e. it meets individual characteristics of the neonate (e.g. gestational age, postnatal age, weight and length) which play an important role in heat transfer mechanisms. The model was validated during thermal neutrality and in a transient thermal environment. During thermal neutrality the model accurately predicted skin and core temperatures. The difference in mean core temperature between measurements and simulations averaged 0.25±0.21°C and that of skin temperature averaged 0.36±0.36°C. During transient thermal conditions, our approach simulated the thermoregulatory dynamics/responses. Here, for all infants, the mean absolute error between core temperatures averaged 0.12±0.11°C and that of skin temperatures hovered around 0.30°C. The mathematical model appears able to predict core and skin temperatures during thermal neutrality and in case of a transient thermal conditions. Copyright © 2016 Elsevier Ltd. All rights reserved.

Mathematical finance theory review and exercises from binomial model to risk measures

CERN Document Server

Gianin, Emanuela Rosazza

2013-01-01

The book collects over 120 exercises on different subjects of Mathematical Finance, including Option Pricing, Risk Theory, and Interest Rate Models. Many of the exercises are solved, while others are only proposed. Every chapter contains an introductory section illustrating the main theoretical results necessary to solve the exercises. The book is intended as an exercise textbook to accompany graduate courses in mathematical finance offered at many universities as part of degree programs in Applied and Industrial Mathematics, Mathematical Engineering, and Quantitative Finance.

The pragmatics of mathematics education vagueness and mathematical discourse

CERN Document Server

Rowland, Tim

2003-01-01

Drawing on philosophy of language and recent linguistic theory, Rowland surveys several approaches to classroom communication in mathematics. Are students intimidated by the nature of mathematics teaching? Many students appear fearful of voicing their understanding - is fear of error part of the linguistics of mathematics? The approaches explored here provide a rationale and a method for exploring and understanding speakers'' motives in classroom mathematics talk. Teacher-student interactions in mathematics are analysed, and this provides a toolkit that teachers can use to respond to the intellectual vulnerability of their students.

Mathematical Modeling of Column-Base Connections under Monotonic Loading

Directory of Open Access Journals (Sweden)

Gholamreza Abdollahzadeh

2014-12-01

Full Text Available Some considerable damage to steel structures during the Hyogo-ken Nanbu Earthquake occurred. Among them, many exposed-type column bases failed in several consistent patterns, such as brittle base plate fracture, excessive bolt elongation, unexpected early bolt failure, and inferior construction work, etc. The lessons from these phenomena led to the need for improved understanding of column base behavior. Joint behavior must be modeled when analyzing semi-rigid frames, which is associated with a mathematical model of the moment–rotation curve. The most accurate model uses continuous nonlinear functions. This article presents three areas of steel joint research: (1 analysis methods of semi-rigid joints; (2 prediction methods for the mechanical behavior of joints; (3 mathematical representations of the moment–rotation curve. In the current study, a new exponential model to depict the moment–rotation relationship of column base connection is proposed. The proposed nonlinear model represents an approach to the prediction of M–θ curves, taking into account the possible failure modes and the deformation characteristics of the connection elements. The new model has three physical parameters, along with two curve-fitted factors. These physical parameters are generated from dimensional details of the connection, as well as the material properties. The M–θ curves obtained by the model are compared with published connection tests and 3D FEM research. The proposed mathematical model adequately comes close to characterizing M–θ behavior through the full range of loading/rotations. As a result, modeling of column base connections using the proposed mathematical model can give crucial beforehand information, and overcome the disadvantages of time consuming workmanship and cost of experimental studies.

INTERSUBJECT CONNECTIONS OF COURSE OF MATHEMATICAL LOGIC AND OTHER MATHEMATICAL COURSES AT PREPARATION OF FUTURE TEACHER OF MATHEMATICS

Directory of Open Access Journals (Sweden)

Yu.I. Sinko

2012-03-01

Full Text Available In this article the interconnections of course of mathematical logic with other mathematical courses – geometry, algebra and theory of numbers, mathematical analysis, and also with the courses of mathematics teaching methodology, history of mathematics in the system of preparation of teachers of mathematics in pedagogical Institute of higher education are analyzed. The presence of connections between the elements of the system and their quality is the important description of the pedagogical system.

Mathematics Connection

African Journals Online (AJOL)

MATHEMATICS CONNECTION aims at providing a forum topromote the development of Mathematics Education in Ghana. Articles that seekto enhance the teaching and/or learning of mathematics at all levels of theeducational system are welcome.

Study on model of onset of nucleate boiling in natural circulation with subcooled boiling using unascertained mathematics

Energy Technology Data Exchange (ETDEWEB)

Zhou Tao [Department of Thermal Engineering, Tsinghua University, Beijing 100084 (China)]. E-mail: zhoutao@mail.tsinghua.edu.cn; Wang Zenghui [Department of Engineering Mechanics, Tsinghua University, Beijing 100084 (China); Yang Ruichang [Department of Thermal Engineering, Tsinghua University, Beijing 100084 (China)

2005-10-01

Experiment data got from onset of nucleate boiling (ONB) in natural circulation is analyzed using unascertained mathematics. Unitary mathematics model of the relation between the temperature and onset of nucleate boiling is built up to analysis ONB. Multiple unascertained mathematics models are also built up with the onset of natural circulation boiling equation based on the experiment. Unascertained mathematics makes that affirmative results are a range of numbers that reflect the fluctuation of experiment data more truly. The fluctuating value with the distribution function F(x) is the feature of unascertained mathematics model and can express fluctuating experimental data. Real status can be actually described through using unascertained mathematics. Thus, for calculation of ONB point, the description of unascertained mathematics model is more precise than common mathematics model. Based on the unascertained mathematics, a new ONB model is developed, which is important for advanced reactor safety analysis. It is conceivable that the unascertained mathematics could be applied to many other two-phase measurements as well.

Study on model of onset of nucleate boiling in natural circulation with subcooled boiling using unascertained mathematics

International Nuclear Information System (INIS)

Zhou Tao; Wang Zenghui; Yang Ruichang

2005-01-01

Experiment data got from onset of nucleate boiling (ONB) in natural circulation is analyzed using unascertained mathematics. Unitary mathematics model of the relation between the temperature and onset of nucleate boiling is built up to analysis ONB. Multiple unascertained mathematics models are also built up with the onset of natural circulation boiling equation based on the experiment. Unascertained mathematics makes that affirmative results are a range of numbers that reflect the fluctuation of experiment data more truly. The fluctuating value with the distribution function F(x) is the feature of unascertained mathematics model and can express fluctuating experimental data. Real status can be actually described through using unascertained mathematics. Thus, for calculation of ONB point, the description of unascertained mathematics model is more precise than common mathematics model. Based on the unascertained mathematics, a new ONB model is developed, which is important for advanced reactor safety analysis. It is conceivable that the unascertained mathematics could be applied to many other two-phase measurements as well

Mathematical Models for Immunology: Current State of the Art and Future Research Directions.

Science.gov (United States)

Eftimie, Raluca; Gillard, Joseph J; Cantrell, Doreen A

2016-10-01

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years.

Logistics of Mathematical Modeling-Focused Projects

Science.gov (United States)

Harwood, R. Corban

2018-01-01

This article addresses the logistics of implementing projects in an undergraduate mathematics class and is intended both for new instructors and for instructors who have had negative experiences implementing projects in the past. Project implementation is given for both lower- and upper-division mathematics courses with an emphasis on mathematical…

Mathematics Anxiety and Prevention Strategy: An Attempt to Support Students and Strengthen Mathematics Education

Directory of Open Access Journals (Sweden)

Aweke Shishigu

2018-02-01

Full Text Available In the process of reaching a medium income country, science, mathematics and technology have become an emphasis of Ethiopia. But, currently, students' interest to study mathematics and ability in mathematics is declining. This study therefore aimed to investigate the prevalence of mathematics anxiety and its effect on students' current mathematics achievement. Additionally, by grounding on the literature, some strategies supposed to reduce the negative effects of math anxiety were identified for practice. The study was conducted on five randomly selected public secondary schools of East Shoa Zone in Oromia region. Math anxiety was measured using a validated instrument called Math Anxiety Rating Scale (MARS, whereas students' current mathematics achievement was measured using achievement test. Structural model was developed to examine causal relationship of the variables treated in the study. The finding revealed that there was a significant negative relationship between mathematics anxiety and achievement. There was also a statistically significant gender difference in mathematics anxiety and current math achievement, with effect size small and typical respectively. Based on the findings of the study, imperative implication for practice and future research were made.

Uncertainty and Complexity in Mathematical Modeling

Science.gov (United States)

Cannon, Susan O.; Sanders, Mark

2017-01-01

Modeling is an effective tool to help students access mathematical concepts. Finding a math teacher who has not drawn a fraction bar or pie chart on the board would be difficult, as would finding students who have not been asked to draw models and represent numbers in different ways. In this article, the authors will discuss: (1) the properties of…

Mathematical model of three winding auto transformer

International Nuclear Information System (INIS)

Volcko, V.; Eleschova, Z.; Belan, A.; Janiga, P.

2012-01-01

This article deals with the design of mathematical model of three-winding auto transformer for steady state analyses. The article is focused on model simplicity for the purposes of the use in complex transmission systems and authenticity of the model taking into account different types of step-voltage regulator. (Authors)

Mathematical Modelling of Intraretinal Oxygen Partial Pressure ...

African Journals Online (AJOL)

Purpose: The aim of our present work is to develop a simple steady state model for intraretinal oxygen partial pressure distribution and to investigate the effect of various model parameters on the partial pressure distribution under adapted conditions of light and darkness.. Method: A simple eight-layered mathematical model ...

Educating mathematics teacher educators

DEFF Research Database (Denmark)

Højgaard, Tomas; Jankvist, Uffe Thomas

2014-01-01

The paper argues for a three-dimensional course design structure for future mathematics teacher educators. More precisely we describe the design and implementation of a course basing itself on: the two mathematical competencies of modelling and problem tackling, this being the first dimension......; the two mathematical topics of differential equations and stochastics, this being the second dimension; and finally a third dimension the purpose of which is to deepen the two others by means of a didactical perspective....

The Conceptualization of the Mathematical Modelling Process in Technology-Aided Environment

Science.gov (United States)

Hidiroglu, Çaglar Naci; Güzel, Esra Bukova

2017-01-01

The aim of the study is to conceptualize the technology-aided mathematical modelling process in the frame of cognitive modelling perspective. The grounded theory approach was adopted in the study. The research was conducted with seven groups consisting of nineteen prospective mathematics teachers. The data were collected from the video records of…

VEDIC MATHEMATICS

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Sead Rešić

2015-09-01

Full Text Available It is very difficult to motivate students when it comes to a school subject like Mathematics. Teachers spend a lot of time trying to find something that will arouse interest in students. It is particularly difficult to find materials that are motivating enough for students that they eagerly wait for the next lesson. One of the solutions may be found in Vedic Mathematics. Traditional methods of teaching Mathematics create fear of this otherwise interesting subject in the majority of students. Fear increases failure. Often the traditional, conventional mathematical methods consist of very long lessons which are difficult to understand. Vedic Mathematics is an ancient system that is very flexible and encourages the development of intuition and innovation. It is a mental calculating tool that does not require a calculator because the calculator is embedded in each of us. Starting from the above problems of fear and failure in Mathematics, the goal of this paper is to do research with the control and the experimental group and to compare the test results. Two tests should be done for each of the groups. The control group would do the tests in the conventional way. The experimental group would do the first test in a conventional manner and then be subjected to different treatment, that is to say, be taught on the basis of Vedic Mathematics. After that, the second group would do the second test according to the principles of Vedic Mathematics. Expectations are that after short lectures on Vedic mathematics results of the experimental group would improve and that students will show greater interest in Mathematics.

Development of Mathematics Learning Strategy Module, Based on Higher Order Thinking Skill (Hots) To Improve Mathematic Communication And Self Efficacy On Students Mathematics Department

Science.gov (United States)

Andriani, Ade; Dewi, Izwita; Halomoan, Budi

2018-03-01

In general, this research is conducted to improve the quality of lectures on mathematics learning strategy in Mathematics Department. The specific objective of this research is to develop learning instrument of mathematics learning strategy based on Higher Order Thinking Skill (HOTS) that can be used to improve mathematical communication and self efficacy of mathematics education students. The type of research is development research (Research & Development), where this research aims to develop a new product or improve the product that has been made. This development research refers to the four-D Model, which consists of four stages: defining, designing, developing, and disseminating. The instrument of this research is the validation sheet and the student response sheet of the instrument.

Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century.

Science.gov (United States)

Ganusov, Vitaly V

2016-01-01

While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest "strong inference in mathematical modeling" as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century.

Strong inference in mathematical modeling: a method for robust science in the 21st century

Directory of Open Access Journals (Sweden)

Vitaly V. Ganusov

2016-07-01

Full Text Available While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers [1], the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions and data. Following the principle of strong inference for experimental sciences proposed by Platt [2], I suggest ``strong inference in mathematical modeling'' as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are 1 to develop multiple alternative models for the phenomenon in question; 2 to compare the models with available experimental data and to determine which of the models are not consistent with the data; 3 to determine reasons why rejected models failed to explain the data, and 4 to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the 21st century.

The Magic of Mathematics Discovering the Spell of Mathematics

CERN Document Server

Pappas, Theoni

2011-01-01

Delves into the world of ideas, explores the spell mathematics casts on our lives, and helps you discover mathematics where you least expect it. Be spellbound by the mathematical designs found in nature. Learn how knots may untie the mysteries of life. Be mesmerized by the computer revolution. Discover how the hidden forces of mathematics hold architectural structures together connect your telephone calls help airplanes get off the ground solve the mysteries of the living cell. See how some artists use a mathematical palette in their works and how many writers draw upon the wealth of its ideas

Long-term development of how students interpret a model; Complementarity of contexts and mathematics

NARCIS (Netherlands)

Vos, Pauline; Roorda, Gerrit; Stillman, Gloria Ann; Blum, Werner; Kaiser, Gabriele

2017-01-01

When students engage in rich mathematical modelling tasks, they have to handle real-world contexts and mathematics in chorus. This is not easy. In this chapter, contexts and mathematics are perceived as complementary, which means they can be integrated. Based on four types of approaches to modelling

Critical Mathematics education: Past, present and future

DEFF Research Database (Denmark)

contribution to the shaping of those concerns in the international community of mathematics educators and mathematics education researchers. This book gathers contributions of researchers from five continents, for whom critical mathematics education has been an inspiration to think about many different topics...... such as the dialogical and political dimensions of teacher education, mathematical modeling, the philosophy of mathematics from social and political perspectives, teaching practices in classrooms, the connection between mathematics and society, the scope and limits of critical thinking in relation to mathematics......Critical mathematics education brings together a series of concerns related to mathematics and its role in society, the practices of teaching and learning of mathematics in educational settings, and the practices of researching mathematics education. The work of Ole Skovsmose has provided a seminal...

Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century

Science.gov (United States)

Ganusov, Vitaly V.

2016-01-01

While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest “strong inference in mathematical modeling” as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century. PMID:27499750