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Sample records for mathematical model consisting

  1. Teaching Mathematical Modeling in Mathematics Education

    Science.gov (United States)

    Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

    2016-01-01

    Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…

  2. 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...

  3. 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.

  4. 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

  5. A comprehensive, consistent and systematic mathematical model of PEM fuel cells

    International Nuclear Information System (INIS)

    Baschuk, J.J.; Li Xianguo

    2009-01-01

    This paper presents a comprehensive, consistent and systematic mathematical model for PEM fuel cells that can be used as the general formulation for the simulation and analysis of PEM fuel cells. As an illustration, the model is applied to an isothermal, steady state, two-dimensional PEM fuel cell. Water is assumed to be in either the gas phase or as a liquid phase in the pores of the polymer electrolyte. The model includes the transport of gas in the gas flow channels, electrode backing and catalyst layers; the transport of water and hydronium in the polymer electrolyte of the catalyst and polymer electrolyte layers; and the transport of electrical current in the solid phase. Water and ion transport in the polymer electrolyte was modeled using the generalized Stefan-Maxwell equations, based on non-equilibrium thermodynamics. Model simulations show that the bulk, convective gas velocity facilitates hydrogen transport from the gas flow channels to the anode catalyst layers, but inhibits oxygen transport. While some of the water required by the anode is supplied by the water produced in the cathode, the majority of water must be supplied by the anode gas phase, making operation with fully humidified reactants necessary. The length of the gas flow channel has a significant effect on the current production of the PEM fuel cell, with a longer channel length having a lower performance relative to a shorter channel length. This lower performance is caused by a greater variation in water content within the longer channel length

  6. 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…

  7. Mathematical modelling

    DEFF Research Database (Denmark)

    Blomhøj, Morten

    2004-01-01

    Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...

  8. 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

  9. 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.

  10. 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.

  11. Mathematical Modeling and Pure Mathematics

    Science.gov (United States)

    Usiskin, Zalman

    2015-01-01

    Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

  12. 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.

  13. Mathematical Modelling Approach in Mathematics Education

    Science.gov (United States)

    Arseven, Ayla

    2015-01-01

    The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

  14. 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 ...

  15. Mathematical modelling

    CERN Document Server

    2016-01-01

    This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.

  16. From virtual clustering analysis to self-consistent clustering analysis: a mathematical study

    Science.gov (United States)

    Tang, Shaoqiang; Zhang, Lei; Liu, Wing Kam

    2018-03-01

    In this paper, we propose a new homogenization algorithm, virtual clustering analysis (VCA), as well as provide a mathematical framework for the recently proposed self-consistent clustering analysis (SCA) (Liu et al. in Comput Methods Appl Mech Eng 306:319-341, 2016). In the mathematical theory, we clarify the key assumptions and ideas of VCA and SCA, and derive the continuous and discrete Lippmann-Schwinger equations. Based on a key postulation of "once response similarly, always response similarly", clustering is performed in an offline stage by machine learning techniques (k-means and SOM), and facilitates substantial reduction of computational complexity in an online predictive stage. The clear mathematical setup allows for the first time a convergence study of clustering refinement in one space dimension. Convergence is proved rigorously, and found to be of second order from numerical investigations. Furthermore, we propose to suitably enlarge the domain in VCA, such that the boundary terms may be neglected in the Lippmann-Schwinger equation, by virtue of the Saint-Venant's principle. In contrast, they were not obtained in the original SCA paper, and we discover these terms may well be responsible for the numerical dependency on the choice of reference material property. Since VCA enhances the accuracy by overcoming the modeling error, and reduce the numerical cost by avoiding an outer loop iteration for attaining the material property consistency in SCA, its efficiency is expected even higher than the recently proposed SCA algorithm.

  17. Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics

    Science.gov (United States)

    Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.

    2016-01-01

    Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…

  18. 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

  19. 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...

  20. A consistent modelling methodology for secondary settling tanks in wastewater treatment.

    Science.gov (United States)

    Bürger, Raimund; Diehl, Stefan; Nopens, Ingmar

    2011-03-01

    The aim of this contribution is partly to build consensus on a consistent modelling methodology (CMM) of complex real processes in wastewater treatment by combining classical concepts with results from applied mathematics, and partly to apply it to the clarification-thickening process in the secondary settling tank. In the CMM, the real process should be approximated by a mathematical model (process model; ordinary or partial differential equation (ODE or PDE)), which in turn is approximated by a simulation model (numerical method) implemented on a computer. These steps have often not been carried out in a correct way. The secondary settling tank was chosen as a case since this is one of the most complex processes in a wastewater treatment plant and simulation models developed decades ago have no guarantee of satisfying fundamental mathematical and physical properties. Nevertheless, such methods are still used in commercial tools to date. This particularly becomes of interest as the state-of-the-art practice is moving towards plant-wide modelling. Then all submodels interact and errors propagate through the model and severely hamper any calibration effort and, hence, the predictive purpose of the model. The CMM is described by applying it first to a simple conversion process in the biological reactor yielding an ODE solver, and then to the solid-liquid separation in the secondary settling tank, yielding a PDE solver. Time has come to incorporate established mathematical techniques into environmental engineering, and wastewater treatment modelling in particular, and to use proven reliable and consistent simulation models. Copyright © 2011 Elsevier Ltd. All rights reserved.

  1. Mathematical modeling

    CERN Document Server

    Eck, Christof; Knabner, Peter

    2017-01-01

    Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.

  2. 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...

  3. 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...

  4. 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)

  5. 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.

  6. Mathematical modelling techniques

    CERN Document Server

    Aris, Rutherford

    1995-01-01

    ""Engaging, elegantly written."" - Applied Mathematical ModellingMathematical modelling is a highly useful methodology designed to enable mathematicians, physicists and other scientists to formulate equations from a given nonmathematical situation. In this elegantly written volume, a distinguished theoretical chemist and engineer sets down helpful rules not only for setting up models but also for solving the mathematical problems they pose and for evaluating models.The author begins with a discussion of the term ""model,"" followed by clearly presented examples of the different types of mode

  7. Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

    Science.gov (United States)

    Mumcu, Hayal Yavuz

    2016-01-01

    The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

  8. Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

    Science.gov (United States)

    Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem

    2014-01-01

    Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…

  9. 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...

  10. MATHEMATICAL MODEL MANIPULATOR ROBOTS

    Directory of Open Access Journals (Sweden)

    O. N. Krakhmalev

    2015-12-01

    Full Text Available A mathematical model to describe the dynamics of manipulator robots. Mathematical model are the implementation of the method based on the Lagrange equation and using the transformation matrices of elastic coordinates. Mathematical model make it possible to determine the elastic deviations of manipulator robots from programmed motion trajectories caused by elastic deformations in hinges, which are taken into account in directions of change of the corresponding generalized coordinates. Mathematical model is approximated and makes it possible to determine small elastic quasi-static deviations and elastic vibrations. The results of modeling the dynamics by model are compared to the example of a two-link manipulator system. The considered model can be used when performing investigations of the mathematical accuracy of the manipulator robots.

  11. Thermodynamically consistent mesoscopic model of the ferro/paramagnetic transition

    Czech Academy of Sciences Publication Activity Database

    Benešová, Barbora; Kružík, Martin; Roubíček, Tomáš

    2013-01-01

    Roč. 64, Č. 1 (2013), s. 1-28 ISSN 0044-2275 R&D Projects: GA AV ČR IAA100750802; GA ČR GA106/09/1573; GA ČR GAP201/10/0357 Grant - others:GA ČR(CZ) GA106/08/1397; GA MŠk(CZ) LC06052 Program:GA; LC Institutional support: RVO:67985556 Keywords : ferro-para-magnetism * evolution * thermodynamics Subject RIV: BA - General Mathematics; BA - General Mathematics (UT-L) Impact factor: 1.214, year: 2013 http://library.utia.cas.cz/separaty/2012/MTR/kruzik-thermodynamically consistent mesoscopic model of the ferro-paramagnetic transition.pdf

  12. 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.

  13. 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.

  14. 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...

  15. 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…

  16. Developing mathematical modelling competence

    DEFF Research Database (Denmark)

    Blomhøj, Morten; Jensen, Tomas Højgaard

    2003-01-01

    In this paper we introduce the concept of mathematical modelling competence, by which we mean being able to carry through a whole mathematical modelling process in a certain context. Analysing the structure of this process, six sub-competences are identified. Mathematical modelling competence...... cannot be reduced to these six sub-competences, but they are necessary elements in the development of mathematical modelling competence. Experience from the development of a modelling course is used to illustrate how the different nature of the sub-competences can be used as a tool for finding...... the balance between different kinds of activities in a particular educational setting. Obstacles of social, cognitive and affective nature for the students' development of mathematical modelling competence are reported and discussed in relation to the sub-competences....

  17. Consistent three-equation model for thin films

    Science.gov (United States)

    Richard, Gael; Gisclon, Marguerite; Ruyer-Quil, Christian; Vila, Jean-Paul

    2017-11-01

    Numerical simulations of thin films of newtonian fluids down an inclined plane use reduced models for computational cost reasons. These models are usually derived by averaging over the fluid depth the physical equations of fluid mechanics with an asymptotic method in the long-wave limit. Two-equation models are based on the mass conservation equation and either on the momentum balance equation or on the work-energy theorem. We show that there is no two-equation model that is both consistent and theoretically coherent and that a third variable and a three-equation model are required to solve all theoretical contradictions. The linear and nonlinear properties of two and three-equation models are tested on various practical problems. We present a new consistent three-equation model with a simple mathematical structure which allows an easy and reliable numerical resolution. The numerical calculations agree fairly well with experimental measurements or with direct numerical resolutions for neutral stability curves, speed of kinematic waves and of solitary waves and depth profiles of wavy films. The model can also predict the flow reversal at the first capillary trough ahead of the main wave hump.

  18. 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.

  19. 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.

  20. An Equivalent Electrical Circuit Model of Proton Exchange Membrane Fuel Cells Based on Mathematical Modelling

    Directory of Open Access Journals (Sweden)

    Dinh An Nguyen

    2012-07-01

    Full Text Available Many of the Proton Exchange Membrane Fuel Cell (PEMFC models proposed in the literature consist of mathematical equations. However, they are not adequately practical for simulating power systems. The proposed model takes into account phenomena such as activation polarization, ohmic polarization, double layer capacitance and mass transport effects present in a PEM fuel cell. Using electrical analogies and a mathematical modeling of PEMFC, the circuit model is established. To evaluate the effectiveness of the circuit model, its static and dynamic performances under load step changes are simulated and compared to the numerical results obtained by solving the mathematical model. Finally, the applicability of our model is demonstrated by simulating a practical system.

  1. 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...

  2. Mathematical Modeling Using MATLAB

    National Research Council Canada - National Science Library

    Phillips, Donovan

    1998-01-01

    .... Mathematical Modeling Using MA MATLAB acts as a companion resource to A First Course in Mathematical Modeling with the goal of guiding the reader to a fuller understanding of the modeling process...

  3. 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.

  4. STP: A mathematically and physically consistent library of steam properties

    International Nuclear Information System (INIS)

    Aguilar, F.; Hutter, A.C.; Tuttle, P.G.

    1982-01-01

    A new FORTRAN library of subroutines has been developed from the fundamental equation of Keenan et al. to evaluate a large set of water properties including derivatives such as sound speed and isothermal compressibility. The STP library uses the true saturation envelope of the Keenan et al. fundamental equation. The evaluation of the true envelope by a continuation method is explained. This envelope, along with other design features, imparts an exceptionally high degree of thermodynamic and mathematical consistency to the STP library, even at the critical point. Accuracy and smoothness, library self-consistency, and designed user convenience make the STP library a reliable and versatile water property package

  5. Mathematical and physical models and radiobiology

    International Nuclear Information System (INIS)

    Lokajicek, M.

    1980-01-01

    The hit theory of the mechanism of biological radiation effects in the cell is discussed with respect to radiotherapy. The mechanisms of biological effects and of intracellular recovery, the cumulative radiation effect and the cumulative biological effect in fractionated irradiation are described. The benefit is shown of consistent application of mathematical and physical models in radiobiology and radiotherapy. (J.P.)

  6. Mathematical Modeling: A Structured Process

    Science.gov (United States)

    Anhalt, Cynthia Oropesa; Cortez, Ricardo

    2015-01-01

    Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…

  7. 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.

  8. Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling

    Science.gov (United States)

    Karali, Diren; Durmus, Soner

    2015-01-01

    The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…

  9. A simple mathematical model of society collapse applied to Easter Island

    Science.gov (United States)

    Bologna, M.; Flores, J. C.

    2008-02-01

    In this paper we consider a mathematical model for the evolution and collapse of the Easter Island society. Based on historical reports, the available primary resources consisted almost exclusively in the trees, then we describe the inhabitants and the resources as an isolated dynamical system. A mathematical, and numerical, analysis about the Easter Island community collapse is performed. In particular, we analyze the critical values of the fundamental parameters and a demographic curve is presented. The technological parameter, quantifying the exploitation of the resources, is calculated and applied to the case of another extinguished civilization (Copán Maya) confirming the consistency of the adopted model.

  10. 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.

  11. Modeling stability of growth between mathematics and science achievement during middle and high school.

    Science.gov (United States)

    Ma, Xin; Ma, Lingling

    2004-04-01

    In this study, the authors introduced a multivariate multilevel model to estimate the consistency among students and schools in the rates of growth between mathematics and science achievement during the entire middle and high school years with data from the Longitudinal Study of American Youth (LSAY). There was no evident consistency in the rates of growth between mathematics and science achievement among students, and this inconsistency was not much influenced by student characteristics and school characteristics. However, there was evident consistency in the average rates of growth between mathematics and science achievement among schools, and this consistency was influenced by student characteristics and school characteristics. Major school-level variables associated with parental involvement did not show any significant impacts on consistency among either students or schools. Results call for educational policies that promote collaboration between mathematics and science departments or teachers.

  12. 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…

  13. Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.

    Science.gov (United States)

    Suppes, Patrick

    This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…

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

    Directory of Open Access Journals (Sweden)

    Edwin Musdi

    2016-02-01

    Full Text Available 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, characteristics of learners, learning management descriptions by junior high school mathematics teacher and relevant research. The development phase is done by developing a draft model (an early prototype model that consists of the syntax, the social system, the principle of reaction, support systems, and the impact and effects of instructional support. Early prototype model contain a draft model, lesson plans, worksheets, and assessments. Tesssmer formative evaluation model used to revise the model. In this study only phase of one to one evaluation conducted. In the ppreliminary phase has produced a theory-based learning RME model, a description of the characteristics of learners in grade VIII Junior High School Padang and the description of teacher teaching in the classroom. The result showed that most students were still not be able to solve the non-routine problem. Teachers did not optimally facilitate students to develop problem-solving skills of students. It was recommended that the model can be applied in the classroom.

  15. 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...

  16. An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers

    Science.gov (United States)

    Thrasher, Emily Plunkett

    2016-01-01

    The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…

  17. 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…

  18. 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

  19. Mathematical Modelling in the Junior Secondary Years: An Approach Incorporating Mathematical Technology

    Science.gov (United States)

    Lowe, James; Carter, Merilyn; Cooper, Tom

    2018-01-01

    Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…

  20. 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…

  1. 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…

  2. Toward a consistent model for glass dissolution

    International Nuclear Information System (INIS)

    Strachan, D.M.; McGrail, B.P.; Bourcier, W.L.

    1994-01-01

    Understanding the process of glass dissolution in aqueous media has advanced significantly over the last 10 years through the efforts of many scientists around the world. Mathematical models describing the glass dissolution process have also advanced from simple empirical functions to structured models based on fundamental principles of physics, chemistry, and thermodynamics. Although borosilicate glass has been selected as the waste form for disposal of high-level wastes in at least 5 countries, there is no international consensus on the fundamental methodology for modeling glass dissolution that could be used in assessing the long term performance of waste glasses in a geologic repository setting. Each repository program is developing their own model and supporting experimental data. In this paper, we critically evaluate a selected set of these structured models and show that a consistent methodology for modeling glass dissolution processes is available. We also propose a strategy for a future coordinated effort to obtain the model input parameters that are needed for long-term performance assessments of glass in a geologic repository. (author) 4 figs., tabs., 75 refs

  3. Precipitation of metal sulphides using gaseous hydrogen sulphide: mathematical modelling

    NARCIS (Netherlands)

    Al Tarazi, M.Y.M.; Heesink, Albertus B.M.; Versteeg, Geert

    2004-01-01

    A mathematical model has been developed that describes the precipitation of metal sulffides in an aqueous solution containing two different heavy metal ions. The solution is assumed to consist of a well-mixed bulk and a boundary layer that is contacted with hydrogen sulphide gas. The model makes use

  4. Precipitation of metal sulphides using gaseous hydrogen sulphide : mathematical modelling

    NARCIS (Netherlands)

    Tarazi, Mousa Al-; Heesink, A. Bert M.; Versteeg, Geert F.

    2004-01-01

    A mathematical model has been developed that describes the precipitation of metal sulphides in an aqueous solution containing two different heavy metal ions. The solution is assumed to consist of a well-mixed bulk and a boundary layer that is contacted with hydrogen sulphide gas. The model makes use

  5. The Development of the Assessment for Learning Model of Mathematics for Rajamangala University of Technology Rattanakosin

    Directory of Open Access Journals (Sweden)

    Wannaree Pansiri

    2016-12-01

    Full Text Available The objectives of this research were 1 to develop the assessment for learning model of Mathematics for Rajamangala University 2 to study the effectivness of assessment for learning model of Mathematics for Rajamagala University of Technology Rattanakosin. The research target group consisted of 72 students from 3 classes and 3 General Mathematics teachers. The data was gathered from observation, worksheets, achievement test and skill of assessment for learning, questionnaire of the assessment for learning model of Mathematics. The statistics that used in this research were Frequency, Percentage, Mean, Standard Deviation, and Growth Score. The results of this research were 1. The assessment of learning model of Mathematics for Rajamangala University of Technology Rattanakosin consisted of 3 components ; 1. Pre-assessment which consisted of 4 activities ; a Preparation b Teacher development c Design and creation the assessment plan and instrument for assessment and d Creation of the learning experience plan 2. The component for assessment process consisted of 4 steps which were a Identifying the learning objectives and criteria b Identifying the learning experience plan and assessment follow the plan c Learning reflection and giving feedback and d Learner development based on information and improve instruction and 3. Giving feedback component. 2. The effective of assessment for learning model found that most students had good score in concentration, honest, responsibilities, group work, task presentation, worksheets, and doing exercises. The development knowledge of learning and knowledge and skill of assessment for learning of lecturers were fairly good. The opinion to the assessment for learning of learners and assessment for learning model of Mathematics of teachers found that was in a good level.

  6. Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics

    Science.gov (United States)

    Wickstrom, Megan H.

    2017-01-01

    This article is a report on a teacher study group that focused on three elementary teachers' perceptions of mathematical modeling in contrast to typical mathematics instruction. Through the theoretical lens of figured worlds, I discuss how mathematics instruction was conceptualized across the classrooms in terms of artifacts, discourse, and…

  7. Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape

    Science.gov (United States)

    Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.

    2014-01-01

    This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…

  8. Topologically Consistent Models for Efficient Big Geo-Spatio Data Distribution

    Science.gov (United States)

    Jahn, M. W.; Bradley, P. E.; Doori, M. Al; Breunig, M.

    2017-10-01

    Geo-spatio-temporal topology models are likely to become a key concept to check the consistency of 3D (spatial space) and 4D (spatial + temporal space) models for emerging GIS applications such as subsurface reservoir modelling or the simulation of energy and water supply of mega or smart cities. Furthermore, the data management for complex models consisting of big geo-spatial data is a challenge for GIS and geo-database research. General challenges, concepts, and techniques of big geo-spatial data management are presented. In this paper we introduce a sound mathematical approach for a topologically consistent geo-spatio-temporal model based on the concept of the incidence graph. We redesign DB4GeO, our service-based geo-spatio-temporal database architecture, on the way to the parallel management of massive geo-spatial data. Approaches for a new geo-spatio-temporal and object model of DB4GeO meeting the requirements of big geo-spatial data are discussed in detail. Finally, a conclusion and outlook on our future research are given on the way to support the processing of geo-analytics and -simulations in a parallel and distributed system environment.

  9. 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…

  10. 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…

  11. 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

  12. 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…

  13. 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.

  14. Mathematical model for spreading dynamics of social network worms

    International Nuclear Information System (INIS)

    Sun, Xin; Liu, Yan-Heng; Han, Jia-Wei; Liu, Xue-Jie; Li, Bin; Li, Jin

    2012-01-01

    In this paper, a mathematical model for social network worm spreading is presented from the viewpoint of social engineering. This model consists of two submodels. Firstly, a human behavior model based on game theory is suggested for modeling and predicting the expected behaviors of a network user encountering malicious messages. The game situation models the actions of a user under the condition that the system may be infected at the time of opening a malicious message. Secondly, a social network accessing model is proposed to characterize the dynamics of network users, by which the number of online susceptible users can be determined at each time step. Several simulation experiments are carried out on artificial social networks. The results show that (1) the proposed mathematical model can well describe the spreading dynamics of social network worms; (2) weighted network topology greatly affects the spread of worms; (3) worms spread even faster on hybrid social networks

  15. 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,…

  16. Mathematical and numerical modelling of fluids at Nano-metric scales

    International Nuclear Information System (INIS)

    Joubaud, R.

    2012-01-01

    This work presents some contributions to the mathematical and numerical modelling of fluids at Nano-metric scales. We are interested in two levels of modelling. The first level consists in an atomic description. We consider the problem of computing the shear viscosity of a fluid from a microscopic description. More precisely, we study the mathematical properties of the nonequilibrium Langevin dynamics allowing to compute the shear viscosity. The second level of description is a continuous description, and we consider a class of continuous models for equilibrium electrolytes, which incorporate on the one hand a confinement by charged solid objects and on the other hand non-ideality effects stemming from electrostatic correlations and steric exclusion phenomena due to the excluded volume effects. First, we perform the mathematical analysis of the case where the free energy is a convex function (mild non-ideality). Second, we consider numerically the case where the free energy is a non convex function (strong non-ideality) leading in particular to phase separation. (author)

  17. 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.

  18. 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.

  19. A mathematical model of crevice and pitting corrosion

    International Nuclear Information System (INIS)

    Sharland, S.M.; Tasker, P.W.

    1985-09-01

    A predictive and self-consistent mathematical model incorporating the electrochemical, chemical and ionic migration processes characterising crevice and pitting corrosion is described. The model predicts full details of the steady-state solution chemistry and electrode kinetics (and hence metal penetration rates) within the corrosion cavities as functions of the many parameters on which these depend such as external electrode potential and crevice dimensions. The crevice is modelled as a parallel-sided slot filled with a dilute sodium chloride solution. Corrosion in both one and two directions is considered. The model includes a solid hydroxide precipitation reaction and assesses the effect on the corrosion rates of consequent changes in the chemical and physical environment within the crevice. A time stepping method is developed for the study of the progression of the corrosion with a precipitation reaction included and is applied to a restricted range of parameters. The applicability of this method is justified in relation to the physical and mathematical approximations made during the construction of the model. (author)

  20. Consistent model driven architecture

    Science.gov (United States)

    Niepostyn, Stanisław J.

    2015-09-01

    The goal of the MDA is to produce software systems from abstract models in a way where human interaction is restricted to a minimum. These abstract models are based on the UML language. However, the semantics of UML models is defined in a natural language. Subsequently the verification of consistency of these diagrams is needed in order to identify errors in requirements at the early stage of the development process. The verification of consistency is difficult due to a semi-formal nature of UML diagrams. We propose automatic verification of consistency of the series of UML diagrams originating from abstract models implemented with our consistency rules. This Consistent Model Driven Architecture approach enables us to generate automatically complete workflow applications from consistent and complete models developed from abstract models (e.g. Business Context Diagram). Therefore, our method can be used to check practicability (feasibility) of software architecture models.

  1. 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...

  2. An upper limb mathematical model of an oil palm harvester

    Science.gov (United States)

    Tumit, N. P.; Rambely, A. S.; BMT, Shamsul; Shahriman A., B.; Ng Y., G.; Deros, B. M.; Zailina, H.; Goh, Y. M.; Arumugam, Manohar; Ismail, I. A.; Abdul Hafiz A., R.

    2014-09-01

    The main purpose of this article is to develop a mathematical model of human body during harvesting via Kane's method. In this paper, a 2-D closed-kinematic biomechanical model that represents a harvesting movement is developed. The model of six segments consisted of upper right arm, right forearm, harvesting equipment, left forearm, upper left arm, and upper part of trunk. Finally, the inverse dynamic equations are represented in matrix form.

  3. Mathematical modeling of microbial growth in milk

    Directory of Open Access Journals (Sweden)

    Jhony Tiago Teleken

    2011-12-01

    Full Text Available A mathematical model to predict microbial growth in milk was developed and analyzed. The model consists of a system of two differential equations of first order. The equations are based on physical hypotheses of population growth. The model was applied to five different sets of data of microbial growth in dairy products selected from Combase, which is the most important database in the area with thousands of datasets from around the world, and the results showed a good fit. In addition, the model provides equations for the evaluation of the maximum specific growth rate and the duration of the lag phase which may provide useful information about microbial growth.

  4. Developing calculus textbook model that supported with GeoGebra to enhancing students’ mathematical problem solving and mathematical representation

    Science.gov (United States)

    Dewi, N. R.; Arini, F. Y.

    2018-03-01

    The main purpose of this research is developing and produces a Calculus textbook model that supported with GeoGebra. This book was designed to enhancing students’ mathematical problem solving and mathematical representation. There were three stages in this research i.e. define, design, and develop. The textbooks consisted of 6 chapters which each chapter contains introduction, core materials and include examples and exercises. The textbook developed phase begins with the early stages of designed the book (draft 1) which then validated by experts. Revision of draft 1 produced draft 2. The data were analyzed with descriptive statistics. The analysis showed that the Calculus textbook model that supported with GeoGebra, valid and fill up the criteria of practicality.

  5. 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

  6. 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…

  7. 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…

  8. 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…

  9. 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…

  10. Multimodal Languaging as a Pedagogical Model--A Case Study of the Concept of Division in School Mathematics

    Science.gov (United States)

    Joutsenlahti, Jorma; Kulju, Pirjo

    2017-01-01

    The purpose of this study is to present a multimodal languaging model for mathematics education. The model consists of mathematical symbolic language, a pictorial language, and a natural language. By applying this model, the objective was to study how 4th grade pupils (N = 21) understand the concept of division. The data was collected over six…

  11. 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.

  12. 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.

  13. 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.

  14. 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.

  15. A theory of drug tolerance and dependence II: the mathematical model.

    Science.gov (United States)

    Peper, Abraham

    2004-08-21

    The preceding paper presented a model of drug tolerance and dependence. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a regulated adaptive process. The oral detection and analysis of exogenous substances is proposed to be the primary stimulus for the mechanism of drug tolerance. Anticipation and environmental cues are in the model considered secondary stimuli, becoming primary in dependence and addiction or when the drug administration bypasses the natural-oral-route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomous tolerance processes. Simulations with the mathematical model demonstrate the model's behaviour to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. The present paper discusses the mathematical model in terms of its design. The model is a nonlinear, learning feedback system, fully satisfying control theoretical principles. It accepts any form of the stimulus-the drug intake-and describes how the physiological processes involved affect the distribution of the drug through the body and the stability of the regulation loop. The mathematical model verifies the proposed theory and provides a basis for the implementation of mathematical models of specific physiological processes.

  16. 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...

  17. 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

  18. Analytic Intermodel Consistent Modeling of Volumetric Human Lung Dynamics.

    Science.gov (United States)

    Ilegbusi, Olusegun; Seyfi, Behnaz; Neylon, John; Santhanam, Anand P

    2015-10-01

    Human lung undergoes breathing-induced deformation in the form of inhalation and exhalation. Modeling the dynamics is numerically complicated by the lack of information on lung elastic behavior and fluid-structure interactions between air and the tissue. A mathematical method is developed to integrate deformation results from a deformable image registration (DIR) and physics-based modeling approaches in order to represent consistent volumetric lung dynamics. The computational fluid dynamics (CFD) simulation assumes the lung is a poro-elastic medium with spatially distributed elastic property. Simulation is performed on a 3D lung geometry reconstructed from four-dimensional computed tomography (4DCT) dataset of a human subject. The heterogeneous Young's modulus (YM) is estimated from a linear elastic deformation model with the same lung geometry and 4D lung DIR. The deformation obtained from the CFD is then coupled with the displacement obtained from the 4D lung DIR by means of the Tikhonov regularization (TR) algorithm. The numerical results include 4DCT registration, CFD, and optimal displacement data which collectively provide consistent estimate of the volumetric lung dynamics. The fusion method is validated by comparing the optimal displacement with the results obtained from the 4DCT registration.

  19. 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

  20. 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...

  1. 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...

  2. 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

  3. 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…

  4. 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.

  5. 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…

  6. 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…

  7. 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…

  8. 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

  9. 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.

  10. 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...

  11. 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…

  12. 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

  13. 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)

  14. Mathematical modelling of the growth of human fetus anatomical structures.

    Science.gov (United States)

    Dudek, Krzysztof; Kędzia, Wojciech; Kędzia, Emilia; Kędzia, Alicja; Derkowski, Wojciech

    2017-09-01

    The goal of this study was to present a procedure that would enable mathematical analysis of the increase of linear sizes of human anatomical structures, estimate mathematical model parameters and evaluate their adequacy. Section material consisted of 67 foetuses-rectus abdominis muscle and 75 foetuses- biceps femoris muscle. The following methods were incorporated to the study: preparation and anthropologic methods, image digital acquisition, Image J computer system measurements and statistical analysis method. We used an anthropologic method based on age determination with the use of crown-rump length-CRL (V-TUB) by Scammon and Calkins. The choice of mathematical function should be based on a real course of the curve presenting growth of anatomical structure linear size Ύ in subsequent weeks t of pregnancy. Size changes can be described with a segmental-linear model or one-function model with accuracy adequate enough for clinical purposes. The interdependence of size-age is described with many functions. However, the following functions are most often considered: linear, polynomial, spline, logarithmic, power, exponential, power-exponential, log-logistic I and II, Gompertz's I and II and von Bertalanffy's function. With the use of the procedures described above, mathematical models parameters were assessed for V-PL (the total length of body) and CRL body length increases, rectus abdominis total length h, its segments hI, hII, hIII, hIV, as well as biceps femoris length and width of long head (LHL and LHW) and of short head (SHL and SHW). The best adjustments to measurement results were observed in the exponential and Gompertz's models.

  15. 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...

  16. 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.

  17. 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…

  18. 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.

  19. 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....

  20. 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…

  1. 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

  2. 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

  3. 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…

  4. 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

  5. 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…

  6. 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...

  7. 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).

  8. 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.

  9. 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.

  10. 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…

  11. Mathematical modeling of tornadoes and squall storms

    Directory of Open Access Journals (Sweden)

    Sergey A. Arsen’yev

    2011-04-01

    Full Text Available Recent advances in modeling of tornadoes and twisters consist of significant achievements in mathematical calculation of occurrence and evolution of a violent F5-class tornado on the Fujita scale, and four-dimensional mathematical modeling of a tornado with the fourth coordinate time multiplied by its characteristic velocity. Such a tornado can arise in a thunderstorm supercell filled with turbulent whirlwinds. A theory of the squall storms is proposed. The squall storm is modeled by running perturbation of the temperature inversion on the lower boundary of cloudiness. This perturbation is induced by the action of strong, hurricane winds in the upper and middle troposphere, and looks like a running solitary wave (soliton; which is developed also in a field of pressure and velocity of a wind. If a soliton of a squall storm gets into the thunderstorm supercell then this soliton is captured by supercell. It leads to additional pressure fall of air inside a storm supercell and stimulate amplification of wind velocity here. As a result, a cyclostrophic balance inside a storm supercell generates a tornado. Comparison of the radial distribution of wind velocity inside a tornado calculated by using the new formulas and equations with radar observations of the wind velocity inside Texas Tornado Dummit in 1995 and inside the 3 May 1999 Oklahoma City Tornado shows good correspondence.

  12. Discovery learning model with geogebra assisted for improvement mathematical visual thinking ability

    Science.gov (United States)

    Juandi, D.; Priatna, N.

    2018-05-01

    The main goal of this study is to improve the mathematical visual thinking ability of high school student through implementation the Discovery Learning Model with Geogebra Assisted. This objective can be achieved through study used quasi-experimental method, with non-random pretest-posttest control design. The sample subject of this research consist of 62 senior school student grade XI in one of school in Bandung district. The required data will be collected through documentation, observation, written tests, interviews, daily journals, and student worksheets. The results of this study are: 1) Improvement students Mathematical Visual Thinking Ability who obtain learning with applied the Discovery Learning Model with Geogebra assisted is significantly higher than students who obtain conventional learning; 2) There is a difference in the improvement of students’ Mathematical Visual Thinking ability between groups based on prior knowledge mathematical abilities (high, medium, and low) who obtained the treatment. 3) The Mathematical Visual Thinking Ability improvement of the high group is significantly higher than in the medium and low groups. 4) The quality of improvement ability of high and low prior knowledge is moderate category, in while the quality of improvement ability in the high category achieved by student with medium prior knowledge.

  13. 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.

  14. 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.

  15. 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

  16. 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...

  17. 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.

  18. 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

  19. 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.

  20. 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...

  1. Mathematical model on Alzheimer's disease.

    Science.gov (United States)

    Hao, Wenrui; Friedman, Avner

    2016-11-18

    Alzheimer disease (AD) is a progressive neurodegenerative disease that destroys memory and cognitive skills. AD is characterized by the presence of two types of neuropathological hallmarks: extracellular plaques consisting of amyloid β-peptides and intracellular neurofibrillary tangles of hyperphosphorylated tau proteins. The disease affects 5 million people in the United States and 44 million world-wide. Currently there is no drug that can cure, stop or even slow the progression of the disease. If no cure is found, by 2050 the number of alzheimer's patients in the U.S. will reach 15 million and the cost of caring for them will exceed $ 1 trillion annually. The present paper develops a mathematical model of AD that includes neurons, astrocytes, microglias and peripheral macrophages, as well as amyloid β aggregation and hyperphosphorylated tau proteins. The model is represented by a system of partial differential equations. The model is used to simulate the effect of drugs that either failed in clinical trials, or are currently in clinical trials. Based on these simulations it is suggested that combined therapy with TNF- α inhibitor and anti amyloid β could yield significant efficacy in slowing the progression of AD.

  2. 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)

  3. Consistent phase-change modeling for CO2-based heat mining operation

    DEFF Research Database (Denmark)

    Singh, Ashok Kumar; Veje, Christian

    2017-01-01

    The accuracy of mathematical modeling of phase-change phenomena is limited if a simple, less accurate equation of state completes the governing partial differential equation. However, fluid properties (such as density, dynamic viscosity and compressibility) and saturation state are calculated using...... a highly accurate, complex equation of state. This leads to unstable and inaccurate simulation as the equation of state and governing partial differential equations are mutually inconsistent. In this study, the volume-translated Peng–Robinson equation of state was used with emphasis to model the liquid......–gas phase transition with more accuracy and consistency. Calculation of fluid properties and saturation state were based on the volume translated Peng–Robinson equation of state and results verified. The present model has been applied to a scenario to simulate a CO2-based heat mining process. In this paper...

  4. 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…

  5. 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…

  6. 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…

  7. 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…

  8. 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...

  9. 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.

  10. 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.

  11. 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...

  12. 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

  13. 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.

  14. 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)

  15. 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

  16. 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...

  17. 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

  18. 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

  19. 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.

  20. Designing of Holistic Mathematic Education Model Based-"System Among" at Low Grade Elementary School

    Science.gov (United States)

    Hayati, R.; Fauzan, A.; Iswari, M.; Khaidir, A.

    2018-04-01

    The purpose of this study was to develop a model of Holistic Mathematics Education (HME) among systems based on low-grade primary school students so that students have a solid foundation when entering a higher behavior. This type of research is desaign research developed by Plomp to have three stages, namely the preliminary research, development or prototyping phase, and assessement Phase. This research resulted in a model Holistic Mathematics Education (HME) -based system is among the primary school students low grade consists of 10 stages, namely 1) Recap through the neighborhood, 2) Discussion groups by exploiting the environment, 3) Demonstration Group, 4) Exercise individuals, 5) mathematical modeling, 6) Demonstration of individuals, 7) Reflections, 8) impressions and messages, and giving meaning, 9) Celebrations and 10) A thorough assessment. Furthermore, this model also produces 7 important components that should be developed teacher, namely 1) constructivism, 2) the nature of nature, 3) independence, 4) parable, 5) inquiry, 6) cooperation, and 7) strengthening. This model will produce a model in the form of books, student books and teacher's guide book as a support system that can help users in its application.

  1. Mathematical Modeling of Vibrio vulnificus Infection in Korea and the Influence of Global Warming.

    Science.gov (United States)

    Chu, Chaeshin; Do, Younghae; Kim, Yongkuk; Saito, Yasuhisa; Lee, Sun-Dong; Park, Haemo; Lee, Jong-Koo

    2011-06-01

    To investigate the possible link between Vibrio vulnificus population size in seawater and water temperature. We collected incidence and water temperature data in coastal regions of Korea and constructed a mathematical model that consisted of three classes; susceptible fish, infected fish available to humans, and infected humans. We developed a mathematical model to connect V. vulnificus incidence with water temperature using estimated bacterial population sizes and actual coastal water temperatures. Increased V. vulnificus population sizes in marine environments may increase the risk of infection in people who eat at coastal restaurants in Korea. Furthermore, we estimated the near-future number of infected patients using our model, which will help to establish a public-health policy to reduce the disease burden.

  2. 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...

  3. Mathematical modeling of the Phoenix Rising pathway.

    Directory of Open Access Journals (Sweden)

    Chad Liu

    2014-02-01

    Full Text Available Apoptosis is a tightly controlled process in mammalian cells. It is important for embryogenesis, tissue homoeostasis, and cancer treatment. Apoptosis not only induces cell death, but also leads to the release of signals that promote rapid proliferation of surrounding cells through the Phoenix Rising (PR pathway. To quantitatively understand the kinetics of interactions of different molecules in this pathway, we developed a mathematical model to simulate the effects of various changes in the PR pathway on the secretion of prostaglandin E2 (PGE2, a key factor for promoting cell proliferation. These changes include activation of caspase 3 (C3, caspase 7 (C7, and nuclear factor κB (NFκB. In addition, we simulated the effects of cyclooxygenase-2 (COX2 inhibition and C3 knockout on the level of secreted PGE2. The model predictions on PGE2 in MEF and 4T1 cells at 48 hours after 10-Gray radiation were quantitatively consistent with the experimental data in the literature. Compared to C7, the model predicted that C3 activation was more critical for PGE2 production. The model also predicted that PGE2 production could be significantly reduced when COX2 expression was blocked via either NFκB inactivation or treatment of cells with exogenous COX2 inhibitors, which led to a decrease in the rate of conversion from arachidonic acid to prostaglandin H2 in the PR pathway. In conclusion, the mathematical model developed in this study yielded new insights into the process of tissue regrowth stimulated by signals from apoptotic cells. In future studies, the model can be used for experimental data analysis and assisting development of novel strategies/drugs for improving cancer treatment or normal tissue regeneration.

  4. Capturing intracellular pH dynamics by coupling its molecular mechanisms within a fully tractable mathematical model.

    Directory of Open Access Journals (Sweden)

    Yann Bouret

    Full Text Available We describe the construction of a fully tractable mathematical model for intracellular pH. This work is based on coupling the kinetic equations depicting the molecular mechanisms for pumps, transporters and chemical reactions, which determine this parameter in eukaryotic cells. Thus, our system also calculates the membrane potential and the cytosolic ionic composition. Such a model required the development of a novel algebraic method that couples differential equations for slow relaxation processes to steady-state equations for fast chemical reactions. Compared to classical heuristic approaches based on fitted curves and ad hoc constants, this yields significant improvements. This model is mathematically self-consistent and allows for the first time to establish analytical solutions for steady-state pH and a reduced differential equation for pH regulation. Because of its modular structure, it can integrate any additional mechanism that will directly or indirectly affect pH. In addition, it provides mathematical clarifications for widely observed biological phenomena such as overshooting in regulatory loops. Finally, instead of including a limited set of experimental results to fit our model, we show examples of numerical calculations that are extremely consistent with the wide body of intracellular pH experimental measurements gathered by different groups in many different cellular systems.

  5. 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...

  6. 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.

  7. 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…

  8. 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.

  9. 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

  10. 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.

  11. 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...

  12. Mathematical Modeling of an Active-Fiber Composite Energy Harvester with Interdigitated Electrodes

    Directory of Open Access Journals (Sweden)

    A. Jemai

    2014-01-01

    Full Text Available The use of active-fiber composites (AFC instead of traditional ceramic piezoelectric materials is motivated by flexibility and relatively high actuation capacity. Nevertheless, their energy harvesting capabilities remain low. As a first step toward the enhancement of AFC’s performances, a mathematical model that accurately simulates the dynamic behavior of the AFC is proposed. In fact, most of the modeling approaches found in the literature for AFC are based on finite element methods. In this work, we use homogenization techniques to mathematically describe piezoelectric properties taking into consideration the composite structure of the AFC. We model the interdigitated electrodes as a series of capacitances and current sources linked in parallel; then we integrate these properties into the structural model of the AFC. The proposed model is incorporated into a vibration based energy harvesting system consisting of a cantilever beam on top of which an AFC patch is attached. Finally, analytical solutions of the dynamic behavior and the harvested voltage are proposed and validated with finite element simulations.

  13. 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.

  14. 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.

  15. 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.

  16. 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)

  17. 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.)

  18. 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 ...

  19. 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.

  20. 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. 

  1. 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…

  2. Warehouse design and product assignment and allocation: A mathematical programming model

    OpenAIRE

    Geraldes, Carla A. S.; Carvalho, Maria Sameiro; Pereira, Guilherme

    2012-01-01

    Warehouses can be considered one of the most important nodes in supply chains. The dynamic nature of today's markets compels organizations to an incessant reassessment in an effort to respond to continuous challenges. Therefore warehouses must be continually re-evaluated to ensure that they are consistent with both market's demands and management's strategies. In this paper we discuss a mathematical programming model aiming to support product assignment and allocation to the functional areas ...

  3. 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

  4. 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.

  5. A Long-Term Mathematical Model for Mining Industries

    Energy Technology Data Exchange (ETDEWEB)

    Achdou, Yves, E-mail: achdou@ljll.univ-paris-diderot.fr [Univ. Paris Diderot, Sorbonne Paris Cité, Laboratoire Jacques-Louis Lions, UMR 7598, UPMC, CNRS (France); Giraud, Pierre-Noel [CERNA, Mines ParisTech (France); Lasry, Jean-Michel [Univ. Paris Dauphine (France); Lions, Pierre-Louis [Collège de France (France)

    2016-12-15

    A parcimonious long term model is proposed for a mining industry. Knowing the dynamics of the global reserve, the strategy of each production unit consists of an optimal control problem with two controls, first the flux invested into prospection and the building of new extraction facilities, second the production rate. In turn, the dynamics of the global reserve depends on the individual strategies of the producers, so the models leads to an equilibrium, which is described by low dimensional systems of partial differential equations. The dimensionality depends on the number of technologies that a mining producer can choose. In some cases, the systems may be reduced to a Hamilton–Jacobi equation which is degenerate at the boundary and whose right hand side may blow up at the boundary. A mathematical analysis is supplied. Then numerical simulations for models with one or two technologies are described. In particular, a numerical calibration of the model in order to fit the historical data is carried out.

  6. A Long-Term Mathematical Model for Mining Industries

    International Nuclear Information System (INIS)

    Achdou, Yves; Giraud, Pierre-Noel; Lasry, Jean-Michel; Lions, Pierre-Louis

    2016-01-01

    A parcimonious long term model is proposed for a mining industry. Knowing the dynamics of the global reserve, the strategy of each production unit consists of an optimal control problem with two controls, first the flux invested into prospection and the building of new extraction facilities, second the production rate. In turn, the dynamics of the global reserve depends on the individual strategies of the producers, so the models leads to an equilibrium, which is described by low dimensional systems of partial differential equations. The dimensionality depends on the number of technologies that a mining producer can choose. In some cases, the systems may be reduced to a Hamilton–Jacobi equation which is degenerate at the boundary and whose right hand side may blow up at the boundary. A mathematical analysis is supplied. Then numerical simulations for models with one or two technologies are described. In particular, a numerical calibration of the model in order to fit the historical data is carried out.

  7. 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 ...

  8. 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...

  9. 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 ...

  10. Methodology for predicting oily mixture properties in the mathematical modeling of molecular distillation

    Directory of Open Access Journals (Sweden)

    M. F. Gayol

    2017-06-01

    Full Text Available A methodology for predicting the thermodynamic and transport properties of a multi-component oily mixture, in which the different mixture components are grouped into a small number of pseudo components is shown. This prediction of properties is used in the mathematical modeling of molecular distillation, which consists of a system of differential equations in partial derivatives, according to the principles of the Transport Phenomena and is solved by an implicit finite difference method using a computer code. The mathematical model was validated with experimental data, specifically the molecular distillation of a deodorizer distillate (DD of sunflower oil. The results obtained were satisfactory, with errors less than 10% with respect to the experimental data in a temperature range in which it is possible to apply the proposed method.

  11. Methodology for predicting oily mixture properties in the mathematical modeling of molecular distillation

    International Nuclear Information System (INIS)

    Gayol, M.F.; Pramparo, M.C.; Miró Erdmann, S.M.

    2017-01-01

    A methodology for predicting the thermodynamic and transport properties of a multi-component oily mixture, in which the different mixture components are grouped into a small number of pseudo components is shown. This prediction of properties is used in the mathematical modeling of molecular distillation, which consists of a system of differential equations in partial derivatives, according to the principles of the Transport Phenomena and is solved by an implicit finite difference method using a computer code. The mathematical model was validated with experimental data, specifically the molecular distillation of a deodorizer distillate (DD) of sunflower oil. The results obtained were satisfactory, with errors less than 10% with respect to the experimental data in a temperature range in which it is possible to apply the proposed method. [es

  12. 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…

  13. 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…

  14. Mathematical modelling of the process of quality control of construction products

    Directory of Open Access Journals (Sweden)

    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.

  15. 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…

  16. 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

  17. Mathematical model for enzymatic hydrolysis and fermentation of cellulose by Trichoderma

    Energy Technology Data Exchange (ETDEWEB)

    Peitersen, N; Ross, Jr, E W

    1979-06-01

    This paper describes a mathematical model for the enzymatic hydrolysis and fermentation of cellulose by Trichoderma reesei. The principal features of the model are the assumption of two forms of cellulose (crystalline and amorphous), two sugars (cellobiose and glucose), and two enzymes (cellulase and ..beta..-glucosidase). An inducer-repressor-messenger RNA mechanism is used to predict enzyme formation, and pH effects are included. The model consists of 12 ordinary differential equations for 12 state variables and contains 38 parameters. The parameters were estimated from four sets of experimental data by optimization. The results appear satisfactory, and the computer programs permit simulation of a variety of system changes.

  18. 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

  19. Mathematical Modelling of Unmanned Aerial Vehicles

    Directory of Open Access Journals (Sweden)

    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

  20. 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)

  1. 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.

  2. 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.

  3. 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.

  4. 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....

  5. 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.

  6. 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

  7. 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.

  8. Numerical study of a mathematical model of internal erosion of soil

    Science.gov (United States)

    Sibin, A.

    2017-10-01

    The process of internal erosion in a three-phase saturated soil is studied. A mathematical model describing the process consists of the equations of mass conservation, Darcy’s law and equation for capillary pressure. The original system of equations is reduced to a system of three equations for porosity, pressure and water saturation. Obtained equation for the water saturation is degenerate. The degenerate problem in an one-dimensional domain is solved numerically using the finite-difference method.

  9. Central Pressure Appraisal: Clinical Validation of a Subject-Specific Mathematical Model.

    Directory of Open Access Journals (Sweden)

    Francesco Tosello

    Full Text Available Current evidence suggests that aortic blood pressure has a superior prognostic value with respect to brachial pressure for cardiovascular events, but direct measurement is not feasible in daily clinical practice.The aim of the present study is the clinical validation of a multiscale mathematical model for non-invasive appraisal of central blood pressure from subject-specific characteristics.A total of 51 young male were selected for the present study. Aortic systolic and diastolic pressure were estimated with a mathematical model and were compared to the most-used non-invasive validated technique (SphygmoCor device, AtCor Medical, Australia. SphygmoCor was calibrated through diastolic and systolic brachial pressure obtained with a sphygmomanometer, while model inputs consist of brachial pressure, height, weight, age, left-ventricular end-systolic and end-diastolic volumes, and data from a pulse wave velocity study.Model-estimated systolic and diastolic central blood pressures resulted to be significantly related to SphygmoCor-assessed central systolic (r = 0.65 p <0.0001 and diastolic (r = 0.84 p<0.0001 blood pressures. The model showed a significant overestimation of systolic pressure (+7.8 (-2.2;14 mmHg, p = 0.0003 and a significant underestimation of diastolic values (-3.2 (-7.5;1.6, p = 0.004, which imply a significant overestimation of central pulse pressure. Interestingly, model prediction errors mirror the mean errors reported in large meta-analysis characterizing the use of the SphygmoCor when non-invasive calibration is performed.In conclusion, multi-scale mathematical model predictions result to be significantly related to SphygmoCor ones. Model-predicted systolic and diastolic aortic pressure resulted in difference of less than 10 mmHg in the 51% and 84% of the subjects, respectively, when compared with SphygmoCor-obtained pressures.

  10. 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.

  11. 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...

  12. 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.

  13. Self-consistent asset pricing models

    Science.gov (United States)

    Malevergne, Y.; Sornette, D.

    2007-08-01

    We discuss the foundations of factor or regression models in the light of the self-consistency condition that the market portfolio (and more generally the risk factors) is (are) constituted of the assets whose returns it is (they are) supposed to explain. As already reported in several articles, self-consistency implies correlations between the return disturbances. As a consequence, the alphas and betas of the factor model are unobservable. Self-consistency leads to renormalized betas with zero effective alphas, which are observable with standard OLS regressions. When the conditions derived from internal consistency are not met, the model is necessarily incomplete, which means that some sources of risk cannot be replicated (or hedged) by a portfolio of stocks traded on the market, even for infinite economies. Analytical derivations and numerical simulations show that, for arbitrary choices of the proxy which are different from the true market portfolio, a modified linear regression holds with a non-zero value αi at the origin between an asset i's return and the proxy's return. Self-consistency also introduces “orthogonality” and “normality” conditions linking the betas, alphas (as well as the residuals) and the weights of the proxy portfolio. Two diagnostics based on these orthogonality and normality conditions are implemented on a basket of 323 assets which have been components of the S&P500 in the period from January 1990 to February 2005. These two diagnostics show interesting departures from dynamical self-consistency starting about 2 years before the end of the Internet bubble. Assuming that the CAPM holds with the self-consistency condition, the OLS method automatically obeys the resulting orthogonality and normality conditions and therefore provides a simple way to self-consistently assess the parameters of the model by using proxy portfolios made only of the assets which are used in the CAPM regressions. Finally, the factor decomposition with the

  14. 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.

  15. 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.

  16. Explorations in Elementary Mathematical Modeling

    Directory of Open Access Journals (Sweden)

    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.

  17. Model-Based Policymaking: A Framework to Promote Ethical “Good Practice” in Mathematical Modeling for Public Health Policymaking

    Science.gov (United States)

    Boden, Lisa A.; McKendrick, Iain J.

    2017-01-01

    Mathematical models are increasingly relied upon as decision support tools, which estimate risks and generate recommendations to underpin public health policies. However, there are no formal agreements about what constitutes professional competencies or duties in mathematical modeling for public health. In this article, we propose a framework to evaluate whether mathematical models that assess human and animal disease risks and control strategies meet standards consistent with ethical “good practice” and are thus “fit for purpose” as evidence in support of policy. This framework is derived from principles of biomedical ethics: independence, transparency (autonomy), beneficence/non-maleficence, and justice. We identify ethical risks associated with model development and implementation and consider the extent to which scientists are accountable for the translation and communication of model results to policymakers so that the strengths and weaknesses of the scientific evidence base and any socioeconomic and ethical impacts of biased or uncertain predictions are clearly understood. We propose principles to operationalize a framework for ethically sound model development and risk communication between scientists and policymakers. These include the creation of science–policy partnerships to mutually define policy questions and communicate results; development of harmonized international standards for model development; and data stewardship and improvement of the traceability and transparency of models via a searchable archive of policy-relevant models. Finally, we suggest that bespoke ethical advisory groups, with relevant expertise and access to these resources, would be beneficial as a bridge between science and policy, advising modelers of potential ethical risks and providing overview of the translation of modeling advice into policy. PMID:28424768

  18. Mathematical models of non-linear phenomena, processes and systems: from molecular scale to planetary atmosphere

    CERN Document Server

    2013-01-01

    This book consists of twenty seven chapters, which can be divided into three large categories: articles with the focus on the mathematical treatment of non-linear problems, including the methodologies, algorithms and properties of analytical and numerical solutions to particular non-linear problems; theoretical and computational studies dedicated to the physics and chemistry of non-linear micro-and nano-scale systems, including molecular clusters, nano-particles and nano-composites; and, papers focused on non-linear processes in medico-biological systems, including mathematical models of ferments, amino acids, blood fluids and polynucleic chains.

  19. 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…

  20. DigitalHuman (DH): An Integrative Mathematical Model ofHuman Physiology

    Science.gov (United States)

    Hester, Robert L.; Summers, Richard L.; lIescu, Radu; Esters, Joyee; Coleman, Thomas G.

    2010-01-01

    Mathematical models and simulation are important tools in discovering the key causal relationships governing physiological processes and improving medical intervention when physiological complexity is a central issue. We have developed a model of integrative human physiology called DigitalHuman (DH) consisting of -5000 variables modeling human physiology describing cardiovascular, renal, respiratory, endocrine, neural and metabolic physiology. Users can view time-dependent solutions and interactively introduce perturbations by altering numerical parameters to investigate new hypotheses. The variables, parameters and quantitative relationships as well as all other model details are described in XML text files. All aspects of the model, including the mathematical equations describing the physiological processes are written in XML open source, text-readable files. Model structure is based upon empirical data of physiological responses documented within the peer-reviewed literature. The model can be used to understand proposed physiological mechanisms and physiological interactions that may not be otherwise intUitively evident. Some of the current uses of this model include the analyses of renal control of blood pressure, the central role of the liver in creating and maintaining insulin resistance, and the mechanisms causing orthostatic hypotension in astronauts. Additionally the open source aspect of the modeling environment allows any investigator to add detailed descriptions of human physiology to test new concepts. The model accurately predicts both qualitative and more importantly quantitative changes in clinically and experimentally observed responses. DigitalHuman provides scientists a modeling environment to understand the complex interactions of integrative physiology. This research was supported by.NIH HL 51971, NSF EPSCoR, and NASA

  1. 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.

  2. 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.

  3. PREFACE: Physics-Based Mathematical Models for Nanotechnology

    Science.gov (United States)

    Voon, Lok C. Lew Yan; Melnik, Roderick; Willatzen, Morten

    2008-03-01

    in the cross-disciplinary research area: low-dimensional semiconductor nanostructures. Since the main properties of two-dimensional heterostructures (such as quantum wells) are now quite well understood, there has been a consistently growing interest in the mathematical physics community to further dimensionality reduction of semiconductor structures. Experimental achievements in realizing one-dimensional and quasi-zero-dimensional heterostructures have opened new opportunities for theory and applications of such low-dimensional semiconductor nanostructures. One of the most important implications of this process has been a critical re-examining of assumptions under which traditional quantum mechanical models have been derived in this field. Indeed, the formation of LDSNs, in particular quantum dots, is a competition between the surface energy in the structure and strain energy. However, current models for bandstructure calculations use quite a simplified analysis of strain relaxation effects, although such effects are in the heart of nanostructure formation. By now, it has been understood that traditional models in this field may not be adequate for modeling realistic objects based on LDSNs due to neglecting many effects that may profoundly influence optoelectronic properties of the nanostructures. Among such effects are electromechanical effects, including strain relaxation, piezoelectric effect, spontaneous polarization, and higher order nonlinear effects. Up to date, major efforts have been concentrated on the analysis of idealized, isolated quantum dots, while a typical self-assembled semiconductor quantum dot nanostructure is an array (or a molecule) of many individual quantum dots sitting on the same `substrate' known as the wetting layer. Each such dot contains several hundred thousand atoms. In order to account for quantum effects accurately in a situation like that, attempts can be made to apply ab initio or atomistic methodologies, but then one would face a

  4. 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,...

  5. Mathematical Modeling of Rotary Blood Pumps in a Pulsatile In Vitro Flow Environment.

    Science.gov (United States)

    Pirbodaghi, Tohid

    2017-08-01

    Nowadays, sacrificing animals to develop medical devices and receive regulatory approval has become more common, which increases ethical concerns. Although in vivo tests are necessary for development and evaluation of new devices, nonetheless, with appropriate in vitro setups and mathematical models, a part of the validation process can be performed using these models to reduce the number of sacrificed animals. The main aim of this study is to present a mathematical model simulating the hydrodynamic function of a rotary blood pump (RBP) in a pulsatile in vitro flow environment. This model relates the pressure head of the RBP to the flow rate, rotational speed, and time derivatives of flow rate and rotational speed. To identify the model parameters, an in vitro setup was constructed consisting of a piston pump, a compliance chamber, a throttle, a buffer reservoir, and the CentriMag RBP. A 40% glycerin-water mixture as a blood analog fluid and deionized water were used in the hydraulic circuit to investigate the effect of viscosity and density of the working fluid on the model parameters. First, model variables were physically measured and digitally acquired. Second, an identification algorithm based on regression analysis was used to derive the model parameters. Third, the completed model was validated with a totally different set of in vitro data. The model is usable for both mathematical simulations of the interaction between the pump and heart and indirect pressure measurement in a clinical context. © 2017 International Center for Artificial Organs and Transplantation and Wiley Periodicals, Inc.

  6. 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.

  7. 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)…

  8. 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

  9. 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...

  10. 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…

  11. 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

  12. 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…

  13. Two-dimensional mathematical model for simulation of the drying process of thick layers of natural materials in a conveyor-belt dryer

    Directory of Open Access Journals (Sweden)

    Salemović Duško R.

    2017-01-01

    Full Text Available This paper presents the mathematical model and numerical analysis of the convective drying process of thick slices of colloidal capillary-porous materials slowly moving through conveyor-belt dryer. A flow of hot moist air was used as drying agent. The drying process has been analyzed in the form of a 2-D mathematical model, in two directions: along the conveyor and perpendicular on it. The mathematical model consists of two non-linear differential equations and one equation with a transcendent character and it is based on the mathematical model developed for drying process in a form of a 1-D thin layer. The appropriate boundary conditions were introduced. The presented model is suitable for the automated control of conveyor-belt dryers. The obtained results with analysis could be useful in predicting the drying kinetics of potato slices and similar natural products.

  14. 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…

  15. 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.

  16. Mathematical models and algorithms for the computer program 'WOLF'

    International Nuclear Information System (INIS)

    Halbach, K.

    1975-12-01

    The computer program FLOW finds the nonrelativistic self- consistent set of two-dimensional ion trajectories and electric fields (including space charges from ions and electrons) for a given set of initial and boundary conditions for the particles and fields. The combination of FLOW with the optimization code PISA gives the program WOLF, which finds the shape of the emitter which is consistent with the plasma forming it, and in addition varies physical characteristics such as electrode position, shapes, and potentials so that some performance characteristics are optimized. The motivation for developing these programs was the desire to design optimum ion source extractor/accelerator systems in a systematic fashion. The purpose of this report is to explain and derive the mathematical models and algorithms which approximate the real physical processes. It serves primarily to document the computer programs. 10 figures

  17. 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.

  18. 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

  19. Mathematical Modelling for Micropiles Embedded in Salt Rock

    Directory of Open Access Journals (Sweden)

    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.

  20. Branch-based model for the diameters of the pulmonary airways: accounting for departures from self-consistency and registration errors.

    Science.gov (United States)

    Neradilek, Moni B; Polissar, Nayak L; Einstein, Daniel R; Glenny, Robb W; Minard, Kevin R; Carson, James P; Jiao, Xiangmin; Jacob, Richard E; Cox, Timothy C; Postlethwait, Edward M; Corley, Richard A

    2012-06-01

    We examine a previously published branch-based approach for modeling airway diameters that is predicated on the assumption of self-consistency across all levels of the tree. We mathematically formulate this assumption, propose a method to test it and develop a more general model to be used when the assumption is violated. We discuss the effect of measurement error on the estimated models and propose methods that take account of error. The methods are illustrated on data from MRI and CT images of silicone casts of two rats, two normal monkeys, and one ozone-exposed monkey. Our results showed substantial departures from self-consistency in all five subjects. When departures from self-consistency exist, we do not recommend using the self-consistency model, even as an approximation, as we have shown that it may likely lead to an incorrect representation of the diameter geometry. The new variance model can be used instead. Measurement error has an important impact on the estimated morphometry models and needs to be addressed in the analysis. Copyright © 2012 Wiley Periodicals, Inc.

  1. 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.

  2. PREFACE: 3rd International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE 2014)

    Science.gov (United States)

    2015-01-01

    The third International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) took place at Madrid, Spain, from Thursday 28 to Sunday 31 August 2014. The Conference was attended by more than 200 participants and hosted about 350 oral, poster, and virtual presentations. More than 600 pre-registered authors were also counted. The third IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical/Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics etc. The scientific program was rather heavy since after the Keynote and Invited Talks in the morning, three parallel oral sessions and one poster session were running every day. However, according to all attendees, the program was excellent with high level of talks and the scientific environment was fruitful, thus all attendees had a creative time. We would like to thank the Keynote Speaker and the Invited Speakers for their significant contribution to IC-MSQUARE. We also would like to thank the Members of the International Advisory and Scientific Committees as well as the Members of the Organizing Committee.

  3. 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.

  4. 5th International Conference on Mathematical Modeling in Physical Sciences (IC-MSquare 2016)

    International Nuclear Information System (INIS)

    Vagenas, Elias C.; Vlachos, Dimitrios S.

    2016-01-01

    The 5th International Conference on Mathematical Modeling in Physical Sciences (IC- MSQUARE) took place at Athens, Greece, from Monday, 23"t"h of May, to Thursday, 26"t"h of May 2016. The Conference was attended by more than 130 participants and hosted about 170 oral, poster, and virtual presentations while counted more than 500 pre-registered authors. The 5"t"h IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical/Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics etc. The scientific program was rather heavy since after the Keynote and Invited Talks in the morning, three parallel oral and one poster session were running every day. However, according to all attendees, the program was excellent with high level talks and the scientific environment was fruitful, thus all attendees had a creative time. We would like to thank the Keynote Speaker and the Invited Speakers for their significant contribution to IC-MSQUARE. We also would like to thank the Members of the International Advisory and Scientific Committees as well as the Members of the Organizing Committee. (paper)

  5. 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...

  6. 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.

  7. 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…

  8. 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

  9. 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-

  10. 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

  11. 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)

  12. 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.

  13. PROBLEMS OF MATHEMATICAL MODELING OF THE ENTERPRISES ORGANIZATIONAL STRUCTURE

    Directory of Open Access Journals (Sweden)

    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

  14. Mathematical modeling based on ordinary differential equations: A promising approach to vaccinology.

    Science.gov (United States)

    Bonin, Carla Rezende Barbosa; Fernandes, Guilherme Cortes; Dos Santos, Rodrigo Weber; Lobosco, Marcelo

    2017-02-01

    New contributions that aim to accelerate the development or to improve the efficacy and safety of vaccines arise from many different areas of research and technology. One of these areas is computational science, which traditionally participates in the initial steps, such as the pre-screening of active substances that have the potential to become a vaccine antigen. In this work, we present another promising way to use computational science in vaccinology: mathematical and computational models of important cell and protein dynamics of the immune system. A system of Ordinary Differential Equations represents different immune system populations, such as B cells and T cells, antigen presenting cells and antibodies. In this way, it is possible to simulate, in silico, the immune response to vaccines under development or under study. Distinct scenarios can be simulated by varying parameters of the mathematical model. As a proof of concept, we developed a model of the immune response to vaccination against the yellow fever. Our simulations have shown consistent results when compared with experimental data available in the literature. The model is generic enough to represent the action of other diseases or vaccines in the human immune system, such as dengue and Zika virus.

  15. 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

  16. High-performance speech recognition using consistency modeling

    Science.gov (United States)

    Digalakis, Vassilios; Murveit, Hy; Monaco, Peter; Neumeyer, Leo; Sankar, Ananth

    1994-12-01

    The goal of SRI's consistency modeling project is to improve the raw acoustic modeling component of SRI's DECIPHER speech recognition system and develop consistency modeling technology. Consistency modeling aims to reduce the number of improper independence assumptions used in traditional speech recognition algorithms so that the resulting speech recognition hypotheses are more self-consistent and, therefore, more accurate. At the initial stages of this effort, SRI focused on developing the appropriate base technologies for consistency modeling. We first developed the Progressive Search technology that allowed us to perform large-vocabulary continuous speech recognition (LVCSR) experiments. Since its conception and development at SRI, this technique has been adopted by most laboratories, including other ARPA contracting sites, doing research on LVSR. Another goal of the consistency modeling project is to attack difficult modeling problems, when there is a mismatch between the training and testing phases. Such mismatches may include outlier speakers, different microphones and additive noise. We were able to either develop new, or transfer and evaluate existing, technologies that adapted our baseline genonic HMM recognizer to such difficult conditions.

  17. Mathematical models to predict rheological parameters of lateritic hydromixtures

    Directory of Open Access Journals (Sweden)

    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.

  18. 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.

  19. 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.

  20. 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

  1. 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...

  2. 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.…

  3. 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.

  4. Modeling and Testing Legacy Data Consistency Requirements

    DEFF Research Database (Denmark)

    Nytun, J. P.; Jensen, Christian Søndergaard

    2003-01-01

    An increasing number of data sources are available on the Internet, many of which offer semantically overlapping data, but based on different schemas, or models. While it is often of interest to integrate such data sources, the lack of consistency among them makes this integration difficult....... This paper addresses the need for new techniques that enable the modeling and consistency checking for legacy data sources. Specifically, the paper contributes to the development of a framework that enables consistency testing of data coming from different types of data sources. The vehicle is UML and its...... accompanying XMI. The paper presents techniques for modeling consistency requirements using OCL and other UML modeling elements: it studies how models that describe the required consistencies among instances of legacy models can be designed in standard UML tools that support XMI. The paper also considers...

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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

  10. 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.

  11. Turbofan engine mathematic model for its static and dynamic characteristics research

    Directory of Open Access Journals (Sweden)

    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.

  12. Developing Learning Model Based on Local Culture and Instrument for Mathematical Higher Order Thinking Ability

    Science.gov (United States)

    Saragih, Sahat; Napitupulu, E. Elvis; Fauzi, Amin

    2017-01-01

    This research aims to develop a student-centered learning model based on local culture and instrument of mathematical higher order thinking of junior high school students in the frame of the 2013-Curriculum in North Sumatra, Indonesia. The subjects of the research are seventh graders which are taken proportionally random consisted of three public…

  13. 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)

  14. 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)

  15. 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...

  16. 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

  17. MATHEMATICAL MODEL OF TRIAXIAL MULTIMODE ATTITUDE AND HEADING REFERENCE SYSTEM

    Directory of Open Access Journals (Sweden)

    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.

  18. 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.

  19. 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.

  20. 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.

  1. 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,.

  2. 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.

  3. 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...

  4. 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.

  5. 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.

  6. 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

  7. 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.

  8. 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.

  9. 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)

  10. 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...

  11. 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...

  12. 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)

  13. A thermodynamically consistent model of shape-memory alloys

    Czech Academy of Sciences Publication Activity Database

    Benešová, Barbora

    2011-01-01

    Roč. 11, č. 1 (2011), s. 355-356 ISSN 1617-7061 R&D Projects: GA ČR GAP201/10/0357 Institutional research plan: CEZ:AV0Z20760514 Keywords : slape memory alloys * model based on relaxation * thermomechanic coupling Subject RIV: BA - General Mathematics http://onlinelibrary.wiley.com/doi/10.1002/pamm.201110169/abstract

  14. PREFACE: 4th International Conference on Mathematical Modeling in Physical Sciences (IC-MSquare2015)

    Science.gov (United States)

    Vlachos, Dimitrios; Vagenas, Elias C.

    2015-09-01

    The 4th International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) took place in Mykonos, Greece, from Friday 5th June to Monday 8th June 2015. The Conference was attended by more than 150 participants and hosted about 200 oral, poster, and virtual presentations. There were more than 600 pre-registered authors. The 4th IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical/Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics etc. The scientific program was rather intense as after the Keynote and Invited Talks in the morning, three parallel oral and one poster session were running every day. However, according to all attendees, the program was excellent with a high quality of talks creating an innovative and productive scientific environment for all attendees. We would like to thank the Keynote Speaker and the Invited Speakers for their significant contribution to IC-MSQUARE. We also would like to thank the Members of the International Advisory and Scientific Committees as well as the Members of the Organizing Committee.

  15. 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…

  16. 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)

  17. Analyzing Mathematics Beliefs of Pre-Service Teachers Using Confirmatory Factor Analysis

    Directory of Open Access Journals (Sweden)

    Mazlini Adnan

    2011-12-01

    Full Text Available Mathematics beliefs play an important role in enhancing the quality and the effectiveness of teaching and learning. This study analyzes the mathematics beliefs of 317 pre-service teachers from six Higher Education Institutions (HEIs (Government Public Universities who were randomly selected to participate in this study. Questionnaires consisting of twenty three items were given to the respondents during the data collection process. The validation of the items was done by using confirmatory factor analysis (CFA. In order to obtain a model fit for the measurement model of mathematics beliefs, several fit index tests such as CMINDF, GFI, AGFI, IFI, NFI, CFI, TLI and RMSEA were used. Constructivist beliefs and traditional beliefs were identified as the contributing factors in the model. The analysis also revealed that mathematics beliefs consist of structures of two hidden variables. The correlation between the two variables (constructivist beliefs and traditional beliefs is at a moderate level. Hence, pre-service teachers should be able to recognize their type of mathematics beliefs in order to become effective mathematics teachers.

  18. 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.…

  19. 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.

  20. 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.

  1. 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

  2. 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 ...

  3. 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).

  4. 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.

  5. 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

  6. 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

  7. 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.

  8. 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.

  9. 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

  10. 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.

  11. 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)

  12. short communication mathematical modelling for magnetite

    African Journals Online (AJOL)

    Preferred Customer

    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:.

  13. 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.

  14. 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.

  15. 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.

  16. IMPROVEMENT OF MATHEMATICAL MODELS FOR ESTIMATION OF TRAIN DYNAMICS

    Directory of Open Access Journals (Sweden)

    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

  17. 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)

  18. 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 ...

  19. 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.

  20. 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

  1. Consistency in the description of diffusion in compacted bentonite

    International Nuclear Information System (INIS)

    Lehikoinen, J.; Muurinen, A.

    2009-01-01

    A macro-level diffusion model, which aims to provide a unifying framework for explaining the experimentally observed co-ion exclusion and greatly controversial counter-ion surface diffusion in a consistent fashion, is presented. It is explained in detail why a term accounting for the non-zero mobility of the counter-ion surface excess is required in the mathematical form of the macroscopic diffusion flux. The prerequisites for the consistency of the model and the problems associated with the interpretation of diffusion in such complex pore geometries as in compacted smectite clays are discussed. (author)

  2. 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…

  3. 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…

  4. Mathematical modeling of CANDU-PHWR

    Energy Technology Data Exchange (ETDEWEB)

    Gaber, F.A.; Aly, R.A.; El-Shal, A.O. [Atomic Energy Authority, Cairo (Egypt)

    2003-07-01

    The paper deals with the transient studies of CANDU 600 pressurized Heavy Water Reactor (PHWR). This study involved mathematical modeling of CANDU-PHWR to study its thermodynamic performances. Modeling of CANDU-PHWR was based on lumped parameter technique. The reactor model includes the neutronic, reactivity, and fuel channel heat transfer. The nuclear reactor power was modelled using the point kinetics equations with six groups of delayed neutrons and the reactivity feed back due to the changes in the fuel temperature and coolant temperature. The CANDU-PHWR model was coded in FORTRAN language and solved by using a standard numerical technique. The adequacy of the model was tested by assessing the physical plausibility of the obtained results. (author)

  5. 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...

  6. 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.

  7. 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)

  8. 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...

  9. 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.

  10. An explicit solution of the mathematical model for osmotic desalination process

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Do Yeon; Gu, Boram; Yang, Dae Ryook [Korea University, Seoul (Korea, Republic of)

    2013-09-15

    Membrane processes such as reverse osmosis and forward osmosis for seawater desalination have gained attention in recent years. Mathematical models have been used to interpret the mechanism of membrane processes. The membrane process model, consisting of flux and concentration polarization (CP) models, is coupled with balance equations and solved simultaneously. This set of model equations is, however, implicit and nonlinear; consequently, the model must be solved iteratively and numerically, which is time- and cost-intensive. We suggest a method to transform implicit equations to their explicit form, in order to avoid an iterative procedure. In addition, the performance of five solving methods, including the method that we suggest, is tested and compared for accuracy, computation time, and robustness based on input conditions. Our proposed method shows the best performance based on the robustness of various simulation conditions, accuracy, and a cost-effective computation time.

  11. 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…

  12. 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

  13. Self-consistent imbedding and the ellipsoidal model model for porous rocks

    International Nuclear Information System (INIS)

    Korringa, J.; Brown, R.J.S.; Thompson, D.D.; Runge, R.J.

    1979-01-01

    Equations are obtained for the effective elastic moduli for a model of an isotropic, heterogeneous, porous medium. The mathematical model used for computation is abstract in that it is not simply a rigorous computation for a composite medium of some idealized geometry, although the computation contains individual steps which are just that. Both the solid part and pore space are represented by ellipsoidal or spherical 'grains' or 'pores' of various sizes and shapes. The strain of each grain, caused by external forces applied to the medium, is calculated in a self-consistent imbedding (SCI) approximation, which replaces the true surrounding of any given grain or pore by an isotropic medium defined by the effective moduli to be computed. The ellipsoidal nature of the shapes allows us to use Eshelby's theoretical treatment of a single ellipsoidal inclusion in an infiinte homogeneous medium. Results are compared with the literature, and discrepancies are found with all published accounts of this problem. Deviations from the work of Wu, of Walsh, and of O'Connell and Budiansky are attributed to a substitution made by these authors which though an identity for the exact quantities involved, is only approximate in the SCI calculation. This reduces the validity of the equations to first-order effects only. Differences with the results of Kuster and Toksoez are attributed to the fact that the computation of these authors is not self-consistent in the sense used here. A result seems to be the stiffening of the medium as if the pores are held apart. For spherical grains and pores, their calculated moduli are those given by the Hashin-Shtrikman upper bounds. Our calculation reproduces, in the case of spheres, an early result of Budiansky. An additional feature of our work is that the algebra is simpler than in earlier work. We also incorporate into the theory the possibility that fluid-filled pores are interconnected

  14. Secondary Teachers’ Mathematics-related Beliefs and Knowledge about Mathematical Problem-solving

    Science.gov (United States)

    E Siswono, T. Y.; Kohar, A. W.; Hartono, S.

    2017-02-01

    This study investigates secondary teachers’ belief about the three mathematics-related beliefs, i.e. nature of mathematics, teaching mathematics, learning mathematics, and knowledge about mathematical problem solving. Data were gathered through a set of task-based semi-structured interviews of three selected teachers with different philosophical views of teaching mathematics, i.e. instrumental, platonist, and problem solving. Those teachers were selected from an interview using a belief-related task from purposively selected teachers in Surabaya and Sidoarjo. While the interviews about knowledge examine teachers’ problem solving content and pedagogical knowledge, the interviews about beliefs examine their views on several cases extracted from each of such mathematics-related beliefs. Analysis included the categorization and comparison on each of beliefs and knowledge as well as their interaction. Results indicate that all the teachers did not show a high consistency in responding views of their mathematics-related beliefs, while they showed weaknesses primarily on problem solving content knowledge. Findings also point out that teachers’ beliefs have a strong relationship with teachers’ knowledge about problem solving. In particular, the instrumental teacher’s beliefs were consistent with his insufficient knowledge about problem-solving, while both platonist and problem-solving teacher’s beliefs were consistent with their sufficient knowledge of either content or pedagogical problem solving.

  15. 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.

  16. Mathematics understanding and anxiety in collaborative teaching

    Science.gov (United States)

    Ansari, B. I.; Wahyu, N.

    2017-12-01

    This study aims to examine students’ mathematical understanding and anxiety using collaborative teaching. The sample consists of 51 students in the 7th-grade of MTs N Jeureula, one of the Islamic public junior high schools in Jeureula, Aceh, Indonesia. A test of mathematics understanding was administered to the students twice during the period of two months. The result suggests that there is a significant increase in mathematical understanding in the pre-test and post-test. We categorized the students into the high, intermediate, and low level of prior mathematics knowledge. In the high-level prior knowledge, there is no difference of mathematical understanding between the experiment and control group. Meanwhile, in the intermediate and low level of prior knowledge, there is a significant difference of mathematical understanding between the experiment and control group. The mathematics anxiety is at an intermediate level in the experiment class and at a high level in the control group. There is no interaction between the learning model and the students’ prior knowledge towards the mathematical understanding, but there are interactions towards the mathematics anxiety. It indicates that the collaborative teaching model and the students’ prior knowledge do not simultaneously impacts on the mathematics understanding but the mathematics anxiety.

  17. A stream-based mathematical model for distributed information processing systems - SysLab system model

    OpenAIRE

    Klein, Cornel; Rumpe, Bernhard; Broy, Manfred

    2014-01-01

    In the SysLab project we develop a software engineering method based on a mathematical foundation. The SysLab system model serves as an abstract mathematical model for information systems and their components. It is used to formalize the semantics of all used description techniques such as object diagrams state automata sequence charts or data-flow diagrams. Based on the requirements for such a reference model, we define the system model including its different views and their relationships.

  18. Mathematical model of information process of protection of the social sector

    Science.gov (United States)

    Novikov, D. A.; Tsarkova, E. G.; Dubrovin, A. S.; Soloviev, A. S.

    2018-03-01

    In work the mathematical model of information protection of society against distribution of extremist moods by means of impact on mass consciousness of information placed in media is investigated. Internal and external channels on which there is a dissemination of information are designated. The problem of optimization consisting in search of the optimum strategy allowing to use most effectively media for dissemination of antiterrorist information with the minimum financial expenses is solved. The algorithm of a numerical method of the solution of a problem of optimization is constructed and also the analysis of results of a computing experiment is carried out.

  19. SOME TRENDS IN MATHEMATICAL MODELING FOR BIOTECHNOLOGY

    Directory of Open Access Journals (Sweden)

    O. M. Klyuchko

    2018-02-01

    Full Text Available The purpose of present research is to demonstrate some trends of development of modeling methods for biotechnology according to contemporary achievements in science and technique. At the beginning the general approaches are outlined, some types of classifications of modeling methods are observed. The role of mathematic methods modeling for biotechnology in present époque of information computer technologies intensive development is studied and appropriate scheme of interrelation of all these spheres is proposed. Further case studies are suggested: some mathematic models in three different spaces (1D, 2D, 3D models are described for processes in living objects of different levels of hierarchic organization. In course of this the main attention was paid to some processes modeling in neurons as well as in their aggregates of different forms, including glioma cell masses (1D, 2D, 3D brain processes models. Starting from the models that have only theoretical importance for today, we describe at the end a model which application may be important for the practice. The work was done after the analysis of approximately 250 current publications in fields of biotechnology, including the authors’ original works.

  20. 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.

  1. PREFACE: 2nd International Conference on Mathematical Modeling in Physical Sciences 2013 (IC-MSQUARE 2013)

    Science.gov (United States)

    2014-03-01

    The second International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) took place at Prague, Czech Republic, from Sunday 1 September to Thursday 5 September 2013. The Conference was attended by more than 280 participants and hosted about 400 oral, poster, and virtual presentations while counted more than 600 pre-registered authors. The second IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical/Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics. The scientific program was rather heavy since after the Keynote and Invited Talks in the morning, three parallel sessions were running every day. However, according to all attendees, the program was excellent with high level of talks and the scientific environment was fruitful, thus all attendees had a creative time. We would like to thank the Keynote Speaker and the Invited Speakers for their significant contribution to IC-MSQUARE. We also would like to thank the Members of the International Advisory and Scientific Committees as well as the Members of the Organizing Committee. Further information on the editors, speakers and committees is available in the attached pdf.

  2. 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,.

  3. 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...

  4. 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

  5. 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

  6. 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.

  7. Does Writing Have Any Effect on Mathematics Success?

    Science.gov (United States)

    Dündar, Sefa

    2016-01-01

    In this study, the relationship between mathematics success and the formal properties and contents of the notebooks in which students take notes during mathematics classes have been examined. The exploratory model, in which quantitative and qualitative data are used together, has been used in this study. This study consists of 176 students from 3…

  8. 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.

  9. 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. 

  10. 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.

  11. Mathematical properties and parameter estimation for transit compartment pharmacodynamic models.

    Science.gov (United States)

    Yates, James W T

    2008-07-03

    One feature of recent research in pharmacodynamic modelling has been the move towards more mechanistically based model structures. However, in all of these models there are common sub-systems, such as feedback loops and time-delays, whose properties and contribution to the model behaviour merit some mathematical analysis. In this paper a common pharmacodynamic model sub-structure is considered: the linear transit compartment. These models have a number of interesting properties as the length of the cascade chain is increased. In the limiting case a pure time-delay is achieved [Milsum, J.H., 1966. Biological Control Systems Analysis. McGraw-Hill Book Company, New York] and the initial behaviour becoming increasingly sensitive to parameter value perturbation. It is also shown that the modelled drug effect is attenuated, though the duration of action is longer. Through this analysis the range of behaviours that such models are capable of reproducing are characterised. The properties of these models and the experimental requirements are discussed in order to highlight how mathematical analysis prior to experimentation can enhance the utility of mathematical modelling.

  12. Modeling Aspects of Activated Sludge Processes Part l l: Mathematical Process Modeling and Biokinetics of Activated Sludge Processes

    Energy Technology Data Exchange (ETDEWEB)

    AbdElHaleem, H S [Cairo Univ.-CivlI Eng. Dept., Giza (Egypt); EI-Ahwany, A H [CairoUlmrsity- Faculty ofEngincering - Chemical Engineering Department, Giza (Egypt); Ibrahim, H I [Helwan University- Faculty of Engineering - Biomedical Engineering Department, Helwan (Egypt); Ibrahim, G [Menofia University- Faculty of Engineering Sbebin EI Kom- Basic Eng. Sc. Dept., Menofia (Egypt)

    2004-07-01

    Mathematical process modeling and biokinetics of activated sludge process were reviewed considering different types of models. It has been evaluated the task group models of ASMI. and 2, and 3 versioned by Henze et al considering the conditions of each model and the different processes of which every model consists. It is revealed that ASMI contains some defects avoided in ASM3. Relied on homogeneity, Models can be classified into homogenous models characterized by taking the activated sludge process as one phase. In this type of models, the internal mass transfer inside the floes was neglected.. Hence, the kinetic parameter produces can be considered inaccurate. The other type of models is the heterogeneous model This type considers the mass transfer operations in addition to the biochemical reaction processes; hence, the resulted kinetic parameters can be considered more accurate than that of homogenous type.

  13. Modeling Aspects of Activated Sludge Processes Part l l: Mathematical Process Modeling and Biokinetics of Activated Sludge Processes

    International Nuclear Information System (INIS)

    AbdElHaleem, H.S.; EI-Ahwany, A. H.; Ibrahim, H.I.; Ibrahim, G.

    2004-01-01

    Mathematical process modeling and biokinetics of activated sludge process were reviewed considering different types of models. It has been evaluated the task group models of ASMI. and 2, and 3 versioned by Henze et al considering the conditions of each model and the different processes of which every model consists. It is revealed that ASMI contains some defects avoided in ASM3. Relied on homogeneity, Models can be classified into homogenous models characterized by taking the activated sludge process as one phase. In this type of models, the internal mass transfer inside the floes was neglected.. Hence, the kinetic parameter produces can be considered inaccurate. The other type of models is the heterogeneous model This type considers the mass transfer operations in addition to the biochemical reaction processes; hence, the resulted kinetic parameters can be considered more accurate than that of homogenous type

  14. A mathematical model of forgetting and amnesia

    NARCIS (Netherlands)

    Murre, J.M.J.; Chessa, A.G.; Meeter, M.

    2013-01-01

    We describe a mathematical model of learning and memory and apply it to the dynamics of forgetting and amnesia. The model is based on the hypothesis that the neural systems involved in memory at different time scales share two fundamental properties: (1) representations in a store decline in

  15. 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

  16. 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.

  17. 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...

  18. A novel mathematical model for controllable near-field electrospinning

    Science.gov (United States)

    Ru, Changhai; Chen, Jie; Shao, Zhushuai; Pang, Ming; Luo, Jun

    2014-01-01

    Near-field electrospinning (NFES) had better controllability than conventional electrospinning. However, due to the lack of guidance of theoretical model, precise deposition of micro/nano fibers could only accomplished by experience. To analyze the behavior of charged jet in NFES using mathematical model, the momentum balance equation was simplified and a new expression between jet cross-sectional radius and axial position was derived. Using this new expression and mass conservation equation, expressions for jet cross-sectional radius and velocity were derived in terms of axial position and initial jet acceleration in the form of exponential functions. Based on Slender-body theory and Giesekus model, a quadratic equation for initial jet acceleration was acquired. With the proposed model, it was able to accurately predict the diameter and velocity of polymer fibers in NFES, and mathematical analysis rather than experimental methods could be applied to study the effects of the process parameters in NFES. Moreover, the movement velocity of the collector stage can be regulated by mathematical model rather than experience. Therefore, the model proposed in this paper had important guiding significance to precise deposition of polymer fibers.

  19. A novel mathematical model for controllable near-field electrospinning

    International Nuclear Information System (INIS)

    Ru, Changhai; Chen, Jie; Shao, Zhushuai; Pang, Ming; Luo, Jun

    2014-01-01

    Near-field electrospinning (NFES) had better controllability than conventional electrospinning. However, due to the lack of guidance of theoretical model, precise deposition of micro/nano fibers could only accomplished by experience. To analyze the behavior of charged jet in NFES using mathematical model, the momentum balance equation was simplified and a new expression between jet cross-sectional radius and axial position was derived. Using this new expression and mass conservation equation, expressions for jet cross-sectional radius and velocity were derived in terms of axial position and initial jet acceleration in the form of exponential functions. Based on Slender-body theory and Giesekus model, a quadratic equation for initial jet acceleration was acquired. With the proposed model, it was able to accurately predict the diameter and velocity of polymer fibers in NFES, and mathematical analysis rather than experimental methods could be applied to study the effects of the process parameters in NFES. Moreover, the movement velocity of the collector stage can be regulated by mathematical model rather than experience. Therefore, the model proposed in this paper had important guiding significance to precise deposition of polymer fibers

  20. A novel mathematical model for controllable near-field electrospinning

    Energy Technology Data Exchange (ETDEWEB)

    Ru, Changhai, E-mail: rchhai@gmail.com, E-mail: luojun@shu.edu.cn [College of Automation, Harbin Engineering University, Harbin 150001 (China); Robotics and Microsystems Center, Soochow University, Suzhou 215021 (China); Chen, Jie; Shao, Zhushuai [Robotics and Microsystems Center, Soochow University, Suzhou 215021 (China); Pang, Ming [College of Automation, Harbin Engineering University, Harbin 150001 (China); Luo, Jun, E-mail: rchhai@gmail.com, E-mail: luojun@shu.edu.cn [School of Mechatronics Engineering and Automation, Shanghai University, Shanghai 200072 (China)

    2014-01-15

    Near-field electrospinning (NFES) had better controllability than conventional electrospinning. However, due to the lack of guidance of theoretical model, precise deposition of micro/nano fibers could only accomplished by experience. To analyze the behavior of charged jet in NFES using mathematical model, the momentum balance equation was simplified and a new expression between jet cross-sectional radius and axial position was derived. Using this new expression and mass conservation equation, expressions for jet cross-sectional radius and velocity were derived in terms of axial position and initial jet acceleration in the form of exponential functions. Based on Slender-body theory and Giesekus model, a quadratic equation for initial jet acceleration was acquired. With the proposed model, it was able to accurately predict the diameter and velocity of polymer fibers in NFES, and mathematical analysis rather than experimental methods could be applied to study the effects of the process parameters in NFES. Moreover, the movement velocity of the collector stage can be regulated by mathematical model rather than experience. Therefore, the model proposed in this paper had important guiding significance to precise deposition of polymer fibers.

  1. Coupling between phosphate and calcium homeostasis: a mathematical model.

    Science.gov (United States)

    Granjon, David; Bonny, Olivier; Edwards, Aurélie

    2017-12-01

    We developed a mathematical model of calcium (Ca) and phosphate (PO 4 ) homeostasis in the rat to elucidate the hormonal mechanisms that underlie the regulation of Ca and PO 4 balance. The model represents the exchanges of Ca and PO 4 between the intestine, plasma, kidneys, bone, and the intracellular compartment, and the formation of Ca-PO 4 -fetuin-A complexes. It accounts for the regulation of these fluxes by parathyroid hormone (PTH), vitamin D 3 , fibroblast growth factor 23, and Ca 2+ -sensing receptors. Our results suggest that the Ca and PO 4 homeostatic systems are robust enough to handle small perturbations in the production rate of either PTH or vitamin D 3 The model predicts that large perturbations in PTH or vitamin D 3 synthesis have a greater impact on the plasma concentration of Ca 2+ ([Ca 2+ ] p ) than on that of PO 4 ([PO 4 ] p ); due to negative feedback loops, [PO 4 ] p does not consistently increase when the production rate of PTH or vitamin D 3 is decreased. Our results also suggest that, following a large PO 4 infusion, the rapidly exchangeable pool in bone acts as a fast, transient storage PO 4 compartment (on the order of minutes), whereas the intracellular pool is able to store greater amounts of PO 4 over several hours. Moreover, a large PO 4 infusion rapidly lowers [Ca 2+ ] p owing to the formation of CaPO 4 complexes. A large Ca infusion, however, has a small impact on [PO 4 ] p , since a significant fraction of Ca binds to albumin. This mathematical model is the first to include all major regulatory factors of Ca and PO 4 homeostasis. Copyright © 2017 the American Physiological Society.

  2. 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.

  3. Mathematic Modeling for Vegetal Coal Activation in a Rotating Cylindrical Furnace

    Directory of Open Access Journals (Sweden)

    Carlos Zalazar-Oliva

    2016-05-01

    Full Text Available The activation of vegetal coal by applying physical or thermal methods is carried out under an atmosphere containing air, carbon dioxide or water vapor at temperatures ranging from 800 °C and 900 °C. This investigation was completed based on the mathematical modeling for the coal activation process in order to estimate the gas distribution and coal temperatures inside a rotating cylindrical kiln. The model consists of a system of non-lineal differential equations and equations to calculate the temperature of the cylinder internal wall and heat transfer coefficients. The 4th order Runge–Kutta method was used for the calculations. The comparison of the results obtained from modeling gas temperatures in the interior of the cylinder and the experimental data indicated that the variation is insignificant with an error margin below 5 %.

  4. 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…

  5. Mathematical modelling of non-isothermal venturi scrubbers

    Energy Technology Data Exchange (ETDEWEB)

    Rahimi, A. [Isfahan Univ., Isfahan (Iran, Islamic Republic of). Dept. of Chemical Engineering; Taheri, M.; Fathikakajahi, J. [Shiraz Univ., Shiraz (Iran, Islamic Republic of). Dept. of Chemical Engineering

    2005-06-01

    Venturi scrubbers collect gaseous pollutants and particulate matter from industrial exhaust. This air pollution control device is highly efficient, easy to maintain and has a low initial cost. However, the high pressure drop through the device results in a high running cost. The main mechanism for collecting particulates is the inertial impaction of the particles on the droplets, which occurs due to high velocity between the gas stream and droplets. Droplet acceleration and irreversible drag-force which results from this high relative velocity are responsible for the high pressure drop in this type of scrubber. While several attempts have been made to mathematically model particulate removal in Venturi scrubbers, most models do not consider simultaneous heat and mass transfer. This factor is important because most Venturi scrubbers operate under non-isothermal conditions where the inlet gas is humidified in order to cool it before entering the scrubber. For that reason, the authors developed a more realistic model to determine the effects of heat and mass transfer on the particulate removal efficiency of a non-isothermal Venturi type scrubber. The model considers the effect of droplet size distribution and liquid film flow on the walls. It consists of differential equations for energy, momentum and material exchange. Model results were compared with data from experimental studies and industrial facilities. It was concluded that the removal efficiency of the scrubber is influenced by the inlet humidity temperature of the inlet gas. 26 refs., 1 tab., 10 figs.

  6. Consistency of the MLE under mixture models

    OpenAIRE

    Chen, Jiahua

    2016-01-01

    The large-sample properties of likelihood-based statistical inference under mixture models have received much attention from statisticians. Although the consistency of the nonparametric MLE is regarded as a standard conclusion, many researchers ignore the precise conditions required on the mixture model. An incorrect claim of consistency can lead to false conclusions even if the mixture model under investigation seems well behaved. Under a finite normal mixture model, for instance, the consis...

  7. 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…

  8. 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…

  9. 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

  10. 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)

  11. Mathematical model and simulations of radiation fluxes from buried radionuclides

    International Nuclear Information System (INIS)

    Ahmad Saat

    1999-01-01

    A mathematical model and a simple Monte Carlo simulations were developed to predict radiation fluxes from buried radionuclides. The model and simulations were applied to measured (experimental) data. The results of the mathematical model showed good acceptable order of magnitude agreement. A good agreement was also obtained between the simple simulations and the experimental results. Thus, knowing the radionuclide distribution profiles in soil from a core sample, it can be applied to the model or simulations to estimate the radiation fluxes emerging from the soil surface. (author)

  12. Mathematical 3D modelling and sensitivity analysis of multipolar radiofrequency ablation in the spine.

    Science.gov (United States)

    Matschek, Janine; Bullinger, Eric; von Haeseler, Friedrich; Skalej, Martin; Findeisen, Rolf

    2017-02-01

    Radiofrequency ablation is a valuable tool in the treatment of many diseases, especially cancer. However, controlled heating up to apoptosis of the desired target tissue in complex situations, e.g. in the spine, is challenging and requires experienced interventionalists. For such challenging situations a mathematical model of radiofrequency ablation allows to understand, improve and optimise the outcome of the medical therapy. The main contribution of this work is the derivation of a tailored, yet expandable mathematical model, for the simulation, analysis, planning and control of radiofrequency ablation in complex situations. The dynamic model consists of partial differential equations that describe the potential and temperature distribution during intervention. To account for multipolar operation, time-dependent boundary conditions are introduced. Spatially distributed parameters, like tissue conductivity and blood perfusion, allow to describe the complex 3D environment representing diverse involved tissue types in the spine. To identify the key parameters affecting the prediction quality of the model, the influence of the parameters on the temperature distribution is investigated via a sensitivity analysis. Simulations underpin the quality of the derived model and the analysis approach. The proposed modelling and analysis schemes set the basis for intervention planning, state- and parameter estimation, and control. Copyright © 2016. Published by Elsevier Inc.

  13. The mathematical model of thread unrolling from a bobbin

    Directory of Open Access Journals (Sweden)

    S. M. Tenenbaum

    2014-01-01

    Full Text Available I. Introduction The subject of research in this work is a process of thread unrolling from a bobbin. The mathematical model of this process considering motion of thread peace on a bobbin and unrolled peace is proposed. The dimension of system of differential equations for this model is constant during deploying.The relevance to simulate this process for design of Heliogyro-like solar sails (Heliogyro [1], BMSTU-Sail [2] is proved. The paper briefly characterizes a blade for such solar sail as a simulation object. It proves the possibility for using a flexible thread model for a long blade because of very small blade thickness (less than 10 μm [3] relative to blade width and the phenomena of Koriolis forces [4] that lead to buckling failure of blade flatness.The major features of the proposed model are:-- simulated as a motion of the thread piece both being on a bobbin and its unrolled peace;-- splitting a thread length into nodes does not depend on the demand to ensure a sufficient number of nodes on a single thread turn on the coil;-- because of avoiding a problem of contact between the thread and bobbin a stable integration of motion equations is provided by the conventional Runge-Kutta method of fourth order with a constant step [5];-- in the course of solution the number of freedom degrees (number of motion equation is constant, thereby simplifying a calculation algorithm.The closest mathematical model is proposed in [6].The scientific novelty of this research is the approach to solving the problem of unrolling thread from a bobbin using a constant number of motion equations while preserving real kinematics coiling process.II. Problem formulationIn this section the problem of unrolling thread with length L from a bobbin of radius r is posed while any kind of forces are acting on the unrolled peace of thread. Moreover, the law of bobbin rotation φ(t assumed to be known with the proviso that the model can be modified if φ(t is the result of

  14. Mathematical Modeling in Combustion Science

    CERN Document Server

    Takeno, Tadao

    1988-01-01

    An important new area of current research in combustion science is reviewed in the contributions to this volume. The complicated phenomena of combustion, such as chemical reactions, heat and mass transfer, and gaseous flows, have so far been studied predominantly by experiment and by phenomenological approaches. But asymptotic analysis and other recent developments are rapidly changing this situation. The contributions in this volume are devoted to mathematical modeling in three areas: high Mach number combustion, complex chemistry and physics, and flame modeling in small scale turbulent flow combustion.

  15. 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…

  16. 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.

  17. 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…

  18. 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…

  19. 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.

  20. A mathematical model of sentimental dynamics accounting for marital dissolution.

    Science.gov (United States)

    Rey, José-Manuel

    2010-03-31

    Marital dissolution is ubiquitous in western societies. It poses major scientific and sociological problems both in theoretical and therapeutic terms. Scholars and therapists agree on the existence of a sort of second law of thermodynamics for sentimental relationships. Effort is required to sustain them. Love is not enough. Building on a simple version of the second law we use optimal control theory as a novel approach to model sentimental dynamics. Our analysis is consistent with sociological data. We show that, when both partners have similar emotional attributes, there is an optimal effort policy yielding a durable happy union. This policy is prey to structural destabilization resulting from a combination of two factors: there is an effort gap because the optimal policy always entails discomfort and there is a tendency to lower effort to non-sustaining levels due to the instability of the dynamics. These mathematical facts implied by the model unveil an underlying mechanism that may explain couple disruption in real scenarios. Within this framework the apparent paradox that a union consistently planned to last forever will probably break up is explained as a mechanistic consequence of the second law.

  1. A mathematical model of sentimental dynamics accounting for marital dissolution.

    Directory of Open Access Journals (Sweden)

    José-Manuel Rey

    Full Text Available BACKGROUND: Marital dissolution is ubiquitous in western societies. It poses major scientific and sociological problems both in theoretical and therapeutic terms. Scholars and therapists agree on the existence of a sort of second law of thermodynamics for sentimental relationships. Effort is required to sustain them. Love is not enough. METHODOLOGY/PRINCIPAL FINDINGS: Building on a simple version of the second law we use optimal control theory as a novel approach to model sentimental dynamics. Our analysis is consistent with sociological data. We show that, when both partners have similar emotional attributes, there is an optimal effort policy yielding a durable happy union. This policy is prey to structural destabilization resulting from a combination of two factors: there is an effort gap because the optimal policy always entails discomfort and there is a tendency to lower effort to non-sustaining levels due to the instability of the dynamics. CONCLUSIONS/SIGNIFICANCE: These mathematical facts implied by the model unveil an underlying mechanism that may explain couple disruption in real scenarios. Within this framework the apparent paradox that a union consistently planned to last forever will probably break up is explained as a mechanistic consequence of the second law.

  2. Mathematical models of granular matter

    CERN Document Server

    Mariano, Paolo; Giovine, Pasquale

    2008-01-01

    Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.

  3. Aspects of Mathematical Modelling of Pressure Retarded Osmosis

    Science.gov (United States)

    Anissimov, Yuri G.

    2016-01-01

    In power generating terms, a pressure retarded osmosis (PRO) energy generating plant, on a river entering a sea or ocean, is equivalent to a hydroelectric dam with a height of about 60 meters. Therefore, PRO can add significantly to existing renewable power generation capacity if economical constrains of the method are resolved. PRO energy generation relies on a semipermeable membrane that is permeable to water and impermeable to salt. Mathematical modelling plays an important part in understanding flows of water and salt near and across semipermeable membranes and helps to optimize PRO energy generation. Therefore, the modelling can help realizing PRO energy generation potential. In this work, a few aspects of mathematical modelling of the PRO process are reviewed and discussed. PMID:26848696

  4. Modeling a Consistent Behavior of PLC-Sensors

    Directory of Open Access Journals (Sweden)

    E. V. Kuzmin

    2014-01-01

    Full Text Available The article extends the cycle of papers dedicated to programming and verificatoin of PLC-programs by LTL-specification. This approach provides the availability of correctness analysis of PLC-programs by the model checking method.The model checking method needs to construct a finite model of a PLC program. For successful verification of required properties it is important to take into consideration that not all combinations of input signals from the sensors can occur while PLC works with a control object. This fact requires more advertence to the construction of the PLC-program model.In this paper we propose to describe a consistent behavior of sensors by three groups of LTL-formulas. They will affect the program model, approximating it to the actual behavior of the PLC program. The idea of LTL-requirements is shown by an example.A PLC program is a description of reactions on input signals from sensors, switches and buttons. In constructing a PLC-program model, the approach to modeling a consistent behavior of PLC sensors allows to focus on modeling precisely these reactions without an extension of the program model by additional structures for realization of a realistic behavior of sensors. The consistent behavior of sensors is taken into account only at the stage of checking a conformity of the programming model to required properties, i. e. a property satisfaction proof for the constructed model occurs with the condition that the model contains only such executions of the program that comply with the consistent behavior of sensors.

  5. Mathematical modeling of a convective textile drying process

    Directory of Open Access Journals (Sweden)

    G. Johann

    2014-12-01

    Full Text Available This study aims to develop a model that accurately represents the convective drying process of textile materials. The mathematical modeling was developed from energy and mass balances and, for the solution of the mathematical model, the technique of finite differences, in Cartesian coordinates, was used. It transforms the system of partial differential equations into a system of ordinary equations, with the unknowns, the temperature and humidity of both the air and the textile material. The simulation results were compared with experimental data obtained from the literature. In the statistical analysis the Shapiro-Wilk test was used to validate the model and, in all cases simulated, the results were p-values greater than 5 %, indicating normality of the data. The R-squared values were above 0.997 and the ratios Fcalculated/Fsimulated, at the 95 % confidence level, higher than five, indicating that the modeling was predictive in all simulations.

  6. 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.

  7. Mathematical Modelling of Surfactant Self-assembly at Interfaces

    KAUST Repository

    Morgan, C. E.

    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 differential equations that couple the rearrangement of surfactant within the multilayer to the surface adsorption kinetics is first derived. This model is then extended to the macroscopic scale by taking the continuum limit that exploits the typically large number of surfactant layers, which results in a novel third-order partial differential equation. The model is generalized to allow for the presence of two adsorbing boundaries, which results in an implicit free-boundary problem. The system predicts physically observed features in multilayer systems such as the initial formation of smaller lamellar structures and the typical number of layers that form in equilibrium.

  8. 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…

  9. On the mathematical modeling of aeolian saltation

    DEFF Research Database (Denmark)

    Jensen, Jens Ledet; Sørensen, Michael

    1983-01-01

    The development of a mathematical model for aeolian saltation is a promising way of obtaining further progress in the field of wind-blown sand. Interesting quantities can be calculated from a model defined in general terms, and a specific model is defined and compared to previously published data...... on aeolian saltation. This comparison points out the necessity of discriminating between pure and real saltation. -Authors...

  10. Taking the mystery out of mathematical model applications to karst aquifers—A primer

    Science.gov (United States)

    Kuniansky, Eve L.

    2014-01-01

    Advances in mathematical model applications toward the understanding of the complex flow, characterization, and water-supply management issues for karst aquifers have occurred in recent years. Different types of mathematical models can be applied successfully if appropriate information is available and the problems are adequately identified. The mathematical approaches discussed in this paper are divided into three major categories: 1) distributed parameter models, 2) lumped parameter models, and 3) fitting models. The modeling approaches are described conceptually with examples (but without equations) to help non-mathematicians understand the applications.

  11. Life insurance mathematics

    CERN Document Server

    Gerber, Hans U

    1997-01-01

    This concise introduction to life contingencies, the theory behind the actuarial work around life insurance and pension funds, will appeal to the reader who likes applied mathematics. In addition to model of life contingencies, the theory of compound interest is explained and it is shown how mortality and other rates can be estimated from observations. The probabilistic model is used consistently throughout the book. Numerous exercises (with answers and solutions) have been added, and for this third edition several misprints have been corrected.

  12. Mathematical models of human cerebellar development in the fetal period.

    Science.gov (United States)

    Dudek, Krzysztof; Nowakowska-Kotas, Marta; Kędzia, Alicja

    2018-04-01

    The evaluation of cerebellar growth in the fetal period forms a part of a widely used examination to identify any features of abnormalities in early stages of human development. It is well known that the development of anatomical structures, including the cerebellum, does not always follow a linear model of growth. The aim of the study was to analyse a variety of mathematical models of human cerebellar development in fetal life to determine their adequacy. The study comprised 101 fetuses (48 males and 53 females) between the 15th and 28th weeks of fetal life. The cerebellum was exposed and measurements of the vermis and hemispheres were performed, together with statistical analyses. The mathematical model parameters of fetal growth were assessed for crown-rump length (CRL) increases, transverse cerebellar diameter and ventrodorsal dimensions of the cerebellar vermis in the transverse plane, and rostrocaudal dimensions of the cerebellar vermis and hemispheres in the frontal plane. A variety of mathematical models were applied, including linear and non-linear functions. Taking into consideration the variance between models and measurements, as well as correlation parameters, the exponential and Gompertz models proved to be the most suitable for modelling cerebellar growth in the second and third trimesters of pregnancy. However, the linear model gave a satisfactory approximation of cerebellar growth, especially in older fetuses. The proposed models of fetal cerebellar growth constructed on the basis of anatomical examination and objective mathematical calculations could be useful in the estimation of fetal development. © 2018 Anatomical Society.

  13. An analysis of mathematical connection ability based on student learning style on visualization auditory kinesthetic (VAK) learning model with self-assessment

    Science.gov (United States)

    Apipah, S.; Kartono; Isnarto

    2018-03-01

    This research aims to analyze the quality of VAK learning with self-assessment toward the ability of mathematical connection performed by students and to analyze students’ mathematical connection ability based on learning styles in VAK learning model with self-assessment. This research applies mixed method type with concurrent embedded design. The subject of this research consists of VIII grade students from State Junior High School 9 Semarang who apply visual learning style, auditory learning style, and kinesthetic learning style. The data of learning style is collected by using questionnaires, the data of mathematical connection ability is collected by performing tests, and the data of self-assessment is collected by using assessment sheets. The quality of learning is qualitatively valued from planning stage, realization stage, and valuation stage. The result of mathematical connection ability test is analyzed quantitatively by mean test, conducting completeness test, mean differentiation test, and mean proportional differentiation test. The result of the research shows that VAK learning model results in well-qualified learning regarded from qualitative and quantitative sides. Students with visual learning style perform the highest mathematical connection ability, students with kinesthetic learning style perform average mathematical connection ability, and students with auditory learning style perform the lowest mathematical connection ability.

  14. A Mathematical Model of Cardiovascular Response to Dynamic Exercise

    National Research Council Canada - National Science Library

    Magosso, E

    2001-01-01

    A mathematical model of cardiovascular response to dynamic exercise is presented, The model includes the pulsating heart, the systemic and pulmonary, circulation, a functional description of muscle...

  15. Modeling Achievement in Mathematics: The Role of Learner and Learning Environment Characteristics

    Science.gov (United States)

    Nasser-Abu Alhija, Fadia; Amasha, Marcel

    2012-01-01

    This study examined a structural model of mathematics achievement among Druze 8th graders in Israel. The model integrates 2 psychosocial theories: goal theory and social learning theory. Variables in the model included gender, father's and mother's education, classroom mastery and performance goal orientation, mathematics self-efficacy and…

  16. Mathematical models in Slowpoke reactor internal irradiation site

    International Nuclear Information System (INIS)

    Raza, J.

    2007-01-01

    The main objective is to build representative mathematical models of neutron activation analysis in a Slowpoke internal irradiation site. Another significant objective is to correct various elements neutron activation analysis measured mass using these models. The neutron flux perturbation is responsible for the measured under-estimation of real masses. We supposed that neutron flux perturbation measurements taken during the Ecole Polytechnique de Montreal Slowpoke reactor first fuel loading were still valid after the second fuelling. .We also supposed that the thermal neutrons spatial and kinetic energies distributions as well as the absorption microscopic cross section dependence on the neutrons kinetic energies were important factors to satisfactorily represent neutron activation analysis results. In addition, we assumed that the neutron flux is isotropic in the laboratory system. We used experimental results from the Slowpoke reactor internal irradiation sites, in order to validate our mathematical models. Our models results are in close agreement with these experimental results..We established an accurate global mathematical correlation of the neutron flux perturbation in function of samples volumes and macroscopic neutron absorption cross sections. It is applicable to sample volumes ranging from 0,1 to 1,3 ml and macroscopic neutron absorption cross section up to 5 moles-b for seven (7) elements with atomic numbers (Z) ranging from 5 to 79. We first came up with a heuristic neutron transport mathematical semi-analytical model, in order to better understand neutrons behaviour in presence of one of several different nuclei samples volumes and mass. In order to well represent the neutron flux perturbation, we combined a neutron transport solution obtained from the spherical harmonics method of a finite cylinder and a mathematical expression combining two cylindrical harmonic functions..With the help of this model and the least squares method, we made extensive

  17. Mathematical models of bipolar disorder

    Science.gov (United States)

    Daugherty, Darryl; Roque-Urrea, Tairi; Urrea-Roque, John; Troyer, Jessica; Wirkus, Stephen; Porter, Mason A.

    2009-07-01

    We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.

  18. А mathematical model study of suspended monorail

    OpenAIRE

    Viktor GUTAREVYCH

    2012-01-01

    The mathematical model of suspended monorail track with allowance for elastic strain which occurs during movement of the monorail carriage was developed. Standard forms for single span and double span of suspended monorail sections were established.

  19. Representing the Electromagnetic Field: How Maxwell's Mathematics Empowered Faraday's Field Theory

    Science.gov (United States)

    Tweney, Ryan D.

    2011-01-01

    James Clerk Maxwell "translated" Michael Faraday's experimentally-based field theory into the mathematical representation now known as "Maxwell's Equations." Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday's theory and brought it into consistency with other…

  20. 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.

  1. 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...

  2. Mathematical modeling of renal hemodynamics in physiology and pathophysiology.

    Science.gov (United States)

    Sgouralis, Ioannis; Layton, Anita T

    2015-06-01

    In addition to the excretion of metabolic waste and toxin, the kidney plays an indispensable role in regulating the balance of water, electrolyte, acid-base, and blood pressure. For the kidney to maintain proper functions, hemodynamic control is crucial. In this review, we describe representative mathematical models that have been developed to better understand the kidney's autoregulatory processes. We consider mathematical models that simulate glomerular filtration, and renal blood flow regulation by means of the myogenic response and tubuloglomerular feedback. We discuss the extent to which these modeling efforts have expanded the understanding of renal functions in health and disease. Copyright © 2015 Elsevier Inc. All rights reserved.

  3. 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.

  4. Thermodynamically Consistent Algorithms for the Solution of Phase-Field Models

    KAUST Repository

    Vignal, Philippe

    2016-02-11

    Phase-field models are emerging as a promising strategy to simulate interfacial phenomena. Rather than tracking interfaces explicitly as done in sharp interface descriptions, these models use a diffuse order parameter to monitor interfaces implicitly. This implicit description, as well as solid physical and mathematical footings, allow phase-field models to overcome problems found by predecessors. Nonetheless, the method has significant drawbacks. The phase-field framework relies on the solution of high-order, nonlinear partial differential equations. Solving these equations entails a considerable computational cost, so finding efficient strategies to handle them is important. Also, standard discretization strategies can many times lead to incorrect solutions. This happens because, for numerical solutions to phase-field equations to be valid, physical conditions such as mass conservation and free energy monotonicity need to be guaranteed. In this work, we focus on the development of thermodynamically consistent algorithms for time integration of phase-field models. The first part of this thesis focuses on an energy-stable numerical strategy developed for the phase-field crystal equation. This model was put forward to model microstructure evolution. The algorithm developed conserves, guarantees energy stability and is second order accurate in time. The second part of the thesis presents two numerical schemes that generalize literature regarding energy-stable methods for conserved and non-conserved phase-field models. The time discretization strategies can conserve mass if needed, are energy-stable, and second order accurate in time. We also develop an adaptive time-stepping strategy, which can be applied to any second-order accurate scheme. This time-adaptive strategy relies on a backward approximation to give an accurate error estimator. The spatial discretization, in both parts, relies on a mixed finite element formulation and isogeometric analysis. The codes are

  5. Mathematical modelling of zirconium salicylate solvent extraction process

    International Nuclear Information System (INIS)

    Smirnova, N.S.; Evseev, A.M.; Fadeeva, V.I.; Kochetkova, S.K.

    1979-01-01

    Mathematical modelling of equilibrium multicomponent physicochemical system at the extraction of zirconium salicylates by chloroform is carried out from HCl aqueous solutions at pH 0.5-4.7. Adequate models, comprising different molecular forms, corresponding to equilibrium phase composition are built

  6. Mathematical modelling of zirconium salicylate solvent extraction process

    Energy Technology Data Exchange (ETDEWEB)

    Smirnova, N S; Evseev, A M; Fadeeva, V I; Kochetkova, S K [Moskovskij Gosudarstvennyj Univ. (USSR)

    1979-11-01

    Mathematical modelling of equilibrium multicomponent physicochemical system at the extraction of zirconium salicylates by chloroform is carried out from HCl aqueous solutions at pH 0.5-4.7. Adequate models, comprising different molecular forms, corresponding to equilibrium phase composition are built.

  7. 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 ...

  8. Mathematical Modeling in the People's Republic of China--Indicators of Participation and Performance on COMAP's Modeling Contest

    Science.gov (United States)

    Tian, Xiaoxi

    2014-01-01

    In recent years, Mainland Chinese teams have been the dominant participants in the two COMAP-sponsored mathematical modeling competitions: the Mathematical Contest in Modeling (MCM) and the Interdisciplinary Contest in Modeling (ICM). This study examines five factors that lead to the Chinese teams' dramatic increase in participation rate and…

  9. Mathematical models for correction of images, obtained at radioisotope scan

    International Nuclear Information System (INIS)

    Glaz, A.; Lubans, A.

    2002-01-01

    The images, which obtained at radioisotope scintigraphy, contain distortions. Distortions appear as a result of absorption of radiation by patient's body's tissues. Two mathematical models for reducing of such distortions are proposed. Image obtained by only one gamma camera is used in the first mathematical model. Unfortunately, this model allows processing of the images only in case, when it can be assumed, that the investigated organ has a symmetric form. The images obtained by two gamma cameras are used in the second model. It gives possibility to assume that the investigated organ has non-symmetric form and to acquire more precise results. (authors)

  10. A Mathematical Model of Marine Diesel Engine Speed Control System

    Science.gov (United States)

    Sinha, Rajendra Prasad; Balaji, Rajoo

    2018-02-01

    Diesel engine is inherently an unstable machine and requires a reliable control system to regulate its speed for safe and efficient operation. Also, the diesel engine may operate at fixed or variable speeds depending upon user's needs and accordingly the speed control system should have essential features to fulfil these requirements. This paper proposes a mathematical model of a marine diesel engine speed control system with droop governing function. The mathematical model includes static and dynamic characteristics of the control loop components. Model of static characteristic of the rotating fly weights speed sensing element provides an insight into the speed droop features of the speed controller. Because of big size and large time delay, the turbo charged diesel engine is represented as a first order system or sometimes even simplified to a pure integrator with constant gain which is considered acceptable in control literature. The proposed model is mathematically less complex and quick to use for preliminary analysis of the diesel engine speed controller performance.

  11. Mathematical modelling in engineering: A proposal to introduce linear algebra concepts

    Directory of Open Access Journals (Sweden)

    Andrea Dorila Cárcamo

    2016-03-01

    Full Text Available The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasize the development of mathematical abilities primarily associated with modelling and interpreting, which aren´t limited only to calculus abilities. Considering this, an instructional design was elaborated based on mathematic modelling and emerging heuristic models for the construction of specific linear algebra concepts:  span and spanning set. This was applied to first year engineering students. Results suggest that this type of instructional design contributes to the construction of these mathematical concepts and can also favour first year engineering students understanding of key linear algebra concepts and potentiate the development of higher order skills.

  12. 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.

  13. Structured Mathematical Modeling of Industrial Boiler

    OpenAIRE

    Aziz, Abdullah Nur; Nazaruddin, Yul Yunazwin; Siregar, Parsaulian; Bindar, Yazid

    2014-01-01

    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. T...

  14. Consistent Estimation of Partition Markov Models

    Directory of Open Access Journals (Sweden)

    Jesús E. García

    2017-04-01

    Full Text Available The Partition Markov Model characterizes the process by a partition L of the state space, where the elements in each part of L share the same transition probability to an arbitrary element in the alphabet. This model aims to answer the following questions: what is the minimal number of parameters needed to specify a Markov chain and how to estimate these parameters. In order to answer these questions, we build a consistent strategy for model selection which consist of: giving a size n realization of the process, finding a model within the Partition Markov class, with a minimal number of parts to represent the process law. From the strategy, we derive a measure that establishes a metric in the state space. In addition, we show that if the law of the process is Markovian, then, eventually, when n goes to infinity, L will be retrieved. We show an application to model internet navigation patterns.

  15. Comparison of Intelligent Systems in Detecting a Child's Mathematical Gift

    Science.gov (United States)

    Pavlekovic, Margita; Zekic-Susac, Marijana; Djurdjevic, Ivana

    2009-01-01

    This paper compares the efficiency of two intelligent methods: expert systems and neural networks, in detecting children's mathematical gift at the fourth grade of elementary school. The input space for the expert system and the neural network model consisted of 60 variables describing five basic components of a child's mathematical gift…

  16. Fun with maths: exploring implications of mathematical models for malaria eradication.

    Science.gov (United States)

    Eckhoff, Philip A; Bever, Caitlin A; Gerardin, Jaline; Wenger, Edward A

    2014-12-11

    Mathematical analyses and modelling have an important role informing malaria eradication strategies. Simple mathematical approaches can answer many questions, but it is important to investigate their assumptions and to test whether simple assumptions affect the results. In this note, four examples demonstrate both the effects of model structures and assumptions and also the benefits of using a diversity of model approaches. These examples include the time to eradication, the impact of vaccine efficacy and coverage, drug programs and the effects of duration of infections and delays to treatment, and the influence of seasonality and migration coupling on disease fadeout. An excessively simple structure can miss key results, but simple mathematical approaches can still achieve key results for eradication strategy and define areas for investigation by more complex models.

  17. А mathematical model study of suspended monorail

    Directory of Open Access Journals (Sweden)

    Viktor GUTAREVYCH

    2012-01-01

    Full Text Available The mathematical model of suspended monorail track with allowance for elastic strain which occurs during movement of the monorail carriage was developed. Standard forms for single span and double span of suspended monorail sections were established.

  18. A mathematical model of fluid and gas flow in nanoporous media.

    Science.gov (United States)

    Monteiro, Paulo J M; Rycroft, Chris H; Barenblatt, Grigory Isaakovich

    2012-12-11

    The mathematical modeling of the flow in nanoporous rocks (e.g., shales) becomes an important new branch of subterranean fluid mechanics. The classic approach that was successfully used in the construction of the technology to develop oil and gas deposits in the United States, Canada, and the Union of Soviet Socialist Republics becomes insufficient for deposits in shales. In the present article a mathematical model of the flow in nanoporous rocks is proposed. The model assumes the rock consists of two components: (i) a matrix, which is more or less an ordinary porous or fissurized-porous medium, and (ii) specific organic inclusions composed of kerogen. These inclusions may have substantial porosity but, due to the nanoscale of pores, tubes, and channels, have extremely low permeability on the order of a nanodarcy (~109-²¹ m² ) or less. These inclusions contain the majority of fluid: oil and gas. Our model is based on the hypothesis that the permeability of the inclusions substantially depends on the pressure gradient. At the beginning of the development of the deposit, boundary layers are formed at the boundaries of the low-permeable inclusions, where the permeability is strongly increased and intensive flow from inclusions to the matrix occurs. The resulting formulae for the production rate of the deposit are presented in explicit form. The formulae demonstrate that the production rate of deposits decays with time following a power law whose exponent lies between -1/2 and -1. Processing of experimental data obtained from various oil and gas deposits in shales demonstrated an instructive agreement with the prediction of the model.

  19. Development of syntax of intuition-based learning model in solving mathematics problems

    Science.gov (United States)

    Yeni Heryaningsih, Nok; Khusna, Hikmatul

    2018-01-01

    The aim of the research was to produce syntax of Intuition Based Learning (IBL) model in solving mathematics problem for improving mathematics students’ achievement that valid, practical and effective. The subject of the research were 2 classes in grade XI students of SMAN 2 Sragen, Central Java. The type of the research was a Research and Development (R&D). Development process adopted Plomp and Borg & Gall development model, they were preliminary investigation step, design step, realization step, evaluation and revision step. Development steps were as follow: (1) Collected the information and studied of theories in Preliminary Investigation step, studied about intuition, learning model development, students condition, and topic analysis, (2) Designed syntax that could bring up intuition in solving mathematics problem and then designed research instruments. They were several phases that could bring up intuition, Preparation phase, Incubation phase, Illumination phase and Verification phase, (3) Realized syntax of Intuition Based Learning model that has been designed to be the first draft, (4) Did validation of the first draft to the validator, (5) Tested the syntax of Intuition Based Learning model in the classrooms to know the effectiveness of the syntax, (6) Conducted Focus Group Discussion (FGD) to evaluate the result of syntax model testing in the classrooms, and then did the revision on syntax IBL model. The results of the research were produced syntax of IBL model in solving mathematics problems that valid, practical and effective. The syntax of IBL model in the classroom were, (1) Opening with apperception, motivations and build students’ positive perceptions, (2) Teacher explains the material generally, (3) Group discussion about the material, (4) Teacher gives students mathematics problems, (5) Doing exercises individually to solve mathematics problems with steps that could bring up students’ intuition: Preparations, Incubation, Illumination, and

  20. Large scale Bayesian nuclear data evaluation with consistent model defects

    International Nuclear Information System (INIS)

    Schnabel, G

    2015-01-01

    Monte Carlo sampling schemes of available evaluation methods. The second improvement concerns Bayesian evaluation methods based on a certain simplification of the nuclear model. These methods were restricted to the consistent evaluation of tens of thousands of observables. In this thesis, a new evaluation scheme has been developed, which is mathematically equivalent to existing methods, but allows the consistent evaluation of dozens of millions of observables. The new scheme is suited for the implementation as a database application. The realization of such an application with public access can help to accelerate the production of reliable nuclear data sets. Furthermore, in combination with the novel treatment of model deficiencies, problems of the model and the experimental data can be tracked down without user interaction. This feature can foster the development of nuclear models with high predictive power. (author) [de

  1. International seminar series on mathematics and applied mathematics and a series of three focused international research workshops on engineering mathematics organised by the Research Environment in Mathematics and Applied Mathematics at Mälardalen University from autumn 2014 to autumn 2015: the International Workshop on Engineering Mathematics for Electromagnetics and Health Technology; the International Workshop on Engineering Mathematics, Algebra, Analysis and Electromagnetics; and the 1st Swedish-Estonian International Workshop on Engineering Mathematics, Algebra, Analysis and Applications

    CERN Document Server

    Rancic, Milica

    2016-01-01

    This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most relevant for applications in modern technologies and engineering. It addresses mathematical methods of algebra, applied matrix analysis, operator analysis, probability theory and stochastic processes, geometry and computational methods in network analysis, data classification, ranking and optimisation. The individual chapters cover both theory and applications, and include a wealth of figures, schemes, algorithms, tables and results of data analysis and simulation. Presenting new methods and results, reviews of cutting-edge research, and open problems for future research, they equip readers to develop new mathematical methods and concepts of their own, and to further compare and analyse the methods and results discussed. The book consists of contributed chapters covering research developed as a result of a focused interna...

  2. Mathematical Model of Age Aggression

    OpenAIRE

    Golovinski, P. A.

    2013-01-01

    We formulate a mathematical model of competition for resources between representatives of different age groups. A nonlinear kinetic integral-differential equation of the age aggression describes the process of redistribution of resources. It is shown that the equation of the age aggression has a stationary solution, in the absence of age-dependency in the interaction of different age groups. A numerical simulation of the evolution of resources for different initial distributions has done. It ...

  3. Mathematical model of the reactor coolant pump

    International Nuclear Information System (INIS)

    Kozuh, M.

    1989-01-01

    The mathematical model of reactor coolant pump is described in this paper. It is based on correlations for centrifugal reactor coolant pumps. This code is one of the elements needed for the simulation of the whole NPP primary system. In subroutine developed according to this model we tried in every possible detail to incorporate plant specific data for Krsko NPP. (author)

  4. 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

  5. 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

  6. 78 FR 20148 - Reporting Procedure for Mathematical Models Selected To Predict Heated Effluent Dispersion in...

    Science.gov (United States)

    2013-04-03

    ... procedure acceptable to the NRC staff for providing summary details of mathematical modeling methods used in... NUCLEAR REGULATORY COMMISSION [NRC-2013-0062] Reporting Procedure for Mathematical Models Selected... Regulatory Guide (RG) 4.4, ``Reporting Procedure for Mathematical Models Selected to Predict Heated Effluent...

  7. 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…

  8. 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.

  9. 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

  10. Mathematical model for dissolved oxygen prediction in Cirata ...

    African Journals Online (AJOL)

    This paper presents the implementation and performance of mathematical model to predict theconcentration of dissolved oxygen in Cirata Reservoir, West Java by using Artificial Neural Network (ANN). The simulation program was created using Visual Studio 2012 C# software with ANN model implemented in it. Prediction ...

  11. Investigation of Predictive Power of Mathematics Anxiety on Mathematics Achievement in Terms of Gender and Class Variables

    Directory of Open Access Journals (Sweden)

    Mustafa İLHAN

    2013-12-01

    Full Text Available This research aims to explore predictive power of mathematics anxiety in terms of gender and class variables. For this purpose relational model was used in the study. Working group of the research consists of 348 secondary school second stage students, 175 of whom are girls and 175 are boys, having education in four elementary schools in central district of Diyarbakır province, during 2011-2012 Academic Year, first Semester. “Math Anxiety Scale for Primary School Students” to determine students’ mathematics anxiety was used. Averages of students’ mathematics notes in the first term of 2011- 2012 academic year are taken as the achievement scores of mathematics. The collected data has been analyzed by SPSS 17.0. The relationship between mathematics achievement and math anxiety was analyzed with pearson correlation. The predictor power of math anxiety for mathematics achievement was determined by the regression analysis. According the research findings %17 of the total variance of mathematics achievement can be explained by math anxiety. It has been determined that predictive power of mathematics anxiety on mathematics success is higher in girls than boys. Furthermore, it has been determined in the research that predictive power of mathematics anxiety on mathematics success increases, as students proceed towards the next grade.

  12. Classical and Weak Solutions for Two Models in Mathematical Finance

    Science.gov (United States)

    Gyulov, Tihomir B.; Valkov, Radoslav L.

    2011-12-01

    We study two mathematical models, arising in financial mathematics. These models are one-dimensional analogues of the famous Black-Scholes equation on finite interval. The main difficulty is the degeneration at the both ends of the space interval. First, classical solutions are studied. Positivity and convexity properties of the solutions are discussed. Variational formulation in weighted Sobolev spaces is introduced and existence and uniqueness of the weak solution is proved. Maximum principle for weak solution is discussed.

  13. Developing Students’ Reflections about the Function and Status of Mathematical Modeling in Different Scientific Practices

    DEFF Research Database (Denmark)

    Kjeldsen, Tinne Hoff; Blomhøj, Morten

    2013-01-01

    position held by the modeler(s) and the practitioners in the extra-mathematical domain. For students to experience the significance of different scientific practices and cultures for the function and status of mathematical modeling in other sciences, students need to be placed in didactical situations......Mathematical models and mathematical modeling play different roles in the different areas and problems in which they are used. The function and status of mathematical modeling and models in the different areas depend on the scientific practice as well as the underlying philosophical and theoretical...... where such differences are exposed and made into explicit objects of their reflections. It can be difficult to create such situations in the teaching of contemporary science in which modeling is part of the culture. In this paper we show how history can serve as a means for students to be engaged...

  14. Physical and mathematical modeling of antimicrobial photodynamic therapy

    Science.gov (United States)

    Bürgermeister, Lisa; López, Fernando Romero; Schulz, Wolfgang

    2014-07-01

    Antimicrobial photodynamic therapy (aPDT) is a promising method to treat local bacterial infections. The therapy is painless and does not cause bacterial resistances. However, there are gaps in understanding the dynamics of the processes, especially in periodontal treatment. This work describes the advances in fundamental physical and mathematical modeling of aPDT used for interpretation of experimental evidence. The result is a two-dimensional model of aPDT in a dental pocket phantom model. In this model, the propagation of laser light and the kinetics of the chemical reactions are described as coupled processes. The laser light induces the chemical processes depending on its intensity. As a consequence of the chemical processes, the local optical properties and distribution of laser light change as well as the reaction rates. The mathematical description of these coupled processes will help to develop treatment protocols and is the first step toward an inline feedback system for aPDT users.

  15. 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

  16. Mathematical modeling for prediction and optimization of TIG welding pool geometry

    Directory of Open Access Journals (Sweden)

    U. Esme

    2009-04-01

    Full Text Available In this work, nonlinear and multi-objective mathematical models were developed to determine the process parameters corresponding to optimum weld pool geometry. The objectives of the developed mathematical models are to maximize tensile load (TL, penetration (P, area of penetration (AP and/or minimize heat affected zone (HAZ, upper width (UW and upper height (UH depending upon the requirements.

  17. Mathematical models from the collections of universities and museums : photograph volume and commentary

    CERN Document Server

    2017-01-01

    This book presents beautiful photos of mathematical models of geometric surfaces made from a variety of materials including plaster, metal, paper, wood, and string. The construction of these models at the time (of Felix Klein and others) was not an end in itself, but was accompanied by mathematical research especially in the field of algebraic geometry. The models were used to illustrate the mathematical objects defined by abstract formulas, either as equations or parameterizations. In the second part of the book, the models are explained by experts in the field of geometry. This book is a reprint thirty years after the original publication in 1986 with a new preface by Gert-Martin Greuel. The models have a timeless appeal and a historical value. The Editor Prof. Dr. Gerd Fischer, Department of Mathematics, Technical University of Munich.

  18. Multiscale mathematical modeling of the hypothalamo-pituitary-gonadal axis.

    Science.gov (United States)

    Clément, Frédérique

    2016-07-01

    Although the fields of systems and integrative biology are in full expansion, few teams are involved worldwide into the study of reproductive function from the mathematical modeling viewpoint. This may be due to the fact that the reproductive function is not compulsory for individual organism survival, even if it is for species survival. Alternatively, the complexity of reproductive physiology may be discouraging. Indeed, the hypothalamo-pituitary-gonadal (HPG) axis involves not only several organs and tissues but also intricate time (from the neuronal millisecond timescale to circannual rhythmicity) and space (from molecules to organs) scales. Yet, mathematical modeling, and especially multiscale modeling, can renew our approaches of the molecular, cellular, and physiological processes underlying the control of reproductive functions. In turn, the remarkable dynamic features exhibited by the HPG axis raise intriguing and challenging questions to modelers and applied mathematicians. In this article, we draw a panoramic review of some mathematical models designed in the framework of the female HPG, with a special focus on the gonadal and central control of follicular development. On the gonadal side, the modeling of follicular development calls to the generic formalism of structured cell populations, that allows one to make mechanistic links between the control of cell fate (proliferation, differentiation, or apoptosis) and that of the follicle fate (ovulation or degeneration) or to investigate how the functional interactions between the oocyte and its surrounding cells shape the follicle morphogenesis. On the central, mainly hypothalamic side, models based on dynamical systems with multiple timescales allow one to represent within a single framework both the pulsatile and surge patterns of the neurohormone GnRH. Beyond their interest in basic research investigations, mathematical models can also be at the source of useful tools to study the encoding and decoding of

  19. Mathematical Model of the Emissions of a selected vehicle

    Directory of Open Access Journals (Sweden)

    Matušů Radim

    2014-10-01

    Full Text Available The article addresses the quantification of exhaust emissions from gasoline engines during transient operation. The main targeted emissions are carbon monoxide and carbon dioxide. The result is a mathematical model describing the production of individual emissions components in all modes (static and dynamic. It also describes the procedure for the determination of emissions from the engine’s operating parameters. The result is compared with other possible methods of measuring emissions. The methodology is validated using the data from an on-road measurement. The mathematical model was created on the first route and validated on the second route.

  20. Potential of mathematical modeling in fruit quality | Vazquez-Cruz ...

    African Journals Online (AJOL)

    A review of mathematical modeling applied to fruit quality showed that these models ranged inresolution from simple yield equations to complex representations of processes as respiration, photosynthesis and assimilation of nutrients. The latter models take into account complex genotype environment interactions to ...

  1. Mathematical modelling of thermal storage systems for the food industry

    Energy Technology Data Exchange (ETDEWEB)

    Lopez, A.; Lacarra, G. [Universidad Publica de Navarra Campus Arrosadia, Pamplona (Spain). Area de Tecnologia de Alimentos

    1999-07-01

    Dynamic mathematical models of two thermal storage systems used in the food industry to produce chilled water are presented; an ice-bank system and a holding tank system. The variability of the refrigeration demand with time was taken into account in the model. A zoned approach using mass and energy balances was applied. Heat transfer phenomena in the evaporator were modelled using empirical correlations. The experimental validation of the mathematical models on an ice-bank system at pilot plant scale, and a centralized refrigeration system with a holding tank in a winery, showed accurate prediction. Simple models are adequate to predict the dynamic behaviour of these refrigeration systems under variable heat loads. (Author)

  2. 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…

  3. Mathematical model of transmission network static state estimation

    Directory of Open Access Journals (Sweden)

    Ivanov Aleksandar

    2012-01-01

    Full Text Available In this paper the characteristics and capabilities of the power transmission network static state estimator are presented. The solving process of the mathematical model containing the measurement errors and their processing is developed. To evaluate difference between the general model of state estimation and the fast decoupled state estimation model, the both models are applied to an example, and so derived results are compared.

  4. Financial model calibration using consistency hints.

    Science.gov (United States)

    Abu-Mostafa, Y S

    2001-01-01

    We introduce a technique for forcing the calibration of a financial model to produce valid parameters. The technique is based on learning from hints. It converts simple curve fitting into genuine calibration, where broad conclusions can be inferred from parameter values. The technique augments the error function of curve fitting with consistency hint error functions based on the Kullback-Leibler distance. We introduce an efficient EM-type optimization algorithm tailored to this technique. We also introduce other consistency hints, and balance their weights using canonical errors. We calibrate the correlated multifactor Vasicek model of interest rates, and apply it successfully to Japanese Yen swaps market and US dollar yield market.

  5. Mathematical rainfall model for hydrographic demarcation of Manabi ...

    African Journals Online (AJOL)

    PROMOTING ACCESS TO AFRICAN RESEARCH ... To achieve this objective, the basins of the Hydrographic Demarcation of Manabí ... Keywords: multiple regression; mathematical model; GIS; Hydrology; rainfall. ... HOW TO USE AJOL.

  6. Mathematical Model for Direct Evaporative Space Cooling Systems ...

    African Journals Online (AJOL)

    This paper deals with the development of a simple mathematical model for experimental validation of the performance of a small evaporative cooling system in a tropical climate. It also presents the coefficient of convective heat transfer of wide range of temperatures based on existing model. Extensive experiments have ...

  7. Mathematical and computational modeling with applications in natural and social sciences, engineering, and the arts

    CERN Document Server

    Melnik, Roderick

    2015-01-01

    Illustrates the application of mathematical and computational modeling in a variety of disciplines With an emphasis on the interdisciplinary nature of mathematical and computational modeling, Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts features chapters written by well-known, international experts in these fields and presents readers with a host of state-of-the-art achievements in the development of mathematical modeling and computational experiment methodology. The book is a valuable guide to the methods, ideas,

  8. Mathematical Modeling of Hybrid Electrical Engineering Systems

    Directory of Open Access Journals (Sweden)

    A. A. Lobaty

    2016-01-01

    Full Text Available A large class of systems that have found application in various industries and households, electrified transportation facilities and energy sector has been classified as electrical engineering systems. Their characteristic feature is a combination of continuous and discontinuous modes of operation, which is reflected in the appearance of a relatively new term “hybrid systems”. A wide class of hybrid systems is pulsed DC converters operating in a pulse width modulation, which are non-linear systems with variable structure. Using various methods for linearization it is possible to obtain linear mathematical models that rather accurately simulate behavior of such systems. However, the presence in the mathematical models of exponential nonlinearities creates considerable difficulties in the implementation of digital hardware. The solution can be found while using an approximation of exponential functions by polynomials of the first order, that, however, violates the rigor accordance of the analytical model with characteristics of a real object. There are two practical approaches to synthesize algorithms for control of hybrid systems. The first approach is based on the representation of the whole system by a discrete model which is described by difference equations that makes it possible to synthesize discrete algorithms. The second approach is based on description of the system by differential equations. The equations describe synthesis of continuous algorithms and their further implementation in a digital computer included in the control loop system. The paper considers modeling of a hybrid electrical engineering system using differential equations. Neglecting the pulse duration, it has been proposed to describe behavior of vector components in phase coordinates of the hybrid system by stochastic differential equations containing generally non-linear differentiable random functions. A stochastic vector-matrix equation describing dynamics of the

  9. The High Level Mathematical Models in Calculating Aircraft Gas Turbine Engine Parameters

    Directory of Open Access Journals (Sweden)

    Yu. A. Ezrokhi

    2017-01-01

    Full Text Available The article describes high-level mathematical models developed to solve special problems arising at later stages of design with regard to calculation of the aircraft gas turbine engine (GTE under real operating conditions. The use of blade row mathematics models, as well as mathematical models of a higher level, including 2D and 3D description of the working process in the engine units and components, makes it possible to determine parameters and characteristics of the aircraft engine under conditions significantly different from the calculated ones.The paper considers application of mathematical modelling methods (MMM for solving a wide range of practical problems, such as forcing the engine by injection of water into the flowing part, estimate of the thermal instability effect on the GTE characteristics, simulation of engine start-up and windmill starting condition, etc. It shows that the MMM use, when optimizing the laws of the compressor stator control, as well as supplying cooling air to the hot turbine components in the motor system, can significantly improve the integral traction and economic characteristics of the engine in terms of its gas-dynamic stability, reliability and resource.It ought to bear in mind that blade row mathematical models of the engine are designed to solve purely "motor" problems and do not replace the existing models of various complexity levels used in calculation and design of compressors and turbines, because in “quality” a description of the working processes in these units is inevitably inferior to such specialized models.It is shown that the choice of the mathematical modelling level of an aircraft engine for solving a particular problem arising in its designing and computational study is to a large extent a compromise problem. Despite the significantly higher "resolution" and information ability the motor mathematical models containing 2D and 3D approaches to the calculation of flow in blade machine

  10. The irradiance and temperature dependent mathematical model for estimation of photovoltaic panel performances

    International Nuclear Information System (INIS)

    Barukčić, M.; Ćorluka, V.; Miklošević, K.

    2015-01-01

    Highlights: • The temperature and irradiance dependent model for the I–V curve estimation is presented. • The purely mathematical model based on the analysis of the I–V curve shape is presented. • The model includes the Gompertz function with temperature and irradiance dependent parameters. • The input data are extracted from the data sheet I–V curves. - Abstract: The temperature and irradiance dependent mathematical model for photovoltaic panel performances estimation is proposed in the paper. The base of the model is the mathematical function of the photovoltaic panel current–voltage curve. The model of the current–voltage curve is based on the sigmoid function with temperature and irradiance dependent parameters. The temperature and irradiance dependencies of the parameters are proposed in the form of analytic functions. The constant parameters are involved in the analytical functions. The constant parameters need to be estimated to get the temperature and irradiance dependent current–voltage curve. The mathematical model contains 12 constant parameters and they are estimated by using the evolutionary algorithm. The optimization problem is defined for this purpose. The optimization problem objective function is based on estimated and extracted (measured) current and voltage values. The current and voltage values are extracted from current–voltage curves given in datasheet of the photovoltaic panels. The new procedure for estimation of open circuit voltage value at any temperature and irradiance is proposed in the model. The performance of the proposed mathematical model is presented for three different photovoltaic panel technologies. The simulation results indicate that the proposed mathematical model is acceptable for estimation of temperature and irradiance dependent current–voltage curve and photovoltaic panel performances within temperature and irradiance ranges

  11. MATHEMATICAL MODELLING OF AIRCRAFT PILOTING PROSSESS UNDER SPECIFIED FLIGHT PATH

    Directory of Open Access Journals (Sweden)

    И. Кузнецов

    2012-04-01

    Full Text Available The author suggests mathematical model of pilot’s activity as follow up system and mathematical methods of pilot’s activity description. The main idea of the model is flight path forming and aircraft stabilization on it during instrument flight. Input of given follow up system is offered to be aircraft deflection from given path observed by pilot by means of sight and output is offered to be pilot’s regulating actions for aircraft stabilization on flight path.

  12. APPLYING PROFESSIONALLY ORIENTED PROBLEMS OF MATHEMATICAL MODELING IN TEACHING STUDENTS OF ENGINEERING DEPARTMENTS

    Directory of Open Access Journals (Sweden)

    Natal’ya Yur’evna Gorbunova

    2017-06-01

    Full Text Available We described several aspects of organizing student research work, as well as solving a number of mathematical modeling problems: professionally-oriented, multi-stage, etc. We underlined the importance of their economic content. Samples of using such problems in teaching Mathematics at agricultural university were given. Several questions connected with information material selection and peculiarities of research problems application were described. Purpose. The author aims to show the possibility and necessity of using professionally-oriented problems of mathematical modeling in teaching Mathematics at agricultural university. The subject of analysis is including such problems into educational process. Methodology. The main research method is dialectical method of obtaining knowledge of finding approaches to selection, writing and using mathematical modeling and professionally-oriented problems in educational process; the methodology is study of these methods of obtaining knowledge. Results. As a result of analysis of literature, students opinions, observation of students work, and taking into account personal teaching experience, it is possible to make conclusion about importance of using mathematical modeling problems, as it helps to systemize theoretical knowledge, apply it to practice, raise students study motivation in engineering sphere. Practical implications. Results of the research can be of interest for teachers of Mathematics in preparing Bachelor and Master students of engineering departments of agricultural university both for theoretical research and for modernization of study courses.

  13. 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…

  14. Attitudes of Mathematics Teachers toward Using Smart Board in Teaching Mathematics

    Science.gov (United States)

    Muhanna, Wafa; Nejem, Khamis Mousa

    2013-01-01

    This study aimed at investigating the attitudes of mathematics teachers toward using a smart board in teaching mathematics and also to determine the effect of gender, experience, and qualification of teachers on their attitudes. The sample of this study consisted of 74 mathematics teachers--35 males and 39 females--from private schools in Amman…

  15. Symmetrization of mathematical model of charge transport in semiconductors

    Directory of Open Access Journals (Sweden)

    Alexander M. Blokhin

    2002-11-01

    Full Text Available A mathematical model of charge transport in semiconductors is considered. The model is a quasilinear system of differential equations. A problem of finding an additional entropy conservation law and system symmetrization are solved.

  16. Mathematical methods and models in composites

    CERN Document Server

    Mantic, Vladislav

    2014-01-01

    This book provides a representative selection of the most relevant, innovative, and useful mathematical methods and models applied to the analysis and characterization of composites and their behaviour on micro-, meso-, and macroscale. It establishes the fundamentals for meaningful and accurate theoretical and computer modelling of these materials in the future. Although the book is primarily concerned with fibre-reinforced composites, which have ever-increasing applications in fields such as aerospace, many of the results presented can be applied to other kinds of composites. The topics cover

  17. Mathematical modeling of earth's dynamical systems a primer

    CERN Document Server

    Slingerland, Rudy

    2011-01-01

    Mathematical Modeling of Earth's Dynamical Systems gives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, the book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables. This book is directed toward upper-level undergraduate students, graduate students, researchers, and professionals who want to learn how to abstract complex systems into sets of dynamic equations. It shows students how to recognize domains of interest and key factors, and how to explain assumptions in formal terms. The book reveals what data best tests ideas of how nature works, and cautions against inadequate transport laws, unconstrained coefficients, and unfalsifiable models. Various examples of processes and systems, and ample illustrations, are provided. Students using this text should be f...

  18. Mathematical Analysis of a Model for Human Immunodeficiency ...

    African Journals Online (AJOL)

    ADOWIE PERE

    ABSTRACT: The objective of this paper is to present a mathematical model formulated to investigate the dynamics of human immunodeficiency virus (HIV). The disease free equilibrium of the model was found to be locally and globally asymptotically stable. The endemic equilibrium point exists and it was discovered that the ...

  19. PRINCIPLES OF DEVELOPMENT MATHEMATICAL MODEL FOR RESEARCHING OF NONPULSATILE FLOW PUMP AND CARDIAC SYSTEM

    Directory of Open Access Journals (Sweden)

    I. V. Bykov

    2013-01-01

    Full Text Available Aim. The presented research uncovers the using of mathematical modeling methods for cardio-vascular system and axial blood pump interaction analysis under heart failure with combined valve pathology. The research will pro- vide data for automated pump control algorithm synthesis. Materials and methods. Mathematical model is build up by using experiments results from mock cardio-vascular circulation loop and mathematical representation of Newtonian fluid dynamics in pulsing circulation loop. The model implemented in modeling environment Simulink (Matlab. Results. Authors implemented mathematical model which describe cardio-vascular system and left-ven- tricular assistive device interaction for intact conditions. Values of parameters for intact conditions were acquired in the experiments on animals with implanted axial pump, experiments were conducted in FRCTAO. The model was verified by comparison of instantaneous blood flowrate values in experiments and in model. Conclusion. The paper present implemented mathematical model of cardio-vascular system and axial pump interaction for intact conditions, where the pump connected between left ventricle and aorta. In the next part of research authors will use the presented model to evaluate using the biotechnical system in conditions of heart failure and valve pathology. 

  20. International Workshop on Mathematical Modeling of Tumor-Immune Dynamics

    CERN Document Server

    Kim, Peter; Mallet, Dann

    2014-01-01

    This collection of papers offers a broad synopsis of state-of-the-art mathematical methods used in modeling the interaction between tumors and the immune system. These papers were presented at the four-day workshop on Mathematical Models of Tumor-Immune System Dynamics held in Sydney, Australia from January 7th to January 10th, 2013. The workshop brought together applied mathematicians, biologists, and clinicians actively working in the field of cancer immunology to share their current research and to increase awareness of the innovative mathematical tools that are applicable to the growing field of cancer immunology. Recent progress in cancer immunology and advances in immunotherapy suggest that the immune system plays a fundamental role in host defense against tumors and could be utilized to prevent or cure cancer. Although theoretical and experimental studies of tumor-immune system dynamics have a long history, there are still many unanswered questions about the mechanisms that govern the interaction betwe...

  1. Does the cognitive reflection test measure cognitive reflection? A mathematical modeling approach.

    Science.gov (United States)

    Campitelli, Guillermo; Gerrans, Paul

    2014-04-01

    We used a mathematical modeling approach, based on a sample of 2,019 participants, to better understand what the cognitive reflection test (CRT; Frederick In Journal of Economic Perspectives, 19, 25-42, 2005) measures. This test, which is typically completed in less than 10 min, contains three problems and aims to measure the ability or disposition to resist reporting the response that first comes to mind. However, since the test contains three mathematically based problems, it is possible that the test only measures mathematical abilities, and not cognitive reflection. We found that the models that included an inhibition parameter (i.e., the probability of inhibiting an intuitive response), as well as a mathematical parameter (i.e., the probability of using an adequate mathematical procedure), fitted the data better than a model that only included a mathematical parameter. We also found that the inhibition parameter in males is best explained by both rational thinking ability and the disposition toward actively open-minded thinking, whereas in females this parameter was better explained by rational thinking only. With these findings, this study contributes to the understanding of the processes involved in solving the CRT, and will be particularly useful for researchers who are considering using this test in their research.

  2. Stability Analysis of a Mathematical Model for Onchocerciaisis ...

    African Journals Online (AJOL)

    ADOWIE PERE

    ABSTRACT: In this work, we propose a Deterministic Mathematical Model that ... blackflies Center for Disease Control and World ... villages located along fast flowing rivers where the ..... distribution of Blackflies (Simulium Species) in.

  3. MATHEMATICAL AND COMPUTATIONAL MODELLING OF RIBOSOMAL MOVEMENT AND PROTEIN SYNTHESIS: AN OVERVIEW

    Directory of Open Access Journals (Sweden)

    Tobias von der Haar

    2012-04-01

    Full Text Available Translation or protein synthesis consists of a complex system of chemical reactions, which ultimately result in decoding of the mRNA and the production of a protein. The complexity of this reaction system makes it difficult to quantitatively connect its input parameters (such as translation factor or ribosome concentrations, codon composition of the mRNA, or energy availability to output parameters (such as protein synthesis rates or ribosome densities on mRNAs. Mathematical and computational models of translation have now been used for nearly five decades to investigate translation, and to shed light on the relationship between the different reactions in the system. This review gives an overview over the principal approaches used in the modelling efforts, and summarises some of the major findings that were made.

  4. Zero-dimensional mathematical model of the torch ignited engine

    International Nuclear Information System (INIS)

    Cruz, Igor William Santos Leal; Alvarez, Carlos Eduardo Castilla; Teixeira, Alysson Fernandes; Valle, Ramon Molina

    2016-01-01

    Highlights: • Publications about the torch ignition system are mostly CFD or experimental research. • A zero-dimensional mathematical model is presented. • The model is based on classical thermodynamic equations. • Approximations are based on empirical functions. • The model is applied to a prototype by means of a computer code. - Abstract: Often employed in the analysis of conventional SI and CI engines, mathematical models can also be applied to engines with torch ignition, which have been researched almost exclusively by CFD or experimentally. The objective of this work is to describe the development and application of a zero-dimensional model of the compression and power strokes of a torch ignited engine. It is an initial analysis that can be used as a basis for future models. The processes of compression, combustion and expansion were described mathematically and applied to an existing prototype by means of a computer code written in MATLAB language. Conservation of energy and mass and the ideal gas law were used in determining gas temperature, pressure, and mass flow rate within the cylinder. Gas motion through the orifice was modelled as an isentropic compressible flow. The thermodynamic properties of the mixture were found by a weighted arithmetic mean of the data for each component, computed by polynomial functions of temperature. Combustion was modelled by the Wiebe function. Heat transfer to the cylinder walls was estimated by Annand’s correlations. Results revealed the behaviour of pressure, temperature, jet velocity, energy transfer, thermodynamic properties, among other variables, and how some of these are influenced by others.

  5. Promoting students’ mathematical problem-solving skills through 7e learning cycle and hypnoteaching model

    Science.gov (United States)

    Saleh, H.; Suryadi, D.; Dahlan, J. A.

    2018-01-01

    The aim of this research was to find out whether 7E learning cycle under hypnoteaching model can enhance students’ mathematical problem-solving skill. This research was quasi-experimental study. The design of this study was pretest-posttest control group design. There were two groups of sample used in the study. The experimental group was given 7E learning cycle under hypnoteaching model, while the control group was given conventional model. The population of this study was the student of mathematics education program at one university in Tangerang. The statistical analysis used to test the hypothesis of this study were t-test and Mann-Whitney U. The result of this study show that: (1) The students’ achievement of mathematical problem solving skill who obtained 7E learning cycle under hypnoteaching model are higher than the students who obtained conventional model; (2) There are differences in the students’ enhancement of mathematical problem-solving skill based on students’ prior mathematical knowledge (PMK) category (high, middle, and low).

  6. Mathematical modelling of dextran filtration through hollow fibre membranes

    DEFF Research Database (Denmark)

    Vinther, Frank; Pinelo, Manuel; Brøns, Morten

    2014-01-01

    In this paper we present a mathematical model of an ultrafiltration process. The results of the model are produced using standard numerical techniques with Comsol Multiphysics. The model describes the fluid flow and separation in hollow fibre membranes. The flow of solute and solvent within the h...

  7. Mathematical Modeling, Sense Making, and the Common Core State Standards

    Science.gov (United States)

    Schoenfeld, Alan H.

    2013-01-01

    On October 14, 2013 the Mathematics Education Department at Teachers College hosted a full-day conference focused on the Common Core Standards Mathematical Modeling requirements to be implemented in September 2014 and in honor of Professor Henry Pollak's 25 years of service to the school. This article is adapted from my talk at this conference…

  8. Mathematical model for hysteresis phenomenon in moisture transport of concrete carbonation process

    International Nuclear Information System (INIS)

    Aiki, Toyohiko; Kumazaki, Kota

    2012-01-01

    From civil engineering point of view it is very important to construct and analyze a mathematical model for a mechanism of concrete carbonation process. On this subject there are several mathematical results concerned with a one-dimensional model, in which hysteresis effects are neglected. Our aim is to give a model with hysteresis effects appearing in carbonation process. In this paper, as the first step of this research we focus only on moisture transport in the process and propose an initial boundary value problem for a system of partial differential equations as a mathematical model. Also, we give results on the existence of a solution to the problem, globally in time and the uniqueness in only one-dimensional case without proofs.

  9. A mathematical model of brain glucose homeostasis

    Directory of Open Access Journals (Sweden)

    Kimura Hidenori

    2009-11-01

    Full Text Available Abstract Background The physiological fact that a stable level of brain glucose is more important than that of blood glucose suggests that the ultimate goal of the glucose-insulin-glucagon (GIG regulatory system may be homeostasis of glucose concentration in the brain rather than in the circulation. Methods In order to demonstrate the relationship between brain glucose homeostasis and blood hyperglycemia in diabetes, a brain-oriented mathematical model was developed by considering the brain as the controlled object while the remaining body as the actuator. After approximating the body compartmentally, the concentration dynamics of glucose, as well as those of insulin and glucagon, are described in each compartment. The brain-endocrine crosstalk, which regulates blood glucose level for brain glucose homeostasis together with the peripheral interactions among glucose, insulin and glucagon, is modeled as a proportional feedback control of brain glucose. Correlated to the brain, long-term effects of psychological stress and effects of blood-brain-barrier (BBB adaptation to dysglycemia on the generation of hyperglycemia are also taken into account in the model. Results It is shown that simulation profiles obtained from the model are qualitatively or partially quantitatively consistent with clinical data, concerning the GIG regulatory system responses to bolus glucose, stepwise and continuous glucose infusion. Simulations also revealed that both stress and BBB adaptation contribute to the generation of hyperglycemia. Conclusion Simulations of the model of a healthy person under long-term severe stress demonstrated that feedback control of brain glucose concentration results in elevation of blood glucose level. In this paper, we try to suggest that hyperglycemia in diabetes may be a normal outcome of brain glucose homeostasis.

  10. Correlation of spacecraft thermal mathematical models to reference data

    Science.gov (United States)

    Torralbo, Ignacio; Perez-Grande, Isabel; Sanz-Andres, Angel; Piqueras, Javier

    2018-03-01

    Model-to-test correlation is a frequent problem in spacecraft-thermal control design. The idea is to determine the values of the parameters of the thermal mathematical model (TMM) that allows reaching a good fit between the TMM results and test data, in order to reduce the uncertainty of the mathematical model. Quite often, this task is performed manually, mainly because a good engineering knowledge and experience is needed to reach a successful compromise, but the use of a mathematical tool could facilitate this work. The correlation process can be considered as the minimization of the error of the model results with regard to the reference data. In this paper, a simple method is presented suitable to solve the TMM-to-test correlation problem, using Jacobian matrix formulation and Moore-Penrose pseudo-inverse, generalized to include several load cases. Aside, in simple cases, this method also allows for analytical solutions to be obtained, which helps to analyze some problems that appear when the Jacobian matrix is singular. To show the implementation of the method, two problems have been considered, one more academic, and the other one the TMM of an electronic box of PHI instrument of ESA Solar Orbiter mission, to be flown in 2019. The use of singular value decomposition of the Jacobian matrix to analyze and reduce these models is also shown. The error in parameter space is used to assess the quality of the correlation results in both models.

  11. Improved Mathematical Models for Particle-Size Distribution Data

    African Journals Online (AJOL)

    BirukEdimon

    School of Civil & Environmental Engineering, Addis Ababa Institute of Technology,. 3. Murray Rix ... two improved mathematical models to describe ... demand further improvement to handle the PSD ... statistics and the range of the optimized.

  12. Rock Burst Mechanics: Insight from Physical and Mathematical Modelling

    Directory of Open Access Journals (Sweden)

    J. Vacek

    2008-01-01

    Full Text Available Rock burst processes in mines are studied by many groups active in the field of geomechanics. Physical and mathematical modelling can be used to better understand the phenomena and mechanisms involved in the bursts. In the present paper we describe both physical and mathematical models of a rock burst occurring in a gallery of a coal mine.For rock bursts (also called bumps to occur, the rock has to possess certain particular rock burst properties leading to accumulation of energy and the potential to release this energy. Such materials may be brittle, or the rock burst may arise at the interfacial zones of two parts of the rock, which have principally different material properties (e.g. in the Poíbram uranium mines.The solution is based on experimental and mathematical modelling. These two methods have to allow the problem to be studied on the basis of three presumptions:· the solution must be time dependent,· the solution must allow the creation of cracks in the rock mass,· the solution must allow an extrusion of rock into an open space (bump effect. 

  13. Improving Mathematics Teaching in Kindergarten with Realistic Mathematical Education

    Science.gov (United States)

    Papadakis, Stamatios; Kalogiannakis, Michail; Zaranis, Nicholas

    2017-01-01

    The present study investigates and compares the influence of teaching Realistic Mathematics on the development of mathematical competence in kindergarten. The sample consisted of 231 Greek kindergarten students. For the implementation of the survey, we conducted an intervention, which included one experimental and one control group. Children in…

  14. A mathematical model for describing the mechanical behaviour of root canal instruments.

    Science.gov (United States)

    Zhang, E W; Cheung, G S P; Zheng, Y F

    2011-01-01

    The purpose of this study was to establish a general mathematical model for describing the mechanical behaviour of root canal instruments by combining a theoretical analytical approach with a numerical finite-element method. Mathematical formulas representing the longitudinal (taper, helical angle and pitch) and cross-sectional configurations and area, the bending and torsional inertia, the curvature of the boundary point and the (geometry of) loading condition were derived. Torsional and bending stresses and the resultant deformation were expressed mathematically as a function of these geometric parameters, modulus of elasticity of the material and the applied load. As illustrations, three brands of NiTi endodontic files of different cross-sectional configurations (ProTaper, Hero 642, and Mani NRT) were analysed under pure torsion and pure bending situation by entering the model into a finite-element analysis package (ANSYS). Numerical results confirmed that mathematical models were a feasible method to analyse the mechanical properties and predict the stress and deformation for root canal instruments during root canal preparation. Mathematical and numerical model can be a suitable way to examine mechanical behaviours as a criterion of the instrument design and to predict the stress and strain experienced by the endodontic instruments during root canal preparation. © 2010 International Endodontic Journal.

  15. Correlation Educational Model in Primary Education Curriculum of Mathematics and Computer Science

    Science.gov (United States)

    Macinko Kovac, Maja; Eret, Lidija

    2012-01-01

    This article gives insight into methodical correlation model of teaching mathematics and computer science. The model shows the way in which the related areas of computer science and mathematics can be supplemented, if it transforms the way of teaching and creates a "joint" lessons. Various didactic materials are designed, in which all…

  16. Mathematical modelling in radionuclide diagnosis of physiologic systems state

    International Nuclear Information System (INIS)

    Narkevich, B.Ya.

    1981-01-01

    It is shown that the development of software for radionuclide functional diagnostics should be carried out in two directions: 1) increasing the accuracy of radiographic measurements proper; 2) increasing clinical and diagnostic informativeness in the interpretation of the results of measurements. The realization of the first problem is reduced to a mathematical model of the measurement process and the computerized selection of optimum radiography parameters and regimes. The second problem is not solved in the general form, as the interpretation of measurement results depends on the specific clinical and diagnostic aim of investigation, indicator type and the way of its administration in the organism, etc. The lecture gives the classification of the mathematical models of indicator transport, techniques of identification of model parameters. Methods promoting the increase in the accuracy of model identification are presented [ru

  17. Evaluation of Mathematical Models for Tankers’ Maneuvering Motions

    Directory of Open Access Journals (Sweden)

    Erhan AKSU

    2017-03-01

    Full Text Available In this study, the maneuvering performance of two tanker ships, KVLCC1 and KVLCC2 which have different stern forms are predicted using a system-based method. Two different 3 DOF (degrees of freedom mathematical models based on the MMG(Maneuvering Modeling Group concept areappliedwith the difference in representing lateral force and yawing moment by second and third order polynomials respectively. Hydrodynamic coefficients and related parameters used in the mathematical models of the same scale models of KVLCC1 and KVLCC2 ships are estimated by using experimental data of NMRI (National Maritime Research Institute. The simulations of turning circle with rudder angle ±35o , zigzag(±10o /±10o and zigzag (±20o /±20o maneuvers are carried out and compared with free running model test data of MARIN (Maritime Research Institute Netherlands in this study. As a result of the analysis, it can be summarised that MMG model based on the third order polynomial is superior to the one based on the second order polynomial in view of estimation accuracy of lateral hull force and yawing moment.

  18. A whole-body mathematical model for intracranial pressure dynamics.

    Science.gov (United States)

    Lakin, William D; Stevens, Scott A; Tranmer, Bruce I; Penar, Paul L

    2003-04-01

    Most attempts to study intracranial pressure using lumped-parameter models have adopted the classical "Kellie-Monro Doctrine," which considers the intracranial space to be a closed system that is confined within the nearly-rigid skull, conserves mass, and has equal inflow and outflow. The present work revokes this Doctrine and develops a mathematical model for the dynamics of intracranial pressures, volumes, and flows that embeds the intracranial system in extensive whole-body physiology. The new model consistently introduces compartments representing the tissues and vasculature of the extradural portions of the body, including both the thoracic region and the lower extremities. In addition to vascular connections, a spinal-subarachnoid cerebrospinal fluid (CSF) compartment bridges intracranial and extracranial physiology allowing explict buffering of intracranial pressure fluctuations by the spinal theca. The model contains cerebrovascular autoregulation, regulation of systemic vascular pressures by the sympathetic nervous system, regulation of CSF production in the choroid plexus, a lymphatic system, colloid osmotic pressure effects, and realistic descriptions of cardiac output. To validate the model in situations involving normal physiology, the model's response to a realistic pulsatile cardiac output is examined. A well-known experimentally-derived intracranial pressure-volume relationship is recovered by using the model to simulate CSF infusion tests, and the effect on cerebral blood flow of a change in body position is also examined. Cardiac arrest and hemorrhagic shock are simulated to demonstrate the predictive capabilities of the model in pathological conditions.

  19. A mathematical look at a physical power prediction model

    Energy Technology Data Exchange (ETDEWEB)

    Landberg, L. [Riso National Lab., Roskilde (Denmark)

    1997-12-31

    This paper 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 the simplifications can be made and where they can not. This paper shows that there is a linear dependence between the geostrophic wind and the wind at the surface, but also that great care must be taken in the selection of the models since physical dependencies play a very important role, e.g. through the dependence of the turning of the wind on the wind speed.

  20. Proceedings – Mathematical Sciences | Indian Academy of Sciences

    Indian Academy of Sciences (India)

    ... consistent model for incompressible two-phase flows with phase transitions is considered mathematically. The model is based on first principles, i.e., balance of mass, momentum and energy. In the isothermal case, this problem is analysed to obtain local well-posedness, stability of non-degenerate equilibria, and global ...

  1. Unlocking the black box: teaching mathematical modeling with popular culture.

    Science.gov (United States)

    Lofgren, Eric T

    2016-10-01

    Mathematical modeling is an important tool in biological research, allowing for the synthesis of results from many studies into an understanding of a system. Despite this, the need for extensive subject matter knowledge and complex mathematics often leaves modeling as an esoteric subspecialty. A 2-fold approach can be used to make modeling more approachable for students and those interested in obtaining a functional knowledge of modeling. The first is the use of a popular culture disease system-a zombie epidemic-to allow for exploration of the concepts of modeling using a flexible framework. The second is the use of available interactive and non-calculus-based tools to allow students to work with and implement models to cement their understanding. © FEMS 2016. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

  2. Thin layer convective solar drying and mathematical modeling of prickly pear peel (Opuntia ficus indica)

    International Nuclear Information System (INIS)

    Lahsasni, Siham; Kouhila, Mohammed; Mahrouz, Mostafa; Idlimam, Ali; Jamali, Abdelkrim

    2004-01-01

    This paper presents the thin layer convective solar drying and mathematical modeling of prickly pear peel. For these purposes, an indirect forced convection solar dryer consisting of a solar air collector, an auxiliary heater, a circulation fan and a drying cabinet is used for drying experiments. Moreover, the prickly pear peel is sufficiently dried in the ranges of 32 to 36 deg. C of ambient air temperature, 50 to 60 deg. C of drying air temperature, 23 to 34% of relative humidity, 0.0277 to 0.0833 m 3 /s of drying air flow rate and 200 to 950 W/m 2 of daily solar radiation. The experimental drying curves show only a falling drying rate period. The main factor in controlling the drying rate was found to be the drying air temperature. The drying rate equation is determined empirically from the characteristic drying curve. Also, the experimental drying curves obtained were fitted to a number of mathematical models. The Midilli-Kucuk drying model was found to satisfactorily describe the solar drying curves of prickly pear peel with a correlation coefficient (r) of 0.9998 and chi-square (χ 2 ) of 4.6572 10 -5

  3. Mathematical modeling of efficacy and safety for anticancer drugs clinical development.

    Science.gov (United States)

    Lavezzi, Silvia Maria; Borella, Elisa; Carrara, Letizia; De Nicolao, Giuseppe; Magni, Paolo; Poggesi, Italo

    2018-01-01

    Drug attrition in oncology clinical development is higher than in other therapeutic areas. In this context, pharmacometric modeling represents a useful tool to explore drug efficacy in earlier phases of clinical development, anticipating overall survival using quantitative model-based metrics. Furthermore, modeling approaches can be used to characterize earlier the safety and tolerability profile of drug candidates, and, thus, the risk-benefit ratio and the therapeutic index, supporting the design of optimal treatment regimens and accelerating the whole process of clinical drug development. Areas covered: Herein, the most relevant mathematical models used in clinical anticancer drug development during the last decade are described. Less recent models were considered in the review if they represent a standard for the analysis of certain types of efficacy or safety measures. Expert opinion: Several mathematical models have been proposed to predict overall survival from earlier endpoints and validate their surrogacy in demonstrating drug efficacy in place of overall survival. An increasing number of mathematical models have also been developed to describe the safety findings. Modeling has been extensively used in anticancer drug development to individualize dosing strategies based on patient characteristics, and design optimal dosing regimens balancing efficacy and safety.

  4. Using the Scientific Method to Engage Mathematical Modeling: An Investigation of pi

    Science.gov (United States)

    Archer, Lester A. C.; Ng, Karen E.

    2016-01-01

    The purpose of this paper is to explain how to use the scientific method as the framework to introduce mathematical model. Two interdisciplinary activities, targeted for students in grade 6 or grade 7, are explained to show the application of the scientific method while building a mathematical model to investigate the relationship between the…

  5. A mathematical model of insulin resistance in Parkinson's disease.

    Science.gov (United States)

    Braatz, Elise M; Coleman, Randolph A

    2015-06-01

    This paper introduces a mathematical model representing the biochemical interactions between insulin signaling and Parkinson's disease. The model can be used to examine the changes that occur over the course of the disease as well as identify which processes would be the most effective targets for treatment. The model is mathematized using biochemical systems theory (BST). It incorporates a treatment strategy that includes several experimental drugs along with current treatments. In the past, BST models of neurodegeneration have used power law analysis and simulation (PLAS) to model the system. This paper recommends the use of MATLAB instead. MATLAB allows for more flexibility in both the model itself and in data analysis. Previous BST analyses of neurodegeneration began treatment at disease onset. As shown in this model, the outcomes of delayed, realistic treatment and full treatment at disease onset are significantly different. The delayed treatment strategy is an important development in BST modeling of neurodegeneration. It emphasizes the importance of early diagnosis, and allows for a more accurate representation of disease and treatment interactions. Copyright © 2015 Elsevier Ltd. All rights reserved.

  6. 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…

  7. An Invitation to Mathematics

    CERN Document Server

    Schleicher, Dierk

    2011-01-01

    This "Invitation to Mathematics" consists of 14 contributions, many from the world's leading mathematicians, which introduce the readers to exciting aspects of current mathematical research. The contributions are as varied as the personalities of active mathematicians, but together they show mathematics as a rich and lively field of research. The contributions are written for interested students at the age of transition between high school and university who know high school mathematics and perhaps competition mathematics and who want to find out what current research mathematics is

  8. Parameters Investigation of Mathematical Model of Productivity for Automated Line with Availability by DMAIC Methodology

    Directory of Open Access Journals (Sweden)

    Tan Chan Sin

    2014-01-01

    Full Text Available Automated line is widely applied in industry especially for mass production with less variety product. Productivity is one of the important criteria in automated line as well as industry which directly present the outputs and profits. Forecast of productivity in industry accurately in order to achieve the customer demand and the forecast result is calculated by using mathematical model. Mathematical model of productivity with availability for automated line has been introduced to express the productivity in terms of single level of reliability for stations and mechanisms. Since this mathematical model of productivity with availability cannot achieve close enough productivity compared to actual one due to lack of parameters consideration, the enhancement of mathematical model is required to consider and add the loss parameters that is not considered in current model. This paper presents the investigation parameters of productivity losses investigated by using DMAIC (Define, Measure, Analyze, Improve, and Control concept and PACE Prioritization Matrix (Priority, Action, Consider, and Eliminate. The investigated parameters are important for further improvement of mathematical model of productivity with availability to develop robust mathematical model of productivity in automated line.

  9. Mathematical models in cell biology and cancer chemotherapy

    CERN Document Server

    Eisen, Martin

    1979-01-01

    The purpose of this book is to show how mathematics can be applied to improve cancer chemotherapy. Unfortunately, most drugs used in treating cancer kill both normal and abnormal cells. However, more cancer cells than normal cells can be destroyed by the drug because tumor cells usually exhibit different growth kinetics than normal cells. To capitalize on this last fact, cell kinetics must be studied by formulating mathematical models of normal and abnormal cell growth. These models allow the therapeutic and harmful effects of cancer drugs to be simulated quantitatively. The combined cell and drug models can be used to study the effects of different methods of administering drugs. The least harmful method of drug administration, according to a given criterion, can be found by applying optimal control theory. The prerequisites for reading this book are an elementary knowledge of ordinary differential equations, probability, statistics, and linear algebra. In order to make this book self-contained, a chapter on...

  10. Mathematical model of the reformer sponge iron cycle

    Energy Technology Data Exchange (ETDEWEB)

    Fraser, S.; Hacker, V.; Evers, B.; Hierzer, J.; Besenhard, J.O. [Graz University of Technology, Graz (Austria). Inst. for Chemical Technology of Inorganic Materials Christian Doppler Pilot-Lab. for Fuel Cell Systems

    2003-07-01

    An innovative hydrogen production process called the Reformer Sponge Iron Cycle (RESC), based on redox reactions of iron ore pellets, was mathematically modeled. The hydrogen is produced by blowing steam over hot iron pellets in the oxidation stage, resulting in the oxidation of the iron. Synthesis gas coming from a reformer mixed with a fraction of recycled off-gas was used to reduce the iron oxide pellets (wuestite and-or magnetite) in the reduction stage, leading once more to iron . Once the mathematical model was developed, it was verified utilizing experimental data. Based on calculations of the equilibrium gas concentrations for reformer and sponge iron reactor (SIR), the model computes mass fluxes, molar fluxes, partial pressures, and variations of them throughout the complete cycle. The recycle rate, which determines the fraction of SIR off-gas recycled and added to the input gas stream, was optimized to maximize the amount of iron oxide reduced for a certain input gas flow. 5 refs., 4 figs.

  11. Recent progress and modern challenges in applied mathematics, modeling and computational science

    CERN Document Server

    Makarov, Roman; Belair, Jacques

    2017-01-01

    This volume is an excellent resource for professionals in various areas of applications of mathematics, modeling, and computational science. It focuses on recent progress and modern challenges in these areas. The volume provides a balance between fundamental theoretical and applied developments, emphasizing the interdisciplinary nature of modern trends and detailing state-of-the-art achievements in Applied Mathematics, Modeling, and Computational Science.  The chapters have been authored by international experts in their respective fields, making this book ideal for researchers in academia, practitioners, and graduate students. It can also serve as a reference in the diverse selected areas of applied mathematics, modelling, and computational sciences, and is ideal for interdisciplinary collaborations.

  12. Mathematical model of the reformer sponge iron cycle

    International Nuclear Information System (INIS)

    Fraser, S.; Hacker, V.; Evers, B.; Hierzer, J.; Besenhard, J.O.

    2003-01-01

    A mathematical model of the Reformer Sponge Iron Cycle (RESC), an innovative hydrogen production process based on redox reactions of iron ore pellets is presented. In the oxidation stage of the RESC, hydrogen is produced by blowing steam over hot iron pellets, hence oxidizing the iron. In the reduction stage, synthesis gas coming from a reformer mixed with a fraction of recycled off-gas is used to reduce the iron oxide pellets (wuestite and/or magnetite) back into iron again. A mathematical model of the complete RESC was developed and verified with experimental data. The model is based on calculations of the equilibrium gas concentrations for reformer and Sponge Iron Reactor (SIR). The current model computes mass fluxes, molar fluxes, partial pressures and variations of the respective throughout the complete cycle. The recycle rate, determining the fraction of SIR off-gas recycled and added to the input gas stream was subsequently optimized in order to maximize the amount of iron oxide reduced for a certain input gas flow. (author)

  13. Mathematical model simulation of a diesel spill in the Potomac River

    International Nuclear Information System (INIS)

    Feng, S.S.; Nicolette, J.P.; Markarian, R.K.

    1995-01-01

    A mathematical modeling technique was used to simulate the transport and fate of approximately 400,000 gallons of spilled diesel fuel and its impact on the aquatic biota in the Potomac River and Sugarland Run. Sugarland Run is a tributary about 21 miles upstream from Washington, DC. The mass balance model predicted the dynamic (spatial and temporal) distribution of spilled oil. The distributions were presented in terms of surface oil slick and sheen, dissolved and undissolved total petroleum hydrocarbons (TPH) in the water surface, water column, river sediments, shoreline and atmosphere. The processes simulated included advective movement, dispersion, dissolution, evaporation, volatilization, sedimentation, shoreline deposition, biodegradation, and removal of oil from cleanup operations. The model predicted that the spill resulted in a water column dissolved TPH concentration range of 0.05 to 18.6 ppm in Sugarland Run. The spilled oil traveled 10 miles along Sugarland Run before it reached the Potomac River. At the Potomac River, the water column TPH concentration was predicted to have decreased to the range of 0.0 to 0.43 ppm. These levels were consistent with field samples. To assess biological injury, the model used 4, 8, 24, 48, and 96-hr LC values in computing the fish injury caused by the fuel oil. The model used the maximum running average of dissolved TPH and exposure time to predict levels of fish mortality in the range of 38 to 40% in Sugarland Run. This prediction was consistent with field fisheries surveys. The model also computed the amount of spilled oil that adsorbed and settled into the river sediments

  14. Nonconvex Model of Material Growth: Mathematical Theory

    Science.gov (United States)

    Ganghoffer, J. F.; Plotnikov, P. I.; Sokolowski, J.

    2018-06-01

    The model of volumetric material growth is introduced in the framework of finite elasticity. The new results obtained for the model are presented with complete proofs. The state variables include the deformations, temperature and the growth factor matrix function. The existence of global in time solutions for the quasistatic deformations boundary value problem coupled with the energy balance and the evolution of the growth factor is shown. The mathematical results can be applied to a wide class of growth models in mechanics and biology.

  15. Development of mathematical model to predict the mechanical properties of friction stir

    Directory of Open Access Journals (Sweden)

    R. Palanivel

    2011-01-01

    Full Text Available This paper presents a systematic approach to develop the mathematical model for predicting the ultimate tensile strength,yield strength, and percentage of elongation of AA6351 aluminum alloy which is widely used in automotive, aircraft anddefense Industries by incorporating (FSW friction stir welding process parameter such as tool rotational speed, weldingspeed, and axial force. FSW has been carried out based on three factors five level central composite rotatable design withfull replications technique. Response surface methodology (RSM is employed to develop the mathematical model. Analysisof variance (ANOVA Technique is used to check the adequacy of the developed mathematical model. The developedmathematical model can be used effectively at 95% confidence level. The effect of FSW process parameter on mechanicalproperties of AA6351 aluminum alloy has been analyzed in detail.

  16. Self-consistent model of confinement

    International Nuclear Information System (INIS)

    Swift, A.R.

    1988-01-01

    A model of the large-spatial-distance, zero--three-momentum, limit of QCD is developed from the hypothesis that there is an infrared singularity. Single quarks and gluons do not propagate because they have infinite energy after renormalization. The Hamiltonian formulation of the path integral is used to quantize QCD with physical, nonpropagating fields. Perturbation theory in the infrared limit is simplified by the absence of self-energy insertions and by the suppression of large classes of diagrams due to vanishing propagators. Remaining terms in the perturbation series are resummed to produce a set of nonlinear, renormalizable integral equations which fix both the confining interaction and the physical propagators. Solutions demonstrate the self-consistency of the concepts of an infrared singularity and nonpropagating fields. The Wilson loop is calculated to provide a general proof of confinement. Bethe-Salpeter equations for quark-antiquark pairs and for two gluons have finite-energy solutions in the color-singlet channel. The choice of gauge is addressed in detail. Large classes of corrections to the model are discussed and shown to support self-consistency

  17. Use of mathematical modelling to assess the impact of vaccines on antibiotic resistance.

    Science.gov (United States)

    Atkins, Katherine E; Lafferty, Erin I; Deeny, Sarah R; Davies, Nicholas G; Robotham, Julie V; Jit, Mark

    2017-11-13

    Antibiotic resistance is a major global threat to the provision of safe and effective health care. To control antibiotic resistance, vaccines have been proposed as an essential intervention, complementing improvements in diagnostic testing, antibiotic stewardship, and drug pipelines. The decision to introduce or amend vaccination programmes is routinely based on mathematical modelling. However, few mathematical models address the impact of vaccination on antibiotic resistance. We reviewed the literature using PubMed to identify all studies that used an original mathematical model to quantify the impact of a vaccine on antibiotic resistance transmission within a human population. We reviewed the models from the resulting studies in the context of a new framework to elucidate the pathways through which vaccination might impact antibiotic resistance. We identified eight mathematical modelling studies; the state of the literature highlighted important gaps in our understanding. Notably, studies are limited in the range of pathways represented, their geographical scope, and the vaccine-pathogen combinations assessed. Furthermore, to translate model predictions into public health decision making, more work is needed to understand how model structure and parameterisation affects model predictions and how to embed these predictions within economic frameworks. Copyright © 2017 Elsevier Ltd. All rights reserved.

  18. Consistent Quantum Theory

    Science.gov (United States)

    Griffiths, Robert B.

    2001-11-01

    Quantum mechanics is one of the most fundamental yet difficult subjects in physics. Nonrelativistic quantum theory is presented here in a clear and systematic fashion, integrating Born's probabilistic interpretation with Schrödinger dynamics. Basic quantum principles are illustrated with simple examples requiring no mathematics beyond linear algebra and elementary probability theory. The quantum measurement process is consistently analyzed using fundamental quantum principles without referring to measurement. These same principles are used to resolve several of the paradoxes that have long perplexed physicists, including the double slit and Schrödinger's cat. The consistent histories formalism used here was first introduced by the author, and extended by M. Gell-Mann, J. Hartle and R. Omnès. Essential for researchers yet accessible to advanced undergraduate students in physics, chemistry, mathematics, and computer science, this book is supplementary to standard textbooks. It will also be of interest to physicists and philosophers working on the foundations of quantum mechanics. Comprehensive account Written by one of the main figures in the field Paperback edition of successful work on philosophy of quantum mechanics

  19. 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.

  20. 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…