Application of differential transformation method for solving dengue transmission mathematical model

Science.gov (United States)

Ndii, Meksianis Z.; Anggriani, Nursanti; Supriatna, Asep K.

2018-03-01

The differential transformation method (DTM) is a semi-analytical numerical technique which depends on Taylor series and has application in many areas including Biomathematics. The aim of this paper is to employ the differential transformation method (DTM) to solve system of non-linear differential equations for dengue transmission mathematical model. Analytical and numerical solutions are determined and the results are compared to that of Runge-Kutta method. We found a good agreement between DTM and Runge-Kutta method.

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

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.

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...

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…

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…

Optimal control for mathematical models of cancer therapies an application of geometric methods

CERN Document Server

Schättler, Heinz

2015-01-01

This book presents applications of geometric optimal control to real life biomedical problems with an emphasis on cancer treatments. A number of mathematical models for both classical and novel cancer treatments are presented as optimal control problems with the goal of constructing optimal protocols. The power of geometric methods is illustrated with fully worked out complete global solutions to these mathematically challenging problems. Elaborate constructions of optimal controls and corresponding system responses provide great examples of applications of the tools of geometric optimal control and the outcomes aid the design of simpler, practically realizable suboptimal protocols. The book blends mathematical rigor with practically important topics in an easily readable tutorial style. Graduate students and researchers in science and engineering, particularly biomathematics and more mathematical aspects of biomedical engineering, would find this book particularly useful.

Justification of the concept of mathematical methods and models in making decisions on taxation

OpenAIRE

KORKUNA NATALIA MIKHAYLOVNA

2017-01-01

The paper presents the concept of the application of mathematical methods and models in making decisions on taxation in Ukraine as a phased process. Its performance result is the selection of an effective decision based on regression and optimization models.

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.

PENDISC: a simple method for constructing a mathematical model from time-series data of metabolite concentrations.

Science.gov (United States)

Sriyudthsak, Kansuporn; Iwata, Michio; Hirai, Masami Yokota; Shiraishi, Fumihide

2014-06-01

The availability of large-scale datasets has led to more effort being made to understand characteristics of metabolic reaction networks. However, because the large-scale data are semi-quantitative, and may contain biological variations and/or analytical errors, it remains a challenge to construct a mathematical model with precise parameters using only these data. The present work proposes a simple method, referred to as PENDISC (Parameter Estimation in a N on- DImensionalized S-system with Constraints), to assist the complex process of parameter estimation in the construction of a mathematical model for a given metabolic reaction system. The PENDISC method was evaluated using two simple mathematical models: a linear metabolic pathway model with inhibition and a branched metabolic pathway model with inhibition and activation. The results indicate that a smaller number of data points and rate constant parameters enhances the agreement between calculated values and time-series data of metabolite concentrations, and leads to faster convergence when the same initial estimates are used for the fitting. This method is also shown to be applicable to noisy time-series data and to unmeasurable metabolite concentrations in a network, and to have a potential to handle metabolome data of a relatively large-scale metabolic reaction system. Furthermore, it was applied to aspartate-derived amino acid biosynthesis in Arabidopsis thaliana plant. The result provides confirmation that the mathematical model constructed satisfactorily agrees with the time-series datasets of seven metabolite concentrations.

Laser filamentation mathematical methods and models

CERN Document Server

Lorin, Emmanuel; Moloney, Jerome

2016-01-01

This book is focused on the nonlinear theoretical and mathematical problems associated with ultrafast intense laser pulse propagation in gases and in particular, in air. With the aim of understanding the physics of filamentation in gases, solids, the atmosphere, and even biological tissue, specialists in nonlinear optics and filamentation from both physics and mathematics attempt to rigorously derive and analyze relevant non-perturbative models. Modern laser technology allows the generation of ultrafast (few cycle) laser pulses, with intensities exceeding the internal electric field in atoms and molecules (E=5x109 V/cm or intensity I = 3.5 x 1016 Watts/cm2 ). The interaction of such pulses with atoms and molecules leads to new, highly nonlinear nonperturbative regimes, where new physical phenomena, such as High Harmonic Generation (HHG), occur, and from which the shortest (attosecond - the natural time scale of the electron) pulses have been created. One of the major experimental discoveries in this nonlinear...

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.

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…

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

Mathematical methods in biology and neurobiology

CERN Document Server

Jost, Jürgen

2014-01-01

Mathematical models can be used to meet many of the challenges and opportunities offered by modern biology. The description of biological phenomena requires a range of mathematical theories. This is the case particularly for the emerging field of systems biology. Mathematical Methods in Biology and Neurobiology introduces and develops these mathematical structures and methods in a systematic manner. It studies:   • discrete structures and graph theory • stochastic processes • dynamical systems and partial differential equations • optimization and the calculus of variations.   The biological applications range from molecular to evolutionary and ecological levels, for example:   • cellular reaction kinetics and gene regulation • biological pattern formation and chemotaxis • the biophysics and dynamics of neurons • the coding of information in neuronal systems • phylogenetic tree reconstruction • branching processes and population genetics • optimal resource allocation • sexual recombi...

Computational mathematics models, methods, and analysis with Matlab and MPI

CERN Document Server

White, Robert E

2004-01-01

Computational Mathematics: Models, Methods, and Analysis with MATLAB and MPI explores and illustrates this process. Each section of the first six chapters is motivated by a specific application. The author applies a model, selects a numerical method, implements computer simulations, and assesses the ensuing results. These chapters include an abundance of MATLAB code. By studying the code instead of using it as a "black box, " you take the first step toward more sophisticated numerical modeling. The last four chapters focus on multiprocessing algorithms implemented using message passing interface (MPI). These chapters include Fortran 9x codes that illustrate the basic MPI subroutines and revisit the applications of the previous chapters from a parallel implementation perspective. All of the codes are available for download from www4.ncsu.edu./~white.This book is not just about math, not just about computing, and not just about applications, but about all three--in other words, computational science. Whether us...

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.

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.

Mathematic models for a ray tracing method and its applications in wireless optical communications.

Science.gov (United States)

Zhang, Minglun; Zhang, Yangan; Yuan, Xueguang; Zhang, Jinnan

2010-08-16

This paper presents a new ray tracing method, which contains a whole set of mathematic models, and its validity is verified by simulations. In addition, both theoretical analysis and simulation results show that the computational complexity of the method is much lower than that of previous ones. Therefore, the method can be used to rapidly calculate the impulse response of wireless optical channels for complicated systems.

Mathematical methods for diffusion MRI processing

International Nuclear Information System (INIS)

Lenglet, C.; Lenglet, C.; Sapiro, G.; Campbell, J.S.W.; Pike, G.B.; Campbell, J.S.W.; Siddiqi, K.; Descoteaux, M.; Haro, G.; Wassermann, D.; Deriche, R.; Wassermann, D.; Anwander, A.; Thompson, P.M.

2009-01-01

In this article, we review recent mathematical models and computational methods for the processing of diffusion Magnetic Resonance Images, including state-of-the-art reconstruction of diffusion models, cerebral white matter connectivity analysis, and segmentation techniques. We focus on Diffusion Tensor Images (DTI) and Q-Ball Images (QBI). (authors)

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...

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…

Mathematical methods for mechanics a handbook with Matlab experiments

CERN Document Server

Gekeler, Eckart W

2008-01-01

This book introduces all the mathematical tools necessary for solving complex problems in the field of mechanics. It also contains various applications of mathematical and numerical methods for modeling comprehensive mechanical-technical practical problems.

Mathematical methods to model rodent behavior in the elevated plus-maze.

Science.gov (United States)

Arantes, Rafael; Tejada, Julián; Bosco, Geraldine G; Morato, Silvio; Roque, Antonio C

2013-11-15

The elevated plus maze is a widely used experimental test to study anxiety-like rodent behavior. It is made of four arms, two open and two closed, connected at a central area forming a plus shaped maze. The whole apparatus is elevated 50 cm from the floor. The anxiety of the animal is usually assessed by the number of entries and duration of stay in each arm type during a 5-min period. Different mathematical methods have been proposed to model the mechanisms that control the animal behavior in the maze, such as factor analysis, statistical inference on Markov chains and computational modeling. In this review we discuss these methods and propose possible extensions of them as a direction for future research. Copyright © 2013 Elsevier B.V. All rights reserved.

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...

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).

Mathematical Modelling Plant Signalling Networks

KAUST Repository

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

2013-01-01

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

Mathematical models for therapeutic approaches to control HIV disease transmission

CERN Document Server

Roy, Priti Kumar

2015-01-01

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

Mathematical modelling 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

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…

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…

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

Science.gov (United States)

Ganusov, Vitaly V

2016-01-01

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

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

Directory of Open Access Journals (Sweden)

Vitaly V. Ganusov

2016-07-01

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

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

11th Biennial Conference on Emerging Mathematical Methods, Models and Algorithms for Science and Technology

CERN Document Server

Manchanda, Pammy; Bhardwaj, Rashmi

2015-01-01

The present volume contains invited talks of 11th biennial conference on “Emerging Mathematical Methods, Models and Algorithms for Science and Technology”. The main message of the book is that mathematics has a great potential to analyse and understand the challenging problems of nanotechnology, biotechnology, medical science, oil industry and financial technology. The book highlights all the features and main theme discussed in the conference. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world.

METHOD OF GREEN FUNCTIONS IN MATHEMATICAL MODELLING FOR TWO-POINT BOUNDARY-VALUE PROBLEMS

Directory of Open Access Journals (Sweden)

E. V. Dikareva

2015-01-01

Full Text Available Summary. In many applied problems of control, optimization, system theory, theoretical and construction mechanics, for problems with strings and nods structures, oscillation theory, theory of elasticity and plasticity, mechanical problems connected with fracture dynamics and shock waves, the main instrument for study these problems is a theory of high order ordinary differential equations. This methodology is also applied for studying mathematical models in graph theory with different partitioning based on differential equations. Such equations are used for theoretical foundation of mathematical models but also for constructing numerical methods and computer algorithms. These models are studied with use of Green function method. In the paper first necessary theoretical information is included on Green function method for multi point boundary-value problems. The main equation is discussed, notions of multi-point boundary conditions, boundary functionals, degenerate and non-degenerate problems, fundamental matrix of solutions are introduced. In the main part the problem to study is formulated in terms of shocks and deformations in boundary conditions. After that the main results are formulated. In theorem 1 conditions for existence and uniqueness of solutions are proved. In theorem 2 conditions are proved for strict positivity and equal measureness for a pair of solutions. In theorem 3 existence and estimates are proved for the least eigenvalue, spectral properties and positivity of eigenfunctions. In theorem 4 the weighted positivity is proved for the Green function. Some possible applications are considered for a signal theory and transmutation operators.

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....

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...

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.

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.

Method of computer generation and projection recording of microholograms for holographic memory systems: mathematical modelling and experimental implementation

International Nuclear Information System (INIS)

Betin, A Yu; Bobrinev, V I; Evtikhiev, N N; Zherdev, A Yu; Zlokazov, E Yu; Lushnikov, D S; Markin, V V; Odinokov, S B; Starikov, S N; Starikov, R S

2013-01-01

A method of computer generation and projection recording of microholograms for holographic memory systems is presented; the results of mathematical modelling and experimental implementation of the method are demonstrated. (holographic memory)

Mathematical analysis and numerical methods for science and technology

CERN Document Server

Dautray, Robert

These 6 volumes - the result of a 10 year collaboration between the authors, two of France's leading scientists and both distinguished international figures - compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems: a model here means a set of equations, which ...

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.

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...

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

The Interval Market Model in Mathematical Finance : Game Theoretic Methods

NARCIS (Netherlands)

Bernhard, P.; Engwerda, J.C.; Roorda, B.; Schumacher, J.M.; Kolokoltsov, V.; Saint-Pierre, P.; Aubin, J.P.

2013-01-01

Toward the late 1990s, several research groups independently began developing new, related theories in mathematical finance. These theories did away with the standard stochastic geometric diffusion “Samuelson” market model (also known as the Black-Scholes model because it is used in that most famous

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.

Mixed Methods Study Using Constructive Learning Team Model for Secondary Mathematics Teachers

Science.gov (United States)

Ritter, Kristy L.

2010-01-01

The constructive learning team model for secondary mathematics teachers (CLTM) was created to provide students with learning opportunities and experiences that address deficiencies in oral and written communication, logical processes and analysis, mathematical operations, independent learning, teamwork, and technology utilization. This study…

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...

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

Science.gov (United States)

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

2018-01-01

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

Mathematical 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

Transient Mathematical Modeling for Liquid Rocket Engine Systems: Methods, Capabilities, and Experience

Science.gov (United States)

Seymour, David C.; Martin, Michael A.; Nguyen, Huy H.; Greene, William D.

2005-01-01

The subject of mathematical modeling of the transient operation of liquid rocket engines is presented in overview form from the perspective of engineers working at the NASA Marshall Space Flight Center. The necessity of creating and utilizing accurate mathematical models as part of liquid rocket engine development process has become well established and is likely to increase in importance in the future. The issues of design considerations for transient operation, development testing, and failure scenario simulation are discussed. An overview of the derivation of the basic governing equations is presented along with a discussion of computational and numerical issues associated with the implementation of these equations in computer codes. Also, work in the field of generating usable fluid property tables is presented along with an overview of efforts to be undertaken in the future to improve the tools use for the mathematical modeling process.

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...

THE INFLUENCE OF THE ASSESSMENT MODEL AND METHOD TOWARD THE SCIENCE LEARNING ACHIEVEMENT BY CONTROLLING THE STUDENTS? PREVIOUS KNOWLEDGE OF MATHEMATICS.

OpenAIRE

Adam rumbalifar; I. g. n. Agung; Burhanuddin tola.

2018-01-01

This research aims to study the influence of the assessment model and method toward the science learning achievement by controlling the students? previous knowledge of mathematics. This study was conducted at SMP East Seram district with the population of 295 students. This study applied a quasi-experimental method with 2 X 2 factorial design using the ANCOVA model. The findings after controlling the students\\' previous knowledge of mathematics show that the science learning achievement of th...

System principles, mathematical models and methods to ensure high reliability of safety systems

Science.gov (United States)

Zaslavskyi, V.

2017-04-01

Modern safety and security systems are composed of a large number of various components designed for detection, localization, tracking, collecting, and processing of information from the systems of monitoring, telemetry, control, etc. They are required to be highly reliable in a view to correctly perform data aggregation, processing and analysis for subsequent decision making support. On design and construction phases of the manufacturing of such systems a various types of components (elements, devices, and subsystems) are considered and used to ensure high reliability of signals detection, noise isolation, and erroneous commands reduction. When generating design solutions for highly reliable systems a number of restrictions and conditions such as types of components and various constrains on resources should be considered. Various types of components perform identical functions; however, they are implemented using diverse principles, approaches and have distinct technical and economic indicators such as cost or power consumption. The systematic use of different component types increases the probability of tasks performing and eliminates the common cause failure. We consider type-variety principle as an engineering principle of system analysis, mathematical models based on this principle, and algorithms for solving optimization problems of highly reliable safety and security systems design. Mathematical models are formalized in a class of two-level discrete optimization problems of large dimension. The proposed approach, mathematical models, algorithms can be used for problem solving of optimal redundancy on the basis of a variety of methods and control devices for fault and defects detection in technical systems, telecommunication networks, and energy systems.

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...

Mathematical methods in time series analysis and digital image processing

CERN Document Server

Kurths, J; Maass, P; Timmer, J

2008-01-01

The aim of this volume is to bring together research directions in theoretical signal and imaging processing developed rather independently in electrical engineering, theoretical physics, mathematics and the computer sciences. In particular, mathematically justified algorithms and methods, the mathematical analysis of these algorithms, and methods as well as the investigation of connections between methods from time series analysis and image processing are reviewed. An interdisciplinary comparison of these methods, drawing upon common sets of test problems from medicine and geophysical/enviromental sciences, is also addressed. This volume coherently summarizes work carried out in the field of theoretical signal and image processing. It focuses on non-linear and non-parametric models for time series as well as on adaptive methods in image processing.

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.

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)

Applied mathematical methods in nuclear thermal hydraulics

International Nuclear Information System (INIS)

Ransom, V.H.; Trapp, J.A.

1983-01-01

Applied mathematical methods are used extensively in modeling of nuclear reactor thermal-hydraulic behavior. This application has required significant extension to the state-of-the-art. The problems encountered in modeling of two-phase fluid transients and the development of associated numerical solution methods are reviewed and quantified using results from a numerical study of an analogous linear system of differential equations. In particular, some possible approaches for formulating a well-posed numerical problem for an ill-posed differential model are investigated and discussed. The need for closer attention to numerical fidelity is indicated

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...

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.

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…

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.

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.

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…

Current Mathematical Methods Used in QSAR/QSPR Studies

Directory of Open Access Journals (Sweden)

Peixun Liu

2009-04-01

Full Text Available This paper gives an overview of the mathematical methods currently used in quantitative structure-activity/property relationship (QASR/QSPR studies. Recently, the mathematical methods applied to the regression of QASR/QSPR models are developing very fast, and new methods, such as Gene Expression Programming (GEP, Project Pursuit Regression (PPR and Local Lazy Regression (LLR have appeared on the QASR/QSPR stage. At the same time, the earlier methods, including Multiple Linear Regression (MLR, Partial Least Squares (PLS, Neural Networks (NN, Support Vector Machine (SVM and so on, are being upgraded to improve their performance in QASR/QSPR studies. These new and upgraded methods and algorithms are described in detail, and their advantages and disadvantages are evaluated and discussed, to show their application potential in QASR/QSPR studies in the future.

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.

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.

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.

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.

Mathematical pointing model establishment of the visual tracking theodolite for satellites in two kinds of observation methods.

Science.gov (United States)

Zhang, Yuncheng

The mathematical pointing model is establishment of the visual tracking theodolite for satellites in two kinds of observation methods at Yunnan Observatory, which is related to the digitalisation reform and the optical-electronic technique reform, is introduced respectively in this paper.

The 24-Hour Mathematical Modeling Challenge

Science.gov (United States)

Galluzzo, Benjamin J.; Wendt, Theodore J.

2015-01-01

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

Mathematical 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…

A mathematical model and an approximate method for calculating the fracture characteristics of nonmetallic materials during laser cutting

Energy Technology Data Exchange (ETDEWEB)

Smorodin, F.K.; Druzhinin, G.V.

1991-01-01

A mathematical model is proposed which describes the fracture behavior of amorphous materials during laser cutting. The model, which is based on boundary layer equations, is reduced to ordinary differential equations with the corresponding boundary conditions. The reduced model is used to develop an approximate method for calculating the fracture characteristics of nonmetallic materials.

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. 

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.

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…

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.

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,.

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…

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…

Applied impulsive mathematical models

CERN Document Server

Stamova, Ivanka

2016-01-01

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

Mathematical 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.

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

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.

MATHEMATICAL MODELING OF ELECTROCHEMICAL PROCESSES IN LITHIUM-ION BATTERIES POTENTIALLY STREAMING METHOD

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S. P. Halutin

2014-01-01

Full Text Available Mathematical models in the electrical parameters of physico-chemical processes in lithium-ion batteries are developed. The developed model parameters (discharge mode are identified out of family of discharging curve. By using of the parameters of this model we get the numerically model of lithium-ion battery.

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…

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…

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 ...

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...

Mathematical modeling of laser lipolysis

Directory of Open Access Journals (Sweden)

Reynaud Jean

2008-02-01

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

Mathematical methods for physical and analytical chemistry

CERN Document Server

Goodson, David Z

2011-01-01

Mathematical Methods for Physical and Analytical Chemistry presents mathematical and statistical methods to students of chemistry at the intermediate, post-calculus level. The content includes a review of general calculus; a review of numerical techniques often omitted from calculus courses, such as cubic splines and Newton's method; a detailed treatment of statistical methods for experimental data analysis; complex numbers; extrapolation; linear algebra; and differential equations. With numerous example problems and helpful anecdotes, this text gives chemistry students the mathematical

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...

Mathematical methods in geometrization of coal field

Science.gov (United States)

Shurygin, D. N.; Kalinchenko, V. M.; Tkachev, V. A.; Tretyak, A. Ya

2017-10-01

In the work, the approach to increase overall performance of collieries on the basis of an increase in accuracy of geometrization of coal thicknesses is considered. The sequence of stages of mathematical modelling of spatial placing of indicators of a deposit taking into account allocation of homogeneous sites of thickness and an establishment of quantitative interrelations between mountain-geological indicators of coal layers is offered. As a uniform mathematical method for modelling of various interrelations, it is offered to use a method of the group accounting of arguments (MGUA), one of versions of the regressive analysis. This approach can find application during delimitation between geological homogeneous sites of coal thicknesses in the form of a linear discriminant function. By an example of division into districts of a mine field in the conditions of mine “Sadkinsky” (East Donbass), the use of the complex approach for forecasting of zones of the small amplitude of disturbance of a coal layer on the basis of the discriminant analysis and MGUA is shown.

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…

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…

Comparative analysis of different methods in mathematical modelling of the recuperative heat exchangers

International Nuclear Information System (INIS)

Debeljkovic, D.Lj.; Stevic, D.Z.; Simeunovic, G.V.; Misic, M.A.

2015-01-01

The heat exchangers are frequently used as constructive elements in various plants and their dynamics is very important. Their operation is usually controlled by manipulating inlet fluid temperatures or mass flow rates. On the basis of the accepted and critically clarified assumptions, a linearized mathematical model of the cross-flow heat exchanger has been derived, taking into account the wall dynamics. The model is based on the fundamental law of energy conservation, covers all heat accumulation storages in the process, and leads to the set of partial differential equations (PDE), which solution is not possible in closed form. In order to overcome the solutions difficulties in this paper are analyzed different methods for modeling the heat exchanger: approach based on Laplace transformation, approximation of partial differential equations based on finite differences, the method of physical discretization and the transport approach. Specifying the input temperatures and output variables, under the constant initial conditions, the step transient responses have been simulated and presented in graphic form in order to compare these results for the four characteristic methods considered in this paper, and analyze its practical significance. (author)

Mathematical methods in systems biology.

Science.gov (United States)

Kashdan, Eugene; Duncan, Dominique; Parnell, Andrew; Schattler, Heinz

2016-12-01

The editors of this Special Issue of Mathematical Biosciences and Engineering were the organizers for the Third International Workshop "Mathematical Methods in System Biology" that took place on June 15-18, 2015 at the University College Dublin in Ireland. As stated in the workshop goals, we managed to attract a good mix of mathematicians and statisticians working on biological and medical applications with biologists and clinicians interested in presenting their challenging problems and looking to find mathematical and statistical tools for their solutions.

Mathematical Modeling in the Undergraduate Curriculum

Science.gov (United States)

Toews, Carl

2012-01-01

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

Teachers' Conceptions of Mathematical Modeling

Science.gov (United States)

Gould, Heather

2013-01-01

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

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.

Problems of Mathematical Finance by Stochastic Control Methods

Science.gov (United States)

Stettner, Łukasz

The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.

Mathematical Modelling of Unmanned Aerial Vehicles with Four Rotors

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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.

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

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.

Mathematical and Statistical Methods for Actuarial Sciences and Finance

CERN Document Server

Legros, Florence; Perna, Cira; Sibillo, Marilena

2017-01-01

This volume gathers selected peer-reviewed papers presented at the international conference "MAF 2016 – Mathematical and Statistical Methods for Actuarial Sciences and Finance”, held in Paris (France) at the Université Paris-Dauphine from March 30 to April 1, 2016. The contributions highlight new ideas on mathematical and statistical methods in actuarial sciences and finance. The cooperation between mathematicians and statisticians working in insurance and finance is a very fruitful field, one that yields unique  theoretical models and practical applications, as well as new insights in the discussion of problems of national and international interest. This volume is addressed to academicians, researchers, Ph.D. students and professionals.

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…

Improved methods for the mathematically controlled comparison of biochemical systems

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Schwacke John H

2004-06-01

Full Text Available Abstract The method of mathematically controlled comparison provides a structured approach for the comparison of alternative biochemical pathways with respect to selected functional effectiveness measures. Under this approach, alternative implementations of a biochemical pathway are modeled mathematically, forced to be equivalent through the application of selected constraints, and compared with respect to selected functional effectiveness measures. While the method has been applied successfully in a variety of studies, we offer recommendations for improvements to the method that (1 relax requirements for definition of constraints sufficient to remove all degrees of freedom in forming the equivalent alternative, (2 facilitate generalization of the results thus avoiding the need to condition those findings on the selected constraints, and (3 provide additional insights into the effect of selected constraints on the functional effectiveness measures. We present improvements to the method and related statistical models, apply the method to a previously conducted comparison of network regulation in the immune system, and compare our results to those previously reported.

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.

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

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.

Moving toward Positive Mathematics Beliefs and Developing Socio-Mathematical Authority: Urban Preservice Teachers in Mathematics Methods Courses

Science.gov (United States)

Saran, Rupam; Gujarati, Joan

2013-01-01

This article explores how preservice elementary teachers change their negative beliefs toward mathematics into positive ones after taking a mathematics methods course that follows the Concrete-Pictorial-Abstract (CPA) instructional method. Also explored is the relationship between those beliefs and sociomathematical authority. By administering…

Methods of mathematical modeling using polynomials of algebra of sets

Science.gov (United States)

Kazanskiy, Alexandr; Kochetkov, Ivan

2018-03-01

The article deals with the construction of discrete mathematical models for solving applied problems arising from the operation of building structures. Security issues in modern high-rise buildings are extremely serious and relevant, and there is no doubt that interest in them will only increase. The territory of the building is divided into zones for which it is necessary to observe. Zones can overlap and have different priorities. Such situations can be described using formulas algebra of sets. Formulas can be programmed, which makes it possible to work with them using computer models.

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...

Mathematical methods in engineering

CERN Document Server

Machado, José

2014-01-01

This book presents a careful selection of the contributions presented at the Mathematical Methods in Engineering (MME10) International Symposium, held at the Polytechnic Institute of Coimbra- Engineering Institute of Coimbra (IPC/ISEC), Portugal, October 21-24, 2010. The volume discusses recent developments about theoretical and applied mathematics toward the solution of engineering problems, thus covering a wide range of topics, such as:  Automatic Control, Autonomous Systems, Computer Science, Dynamical Systems and Control,  Electronics, Finance and Economics, Fluid Mechanics and Heat Transfer, Fractional Mathematics, Fractional Transforms and Their Applications,  Fuzzy Sets and Systems, Image and Signal Analysis, Image Processing, Mechanics, Mechatronics, Motor Control and Human Movement Analysis, Nonlinear Dynamics, Partial Differential Equations, Robotics, Acoustics, Vibration and Control, and Wavelets.

Learners with learning difficulties in mathematics : attitudes, curriculum and methods of teaching mathematics

OpenAIRE

2012-01-01

D.Ed. The aim of this theses is to find out whether there is any relationship between learners' attitudes and learning difficulties in mathematics: To investigate whether learning difficulties in mathematics are associated with learners' gender. To establish the nature of teachers' perceptions of the learning problem areas in the mathematics curriculum. To find out about the teachers' views on the methods of teaching mathematics, resources, learning of mathematics, extra curricular activit...

Mathematical modelling of the laser processing of compose materials

International Nuclear Information System (INIS)

Gromyko, G.F.; Matsuka, N.P.

2009-01-01

Expansion of the protective coating scope led to the necessity to work out lower priced methods of treatment of machine elements. Making of an adequate, agreed with process features, mathematical model and development of effective methods of its solving are promising directions in this fields. In this paper the mathematical model of high-temperature laser treatment via moving source of pre-sprayed with composite powder padding is developed. Presented model describes accurately enough the heat processes taking place by laser processing of machine elements. Varying input parameters of model (laser power, temperature and composition of environment, characteristics and quantitative composition of using materials, etc.) one can get a cheap tool of preliminary estimates for wide range of similar problems. Difference method, based on process physical features and taking into account main process-dependent parameters had been developed for solving of the built system of nonlinear equations. (authors)

Mathematical modelling of the growth of human fetus anatomical structures.

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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.

Mathematical modeling and hydrodynamics of Electrochemical deburring process

Science.gov (United States)

Prabhu, Satisha; Abhishek Kumar, K., Dr

2018-04-01

The electrochemical deburring (ECD) is a variation of electrochemical machining is considered as one of the efficient methods for deburring of intersecting features and internal parts. Since manual deburring costs are comparatively high one can potentially use this method in both batch production and flow production. The other advantage of this process is that time of deburring as is on the order of seconds as compared to other methods. In this paper, the mathematical modeling of Electrochemical deburring is analysed from its deburring time and base metal removal point of view. Simultaneously material removal rate is affected by electrolyte temperature and bubble formation. The mathematical model and hydrodynamics of the process throw limelight upon optimum velocity calculations which can be theoretically determined. The analysis can be the powerful tool for prediction of the above-mentioned parameters by experimentation.

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...

Causal Bayes Model of Mathematical Competence in Kindergarten

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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.

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

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.

Mathematical Modeling of Column-Base Connections under Monotonic Loading

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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.

Genomic similarity and kernel methods I: advancements by building on mathematical and statistical foundations.

Science.gov (United States)

Schaid, Daniel J

2010-01-01

Measures of genomic similarity are the basis of many statistical analytic methods. We review the mathematical and statistical basis of similarity methods, particularly based on kernel methods. A kernel function converts information for a pair of subjects to a quantitative value representing either similarity (larger values meaning more similar) or distance (smaller values meaning more similar), with the requirement that it must create a positive semidefinite matrix when applied to all pairs of subjects. This review emphasizes the wide range of statistical methods and software that can be used when similarity is based on kernel methods, such as nonparametric regression, linear mixed models and generalized linear mixed models, hierarchical models, score statistics, and support vector machines. The mathematical rigor for these methods is summarized, as is the mathematical framework for making kernels. This review provides a framework to move from intuitive and heuristic approaches to define genomic similarities to more rigorous methods that can take advantage of powerful statistical modeling and existing software. A companion paper reviews novel approaches to creating kernels that might be useful for genomic analyses, providing insights with examples [1]. Copyright © 2010 S. Karger AG, Basel.

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

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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.

IMPROVEMENT OF MATHEMATICAL MODELS FOR ESTIMATION OF TRAIN DYNAMICS

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L. V. Ursulyak

2017-12-01

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

The sensitivity research of multiparameter biosensors based on HEMT by the mathematic modeling method

Science.gov (United States)

Tikhomirov, V. G.; Gudkov, A. G.; Agasieva, S. V.; Gorlacheva, E. N.; Shashurin, V. D.; Zybin, A. A.; Evseenkov, A. S.; Parnes, Y. M.

2017-11-01

The numerical impact modeling of some external effects on the CVC of biosensors based on AlGaN/GaN heterostructures (HEMT) was carried out. The mathematical model was created that allowed to predict the behavior of the drain current depending on condition changes on the heterostructure surface in the gate region and to start the process of directed construction optimization of the biosensors based on AlGaN/GaN HEMT with the aim of improving their performance. The calculation of the drain current of the biosensor construction was carried out to confirm the reliability of the developed mathematical model and obtained results.

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

Science.gov (United States)

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

2014-08-28

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

Mathematical models in medicine: Diseases and epidemics

International Nuclear Information System (INIS)

Witten, M.

1987-01-01

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

Mathematical optics classical, quantum, and computational methods

CERN Document Server

Lakshminarayanan, Vasudevan

2012-01-01

Going beyond standard introductory texts, Mathematical Optics: Classical, Quantum, and Computational Methods brings together many new mathematical techniques from optical science and engineering research. Profusely illustrated, the book makes the material accessible to students and newcomers to the field. Divided into six parts, the text presents state-of-the-art mathematical methods and applications in classical optics, quantum optics, and image processing. Part I describes the use of phase space concepts to characterize optical beams and the application of dynamic programming in optical wave

Authentic Teaching Experiences in Secondary Mathematics Methods

Science.gov (United States)

Stickles, Paula R.

2015-01-01

Often secondary mathematics methods courses include classroom peer teaching, but many pre-service teachers find it challenging to teach their classmate peers as there are no discipline issues and little mathematical discourse as the "students" know the content. We will share a recent change in our methods course where pre-service…

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.

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

International Nuclear Information System (INIS)

Easters, D J

2014-01-01

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

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

Science.gov (United States)

Easters, D. J.

2014-03-01

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

Effectiveness of discovery learning model on mathematical problem solving

Science.gov (United States)

Herdiana, Yunita; Wahyudin, Sispiyati, Ririn

2017-08-01

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

Mathematical 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…

Mathematical methods for physicists a comprehensive guide

CERN Document Server

Arfken, George B; Harris, Frank E

2012-01-01

Now in its 7th edition, Mathematical Methods for Physicists continues to provide all the mathematical methods that aspiring scientists and engineers are likely to encounter as students and beginning researchers. This bestselling text provides mathematical relations and their proofs essential to the study of physics and related fields. While retaining the key features of the 6th edition, the new edition provides a more careful balance of explanation, theory, and examples. Taking a problem-solving-skills approach to incorporating theorems with applications, the book's improved focus w

Mathematical modeling and numerical simulation of Czochralski Crystal Growth

Energy Technology Data Exchange (ETDEWEB)

Jaervinen, J.; Nieminen, R. [Center for Scientific Computing, Espoo (Finland)

1996-12-31

A detailed mathematical model and numerical simulation tools based on the SUPG Finite Element Method for the Czochralski crystal growth has been developed. In this presentation the mathematical modeling and numerical simulation of the melt flow and the temperature distribution in a rotationally symmetric crystal growth environment is investigated. The temperature distribution and the position of the free boundary between the solid and liquid phases are solved by using the Enthalpy method. Heat inside of the Czochralski furnace is transferred by radiation, conduction and convection. The melt flow is governed by the incompressible Navier-Stokes equations coupled with the enthalpy equation. The melt flow is numerically demonstrated and the temperature distribution in the whole Czochralski furnace. (author)

Mathematical modeling and numerical simulation of Czochralski Crystal Growth

Energy Technology Data Exchange (ETDEWEB)

Jaervinen, J; Nieminen, R [Center for Scientific Computing, Espoo (Finland)

1997-12-31

A detailed mathematical model and numerical simulation tools based on the SUPG Finite Element Method for the Czochralski crystal growth has been developed. In this presentation the mathematical modeling and numerical simulation of the melt flow and the temperature distribution in a rotationally symmetric crystal growth environment is investigated. The temperature distribution and the position of the free boundary between the solid and liquid phases are solved by using the Enthalpy method. Heat inside of the Czochralski furnace is transferred by radiation, conduction and convection. The melt flow is governed by the incompressible Navier-Stokes equations coupled with the enthalpy equation. The melt flow is numerically demonstrated and the temperature distribution in the whole Czochralski furnace. (author)

Summer Camp of Mathematical Modeling in China

Science.gov (United States)

Tian, Xiaoxi; Xie, Jinxing

2013-01-01

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

Mathematical modeling of ignition of woodlands resulted from accident on the pipeline

Science.gov (United States)

Perminov, V. A.; Loboda, E. L.; Reyno, V. V.

2014-11-01

Accidents occurring at the sites of pipelines, accompanied by environmental damage, economic loss, and sometimes loss of life. In this paper we calculated the sizes of the possible ignition zones in emergency situations on pipelines located close to the forest, accompanied by the appearance of fireballs. In this paper, using the method of mathematical modeling calculates the maximum size of the ignition zones of vegetation as a result of accidental releases of flammable substances. The paper suggested in the context of the general mathematical model of forest fires give a new mathematical setting and method of numerical solution of a problem of a forest fire modeling. The boundary-value problem is solved numerically using the method of splitting according to physical processes. The dependences of the size of the forest fuel for different amounts of leaked flammable substances and moisture content of vegetation.

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…

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)

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...

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…

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.

Mathematical Modeling of Neuro-Vascular Coupling in Rat Cerebellum

DEFF Research Database (Denmark)

Rasmussen, Tina

Activity in the neurons called climbing fibers causes blood flow changes. But the physiological mechanisms which mediate the coupling are not well understood. This PhD thesis investigates the mechanisms of neuro-vascular coupling by means of mathematical methods. In experiments, the extracellularly...... measured field potential is used as an indicator of neuronal activity, and the cortical blood flow is measured by means of laser-Doppler flowmetry. Using system identification methods, these measurements have been used to construct and validate parametric mathematical models of the neuro-vascular system...

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...

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…

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...

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. 

Theory and Examples of Mathematical Modeling for Fine Weave Pierced Fabric

Directory of Open Access Journals (Sweden)

ZHOU Yu-bo

2017-04-01

Full Text Available A mathematical abstraction and three-dimensional modeling method of three-dimensional woven fabric structure was developed for the fine weave pierced fabric, taking parametric continuity splines as the track function of tow. Based on the significant parameters of fine weave pierced fabric measured by MicroCT, eight kinds of the three-dimensional digital models of the fabric structure were established with two kinds of tow sections and four kinds of tow trajectory characteristic functions. There is a good agreement between the three-dimensional digital models and real fabric by comparing their structures and porosities. This mathematical abstraction and three-dimensional modeling method can be applied in micro models for sub unit cell and macro models for macroscopic scale fabrics, with high adaptability.

Application of mathematical model methods for optimization tasks in construction materials technology

Science.gov (United States)

Fomina, E. V.; Kozhukhova, N. I.; Sverguzova, S. V.; Fomin, A. E.

2018-05-01

In this paper, the regression equations method for design of construction material was studied. Regression and polynomial equations representing the correlation between the studied parameters were proposed. The logic design and software interface of the regression equations method focused on parameter optimization to provide the energy saving effect at the stage of autoclave aerated concrete design considering the replacement of traditionally used quartz sand by coal mining by-product such as argillite. The mathematical model represented by a quadric polynomial for the design of experiment was obtained using calculated and experimental data. This allowed the estimation of relationship between the composition and final properties of the aerated concrete. The surface response graphically presented in a nomogram allowed the estimation of concrete properties in response to variation of composition within the x-space. The optimal range of argillite content was obtained leading to a reduction of raw materials demand, development of target plastic strength of aerated concrete as well as a reduction of curing time before autoclave treatment. Generally, this method allows the design of autoclave aerated concrete with required performance without additional resource and time costs.

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

Modelling Of Flotation Processes By Classical Mathematical Methods - A Review

Science.gov (United States)

Jovanović, Ivana; Miljanović, Igor

2015-12-01

Flotation process modelling is not a simple task, mostly because of the process complexity, i.e. the presence of a large number of variables that (to a lesser or a greater extent) affect the final outcome of the mineral particles separation based on the differences in their surface properties. The attempts toward the development of the quantitative predictive model that would fully describe the operation of an industrial flotation plant started in the middle of past century and it lasts to this day. This paper gives a review of published research activities directed toward the development of flotation models based on the classical mathematical rules. The description and systematization of classical flotation models were performed according to the available references, with emphasize exclusively given to the flotation process modelling, regardless of the model application in a certain control system. In accordance with the contemporary considerations, models were classified as the empirical, probabilistic, kinetic and population balance types. Each model type is presented through the aspects of flotation modelling at the macro and micro process levels.

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

Literature Review of Applying Visual Method to Understand Mathematics

Directory of Open Access Journals (Sweden)

Yu Xiaojuan

2015-01-01

Full Text Available As a new method to understand mathematics, visualization offers a new way of understanding mathematical principles and phenomena via image thinking and geometric explanation. It aims to deepen the understanding of the nature of concepts or phenomena and enhance the cognitive ability of learners. This paper collates and summarizes the application of this visual method in the understanding of mathematics. It also makes a literature review of the existing research, especially with a visual demonstration of Euler’s formula, introduces the application of this method in solving relevant mathematical problems, and points out the differences and similarities between the visualization method and the numerical-graphic combination method, as well as matters needing attention for its application.

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

Teaching mathematical modelling through project work

DEFF Research Database (Denmark)

Blomhøj, Morten; Kjeldsen, Tinne Hoff

2006-01-01

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

Mathematical modelling of scour: A review

DEFF Research Database (Denmark)

Sumer, B. Mutlu

2007-01-01

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

Mathematical modeling a chemical engineer's perspective

CERN Document Server

Rutherford, Aris

1999-01-01

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

Engineering Mathematical Analysis Method for Productivity Rate in Linear Arrangement Serial Structure Automated Flow Assembly Line

Directory of Open Access Journals (Sweden)

Tan Chan Sin

2015-01-01

Full Text Available Productivity rate (Q or production rate is one of the important indicator criteria for industrial engineer to improve the system and finish good output in production or assembly line. Mathematical and statistical analysis method is required to be applied for productivity rate in industry visual overviews of the failure factors and further improvement within the production line especially for automated flow line since it is complicated. Mathematical model of productivity rate in linear arrangement serial structure automated flow line with different failure rate and bottleneck machining time parameters becomes the basic model for this productivity analysis. This paper presents the engineering mathematical analysis method which is applied in an automotive company which possesses automated flow assembly line in final assembly line to produce motorcycle in Malaysia. DCAS engineering and mathematical analysis method that consists of four stages known as data collection, calculation and comparison, analysis, and sustainable improvement is used to analyze productivity in automated flow assembly line based on particular mathematical model. Variety of failure rate that causes loss of productivity and bottleneck machining time is shown specifically in mathematic figure and presents the sustainable solution for productivity improvement for this final assembly automated flow line.

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…

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.

The Optimal Design Method and Standardized Mathematical Model of Tooth Profile Modification of Spur Gear

Directory of Open Access Journals (Sweden)

Wenjie Mei

2016-01-01

Full Text Available The paper reports a tooth profile modification method of spur gear. After establishing a standardized mathematical model for optimized tooth profile and simulating meshing process with ANSYS finite element analysis, we obtained 625 groups of gear models with different modification parameters. The group with minimum transmission errors owns the optimal parameters. Genetic algorithm was adopted in the entire process for the purpose of reducing the variation of transmission errors in meshing process. The arc and parabolic modification were doing the same processing. After comparing the transmission errors fluctuation produced by the meshing process of gear of nonmodification with arc modification and parabolic modification, we found that the best modification effects of arc modification and parabolic modification were both reduced by 90%. The modification method makes the gear drive process more stable and efficient, and it is also promising in general application for gear drive.

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

Science.gov (United States)

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

2016-01-01

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

MATHEMATICAL 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.

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.

Nuclear physics mathematical methods

International Nuclear Information System (INIS)

Balian, R.; Gervois, A.; Giannoni, M.J.; Levesque, D.; Maille, M.

1984-01-01

The nuclear physics mathematical methods, applied to the collective motion theory, to the reduction of the degrees of freedom and to the order and disorder phenomena; are investigated. In the scope of the study, the following aspects are discussed: the entropy of an ensemble of collective variables; the interpretation of the dissipation, applying the information theory; the chaos and the universality; the Monte-Carlo method applied to the classical statistical mechanics and quantum mechanics; the finite elements method, and the classical ergodicity [fr

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,

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…

Mathematical model of rolling an elastic wheel over deformable support base

Science.gov (United States)

Volskaia, V. N.; Zhileykin, M. M.; Zakharov, A. Y.

2018-02-01

One of the main direction of economic growth in Russia remains to be a speedy development of north and northeast regions that are the constituents of the 60 percent of the country territory. The further development of these territories requires new methods and technologies for solving transport and technological problems when off-road transportation of cargoes and people is conducting. One of the fundamental methods of patency prediction is imitation modeling of wheeled vehicles movement in different operating conditions. Both deformable properties of tires and physical and mechanical properties of the ground: normal tire deflection and gauge depth; variation of contact patch area depending on the load and pressure of air in the tire; existence of hysteresis losses in the tire material which are influencing on the rolling resistance due to friction processes between tire and ground in the contact patch; existence of the tangential reaction from the ground by entire contact area influence on the tractive patency. Nowadays there are two main trends in theoretical research of interaction wheeled propulsion device with ground: analytical method involving mathematical description of explored process and finite element method based on computational modeling. Mathematical models of interaction tire with the ground are used both in processes of interaction individual wheeled propulsion device with ground and researches of mobile vehicle dynamical models operated in specific road and climate conditions. One of the most significant imperfection of these models is the description of interaction wheel with flat deformable support base whereas profile of real support base surface has essential height of unevenness which is commensurate with radius of the wheel. The description of processes taking place in the ground under influence of the wheeled propulsion device using the finite element method is relatively new but most applicable lately. The application of this method allows

Mathematical and statistical methods for actuarial sciences and finance

CERN Document Server

Sibillo, Marilena

2014-01-01

The interaction between mathematicians and statisticians working in the actuarial and financial fields is producing numerous meaningful scientific results. This volume, comprising a series of four-page papers, gathers new ideas relating to mathematical and statistical methods in the actuarial sciences and finance. The book covers a variety of topics of interest from both theoretical and applied perspectives, including: actuarial models; alternative testing approaches; behavioral finance; clustering techniques; coherent and non-coherent risk measures; credit-scoring approaches; data envelopment analysis; dynamic stochastic programming; financial contagion models; financial ratios; intelligent financial trading systems; mixture normality approaches; Monte Carlo-based methodologies; multicriteria methods; nonlinear parameter estimation techniques; nonlinear threshold models; particle swarm optimization; performance measures; portfolio optimization; pricing methods for structured and non-structured derivatives; r...

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.

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.

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…

Mathematical models of hysteresis

International Nuclear Information System (INIS)

1998-01-01

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

Mathematical models of hysteresis

Energy Technology Data Exchange (ETDEWEB)

NONE

1998-08-01

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

The possibilities of a modelling perspective for school mathematics

Directory of Open Access Journals (Sweden)

Dirk Wessels

2009-09-01

Full Text Available The findings of the international TIMSS investigations of a few years ago into the position and application of problem solving strategies in school mathematics in about 50 countries caused serious concern globally. During each survey South Africa was found to be among the poorest performers of the participating countries. The main problem was that the majority of school learners in South Africa do not have the ability to solve mathematical problems; in fact, it would appear that they lack the total spectrum of mathematical problem solving competencies. The present school system does not develop their mathematical abilities or competencies. While Outcomes-based education, which became very popular in the Western world, has the ability to improve participants’ affective values of mathematics, it proved to be inadequate in improving the quality of their mathematical performances. Mathematics teachers are unsuccessful in teaching in a manner that will make a difference with respect to the way learners do, learn or perform in mathematics. The pedagogical and mathematics content knowledge of the teachers are lacking in conceptual depth, clarity and connectedness (integration. The language proficiency of the learners is poor, which means that they do not understand what they should do with a problem and how to interpret, present and verify their findings. Learners still do not know how to handle mathematics and how to utilise mathematics in order to solve problems. They seriously lack the ability to approach problems in a meaningful and constructive way. Real-life and open-ended problems are being perceived as huge obstacles to most learners. Teachers are not trained and educated to assist their learners in bridging this gap. The teaching methodology that will make a difference in the classroom falls in the broad category of problem solving. The day-to-day teaching method should be the problem-centred teaching and learning approach. This rather

Mathematical methods for hydrodynamic limits

CERN Document Server

Masi, Anna

1991-01-01

Entropy inequalities, correlation functions, couplings between stochastic processes are powerful techniques which have been extensively used to give arigorous foundation to the theory of complex, many component systems and to its many applications in a variety of fields as physics, biology, population dynamics, economics, ... The purpose of the book is to make theseand other mathematical methods accessible to readers with a limited background in probability and physics by examining in detail a few models where the techniques emerge clearly, while extra difficulties arekept to a minimum. Lanford's method and its extension to the hierarchy of equations for the truncated correlation functions, the v-functions, are presented and applied to prove the validity of macroscopic equations forstochastic particle systems which are perturbations of the independent and of the symmetric simple exclusion processes. Entropy inequalities are discussed in the frame of the Guo-Papanicolaou-Varadhan technique and of theKipnis-Oll...

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...

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…

The many faces of the mathematical modeling cycle

NARCIS (Netherlands)

Perrenet, J.C.; Zwaneveld, B.

2012-01-01

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

Mathematical 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)

Mathematic modeling of the method of measurement relative dielectric permeability

Science.gov (United States)

Plotnikova, I. V.; Chicherina, N. V.; Stepanov, A. B.

2018-05-01

The method of measuring relative permittivity’s and the position of the interface between layers of a liquid medium is considered in the article. An electric capacitor is a system consisting of two conductors that are separated by a dielectric layer. It is mathematically proven that at any given time it is possible to obtain the values of the relative permittivity in the layers of the liquid medium and to determine the level of the interface between the layers of the two-layer liquid. The estimation of measurement errors is made.

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.

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

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.

Mathematical modelling a case studies approach

CERN Document Server

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

2004-01-01

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

Mathematical modelling and numerical simulation of oil pollution problems

CERN Document Server

2015-01-01

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

Mathematical Model Taking into Account Nonlocal Effects of Plasmonic Structures on the Basis of the Discrete Source Method

Science.gov (United States)

Eremin, Yu. A.; Sveshnikov, A. G.

2018-04-01

The discrete source method is used to develop and implement a mathematical model for solving the problem of scattering electromagnetic waves by a three-dimensional plasmonic scatterer with nonlocal effects taken into account. Numerical results are presented whereby the features of the scattering properties of plasmonic particles with allowance for nonlocal effects are demonstrated depending on the direction and polarization of the incident wave.

A course in mathematical methods for physicists

CERN Document Server

Herman, Russell L

2014-01-01

Based on the author’s junior-level undergraduate course, this introductory textbook is designed for a course in mathematical physics. Focusing on the physics of oscillations and waves, A Course in Mathematical Methods for Physicists helps students understand the mathematical techniques needed for their future studies in physics. It takes a bottom-up approach that emphasizes physical applications of the mathematics. The book offers: •A quick review of mathematical prerequisites, proceeding to applications of differential equations and linear algebra •Classroom-tested explanations of complex and Fourier analysis for trigonometric and special functions •Coverage of vector analysis and curvilinear coordinates for solving higher dimensional problems •Sections on nonlinear dynamics, variational calculus, numerical solutions of differential equations, and Green's functions

Mathematical methods in medicine: neuroscience, cardiology and pathology

Science.gov (United States)

Amigó, José M.

2017-01-01

The application of mathematics, natural sciences and engineering to medicine is gaining momentum as the mutual benefits of this collaboration become increasingly obvious. This theme issue is intended to highlight the trend in the case of mathematics. Specifically, the scope of this theme issue is to give a general view of the current research in the application of mathematical methods to medicine, as well as to show how mathematics can help in such important aspects as understanding, prediction, treatment and data processing. To this end, three representative specialties have been selected: neuroscience, cardiology and pathology. Concerning the topics, the 12 research papers and one review included in this issue cover biofluids, cardiac and virus dynamics, computational neuroscience, functional magnetic resonance imaging data processing, neural networks, optimization of treatment strategies, time-series analysis and tumour growth. In conclusion, this theme issue contains a collection of fine contributions at the intersection of mathematics and medicine, not as an exercise in applied mathematics but as a multidisciplinary research effort that interests both communities and our society in general. This article is part of the themed issue ‘Mathematical methods in medicine: neuroscience, cardiology and pathology’. PMID:28507240

Mathematical methods in medicine: neuroscience, cardiology and pathology.

Science.gov (United States)

Amigó, José M; Small, Michael

2017-06-28

The application of mathematics, natural sciences and engineering to medicine is gaining momentum as the mutual benefits of this collaboration become increasingly obvious. This theme issue is intended to highlight the trend in the case of mathematics. Specifically, the scope of this theme issue is to give a general view of the current research in the application of mathematical methods to medicine, as well as to show how mathematics can help in such important aspects as understanding, prediction, treatment and data processing. To this end, three representative specialties have been selected: neuroscience, cardiology and pathology. Concerning the topics, the 12 research papers and one review included in this issue cover biofluids, cardiac and virus dynamics, computational neuroscience, functional magnetic resonance imaging data processing, neural networks, optimization of treatment strategies, time-series analysis and tumour growth. In conclusion, this theme issue contains a collection of fine contributions at the intersection of mathematics and medicine, not as an exercise in applied mathematics but as a multidisciplinary research effort that interests both communities and our society in general.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'. © 2017 The Author(s).

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.

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 ...

Mathematical modeling and visualization of functional neuroimages

DEFF Research Database (Denmark)

Rasmussen, Peter Mondrup

This dissertation presents research results regarding mathematical modeling in the context of the analysis of functional neuroimages. Specifically, the research focuses on pattern-based analysis methods that recently have become popular within the neuroimaging community. Such methods attempt...... sets are characterized by relatively few data observations in a high dimensional space. The process of building models in such data sets often requires strong regularization. Often, the degree of model regularization is chosen in order to maximize prediction accuracy. We focus on the relative influence...... be carefully selected, so that the model and its visualization enhance our ability to interpret the brain. The second part concerns interpretation of nonlinear models and procedures for extraction of ‘brain maps’ from nonlinear kernel models. We assess the performance of the sensitivity map as means...

Mathematical modeling and visualization of functional neuroimages

DEFF Research Database (Denmark)

Rasmussen, Peter Mondrup

This dissertation presents research results regarding mathematical modeling in the context of the analysis of functional neuroimages. Specifically, the research focuses on pattern-based analysis methods that recently have become popular analysis tools within the neuroimaging community. Such methods...... neuroimaging data sets are characterized by relatively few data observations in a high dimensional space. The process of building models in such data sets often requires strong regularization. Often, the degree of model regularization is chosen in order to maximize prediction accuracy. We focus on the relative...... be carefully selected, so that the model and its visualization enhance our ability to interpret brain function. The second part concerns interpretation of nonlinear models and procedures for extraction of ‘brain maps’ from nonlinear kernel models. We assess the performance of the sensitivity map as means...

A Mixed Methods Study of Teach for America Teachers' Mathematical Beliefs, Knowledge, and Classroom Teaching Practices during a Reform-Based University Mathematics Methods Course

Science.gov (United States)

Swars, Susan Lee

2015-01-01

This mixed methods study examined the mathematical preparation of elementary teachers in a Teach for America (TFA) program, focal participants for whom there is scant extant research. Data collection occurred before and after a university mathematics methods course, with a particular focus on the participants' (n = 22) mathematical beliefs,…

APPLICATION OF METHODS OF MATHEMATICAL MODELING IN THE FORECAST OF DEVELOPMENT OF ADVERSE CURRENT OF ARTERIAL HYPERTENSION IN WOMEN

Directory of Open Access Journals (Sweden)

Roman Anatolyevich Yaskevich

2017-12-01

Full Text Available The purpose of the study. Studying the possibility of using mathematical modeling methods for predicting the clinical course of arterial hypertension in women. Materials and methods. 84 women aged 20–60 years (mean age 45,3 years were examined. The survey included clinical, instrumental and laboratory methods of investigation. As a mathematical basis, we used a technique for structuring and analyzing heterogeneous statistical data under conditions of nonparametric uncertainty. Results. In the course of the conducted research on the results of mathematical modeling, using the pattern recognition technique, an individual set of signs (risk factors was formed from the list of indicators that predetermined the risk of development of the predicted state (complicated course of hypertension, which made it possible to construct forecast nomograms, medium and high risk of adverse course of AH in women, which will not only allow us to calculate the degree of risk, but also to determine the parameters of the required change of the level of managed risk factors that determine the presence in a high-risk zone, and, by influencing them to carry out preventive measures. It was found that the clinical course of hypertension in women is influenced by an increase in insulinemia, fasting and postprandial glycemia, BMI, OXC, and blood pressure, that is, a simtomocomplex of the metabolic syndrome. The conclusion. The use of the method of restructuring and analysis of heterogeneous statistical data in conditions of non-parametric uncertainty makes it possible to predict and evaluate the severity of the clinical course of AH in women. The most significant factors affecting the severity of the clinical course of hypertension in men are the indicators of insulinemia, glycemia, BMI, OXC, blood pressure levels.

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…

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.

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....

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…

SOME ASPECTS OF THE USE OF MATHEMATICAL-STATISTICAL METHODS IN THE ANALYSIS OF SOCIO-HUMANISTIC TEXTS Humanities and social text, mathematics, method, statistics, probability

Directory of Open Access Journals (Sweden)

Zaira M Alieva

2016-01-01

Full Text Available The article analyzes the application of mathematical and statistical methods in the analysis of socio-humanistic texts. The essence of mathematical and statistical methods, presents examples of their use in the study of Humanities and social phenomena. Considers the key issues faced by the expert in the application of mathematical-statistical methods in socio-humanitarian sphere, including the availability of sustainable contrasting socio-humanitarian Sciences and mathematics; the complexity of the allocation of the object that is the bearer of the problem; having the use of a probabilistic approach. The conclusion according to the results of the study.

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

(Re)Envisioning Mathematics Education: Examining Equity and Social Justice in an Elementary Mathematics Methods Course

Science.gov (United States)

Koestler, Courtney

2010-01-01

In this dissertation, I present my attempts at designing an elementary mathematics methods course to support prospective teachers in developing an understanding of how to teach all students in learning powerful mathematics. To do this, I introduced them to teaching mathematics for equity and social justice by discussing ways to support students'…

The Effectiveness of MURDER Cooperative Model towards Students' Mathematics Reasoning Ability and Self Concept of Ten Grade

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Sofan Tri Prasetiyo

2017-08-01

Full Text Available The purpose of this research was to know the effectiveness of MURDER cooperative model towards students’ mathematics reasoning ability and self concept of ten grade. Population of this research were students of MIA ten grade Senior High School 1 Kebumen in the academic year 2016/1017. Sampling technique using simple random sampling technique. The data collected by the method of documentation, test methods, observation methods, and questionnaire methods. The analyzed of data are used completeness test and average different test. The results showed that: (1 mathematics reasoning ability of students that following MURDER cooperative model have completed individual and classical study completeness; (2 mathematics reasoning ability of students that following MURDER cooperative model better than mathematics reasoning ability of students that following ekspository learning; (3 self concept of students that following MURDER cooperative model better than self concept of students that following ekspository learning.

Mathematics for natural scientists II advanced methods

CERN Document Server

Kantorovich, Lev

2016-01-01

This book covers the advanced mathematical techniques useful for physics and engineering students, presented in a form accessible to physics students, avoiding precise mathematical jargon and laborious proofs. Instead, all proofs are given in a simplified form that is clear and convincing for a physicist. Examples, where appropriate, are given from physics contexts. Both solved and unsolved problems are provided in each chapter. Mathematics for Natural Scientists II: Advanced Methods is the second of two volumes. It follows the first volume on Fundamentals and Basics.

Keystone Method: A Learning Paradigm in Mathematics

Science.gov (United States)

Siadat, M. Vali; Musial, Paul M.; Sagher, Yoram

2008-01-01

This study reports the effects of an integrated instructional program (the Keystone Method) on the students' performance in mathematics and reading, and tracks students' persistence and retention. The subject of the study was a large group of students in remedial mathematics classes at the college, willing to learn but lacking basic educational…

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.

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.

Mathematical modelling of the decomposition of explosives

International Nuclear Information System (INIS)

Smirnov, Lev P

2010-01-01

Studies on mathematical modelling of the molecular and supramolecular structures of explosives and the elementary steps and overall processes of their decomposition are analyzed. Investigations on the modelling of combustion and detonation taking into account the decomposition of explosives are also considered. It is shown that solution of problems related to the decomposition kinetics of explosives requires the use of a complex strategy based on the methods and concepts of chemical physics, solid state physics and theoretical chemistry instead of empirical approach.

Mathematical model for optimization of multilayer submerged-arc welding of frame equipment of power units

International Nuclear Information System (INIS)

Pankov, V.V.; Chernyshev, G.G.; Kozlov, N.E.

1987-01-01

A mathematical model for optimization of multilayer submerged arc welding of frame equipment of power units is constructed. The variation-energy method permits to construct the universal mathematical model for strengthening formation of a single bead; the method is reasonable for simulation of a multilayer welded joint. Minimization of the distance between maximum and minimum layer height of a built-up metal is the necessary condition for qualitative formation of the multilayer joint. One can calculate in real time scale the optimal vector of maximally ten parameters under the multilayer welding condition immediately after change in the grooving width using the developed mathematical model of optimization

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…

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

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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

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

Science.gov (United States)

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

2016-01-01

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

Mathematical 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...

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...

MATHEMATICAL AND CHEMOMETRICAL MODELS – TOOLS TO EVALUATE HEAVY METALS CONTAMINATION

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Despina Maria Bordean

2017-11-01

Full Text Available The aim of the this study is to present a combined view of bio – geo - chemistry, soil – plant interactions, mathematic models and statistic analysis, based on the correlation between the levels of soil contamination, and the remanence of polluting substances in soil and respectively in harvested fruits and vegetables. Most of the mathematical models which describe plant - soil interactions are integrated in plant growth models or climate change models. The models presented by this paper are Soil – Plant Interaction Models, Pollution Indices, The Indices for Evaluating the Adaptative Strategies of Plants and Chemo-metrical Methods, and they have the role to synthesize and evaluate the information regarding heavy metals contamination.

Using Mathematical Modeling Methods for Estimating Entrance Flow Heterogeneity Impact on Aviation GTE Parameters and Performances

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Yu. A. Ezrokhi

2017-01-01

Full Text Available The paper considers methodological approaches to the mathematical models (MM of various levels, dedicated to estimate an impact of the entrance flow heterogeneity on the main parameters and performances of the aviation GTE and it units. By an example of calculation of a twin-shaft turbofan engine in cruiser mode, demonstrates engineering mathematical model capabilities to define the impact of the total pressure field distortion on engine trust and air flow parameters, and also gas dynamic stability margin of the both compressors.It is shown that the presented first level mathematical model allows us to estimate sufficiently the impact of entrance total pressure heterogeneity on the engine parameters. Here reliability of calculations is proved to be true by their comparison with the results, obtained owing to well fulfilled 2D & 3D mathematical models of the engine, which have been repeatedly identified by the results of experiments.It is shown that received results including those on decreasing values of stability margin of both compressors can be used for tentative estimates when choosing a desirable stability margin, providing steady operation of compressors and engine in an entire range of its operating modes. Carrying out a definitive testing calculation using the specialized engine MM of a higher level will not only confirm the results obtained, but also reduce their expected error with regard to the real values reached as a result of tests.

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.

A study of symbol segmentation method for handwritten mathematical formula recognition using mathematical structure information

OpenAIRE

Toyozumi, Kenichi; Yamada, Naoya; Kitasaka, Takayuki; Mori, Kensaku; Suenaga, Yasuhito; Mase, Kenji; Takahashi, Tomoichi

2004-01-01

Symbol segmentation is very important in handwritten mathematical formula recognition, since it is the very first portion of the recognition, since it is the very first portion of the recognition process. This paper proposes a new symbol segmentation method using mathematical structure information. The base technique of symbol segmentation employed in theexisting methods is dynamic programming which optimizes the overall results of individual symbol recognition. The new method we propose here...

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

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.

Development and Validation of a Mathematical Model for Olive Oil Oxidation

Science.gov (United States)

Rahmouni, K.; Bouhafa, H.; Hamdi, S.

2009-03-01

A mathematical model describing the stability or the susceptibility to oxidation of extra virgin olive oil has been developed. The model has been resolved by an iterative method using differential finite method. It was validated by experimental data of extra virgin olive oil (EVOO) oxidation. EVOO stability was tested by using a Rancimat at four different temperatures 60, 70, 80 and 90° C until peroxide accumulation reached 20 [meq/kg]. Peroxide formation is speed relatively slow; fits zero order reaction with linear regression coefficients varying from 0, 98 to 0, 99. The mathematical model was used to predict the shelf life of bulk conditioned olive oil. This model described peroxide accumulation inside a container in excess of oxygen as a function of time at various positions from the interface air/oil. Good correlations were obtained between theoretical and experimental values.

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…

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...

Mathematical model of kinetostatithic calculation of flat lever mechanisms

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A. S. Sidorenko

2016-01-01

Full Text Available Currently widely used graphical-analytical methods of analysis largely obsolete, replaced by various analytical methods using computer technology. Therefore, of particular interest is the development of a mathematical model kinetostatical calculation mechanisms in the form of library procedures of calculation for all powered two groups Assyrians (GA and primary level. Before resorting to the appropriate procedure that computes all the forces in the kinematic pairs, you need to compute inertial forces, moments of forces of inertia and all external forces and moments acting on this GA. To this end shows the design diagram of the power analysis for each species GA of the second class, as well as the initial link. Finding reactions in the internal and external kinematic pairs based on equilibrium conditions with the account of forces of inertia and moments of inertia forces (Dalembert principle. Thus obtained equations of kinetostatical for their versatility have been solved by the Cramer rule. Thus, for each GA of the second class were found all 6 unknowns: the forces in the kinematic pairs, the directions of these forces as well as forces the shoulders. If we study kinetostatic mechanism with parallel consolidation of two GA in the initial link, in this case, power is the geometric sum of the forces acting on the primary link from the discarded GA. Thus, the obtained mathematical model kinetostatical calculation mechanisms in the form of libraries of mathematical procedures for determining reactions of all GA of the second class. The mathematical model kinetostatical calculation makes it relatively simple to implement its software implementation.

Explorative methods in linear models

DEFF Research Database (Denmark)

Høskuldsson, Agnar

2004-01-01

The author has developed the H-method of mathematical modeling that builds up the model by parts, where each part is optimized with respect to prediction. Besides providing with better predictions than traditional methods, these methods provide with graphic procedures for analyzing different feat...... features in data. These graphic methods extend the well-known methods and results of Principal Component Analysis to any linear model. Here the graphic procedures are applied to linear regression and Ridge Regression....

A Mathematical Model of the Thermo-Anemometric Flowmeter.

Science.gov (United States)

Korobiichuk, Igor; Bezvesilna, Olena; Ilchenko, Andriі; Shadura, Valentina; Nowicki, Michał; Szewczyk, Roman

2015-09-11

A thermo-anemometric flowmeter design and the principles of its work are presented in the article. A mathematical model of the temperature field in a stream of biofuel is proposed. This model allows one to determine the fuel consumption with high accuracy. Numerical modeling of the heater heat balance in the fuel flow of a thermo-anemometric flowmeter is conducted and the results are analyzed. Methods for increasing the measurement speed and accuracy of a thermo-anemometric flowmeter are proposed.

Mathematical methods for physicists and engineers

CERN Document Server

Collins, Royal Eugene

2011-01-01

This practical, highly readable text provides physics and engineering students with the essential mathematical tools for thorough comprehension of their disciplines. Featuring all the necessary topics in applied mathematics in the form of programmed instruction, the text can be understood by advanced undergraduates and beginning graduate students without any assistance from the instructor. Topics include elementary vector calculus, matrix algebra, and linear vector operations; the many and varied methods of solving linear boundary value problems, including the more common special functions o

Models and methods in thermoluminescence

International Nuclear Information System (INIS)

Furetta, C.

2005-01-01

This work contains a conference that was treated about the principles of the luminescence phenomena, the mathematical treatment concerning the thermoluminescent emission of light as well as the Randall-Wilkins model, the Garlick-Gibson model, the Adirovitch model, the May-Partridge model, the Braunlich-Scharman model, the mixed first and second order kinetics, the methods for evaluating the kinetics parameters such as the initial rise method, the various heating rates method, the isothermal decay method and those methods based on the analysis of the glow curve shape. (Author)

Models and methods in thermoluminescence

Energy Technology Data Exchange (ETDEWEB)

Furetta, C. [ICN, UNAM, A.P. 70-543, Mexico D.F. (Mexico)

2005-07-01

This work contains a conference that was treated about the principles of the luminescence phenomena, the mathematical treatment concerning the thermoluminescent emission of light as well as the Randall-Wilkins model, the Garlick-Gibson model, the Adirovitch model, the May-Partridge model, the Braunlich-Scharman model, the mixed first and second order kinetics, the methods for evaluating the kinetics parameters such as the initial rise method, the various heating rates method, the isothermal decay method and those methods based on the analysis of the glow curve shape. (Author)

Model answers in pure mathematics for a-level students

CERN Document Server

Pratt, GA; Schofield, C W

1967-01-01

Model Answers in Pure Mathematics for A-Level Students provides a set of solutions that indicate what is required and expected in an Advanced Level examination in Pure Mathematics. This book serves as a guide to the length of answer required, layout of the solution, and methods of selecting the best approach to any particular type of math problem. This compilation intends to supplement, not replace, the normal textbook and provides a varied selection of questions for practice in addition to the worked solutions. The subjects covered in this text include algebra, trigonometry, coordinate geomet

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.

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)

Linear models in the mathematics of uncertainty

CERN Document Server

Mordeson, John N; Clark, Terry D; Pham, Alex; Redmond, Michael A

2013-01-01

The purpose of this book is to present new mathematical techniques for modeling global issues. These mathematical techniques are used to determine linear equations between a dependent variable and one or more independent variables in cases where standard techniques such as linear regression are not suitable. In this book, we examine cases where the number of data points is small (effects of nuclear warfare), where the experiment is not repeatable (the breakup of the former Soviet Union), and where the data is derived from expert opinion (how conservative is a political party). In all these cases the data  is difficult to measure and an assumption of randomness and/or statistical validity is questionable.  We apply our methods to real world issues in international relations such as  nuclear deterrence, smart power, and cooperative threat reduction. We next apply our methods to issues in comparative politics such as successful democratization, quality of life, economic freedom, political stability, and fail...

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

Three dimensional mathematical model of tooth for finite element analysis

Directory of Open Access Journals (Sweden)

Puškar Tatjana

2010-01-01

Full Text Available Introduction. The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects in programmes for solid modeling. Objective. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. Methods. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analyzing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body into simple geometric bodies (cylinder, cone, pyramid,.... Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Results. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Conclusion Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.

Mathematical models in marketing a collection of abstracts

CERN Document Server

Funke, Ursula H

1976-01-01

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

Mathematical methods of many-body quantum field theory

CERN Document Server

Lehmann, Detlef

2004-01-01

Mathematical Methods of Many-Body Quantum Field Theory offers a comprehensive, mathematically rigorous treatment of many-body physics. It develops the mathematical tools for describing quantum many-body systems and applies them to the many-electron system. These tools include the formalism of second quantization, field theoretical perturbation theory, functional integral methods, bosonic and fermionic, and estimation and summation techniques for Feynman diagrams. Among the physical effects discussed in this context are BCS superconductivity, s-wave and higher l-wave, and the fractional quantum Hall effect. While the presentation is mathematically rigorous, the author does not focus solely on precise definitions and proofs, but also shows how to actually perform the computations.Presenting many recent advances and clarifying difficult concepts, this book provides the background, results, and detail needed to further explore the issue of when the standard approximation schemes in this field actually work and wh...

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…

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.

One possible method of mathematical modeling of turbulent transport processes in plasma

International Nuclear Information System (INIS)

Skvortsova, Nina N.; Batanov, German M.; Petrov, Alexander E.; Pshenichnikov, Anton A.; Sarksyan, Karen A.; Kharchev, Nikolay K.; Bening, Vladimir E.; Korolev, Victor Yu.

2003-01-01

It is proposed to use the mathematical modeling of the increments of fluctuating plasma variables to analyzing the probability characteristics of turbulent transport processes in plasma. It is shown that, in plasma of the L-2M stellarator and the TAU-1 linear device, the increments of the process of local fluctuating particle flux are stochastic in nature and their distribution is a scale mixture of Gaussians. (author)

Mathematical models and methods of assisting state subsidy distribution at the regional level

Science.gov (United States)

Bondarenko, Yu V.; Azarnova, T. V.; Kashirina, I. L.; Goroshko, I. V.

2018-03-01

One of the most common forms of state support in the world is subsidization. By providing direct financial support to businesses, local authorities get an opportunity to set certain performance targets. Successful achievement of such targets depends not only on the amount of the budgetary allocations, but also on the distribution mechanisms adopted by the regional authorities. Analysis of the existing mechanisms of subsidies distribution in Russian regions shows that in most cases the choice of subsidy calculation formula and its parameters depends on the experts’ subjective opinion. The authors offer a new approach to assisting subsidy distribution at the regional level, which is based on mathematical models and methods, allowing to evaluate the influence of subsidy distribution on the region’s social and economic development. The results of calculations were discussed with the regional administration representatives who confirmed their significance for decision-making in the sphere of state control.

Experimentally supported mathematical modeling of continuous baking processes

DEFF Research Database (Denmark)

Stenby Andresen, Mette

and temperature) and control the process (air flow, temperature, and humidity) are therefore emphasized. The oven is furthermore designed to work outside the range of standard tunnel ovens, making it interesting for manufacturers of both baking products and baking equipment. A mathematical model describing......The scope of the PhD project was to increase knowledge on the process-to-product interactions in continuous tunnel ovens. The work has focused on five main objectives. These objectives cover development of new experimental equipment for pilot plant baking experiments, mathematical modeling of heat...... and mass transfer in a butter cookie product, and evaluation of quality assessment methods. The pilot plant oven is a special batch oven designed to emulate continuous convection tunnel oven baking. The design, construction, and validation of the oven has been part of the project and is described...

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.

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...

Mathematical modelling of plant transients in the PWR for simulator purposes

International Nuclear Information System (INIS)

Hartel, K.

1984-01-01

This chapter presents the results of the testing of anticipated and abnormal plant transients in pressurized water reactors (PWRs) of the type WWER 440 by means of the numerical simulation of 32 different, stationary and nonstationary, operational regimes. Topics considered include the formation of the PWR mathematical model, the physical approximation of the reactor core, the structure of the reactor core model, a mathematical approximation of the reactor model, the selection of numerical methods, and a computerized simulation system. The necessity of a PWR simulator in Czechoslovakia is justified by the present status and the outlook for the further development of the Czechoslovak nuclear power complex

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. 

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)

Leading Undergraduate Research Projects in Mathematical Modeling

Science.gov (United States)

Seshaiyer, Padmanabhan

2017-01-01

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

Scaffolding Mathematical Modelling with a Solution Plan

Science.gov (United States)

Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner

2015-01-01

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

Mathematical model for estimating of technical and technological indicators of railway stations operation

Directory of Open Access Journals (Sweden)

D.M. Kozachenko

2013-06-01

Full Text Available Purpose. The article aims to create a mathematical model of the railway station functioning for the solving of problems of station technology development on the plan-schedule basis. Methodology. The methods of graph theory and object-oriented analysis are used as research methods. The model of the station activity plan-schedule includes a model of technical equipment of the station (plan-schedule net and a model of the station functioning , which are formalized on the basis of parametric graphs. Findings. The presented model is implemented as an application to the graphics package AutoCAD. The software is developed in Visual LISP and Visual Basic. Taking into account that the construction of the plan-schedule is mostly a traditional process of adding, deleting, and modifying of icons, the developed interface is intuitively understandable for a technologist and practically does not require additional training. Originality. A mathematical model was created on the basis of the theory of graphs and object-oriented analysis in order to evaluate the technical and process of railway stations indicators; it is focused on solving problems of technology development of their work. Practical value. The proposed mathematical model is implemented as an application to the graphics package of AutoCAD. The presence of a mathematical model allows carrying out an automatic analysis of the plan-schedule and, thereby, reducing the period of its creation more than twice.

Improving science and mathematics education with computational modelling in interactive engagement environments

Science.gov (United States)

Neves, Rui Gomes; Teodoro, Vítor Duarte

2012-09-01

A teaching approach aiming at an epistemologically balanced integration of computational modelling in science and mathematics education is presented. The approach is based on interactive engagement learning activities built around computational modelling experiments that span the range of different kinds of modelling from explorative to expressive modelling. The activities are designed to make a progressive introduction to scientific computation without requiring prior development of a working knowledge of programming, generate and foster the resolution of cognitive conflicts in the understanding of scientific and mathematical concepts and promote performative competency in the manipulation of different and complementary representations of mathematical models. The activities are supported by interactive PDF documents which explain the fundamental concepts, methods and reasoning processes using text, images and embedded movies, and include free space for multimedia enriched student modelling reports and teacher feedback. To illustrate, an example from physics implemented in the Modellus environment and tested in undergraduate university general physics and biophysics courses is discussed.

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.

Silent method for mathematics instruction: An overview of teaching subsets

Science.gov (United States)

Sugiman, Apino, Ezi

2017-05-01

Generally, teachers use oral communication for teaching mathematics. Taking an opposite perspective, this paper describes how instructional practices for mathematics can be carried out namely a silent method. Silent method uses body language, written, and oral communication for classroom interaction. This research uses a design research approach consisting of four phases: preliminary, prototyping and developing the instruction, and assessment. There are four stages of silent method. The first stage is conditioning stage in which the teacher introduces the method and makes agreement about the `rule of the game'. It is followed by the second one, elaborating stage, where students guess and explore alternative answers. The third stage is developing mathematical thinking by structuring and symbolizing. Finally, the method is ended by reinforcing stage which aims at strengthening and reflecting student's understanding. In this paper, every stage is described on the basis of practical experiences in a real mathematics classroom setting.

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...

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…

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…

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.

Geomechanical problems of an underground storage of spent nuclear fuel and their mathematic modelling

Directory of Open Access Journals (Sweden)

Antonín Hájek

2007-01-01

Full Text Available The paper is devoted to the use of mathematical modelling for analysis of the thermo-mechanical (T-M processes, which are relevant for the assessment of underground repositories of the spent nuclear fuel. Wes shall discuss mathematical formulation, numerical methods and parallel alghorithms, which are capable to solve large-scale complicated and coupled 3D problems. Particularly, we show an application of the described methods and parallel computer simulations for analysis of model problems concerning the Swedish KBS3 concept of underground repository.

Mathematical models of thermohydraulic disturbance sources in the NPP circuits

International Nuclear Information System (INIS)

Proskuryakov, K.N.

1999-01-01

Methods and means of diagnostics of equipment and processes at NPPs allowing one to substantially increase safety and economic efficiency of nuclear power plant operation are considered. Development of mathematical models, describing the occurrence and propagation of violations is conducted

Numerical methods of mathematical optimization with Algol and Fortran programs

CERN Document Server

Künzi, Hans P; Zehnder, C A; Rheinboldt, Werner

1971-01-01

Numerical Methods of Mathematical Optimization: With ALGOL and FORTRAN Programs reviews the theory and the practical application of the numerical methods of mathematical optimization. An ALGOL and a FORTRAN program was developed for each one of the algorithms described in the theoretical section. This should result in easy access to the application of the different optimization methods.Comprised of four chapters, this volume begins with a discussion on the theory of linear and nonlinear optimization, with the main stress on an easily understood, mathematically precise presentation. In addition

Selecting and Using Mathematics Methods Texts: Nontrivial Tasks

Science.gov (United States)

Harkness, Shelly Sheats; Brass, Amy

2017-01-01

Mathematics methods textbooks/texts are important components of many courses for preservice teachers. Researchers should explore how these texts are selected and used. Within this paper we report the findings of a survey administered electronically to 132 members of the Association of Mathematics Teacher Educators (AMTE) in order to answer the…

Mathematical Modelling, Simulation, and Optimal Control of the 2014 Ebola Outbreak in West Africa

Directory of Open Access Journals (Sweden)

Amira Rachah

2015-01-01

it is crucial to modelize the virus and simulate it. In this paper, we begin by studying a simple mathematical model that describes the 2014 Ebola outbreak in Liberia. Then, we use numerical simulations and available data provided by the World Health Organization to validate the obtained mathematical model. Moreover, we develop a new mathematical model including vaccination of individuals. We discuss different cases of vaccination in order to predict the effect of vaccination on the infected individuals over time. Finally, we apply optimal control to study the impact of vaccination on the spread of the Ebola virus. The optimal control problem is solved numerically by using a direct multiple shooting method.

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

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.

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)

Mathematical models of electrical network systems theory and applications : an introduction

CERN Document Server

Kłos, Andrzej

2017-01-01

This book is for all those who are looking for a non-conventional mathematical model of electrical network systems. It presents a modern approach using linear algebra and derives various commonly unknown quantities and interrelations of network analysis. It also explores some applications of algebraic network model of and solves some examples of previously unsolved network problems in planning and operation of network systems. Complex mathematical aspects are illustrated and described in a way that is understandable for non-mathematicians. Discussing interesting concepts and practically useful methods of network analysis, it is a valuable resource for lecturers, students, engineers and research workers. .

Mathematical interpretation of Brownian motor model: Limit cycles and directed transport phenomena

Science.gov (United States)

Yang, Jianqiang; Ma, Hong; Zhong, Suchuang

2018-03-01

In this article, we first suggest that the attractor of Brownian motor model is one of the reasons for the directed transport phenomenon of Brownian particle. We take the classical Smoluchowski-Feynman (SF) ratchet model as an example to investigate the relationship between limit cycles and directed transport phenomenon of the Brownian particle. We study the existence and variation rule of limit cycles of SF ratchet model at changing parameters through mathematical methods. The influences of these parameters on the directed transport phenomenon of a Brownian particle are then analyzed through numerical simulations. Reasonable mathematical explanations for the directed transport phenomenon of Brownian particle in SF ratchet model are also formulated on the basis of the existence and variation rule of the limit cycles and numerical simulations. These mathematical explanations provide a theoretical basis for applying these theories in physics, biology, chemistry, and engineering.

Numerical methods and modelling for engineering

CERN Document Server

Khoury, Richard

2016-01-01

This textbook provides a step-by-step approach to numerical methods in engineering modelling. The authors provide a consistent treatment of the topic, from the ground up, to reinforce for students that numerical methods are a set of mathematical modelling tools which allow engineers to represent real-world systems and compute features of these systems with a predictable error rate. Each method presented addresses a specific type of problem, namely root-finding, optimization, integral, derivative, initial value problem, or boundary value problem, and each one encompasses a set of algorithms to solve the problem given some information and to a known error bound. The authors demonstrate that after developing a proper model and understanding of the engineering situation they are working on, engineers can break down a model into a set of specific mathematical problems, and then implement the appropriate numerical methods to solve these problems. Uses a “building-block” approach, starting with simpler mathemati...

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)

Applied mathematics

CERN Document Server

Logan, J David

2013-01-01

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

Mathematical Model of Thyristor Inverter Including a Series-parallel Resonant Circuit

OpenAIRE

Miroslaw Luft; Elzbieta Szychta

2008-01-01

The article presents a mathematical model of thyristor inverter including a series-parallel resonant circuit with theaid of state variable method. Maple procedures are used to compute current and voltage waveforms in the inverter.

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

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

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.

Mathematical model of thyristor inverter including a series-parallel resonant circuit

OpenAIRE

Luft, M.; Szychta, E.

2008-01-01

The article presents a mathematical model of thyristor inverter including a series-parallel resonant circuit with the aid of state variable method. Maple procedures are used to compute current and voltage waveforms in the inverter.

Generalized dynamics of soft-matter quasicrystals mathematical models and solutions

CERN Document Server

Fan, Tian-You

2017-01-01

The book systematically introduces the mathematical models and solutions of generalized hydrodynamics of soft-matter quasicrystals (SMQ). It provides methods for solving the initial-boundary value problems in these systems. The solutions obtained demonstrate the distribution, deformation and motion of the soft-matter quasicrystals, and determine the stress, velocity and displacement fields. The interactions between phonons, phasons and fluid phonons are discussed in some fundamental materials samples. Mathematical solutions for solid and soft-matter quasicrystals are compared, to help readers to better understand the featured properties of SMQ.

Mathematical modeling and multicriterion optimization for photonuclear production of the 67cu isotope

International Nuclear Information System (INIS)

Dikij, N.P.; Rudychev, Y.V.; Fedorchenko, D.V.; Khazhmuradov, M.A.

2014-01-01

This paper considers a method for 67 Cu isotope production using electron bremsstrahlung by the 68 Zn(gamma, p) 67 Cu reaction. The facility for 67 Cu isotope production contains an electron accelerator, electron-gamma converter and zinc target. To optimize this facility we developed three-dimensional model of the converter and the target. Using this model, we performed the mathematical modeling of zinc target irradiation and thermal-hydraulic processes inside the target for various parameters of the electron beam and converter configurations. For mathematical modeling of radiation processes we used the MCNPX software. Thermal-hydraulic simulation utilized the commercial SolidWorks software with Flow Simulation module. Mathematical modeling revealed that efficient 67 Cu isotope production needs smaller beam diameter and higher electron energy. Under these conditions target heat power also increases, thus additional cooling is necessary. If the beam diameter and the electron energy are fixed the most effective method to satisfy the operating parameters and retain an efficient isotope yield is to optimize photonuclear spectra of the target by variation of converter thickness. We developed an algorithm for multicriterion optimization and performed the optimization of the facility with account to coupled radiation and heat transfer processes.

Mathematical modeling of alcohol distillation columns

Directory of Open Access Journals (Sweden)

Ones Osney Pérez

2011-04-01

Full Text Available New evaluation modules are proposed to extend the scope of a modular simulator oriented to the sugar cane industry, called STA 4.0, in a way that it can be used to carry out x calculation and analysis in ethanol distilleries. Calculation modules were developed for the simulation of the columns that are combined in the distillation area. Mathematical models were supported on materials and energy balances, equilibrium relations and thermodynamic properties of the ethanol-water system. Ponchon-Savarit method was used for the evaluation of the theoretical stages in the columns. A comparison between the results using Ponchon- Savarit method and those obtained applying McCabe-Thiele method was done for a distillation column. These calculation modules for ethanol distilleries were applied to a real case for validation.

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.

Interfacial Fluid Mechanics A Mathematical Modeling Approach

CERN Document Server

Ajaev, Vladimir S

2012-01-01

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

Mathematical Models of Tuberculosis Reactivation and Relapse

Directory of Open Access Journals (Sweden)

Robert Steven Wallis

2016-05-01

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

Mathematical model development of heat and mass exchange processes in the outdoor swimming pool

Directory of Open Access Journals (Sweden)

M. V. Shaptala

2014-12-01

Full Text Available Purpose. Currently exploitation of outdoor swimming pools is often not cost-effective and, despite of their relevance, such pools are closed in large quantities. At this time there is no the whole mathematical model which would allow assessing qualitatively the effect of energy-saving measures. The aim of this work is to develop a mathematical model of heat and mass exchange processes for calculating basic heat and mass losses that occur during its exploitation. Methodology. The method for determination of heat and mass loses based on the theory of similarity criteria equations is used. Findings. The main types of heat and mass losses of outdoor pool were analyzed. The most significant types were allocated and mathematically described. Namely: by evaporation of water from the surface of the pool, by natural and forced convection, by radiation to the environment, heat consumption for water heating. Originality. The mathematical model of heat and mass exchange process of the outdoor swimming pool was developed, which allows calculating the basic heat and mass loses that occur during its exploitation. Practical value. The method of determining heat and mass loses of outdoor swimming pool as a software system was developed and implemented. It is based on the mathematical model proposed by the authors. This method can be used for the conceptual design of energy-efficient structures of outdoor pools, to assess their use of energy-intensive and selecting the optimum energy-saving measures. A further step in research in this area is the experimental validation of the method of calculation of heat losses in outdoor swimming pools with its use as an example the pool of Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan. The outdoor pool, with water heating- up from the boiler room of the university, is operated year-round.

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…

An aqueous physical and mathematical modelling of ultrasonic degassing of molten metals

International Nuclear Information System (INIS)

Meidani, A.R.N.; Hasan, M.

1999-01-01

A comprehensive mathematical model, combined with an aqueous physical modelling, have been developed to simulate the ultrasonic degassing of a gassy liquid. The mathematical model forms a set of coupled, highly nonlinear and stiff differential equations. Therefore, the modified Gear method, which is a good numerical scheme for solving extremely fast moving boundary problems is applied. The threshold pressure and the effects of ultrasonic specifications on rectified diffusion of the dissolved air in water with different initial concentrations are studied. The results show that the air bubble grows when the ultrasonic pressure amplitude is more than the threshold pressure. In this case, the bubble volume reaches several times of its initial value in a fraction of second and the gas bubble may float to the surface due to the buoyancy force. A parametric study on the present model is carried out. The results of aqueous physical modelling for bubble growth are compared to the results of the mathematical model which show a reasonable agreement between the experiments and the predictions. (author)

The role of problem solving method on the improvement of mathematical learning

Directory of Open Access Journals (Sweden)

Saeed Mokhtari-Hassanabad

2012-10-01

Full Text Available In history of education, problem solving is one of the important educational goals and teachers or parents have intended that their students have capacity of problem solving. In present research, it is tried that study the problem solving method for mathematical learning. This research is implemented via quasi-experimental method on 49 boy students at high school. The results of Leven test and T-test indicated that problem solving method has more effective on the improvement of mathematical learning than traditional instruction method. Therefore it seems that teachers of mathematics must apply the problem solving method in educational systems till students became self-efficiency in mathematical problem solving.

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

OpenAIRE

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

2016-01-01

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

The Mathematical Modelling of Heat Transfer in Electrical Cables

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Bugajev Andrej

2014-05-01

Full Text Available This paper describes a mathematical modelling approach for heat transfer calculations in underground high voltage and middle voltage electrical power cables. First of the all typical layout of the cable in the sand or soil is described. Then numerical algorithms are targeted to the two-dimensional mathematical models of transient heat transfer. Finite Volume Method is suggested for calculations. Different strategies of nonorthogonality error elimination are considered. Acute triangles meshes were applied in two-dimensional domain to eliminate this error. Adaptive mesh is also tried. For calculations OpenFOAM open source software which uses Finite Volume Method is applied. To generate acute triangles meshes aCute library is used. The efficiency of the proposed approach is analyzed. The results show that the second order of convergence or close to that is achieved (in terms of sizes of finite volumes. Also it is shown that standard strategy, used by OpenFOAM is less efficient than the proposed approach. Finally it is concluded that for solving real problem a spatial adaptive mesh is essential and adaptive time steps also may be needed.

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

Mathematical Model of Thyristor Inverter Including a Series-parallel Resonant Circuit

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Miroslaw Luft

2008-01-01

Full Text Available The article presents a mathematical model of thyristor inverter including a series-parallel resonant circuit with theaid of state variable method. Maple procedures are used to compute current and voltage waveforms in the inverter.

Mathematical modeling models, analysis and applications

CERN Document Server

Banerjee, Sandip

2014-01-01

""…the reader may find quite a few interesting examples illustrating several important methods used in applied mathematics. … it may be well used as a valuable source of interesting examples as well as complementary reading in a number of courses.""-Svitlana P. Rogovchenko, Zentralblatt MATH 1298

A mathematical model for batch and continuous thickening of flocculent suspensions in vessels with varying section

Energy Technology Data Exchange (ETDEWEB)

Buerger, R.; Damasceno, J.J.R.; Karlesen, K.H.

2001-10-01

The phenomenological theory of continuous thickening of flocculated suspensions in an ideal cylindrical thickener is extended to vessels having varying cross-section, including divergent or convergent conical vessels. The purpose of this contribution is to draw attention to the corresponding mathematical model, whose key ingredient is a strongly degenerate parabolic partial differential equation. For ideal (non-flocculated) suspensions, which do not form co compressible sediments, the mathematical model reduces to the kinematic approach by Anestis, who developed a method of construction of exact solution by the method of characteristics. The difficulty lies in the fact that characteristics and iso-concentration lines, unlike the conventional Kynch model for cylindrical vessels, do not coincide, and one has to resort to numerical methods to simulate the thickening process. A numerical algorithm is presented and employed for simulations of continuous thickening. Implications of the mathematical model are also demonstrated by steady-state calculations, which lead to new possibilities in thickener design. (author)

Mathematical methods for elastic plates

CERN Document Server

Constanda, Christian

2014-01-01

Mathematical models of deformation of elastic plates are used by applied mathematicians and engineers in connection with a wide range of practical applications, from microchip production to the construction of skyscrapers and aircraft. This book employs two important analytic techniques to solve the fundamental boundary value problems for the theory of plates with transverse shear deformation, which offers a more complete picture of the physical process of bending than Kirchhoff’s classical one.   The first method transfers the ellipticity of the governing system to the boundary, leading to singular integral equations on the contour of the domain. These equations, established on the basis of the properties of suitable layer potentials, are then solved in spaces of smooth (Hölder continuous and Hölder continuously differentiable) functions.   The second technique rewrites the differential system in terms of complex variables and fully integrates it, expressing the solution as a combination of complex ana...

Infusing Mathematics Content into a Methods Course: Impacting Content Knowledge for Teaching

Science.gov (United States)

Burton, Megan; Daane, C. J.; Giesen, Judy

2008-01-01

This study compared content knowledge for teaching mathematics differences between elementary pre-service teachers in a traditional versus an experimental mathematics methods course. The experimental course replaced 20 minutes of traditional methods, each class, with an intervention of elementary mathematics content. The difference between groups…

EXPERIMENTAL VALIDATION FOR THE TRAINING METHOD AND MATHEMATICAL MODEL OF THE PILOT SKILL FORMATION IN MAINTENANCE OF ATTITUDE ORIENTATION

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Maksim BARABANOV

2017-12-01

Full Text Available In order to overcome the drawbacks in artificial horizon indicator (HI of inside-in type (a view from an aircraft (A/C, where pilots produce mistakes in maintenance of attitude orientation most of all, the authors offer a novel training method. The method is based on the hypothesis that the manipulative ability of a human visual system can be trained. A mathematical model for the data accumulation during the corresponding training procedure has been proposed. Construction, design and results of the model evaluation are presented in the article. The experimental results revealed the increase of the probability of faultless operation by the test group of up to 0,892, whereas the faultless operation probability of a control group was 0,726. Thus, the trainee-students have statistically increased the reliability for the maintenance of attitude orientation thanks to the proposed method, and the hypothesis was confirmed.

On the mathematical modeling of memristors

KAUST Repository

Radwan, Ahmed G.

2012-10-06

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

Mathematical Properties Relevant to Geomagnetic Field Modeling

DEFF Research Database (Denmark)

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

2010-01-01

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

Mathematical Properties Relevant to Geomagnetic Field Modeling

DEFF Research Database (Denmark)

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

2014-01-01

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

Mathematical Modeling of Hybrid Electrical Engineering Systems

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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

Perception of mathematics teachers on cooperative learning method in the 21st century

Science.gov (United States)

Taufik, Nurshahira Alwani Mohd; Maat, Siti Mistima

2017-05-01

Mathematics education is one of the branches to be mastered by students to help them compete with the upcoming challenges that are very challenging. As such, all parties should work together to help increase student achievement in Mathematics education in line with the Malaysian Education Blueprint (MEB) 2010-2025. Teaching methods play a very important role in attracting and fostering student understanding and interested in learning Mathematics. Therefore, this study was conducted to identify the perceptions of teachers in carrying out cooperative methods in the teaching and learning of mathematics. Participants of this study involving 4 teachers who teach Mathematics in primary schools around the state of Negeri Sembilan. Interviews are used as a method for gathering data. The findings indicate that cooperative methods help increasing interest and understanding in the teaching and learning of mathematics. In conclusion, the teaching methods affect the interest and understanding of students in the learning of Mathematics in the classroom.

SELECT NUMERICAL METHODS FOR MODELING THE DYNAMICS SYSTEMS

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Tetiana D. Panchenko

2016-07-01

Full Text Available The article deals with the creation of methodical support for mathematical modeling of dynamic processes in elements of the systems and complexes. As mathematical models ordinary differential equations have been used. The coefficients of the equations of the models can be nonlinear functions of the process. The projection-grid method is used as the main tool. It has been described iterative method algorithms taking into account the approximate solution prior to the first iteration and proposed adaptive control computing process. The original method of estimation error in the calculation solutions as well as for a given level of error of the technique solutions purpose adaptive method for solving configuration parameters is offered. A method for setting an adaptive method for solving the settings for a given level of error is given. The proposed method can be used for distributed computing.

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

Energy Technology Data Exchange (ETDEWEB)

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

1985-01-01

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

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)

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.)

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 ...

Nonlinear dynamics mathematical models for rigid bodies with a liquid

CERN Document Server

Lukovsky, Ivan A

2015-01-01

This book is devoted to analytically approximate methods in the nonlinear dynamics of a rigid body with cavities partly filled by liquid. It combines several methods and compares the results with experimental data. It is useful for experienced and early-stage readers interested in analytical approaches to fluid-structure interaction problems, the fundamental mathematical background and modeling the dynamics of such complex mechanical systems.

MATHEMATICAL MODELING OF UNSTEADY HEAT EXCHANGE IN A PASSENGER CAR

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I. Yu. Khomenko

2013-07-01

Full Text Available Purpose.Existing mathematicalmodelsofunsteadyheatexchangeinapassengercardonotsatisfytheneedofthedifferentconstructivedecisionsofthelifesupportsystemefficiencyestimation. They also don’t allow comparing new and old life support system constructions influence on the inner environment conditions. Moreoverquite frequently unsteady heat exchange processes were studied at the initial car motion stage. Due to the new competitive engineering decisionsof the lifesupportsystemthe need of a new mathematical instrument that would satisfy the mentioned features and their influence on the unsteadyheatexchangeprocesses during the whole time of the road appeared. The purpose of this work is creation of the mathematicalmodel ofunsteadyheatexchangeinapassengercarthatcan satisfythe above-listed requirements. Methodology. Fortheassigned task realizationsystemofdifferentialequationsthatcharacterizesunsteadyheatexchangeprocessesinapassengercarwascomposed; forthesystemof equationssolution elementary balance method was used. Findings. Computational algorithm was developed andcomputer program for modeling transitional heat processes in the car was designed. It allows comparing different life support system constructions influence on the inner environment conditionsand unsteady heat exchange processes can be studied at every car motion stage. Originality.Mathematicalmodelofunsteadyheatexchangeinapassengercarwasimproved. That is why it can be used for the heat engineering studying of the inner car state under various conditions and for the operation of the different life support systems of passenger cars comparison. Mathematicalmodelingofunsteadyheatexchangeinapassengercarwas made by the elementary balance method. Practical value. Created mathematical model gives the possibility to simulate temperature changes in passenger car on unsteady thermal conditions with enough accuracy and to introduce and remove additional elements to the designed model. Thus different

Mathematical modeling and computational prediction of cancer drug resistance.

Science.gov (United States)

Sun, Xiaoqiang; Hu, Bin

2017-06-23

Diverse forms of resistance to anticancer drugs can lead to the failure of chemotherapy. Drug resistance is one of the most intractable issues for successfully treating cancer in current clinical practice. Effective clinical approaches that could counter drug resistance by restoring the sensitivity of tumors to the targeted agents are urgently needed. As numerous experimental results on resistance mechanisms have been obtained and a mass of high-throughput data has been accumulated, mathematical modeling and computational predictions using systematic and quantitative approaches have become increasingly important, as they can potentially provide deeper insights into resistance mechanisms, generate novel hypotheses or suggest promising treatment strategies for future testing. In this review, we first briefly summarize the current progress of experimentally revealed resistance mechanisms of targeted therapy, including genetic mechanisms, epigenetic mechanisms, posttranslational mechanisms, cellular mechanisms, microenvironmental mechanisms and pharmacokinetic mechanisms. Subsequently, we list several currently available databases and Web-based tools related to drug sensitivity and resistance. Then, we focus primarily on introducing some state-of-the-art computational methods used in drug resistance studies, including mechanism-based mathematical modeling approaches (e.g. molecular dynamics simulation, kinetic model of molecular networks, ordinary differential equation model of cellular dynamics, stochastic model, partial differential equation model, agent-based model, pharmacokinetic-pharmacodynamic model, etc.) and data-driven prediction methods (e.g. omics data-based conventional screening approach for node biomarkers, static network approach for edge biomarkers and module biomarkers, dynamic network approach for dynamic network biomarkers and dynamic module network biomarkers, etc.). Finally, we discuss several further questions and future directions for the use of

Pengembangan Model dan Media Pembelajaran Matematika Ekonomi dan Bisnis dengan Aplikasi Microsoft Mathematics

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Mohammad Arief

2015-09-01

Full Text Available The purpose of this research was to produce: 1 Computer-assisted learning model (Computer Assisted Instruction/CAI using Microsoft Mathematics Application for task completion in the Economic Mathematic and Business course; 2 the development (production interactive multimedia for learning in Economic Mathematic and Business course; 3 Dissemination of results model development and learning media CAI into learning of the Economic Mathematic and Business course in the department of management Economics Faculty UM. The research method that used in this study is qualitative method with Class Action Research (CAR. To collecting data observation that are; 1 observation; 2 questionnaire; 3 photo documentation; 4 application. Research subject was student Management S-1 of academic years 2011/2012 on the odd semester of 2011/2012 who are taking Economic Mathematic and Business courses that are 43 students. The result of development model activities and learning media of Economic Mathematic and Business shown that even though they are beginner using this software, however its ease to use and better outcome expectation with the appropriate learning model, it’s very helpful to achieve learning objective of Economic Mathematic and Business course. Important suggestion is the time in mid semester examination or final semester examination in task completion should be use conventional way, because mastery concept of mathematic which associated and economic phenomena and business not all them can be explained through application program. Abstrak: Tujuan penelitian ini adalah untuk menghasilkan: 1 Model pembelajaran berbantuan komputer ( Computer Assisted Instruction / CAI dengan memanfaatkan Aplikasi Microsoft Mathematics untuk penyelesaian soal dalam mata kuliah Matematika Ekonomi dan Bisnis; 2 Pengembangan multimedia interaktif untuk pembelajaran mata kuliah Matematika Ekonomi dan Bisnis; 3 Diseminasi hasil pengembangan model dan media pembelajaran CAI ke

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…

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

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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

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

CERN Document Server

Rudolph, Lee

2012-01-01

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

Mathematical 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.

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 ...

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 ...

Mathematical model predicts the elastic behavior of composite materials

Directory of Open Access Journals (Sweden)

Zoroastro de Miranda Boari

2005-03-01

Full Text Available Several studies have found that the non-uniform distribution of reinforcing elements in a composite material can markedly influence its characteristics of elastic and plastic deformation and that a composite's overall response is influenced by the physical and geometrical properties of its reinforcing phases. The finite element method, Eshelby's method and dislocation mechanisms are usually employed in formulating a composite's constitutive response. This paper discusses a composite material containing SiC particles in an aluminum matrix. The purpose of this study was to find the correlation between a composite material's particle distribution and its resistance, and to come up with a mathematical model to predict the material's elastic behavior. The proposed formulation was applied to establish the thermal stress field in the aluminum-SiC composite resulting from its fabrication process, whereby the mixture is prepared at 600 °C and the composite material is used at room temperature. The analytical results, which are presented as stress probabilities, were obtained from the mathematical model proposed herein. These results were compared with the numerical ones obtained by the FEM method. A comparison of the results of the two methods, analytical and numerical, reveals very similar average thermal stress values. It is also shown that Maxwell-Boltzmann's distribution law can be applied to identify the correlation between the material's particle distribution and its resistance, using Eshelby's thermal stresses.

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…

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

Science.gov (United States)

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

2016-02-01

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

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 ...

Mathematical Methods of System Analysis in Construction Materials

Science.gov (United States)

Garkina, Irina; Danilov, Alexander

2017-10-01

modules and their levels (the mathematical description, a decision algorithm) are defined. Adequacy is established (compliance of results of modelling to experimental data; is defined by the level of knowledge of process and validity of the accepted assumptions). The global criterion of quality of material is considered as a set of private criteria (properties). Synthesis of material is carried out on the basis of one-criteria optimization on each of the chosen private criteria. Results of one-criteria optimization are used at multicriteria optimization. The methods of developing materials as single-purpose, multi-purpose, including contradictory, systems are indicated. The scheme of synthesis of composite materials as difficult systems is developed. The specified system approach effectively was used in case of synthesis of composite materials with special properties.

Mathematical methods for physicists

CERN Document Server

Arfken, George B

2005-01-01

This best-selling title provides in one handy volume the essential mathematical tools and techniques used to solve problems in physics. It is a vital addition to the bookshelf of any serious student of physics or research professional in the field. The authors have put considerable effort into revamping this new edition.* Updates the leading graduate-level text in mathematical physics* Provides comprehensive coverage of the mathematics necessary for advanced study in physics and engineering* Focuses on problem-solving skills and offers a vast array of exercises * Clearly illustrates and proves mathematical relationsNew in the Sixth Edition:* Updated content throughout, based on users'' feedback * More advanced sections, including differential forms and the elegant forms of Maxwell''s equations* A new chapter on probability and statistics* More elementary sections have been deleted

Analysis mathematical literacy skills in terms of the students’ metacognition on PISA-CPS model

Science.gov (United States)

Ovan; Waluya, S. B.; Nugroho, S. E.

2018-03-01

This research was aimed to know the effectiveness of PISA-CPS model and desceibe the mathematical literacy skills (KLM) in terms of the students’ metacognition. This study used Mixed Methods approaches with the concurrent embedded desaign. The technique of data analysis on quantitative research done analysis of lesson plan, prerequisite test, test hypotesis 1 and hypotesis test. While qualitative research done data reduction, data presentation, and drawing conclution and data verification. The subject of this study was the students of Grade Eight (VIII) of SMP Islam Sultan Agung 4 Semarang, Central Java. The writer analyzed the data with quantitative and qualitative approaches based on the metacognition of the students in low, medium and high groups. Subsequently, taken the mathematical literacy skills (KLM) from students’ metacognition in low, medium, and high . The results of the study showed that the PISA-CPS model was complete and the students’ mathematical literacy skills in terms of the students’ metacognition taught by the PISA-CPS model was higher than the expository learning. metacognitions’ students classified low hadmathematical literacy skills (KLM) less good, metacognitions’ students classified medium had mathematical literacy skills (KLM) good enough, metacognitions’ students classified high had mathematical literacy skills (KLM) very good. Based onresult analysis got conclusion that the PISA-CPS model was effective toward the students’ mathematical literacy skills (KLM). To increase the students’ mathematical literacy skills (KLM), the teachers need to provide reinforcements in the form of the exercises so that the student’s mathematical literacy was achieved at level 5 and level 6.

A new mathematical model for coal flotation kinetics

OpenAIRE

Guerrero-Pérez, Juan Sebastián; Barraza-Burgos, Juan Manuel

2017-01-01

Abstract This study describes the development and formulation of a novel mathematical model for coal flotation kinetic. The flotation rate was considered as a function of chemical, operating and petrographic parameters for a global flotation order n. The equation for flotation rate was obtained by dimensional analysis using the Rayleigh method. It shows the dependency of flotation kinetic on operating parameters, such as air velocity and particle size; chemical parameters, such as reagents do...

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…

Mathematical methods and the computer in oil and gas geology. Matematicheskiye metody i EVM v neftegazovoy geologii

Energy Technology Data Exchange (ETDEWEB)

Dement' yev, L.F.

1983-01-01

Fundamental questions are presented for mathematical modeling in geology. Tasks are examined for describing and grouping geological objects, separating and correlating the sections, analyzing interrelationships between the signs and spatial laws governing their change, organization of collection of automated processing of geological information. Fundamental attention is focused on methodology of using mathematical methods and computers.

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

Selection of productivity improvement techniques via mathematical modeling

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Mahassan M. Khater

2011-07-01

Full Text Available This paper presents a new mathematical model to select an optimal combination of productivity improvement techniques. The proposed model of this paper considers four-stage cycle productivity and the productivity is assumed to be a linear function of fifty four improvement techniques. The proposed model of this paper is implemented for a real-world case study of manufacturing plant. The resulted problem is formulated as a mixed integer programming which can be solved for optimality using traditional methods. The preliminary results of the implementation of the proposed model of this paper indicate that the productivity can be improved through a change on equipments and it can be easily applied for both manufacturing and service industries.

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

A mathematical model for iodine kinetics

International Nuclear Information System (INIS)

Silva, E.A.T. da.

1976-01-01

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

Mathematical 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

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)

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.

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.

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....

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.

A mathematical model for postirradiation immunity

International Nuclear Information System (INIS)

Smirnova, O.A.

1988-01-01

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

MATHEMATICAL METHODS AND TOOLS OF TRENDS’ RESEARCH IN THE EVOLUTIONARY DEVELOPMENT OF THE NATURAL AND ECONOMIC PROCESSES

OpenAIRE

Kymratova A. M.

2015-01-01

The present study was carried out in the view of the fact that there is no more or less complete theory of time series prediction memory to date. This determines the urgency and necessity of the development of new mathematical methods and algorithms to detect possible potential predictability of the series with the memory and the construction of adequate predictive models. Classical methods of forecasting economic time series are based on the mathematical apparatus of econometrics. It is carr...

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.

Current problems in applied mathematics and mathematical physics

Science.gov (United States)

Samarskii, A. A.

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

Improving students’ mathematical critical thinking through rigorous teaching and learning model with informal argument

Science.gov (United States)

Hamid, H.

2018-01-01

The purpose of this study is to analyze an improvement of students’ mathematical critical thinking (CT) ability in Real Analysis course by using Rigorous Teaching and Learning (RTL) model with informal argument. In addition, this research also attempted to understand students’ CT on their initial mathematical ability (IMA). This study was conducted at a private university in academic year 2015/2016. The study employed the quasi-experimental method with pretest-posttest control group design. The participants of the study were 83 students in which 43 students were in the experimental group and 40 students were in the control group. The finding of the study showed that students in experimental group outperformed students in control group on mathematical CT ability based on their IMA (high, medium, low) in learning Real Analysis. In addition, based on medium IMA the improvement of mathematical CT ability of students who were exposed to RTL model with informal argument was greater than that of students who were exposed to CI (conventional instruction). There was also no effect of interaction between RTL model and CI model with both (high, medium, and low) IMA increased mathematical CT ability. Finally, based on (high, medium, and low) IMA there was a significant improvement in the achievement of all indicators of mathematical CT ability of students who were exposed to RTL model with informal argument than that of students who were exposed to CI.

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.

Curve fitting methods for solar radiation data modeling

Energy Technology Data Exchange (ETDEWEB)

Karim, Samsul Ariffin Abdul, E-mail: samsul-ariffin@petronas.com.my, E-mail: balbir@petronas.com.my; Singh, Balbir Singh Mahinder, E-mail: samsul-ariffin@petronas.com.my, E-mail: balbir@petronas.com.my [Department of Fundamental and Applied Sciences, Faculty of Sciences and Information Technology, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak Darul Ridzuan (Malaysia)

2014-10-24

This paper studies the use of several type of curve fitting method to smooth the global solar radiation data. After the data have been fitted by using curve fitting method, the mathematical model of global solar radiation will be developed. The error measurement was calculated by using goodness-fit statistics such as root mean square error (RMSE) and the value of R{sup 2}. The best fitting methods will be used as a starting point for the construction of mathematical modeling of solar radiation received in Universiti Teknologi PETRONAS (UTP) Malaysia. Numerical results indicated that Gaussian fitting and sine fitting (both with two terms) gives better results as compare with the other fitting methods.

Curve fitting methods for solar radiation data modeling

Science.gov (United States)

Karim, Samsul Ariffin Abdul; Singh, Balbir Singh Mahinder

2014-10-01

This paper studies the use of several type of curve fitting method to smooth the global solar radiation data. After the data have been fitted by using curve fitting method, the mathematical model of global solar radiation will be developed. The error measurement was calculated by using goodness-fit statistics such as root mean square error (RMSE) and the value of R2. The best fitting methods will be used as a starting point for the construction of mathematical modeling of solar radiation received in Universiti Teknologi PETRONAS (UTP) Malaysia. Numerical results indicated that Gaussian fitting and sine fitting (both with two terms) gives better results as compare with the other fitting methods.

Curve fitting methods for solar radiation data modeling

International Nuclear Information System (INIS)

Karim, Samsul Ariffin Abdul; Singh, Balbir Singh Mahinder

2014-01-01

This paper studies the use of several type of curve fitting method to smooth the global solar radiation data. After the data have been fitted by using curve fitting method, the mathematical model of global solar radiation will be developed. The error measurement was calculated by using goodness-fit statistics such as root mean square error (RMSE) and the value of R 2 . The best fitting methods will be used as a starting point for the construction of mathematical modeling of solar radiation received in Universiti Teknologi PETRONAS (UTP) Malaysia. Numerical results indicated that Gaussian fitting and sine fitting (both with two terms) gives better results as compare with the other fitting methods

Mathematical modeling of reciprocating pump

International Nuclear Information System (INIS)

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

2015-01-01

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

Explorations in Elementary Mathematical Modeling

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.

Mathematical model of heat transfer to predict distribution of hardness through the Jominy bar

International Nuclear Information System (INIS)

Lopez, E.; Hernandez, J. B.; Solorio, G.; Vergara, H. J.; Vazquez, O.; Garnica, F.

2013-01-01

The heat transfer coefficient was estimated at the bottom surface at Jominy bar end quench specimen by solution of the heat inverse conduction problem. A mathematical model based on the finite-difference method was developed to predict thermal paths and volume fraction of transformed phases. The mathematical model was codified in the commercial package Microsoft Visual Basic v. 6. The calculated thermal path and final phase distribution were used to evaluate the hardness distribution along the AISI 4140 Jominy bar. (Author)

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…

Mathematical model of one-man air revitalization system

Science.gov (United States)

1976-01-01

A mathematical model was developed for simulating the steady state performance in electrochemical CO2 concentrators which utilize (NMe4)2 CO3 (aq.) electrolyte. This electrolyte, which accommodates a wide range of air relative humidity, is most suitable for one-man air revitalization systems. The model is based on the solution of coupled nonlinear ordinary differential equations derived from mass transport and rate equations for the processes which take place in the cell. The boundary conditions are obtained by solving the mass and energy transport equations. A shooting method is used to solve the differential equations.

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.

About the Effectiveness of the Training Technology Model of Trigonometry Teaching for the Mathematical Profile Students

Directory of Open Access Journals (Sweden)

N. I. Popov

2013-01-01

Full Text Available The paper is devoted to trigonometry teaching in higher school as a part of the elementary mathematics course with a complex hierarchical structure. Due to the complicated content of the given discipline,each of its modules can be divided into separate themes; though, the teacher should emphasize their interrelations, as well as the links with the coordinate method, geometry and mathematical analysis.The recommended training technology model allows the teacher to build up and control the training process, and achieve good results in accordance with the assigned tasks. In the course of the model approbation, theauthor developed the e-learning resource and identification method for selecting the key mathematical examples and exercises for each theme and module. The analysis of students’ tests and questionnaires conducted for several years proves the effectiveness of the designed model for the senior university students of mathematical profile. Based on the research findings, the author developed the educational methodology complex for the Basics of Trigonometry course.

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.

Scattering theory in quantum mechanics. Physical principles and mathematical methods

International Nuclear Information System (INIS)

Amrein, W.O.; Jauch, J.M.; Sinha, K.B.

1977-01-01

A contemporary approach is given to the classical topics of physics. The purpose is to explain the basic physical concepts of quantum scattering theory, to develop the necessary mathematical tools for their description, to display the interrelation between the three methods (the Schroedinger equation solutions, stationary scattering theory, and time dependence) to derive the properties of various quantities of physical interest with mathematically rigorous methods

Introductory mathematics for earth scientists

CERN Document Server

Yang, Xin-She

2009-01-01

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

Mathematical 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,...

A mathematical model for malaria transmission relating global warming and local socioeconomic conditions

Directory of Open Access Journals (Sweden)

Hyun M Yang

2001-06-01

Full Text Available OBJECTIVE: Sensitivity analysis was applied to a mathematical model describing malaria transmission relating global warming and local socioeconomic conditions. METHODS: A previous compartment model was proposed to describe the overall transmission of malaria. This model was built up on several parameters and the prevalence of malaria in a community was characterized by the values assigned to them. To assess the control efforts, the model parameters can vary on broad intervals. RESULTS: By performing the sensitivity analysis on equilibrium points, which represent the level of malaria infection in a community, the different possible scenarios are obtained when the parameters are changed. CONCLUSIONS: Depending on malaria risk, the efforts to control its transmission can be guided by a subset of parameters used in the mathematical model.

Physical and mathematical models for diffusion of thermal pollutants in water

International Nuclear Information System (INIS)