Mathematical modeling of acid-base physiology.
Occhipinti, Rossana; Boron, Walter F
2015-01-01
pH is one of the most important parameters in life, influencing virtually every biological process at the cellular, tissue, and whole-body level. Thus, for cells, it is critical to regulate intracellular pH (pHi) and, for multicellular organisms, to regulate extracellular pH (pHo). pHi regulation depends on the opposing actions of plasma-membrane transporters that tend to increase pHi, and others that tend to decrease pHi. In addition, passive fluxes of uncharged species (e.g., CO2, NH3) and charged species (e.g., HCO3(-), [Formula: see text] ) perturb pHi. These movements not only influence one another, but also perturb the equilibria of a multitude of intracellular and extracellular buffers. Thus, even at the level of a single cell, perturbations in acid-base reactions, diffusion, and transport are so complex that it is impossible to understand them without a quantitative model. Here we summarize some mathematical models developed to shed light onto the complex interconnected events triggered by acids-base movements. We then describe a mathematical model of a spherical cells-which to our knowledge is the first one capable of handling a multitude of buffer reactions-that our team has recently developed to simulate changes in pHi and pHo caused by movements of acid-base equivalents across the plasma membrane of a Xenopus oocyte. Finally, we extend our work to a consideration of the effects of simultaneous CO2 and HCO3(-) influx into a cell, and envision how future models might extend to other cell types (e.g., erythrocytes) or tissues (e.g., renal proximal-tubule epithelium) important for whole-body pH homeostasis. Copyright © 2015 Elsevier Ltd. All rights reserved.
Mathematical modeling creation for curriculum based on ontology. Part 1
PIYAVSKY S.A.; LARUKHIN V.B.
2012-01-01
This article delivers a mathematical optimal formation model of curriculum based on the solution of multi-criteria optimization problem. A mathematical model of optimal curriculum shaping based on the solution of multi-criteria optimization. In combination with the previously developed ontology of the educational process, it allows us to offer information technology of forming curriculum at various levels of training in universities personalized for each students
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.
DEFF Research Database (Denmark)
Blomhøj, Morten
2004-01-01
modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive......Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...
Mathematical Modeling of Column-Base Connections under Monotonic Loading
Directory of Open Access Journals (Sweden)
Gholamreza Abdollahzadeh
2014-12-01
Full Text Available Some considerable damage to steel structures during the Hyogo-ken Nanbu Earthquake occurred. Among them, many exposed-type column bases failed in several consistent patterns, such as brittle base plate fracture, excessive bolt elongation, unexpected early bolt failure, and inferior construction work, etc. The lessons from these phenomena led to the need for improved understanding of column base behavior. Joint behavior must be modeled when analyzing semi-rigid frames, which is associated with a mathematical model of the moment–rotation curve. The most accurate model uses continuous nonlinear functions. This article presents three areas of steel joint research: (1 analysis methods of semi-rigid joints; (2 prediction methods for the mechanical behavior of joints; (3 mathematical representations of the moment–rotation curve. In the current study, a new exponential model to depict the moment–rotation relationship of column base connection is proposed. The proposed nonlinear model represents an approach to the prediction of M–θ curves, taking into account the possible failure modes and the deformation characteristics of the connection elements. The new model has three physical parameters, along with two curve-fitted factors. These physical parameters are generated from dimensional details of the connection, as well as the material properties. The M–θ curves obtained by the model are compared with published connection tests and 3D FEM research. The proposed mathematical model adequately comes close to characterizing M–θ behavior through the full range of loading/rotations. As a result, modeling of column base connections using the proposed mathematical model can give crucial beforehand information, and overcome the disadvantages of time consuming workmanship and cost of experimental studies.
2016-01-01
This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.
Eck, Christof; Knabner, Peter
2017-01-01
Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.
Information system based on the mathematical model of the EPS
Kalimoldayev, Maksat N.; Abdildayeva, Assel A.; Mamyrbayev, Orken Zh.; Akhmetzhanov, Maksat
2016-11-01
This article discusses the structure of an information system, the mathematical and information models of electric power systems. Currently, the major application areas include system relaying data communication systems and automation, automated dispatching and technological management of electric power facilities, as well as computer-aided calculation of energy resources. Automatic control of excitation (ARV) synchronous machines is one of the most effective ways to ensure the stability of power systems. However, the variety of possible options and modes even in a single grid pose significant obstacles to the development of the best means of ensuring sustainability. Thus, the use of ARVs to ensure stability in some cases may not be sufficient. Therefore, there is a need to develop an information system based on a mathematical model.
Mathematical Modeling and Pure Mathematics
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…
PREFACE: Physics-Based Mathematical Models for Nanotechnology
Voon, Lok C. Lew Yan; Melnik, Roderick; Willatzen, Morten
2008-03-01
stain-resistant clothing, but with thousands more anticipated. The focus of this interdisciplinary workshop was on determining what kind of new theoretical and computational tools will be needed to advance the science and engineering of nanomaterials and nanostructures. Thanks to the stimulating environment of the BIRS, participants of the workshop had plenty of opportunity to exchange new ideas on one of the main topics of this workshop—physics-based mathematical models for the description of low-dimensional semiconductor nanostructures (LDSNs) that are becoming increasingly important in technological innovations. The main objective of the workshop was to bring together some of the world leading experts in the field from each of the key research communities working on different aspects of LDSNs in order to (a) summarize the state-of-the-art models and computational techniques for modeling LDSNs, (b) identify critical problems of major importance that require solution and prioritize them, (c) analyze feasibility of existing mathematical and computational methodologies for the solution of some such problems, and (d) use some of the workshop working sessions to explore promising approaches in addressing identified challenges. With the possibility of growing practically any shape and size of heterostructures, it becomes essential to understand the mathematical properties of quantum-confined structures including properties of bulk states, interface states, and surface states as a function of shape, size, and internal strain. This workshop put strong emphasis on discussions of the new mathematics needed in nanotechnology especially in relation to geometry and material-combination optimization of device properties such as electronic, optical, and magnetic properties. The problems that were addressed at this meeting are of immense importance in determining such quantum-mechanical properties and the group of invited participants covered very well all the relevant disciplines
Hybrid modelling framework by using mathematics-based and information-based methods
International Nuclear Information System (INIS)
Ghaboussi, J; Kim, J; Elnashai, A
2010-01-01
Mathematics-based computational mechanics involves idealization in going from the observed behaviour of a system into mathematical equations representing the underlying mechanics of that behaviour. Idealization may lead mathematical models that exclude certain aspects of the complex behaviour that may be significant. An alternative approach is data-centric modelling that constitutes a fundamental shift from mathematical equations to data that contain the required information about the underlying mechanics. However, purely data-centric methods often fail for infrequent events and large state changes. In this article, a new hybrid modelling framework is proposed to improve accuracy in simulation of real-world systems. In the hybrid framework, a mathematical model is complemented by information-based components. The role of informational components is to model aspects which the mathematical model leaves out. The missing aspects are extracted and identified through Autoprogressive Algorithms. The proposed hybrid modelling framework has a wide range of potential applications for natural and engineered systems. The potential of the hybrid methodology is illustrated through modelling highly pinched hysteretic behaviour of beam-to-column connections in steel frames.
Mathematical modeling in realistic mathematics education
Riyanto, B.; Zulkardi; Putri, R. I. I.; Darmawijoyo
2017-12-01
The purpose of this paper is to produce Mathematical modelling in Realistics Mathematics Education of Junior High School. This study used development research consisting of 3 stages, namely analysis, design and evaluation. The success criteria of this study were obtained in the form of local instruction theory for school mathematical modelling learning which was valid and practical for students. The data were analyzed using descriptive analysis method as follows: (1) walk through, analysis based on the expert comments in the expert review to get Hypothetical Learning Trajectory for valid mathematical modelling learning; (2) analyzing the results of the review in one to one and small group to gain practicality. Based on the expert validation and students’ opinion and answers, the obtained mathematical modeling problem in Realistics Mathematics Education was valid and practical.
Hafiz, M.; Darhim; Dahlan, J. A.
2017-09-01
Mathematical resilience is very important thing in learning mathematics. It is a positive attitude in order to make student not easily give up in the face of adversity when solving mathematics problems through discussion and research about mathematics. The purpose of this study was to examine comparison of mathematical resilience among students receiving problem based learning model and the students who received guided discovery learning model. This research was conducted at one junior high school in Jakarta. The method was used in this study is quasi-experimental with 66 students as the samples. The instrument which was used in this research is mathematical resilience scale with 24 items of statements. The result of this research is mathematical resilience between the students who received problem based learning model is better than the students who received guided discovery learning model. According to this study result the authors presented some suggestions that: 1) problem based learning and guided discovery learning model can both develop mathematical resilience, but problem based learning is more recommended to use, 2) in order to achieve mathematical resilience better than this findings, it needs to do the next research that combine problem based learning with other treatment.
Finite mathematics models and applications
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.
Directory of Open Access Journals (Sweden)
Edwin Musdi
2016-02-01
Full Text Available This research aims to develop a mathematics instructional model based realistic mathematics education (RME to promote students' problem-solving abilities. The design research used Plomp models, which consists of preliminary phase, development or proto-typing phase and assessment phase. At this study, only the first two phases conducted. The first phase, a preliminary investigation, carried out with a literature study to examine the theory-based instructional learning RME model, characteristics of learners, learning management descriptions by junior high school mathematics teacher and relevant research. The development phase is done by developing a draft model (an early prototype model that consists of the syntax, the social system, the principle of reaction, support systems, and the impact and effects of instructional support. Early prototype model contain a draft model, lesson plans, worksheets, and assessments. Tesssmer formative evaluation model used to revise the model. In this study only phase of one to one evaluation conducted. In the ppreliminary phase has produced a theory-based learning RME model, a description of the characteristics of learners in grade VIII Junior High School Padang and the description of teacher teaching in the classroom. The result showed that most students were still not be able to solve the non-routine problem. Teachers did not optimally facilitate students to develop problem-solving skills of students. It was recommended that the model can be applied in the classroom.
Directory of Open Access Journals (Sweden)
Melike TURAL SÖNMEZ
2017-12-01
Full Text Available The purpose of this study is to examine the construction of mathematical modelling problems process in the content of financial literacy. It is also aimed to create design proposals for construction of mathematical modelling problems. A design based research method was used in this study. The participants were three seventh grade students, six finance experts and nine mathematics education experts. Data collection tools were transcription of video and tapes group discussions, presentations and worksheets during mathematical modelling activities, and participant experts’ feedback form about mathematical modelling problems. There were three stages in this study. First stage was application of preliminary study. This stage gave information about convenience of problems to grade level, students’ timing for solution of problems, clarity of problems and students’ background about content. In second stage, finance experts commented on convenience of mathematical modelling problems to financial literacy standards. In third stage, mathematics education experts commented on convenience of problems to students’ grade level, mathematical modelling principles and seventh grade mathematics lesson objectives. They also gave suggestion on progress. The frequency value of theme in feedback forms was calculated and experts’ expressions were given as citation. It was given suggestion about stages and application of the design guide
Mathematical models of morphogenesis
Directory of Open Access Journals (Sweden)
Dilão Rui
2015-01-01
Full Text Available Morphogenesis is the ensemble of phenomena that generates the form and shape of organisms. Organisms are classified according to some of its structural characteristics, to its metabolism and to its form. In particular, the empirical classification associated with the phylum concept is related with the form and shape of organisms. In the first part of this talk, we introduce the class of mathematical models associated the Turing approach to pattern formation. In the Turing approach, morphogenesis models are described by reaction-diffusion parabolic partial differential equations. Based on this formalism, we present a mathematical model describing the first two hours of development of the fruit fly Drosophila. In the second part of this talk, we present results on Pareto optimality to calibrate and validate mathematical models.
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...
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.
Optimization of Roller Velocity for Quenching Machine Based on Heat Transfer Mathematical Model
Directory of Open Access Journals (Sweden)
Yunfeng He
2017-01-01
Full Text Available During quenching process of steel plate, control parameters are important to product quality. In this work, heat transfer mathematical model has been developed for roller-type quenching machine to predict the temperature field of plate at first, and then an optimization schedule considering quenching technology and equipment limitations is developed firstly based on the heat transfer mathematical model with considering the shortest quenching time. A numerical simulation is performed during optimization process to investigate the effects of roller velocity on the temperature of representative plate. Based on the optimization method, study is also performed for different thickness of plate to obtain the corresponding roller velocity. The results show that the optimized roller velocity can be achieved for the roller-type continuous quenching machine based on the heat transfer mathematical model. With the increasing of plate’s thickness, the optimized roller velocity decreases exponentially.
Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.
Said, Nadia; Engelhart, Michael; Kirches, Christian; Körkel, Stefan; Holt, Daniel V
2016-01-01
Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods.
Lee, Young-Jin
2017-01-01
Purpose: The purpose of this paper is to develop a quantitative model of problem solving performance of students in the computer-based mathematics learning environment. Design/methodology/approach: Regularized logistic regression was used to create a quantitative model of problem solving performance of students that predicts whether students can…
Development of syntax of intuition-based learning model in solving mathematics problems
Yeni Heryaningsih, Nok; Khusna, Hikmatul
2018-01-01
The aim of the research was to produce syntax of Intuition Based Learning (IBL) model in solving mathematics problem for improving mathematics students’ achievement that valid, practical and effective. The subject of the research were 2 classes in grade XI students of SMAN 2 Sragen, Central Java. The type of the research was a Research and Development (R&D). Development process adopted Plomp and Borg & Gall development model, they were preliminary investigation step, design step, realization step, evaluation and revision step. Development steps were as follow: (1) Collected the information and studied of theories in Preliminary Investigation step, studied about intuition, learning model development, students condition, and topic analysis, (2) Designed syntax that could bring up intuition in solving mathematics problem and then designed research instruments. They were several phases that could bring up intuition, Preparation phase, Incubation phase, Illumination phase and Verification phase, (3) Realized syntax of Intuition Based Learning model that has been designed to be the first draft, (4) Did validation of the first draft to the validator, (5) Tested the syntax of Intuition Based Learning model in the classrooms to know the effectiveness of the syntax, (6) Conducted Focus Group Discussion (FGD) to evaluate the result of syntax model testing in the classrooms, and then did the revision on syntax IBL model. The results of the research were produced syntax of IBL model in solving mathematics problems that valid, practical and effective. The syntax of IBL model in the classroom were, (1) Opening with apperception, motivations and build students’ positive perceptions, (2) Teacher explains the material generally, (3) Group discussion about the material, (4) Teacher gives students mathematics problems, (5) Doing exercises individually to solve mathematics problems with steps that could bring up students’ intuition: Preparations, Incubation, Illumination, and
Mathematical modeling using Maple
Beauchamp, Robert Edward.
1996-01-01
The area of higher mathematics begins with successive courses in calculus; however, rarely does the calculus student recognize the applications or impetus for the mathematical skills that are taught. Giordano and Weir produced A First Course in Mathematical Modeling, the first text which addressed this shortcoming in the curriculum of every science and engineering field. With the advent of powerful classroom computers, Fox, Maddox, Giordano and Weir produced Mathematical Modeling With Minitab...
Mathematical Modelling Approach in Mathematics Education
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…
Teaching Mathematical Modeling in Mathematics Education
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…
Modelers' perception of mathematical modeling in epidemiology: a web-based survey.
Directory of Open Access Journals (Sweden)
Gilles Hejblum
Full Text Available BACKGROUND: Mathematical modeling in epidemiology (MME is being used increasingly. However, there are many uncertainties in terms of definitions, uses and quality features of MME. METHODOLOGY/PRINCIPAL FINDINGS: To delineate the current status of these models, a 10-item questionnaire on MME was devised. Proposed via an anonymous internet-based survey, the questionnaire was completed by 189 scientists who had published in the domain of MME. A small minority (18% of respondents claimed to have in mind a concise definition of MME. Some techniques were identified by the researchers as characterizing MME (e.g. Markov models, while others-at the same level of sophistication in terms of mathematics-were not (e.g. Cox regression. The researchers' opinions were also contrasted about the potential applications of MME, perceived as highly relevant for providing insight into complex mechanisms and less relevant for identifying causal factors. The quality criteria were those of good science and were not related to the size and the nature of the public health problems addressed. CONCLUSIONS/SIGNIFICANCE: This study shows that perceptions on the nature, uses and quality criteria of MME are contrasted, even among the very community of published authors in this domain. Nevertheless, MME is an emerging discipline in epidemiology and this study underlines that it is associated with specific areas of application and methods. The development of this discipline is likely to deserve a framework providing recommendations and guidance at various steps of the studies, from design to report.
The human body metabolism process mathematical simulation based on Lotka-Volterra model
Oliynyk, Andriy; Oliynyk, Eugene; Pyptiuk, Olexandr; DzierŻak, RóŻa; Szatkowska, Małgorzata; Uvaysova, Svetlana; Kozbekova, Ainur
2017-08-01
The mathematical model of metabolism process in human organism based on Lotka-Volterra model has beeng proposed, considering healing regime, nutrition system, features of insulin and sugar fragmentation process in the organism. The numerical algorithm of the model using IV-order Runge-Kutta method has been realized. After the result of calculations the conclusions have been made, recommendations about using the modeling results have been showed, the vectors of the following researches are defined.
Fasni, Nurli; Fatimah, Siti; Yulanda, Syerli
2017-05-01
This research aims to achieve some purposes such as: to know whether mathematical problem solving ability of students who have learned mathematics using Multiple Intelligences based teaching model is higher than the student who have learned mathematics using cooperative learning; to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using Multiple Intelligences based teaching model., to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using cooperative learning; to know the attitude of the students to Multiple Intelligences based teaching model. The method employed here is quasi-experiment which is controlled by pre-test and post-test. The population of this research is all of VII grade in SMP Negeri 14 Bandung even-term 2013/2014, later on two classes of it were taken for the samples of this research. A class was taught using Multiple Intelligences based teaching model and the other one was taught using cooperative learning. The data of this research were gotten from the test in mathematical problem solving, scale questionnaire of the student attitudes, and observation. The results show the mathematical problem solving of the students who have learned mathematics using Multiple Intelligences based teaching model learning is higher than the student who have learned mathematics using cooperative learning, the mathematical problem solving ability of the student who have learned mathematics using cooperative learning and Multiple Intelligences based teaching model are in intermediate level, and the students showed the positive attitude in learning mathematics using Multiple Intelligences based teaching model. As for the recommendation for next author, Multiple Intelligences based teaching model can be tested on other subject and other ability.
Directory of Open Access Journals (Sweden)
Dinh An Nguyen
2012-07-01
Full Text Available Many of the Proton Exchange Membrane Fuel Cell (PEMFC models proposed in the literature consist of mathematical equations. However, they are not adequately practical for simulating power systems. The proposed model takes into account phenomena such as activation polarization, ohmic polarization, double layer capacitance and mass transport effects present in a PEM fuel cell. Using electrical analogies and a mathematical modeling of PEMFC, the circuit model is established. To evaluate the effectiveness of the circuit model, its static and dynamic performances under load step changes are simulated and compared to the numerical results obtained by solving the mathematical model. Finally, the applicability of our model is demonstrated by simulating a practical system.
MATHEMATICAL MODELLING FOR MAGNETITE (CRUDE ...
African Journals Online (AJOL)
The present research focuses to develop mathematical model for the removal of iron (magnetite) by ion-exchange resin from primary heat transfer loop of process industries. This mathematical model is based on operating capacities (that's provide more effective design as compared to loading capacity) from static laboratory ...
Saragih, Sahat; Napitupulu, E. Elvis; Fauzi, Amin
2017-01-01
This research aims to develop a student-centered learning model based on local culture and instrument of mathematical higher order thinking of junior high school students in the frame of the 2013-Curriculum in North Sumatra, Indonesia. The subjects of the research are seventh graders which are taken proportionally random consisted of three public…
Petersen, Richard H.
1997-01-01
The objectives of the Institute were: (a) increase participants' content knowledge about aeronautics, science, mathematics, and technology, (b) model and promote the use of scientific inquiry through problem-based learning, (c) investigate the use of instructional technologies and their applications to curricula, and (d) encourage the dissemination of TEI experiences to colleagues, students, and parents.
Mathematical modelling in science and mathematics education
Teodoro, Vítor Duarte; Neves, Rui Gomes
2011-01-01
Scientific research involves mathematical modelling in the context of an interactive balance between theory, experiment and computation. However, computational methods and tools are still far from being appropriately integrated in the high school and university curricula in science and mathematics. In this paper, it is discussed the relevance of mathematical modelling and illustrated how a computer modelling tool (Modellus, a free tool available on the Internet and developed at FCTUNL) can be used to embed modelling in high school and undergraduate courses. Modellus allows students to create and explore mathematical models using functions, differential and iterative equations, and visualize the behaviour of mathematical objects.
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....
Directory of Open Access Journals (Sweden)
Dina V. Lazareva
2015-06-01
Full Text Available A new mathematical model of asymmetric support structure frame type is built on the basis of numerical-analytical boundary elements method (BEM. To describe the design scheme used is the graph theory. Building the model taken into account is the effect of frame members restrained torsion, which presence is due to the fact that these elements are thin-walled. The built model represents a real object as a two-axle semi-trailer platform. To implement the BEM algorithm obtained are analytical expressions of the fundamental functions and vector load components. The effected calculations are based on the semi-trailer two different models, using finite elements and boundary elements methods. The analysis showed that the error between the results obtained on the basis of two numerical methods and experimental data is about 4%, that indicates the adequacy of the proposed mathematical model.
Mathematical modeling of cross-linking monomer elution from resin-based dental composites.
Manojlovic, Dragica; Radisic, Marina; Lausevic, Mila; Zivkovic, Slavoljub; Miletic, Vesna
2013-01-01
Elution of potentially toxic substances, including monomers, from resin-based dental composites may affect the biocompatibility of these materials in clinical conditions. In addition to the amounts of eluted monomers, mathematical modeling of elution kinetics reveals composite restorations as potential chronic sources of leachable monomers. The aim of this work was to experimentally quantify elution of main cross-linking monomers from four commercial composites and offer a mathematical model of elution kinetics. Composite samples (n = 7 per group) of Filtek Supreme XT (3M ESPE), Tetric EvoCeram (Ivoclar Vivadent), Admira (Voco), and Filtek Z250 (3M ESPE) were prepared in 2-mm thick Teflon moulds and cured with halogen or light-emitting diode light. Monomer elution in ethanol and water was analyzed using high-performance liquid chromatography up to 28 days postimmersion. The mathematical model was expressed as a sum of two exponential regression functions representing the first-order kinetics law. Elution kinetics in all cases followed the same mathematical model though differences in rate constants as well as the extent of monomer elution were material-, LCU-, medium-dependent. The proposed mechanisms of elution indicate fast elution from surface and subsurface layers and up to 100 times slower monomer extraction from the bulk polymer. Copyright © 2012 Wiley Periodicals, Inc.
Mathematical modelling techniques
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
Munahefi, D. N.; Waluya, S. B.; Rochmad
2018-03-01
The purpose of this research identified the effectiveness of Problem Based Learning (PBL) models based on Self Regulation Leaning (SRL) on the ability of mathematical creative thinking and analyzed the ability of mathematical creative thinking of high school students in solving mathematical problems. The population of this study was students of grade X SMA N 3 Klaten. The research method used in this research was sequential explanatory. Quantitative stages with simple random sampling technique, where two classes were selected randomly as experimental class was taught with the PBL model based on SRL and control class was taught with expository model. The selection of samples at the qualitative stage was non-probability sampling technique in which each selected 3 students were high, medium, and low academic levels. PBL model with SRL approach effectived to students’ mathematical creative thinking ability. The ability of mathematical creative thinking of low academic level students with PBL model approach of SRL were achieving the aspect of fluency and flexibility. Students of academic level were achieving fluency and flexibility aspects well. But the originality of students at the academic level was not yet well structured. Students of high academic level could reach the aspect of originality.
An introduction to mathematical modeling
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
Simulation of dynamic mathematical modeling for PWR nuclear power plant core based on PSASP
International Nuclear Information System (INIS)
Shi Xi; Liu Dichen; Wu Ping; Zhao Jie; Xiong Li; Zhang Yuanyuan; Zhao Zunlian
2009-01-01
Neutron dynamic model and fuel/coolant thermal output dynamic model were implemented in PSASP through a user-defined program. Based on the mathematical models of different orders, the dynamic behaviors of the NPP core under the input of step disturbance of reactivity and cool-line temperature were simulated in PSASP respectively. The simulation results demonstrate the self-stability of NPP core with temperature effect and poisoning effect, which is consistent with the real-world data. Moreover, the simulation validated the proposed core model, and it can be further used in dynamic calculation of the power system. (authors)
Applied impulsive mathematical models
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.
Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.
Directory of Open Access Journals (Sweden)
Nadia Said
Full Text Available Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods.
Tumanov, Aleksandr; Gumenyuk, Vasily; Tumanov, Vladimir
2017-10-01
The article is devoted to the development of mathematical model for assessing the harm accidents on potentially-dangerous sea-based energy object. Made choice of regression mathematical model that best represents the relationship of the integral indicator with a set of risk factors of emergency situations their probabilities. Shows the main parameters of the model and result indicators. A mathematical model in which risk assessment in addition to the probability of the adverse events, risk factors and possible consequences taken into account the vulnerability of the object.
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...... 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...... availability of genomic information and powerful analytical techniques, mathematical models also serve as a tool for understanding the cellular metabolism and physiology....
Mathematical model of rolling an elastic wheel over deformable support base
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
Principles of mathematical modeling
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...
Perspectives of IT Artefacts: Information Systems based on Complex Mathematical Models
DEFF Research Database (Denmark)
Carugati, Andrea
2002-01-01
A solution for production scheduling that is lately attracting the interests of the manufacturing industry involves the use of complex mathematical modeling techniques in scheduling software. However this technology is fairly unknown among manufacturing practitioners, as are the social problems...... of its development and use. The aim of this article is to show how an approach based on multiple perspectives can help understand the emergence of complex software and help understand why and how the reasons and motives of the different stakeholders are, at times, incompatible....
DEFF Research Database (Denmark)
Carugati, Andrea
2002-01-01
has been initiated with the scope of investigating the questions that mathematical modelling technology poses to traditional information systems development projects. Based on the past body of research, this study proposes a framework to guide decision making for managing projects of information...... systems development. In a presented case the indications of the model are compared with the decisions taken during the development. The results highlight discrepancies between the structure and predictions of the model and the case observations, especially with regard to the importance given to the users......’ skills in the development process. Further observations also indicate that flexibility and adaptability, based on grounded theory, are valuable tools when information systems development involves a new technology....
Charafi, My. M.; Sadok, A.; Kamal, A.; Menai, A.
A quasi-three-dimensional mathematical model has been developed to study the morphological processes based on equilibrium sediment transport method. The flow velocities are computed by a two-dimensional horizontal depth-averaged flow model (H2D) in combination with logarithmic velocity profiles. The transport of sediment particles by a flow water has been considered in the form of bed load and suspended load. The bed load transport rate is defined as the transport of particles by rolling and saltating along the bed surface and is given by the Van Rijn relationship (1987). The equilibrium suspended load transport is described in terms of an equilibrium sediment concentration profile (ce) and a logarithmic velocity (u). Based on the equilibrium transport, the bed change rate is given by integration of the sediment mass-balance equation. The model results have been compared with a Van Rijn results (equilibrium approach) and good agreement has been found.
Habsah, Fitria
2017-01-01
This research aims to produce mathematics textbook for grade VII junior high school students based on realistic mathematics and oriented to the mathematical reasoning and mathematical communication. The quality is determined based on Nieveen criteria, including validity, practicality, and effectiveness.This study was a research and development and used Borg & Gall model. The subject of this research were the students of SMPN 2 Pujon-Kabupaten Malang, that is 30 students in an experimental cla...
Concepts of mathematical modeling
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
Firefly Optimization and Mathematical Modeling of a Vehicle Crash Test Based on Single-Mass
Directory of Open Access Journals (Sweden)
Andreas Klausen
2014-01-01
Full Text Available In this paper mathematical modeling of a vehicle crash test based on a single-mass is studied. The model under consideration consists of a single-mass coupled with a spring and/or a damper. The parameters for the spring and damper are obtained by analyzing the measured acceleration in the center of gravity of the vehicle during a crash. A model with a nonlinear spring and damper is also proposed and the parameters will be optimized with different damper and spring characteristics and optimization algorithms. The optimization algorithms used are interior-point and firefly algorithm. The objective of this paper is to compare different methods used to establish a simple model of a car crash and validate the results against real crash data.
Energy Technology Data Exchange (ETDEWEB)
Salloum, Maher N. [Sandia National Lab. (SNL-CA), Livermore, CA (United States); Gharagozloo, Patricia E. [Sandia National Lab. (SNL-CA), Livermore, CA (United States)
2013-10-01
Metal particle beds have recently become a major technique for hydrogen storage. In order to extract hydrogen from such beds, it is crucial to understand the decomposition kinetics of the metal hydride. We are interested in obtaining a a better understanding of the uranium hydride (UH3) decomposition kinetics. We first developed an empirical model by fitting data compiled from different experimental studies in the literature and quantified the uncertainty resulting from the scattered data. We found that the decomposition time range predicted by the obtained kinetics was in a good agreement with published experimental results. Secondly, we developed a physics based mathematical model to simulate the rate of hydrogen diffusion in a hydride particle during the decomposition. We used this model to simulate the decomposition of the particles for temperatures ranging from 300K to 1000K while propagating parametric uncertainty and evaluated the kinetics from the results. We compared the kinetics parameters derived from the empirical and physics based models and found that the uncertainty in the kinetics predicted by the physics based model covers the scattered experimental data. Finally, we used the physics-based kinetics parameters to simulate the effects of boundary resistances and powder morphological changes during decomposition in a continuum level model. We found that the species change within the bed occurring during the decomposition accelerates the hydrogen flow by increasing the bed permeability, while the pressure buildup and the thermal barrier forming at the wall significantly impede the hydrogen extraction.
Mathematical Modeling: A Structured Process
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…
Sheu, Yun Robert; Feder, Elie; Balsim, Igor; Levin, Victor F; Bleicher, Andrew G; Branstetter, Barton F
2010-06-01
Peer review is an essential process for physicians because it facilitates improved quality of patient care and continuing physician learning and improvement. However, peer review often is not well received by radiologists who note that it is time intensive, is subjective, and lacks a demonstrable impact on patient care. Current advances in peer review include the RADPEER() system, with its standardization of discrepancies and incorporation of the peer-review process into the PACS itself. The purpose of this study was to build on RADPEER and similar systems by using a mathematical model to optimally select the types of cases to be reviewed, for each radiologist undergoing review, on the basis of the past frequency of interpretive error, the likelihood of morbidity from an error, the financial cost of an error, and the time required for the reviewing radiologist to interpret the study. The investigators compiled 612,890 preliminary radiology reports authored by residents and attending radiologists at a large tertiary care medical center from 1999 to 2004. Discrepancies between preliminary and final interpretations were classified by severity and validated by repeat review of major discrepancies. A mathematical model was then used to calculate, for each author of a preliminary report, the combined morbidity and financial costs of expected errors across 3 modalities (MRI, CT, and conventional radiography) and 4 departmental divisions (neuroradiology, abdominal imaging, musculoskeletal imaging, and thoracic imaging). A customized report was generated for each on-call radiologist that determined the category (modality and body part) with the highest total cost function. A universal total cost based on probability data from all radiologists was also compiled. The use of mathematical models to guide case selection could optimize the efficiency and effectiveness of physician time spent on peer review and produce more concrete and meaningful feedback to radiologists
Directory of Open Access Journals (Sweden)
Sayantan Nath
2015-09-01
Full Text Available In this paper, integration between multiple functions of image processing and its statistical parameters for intelligent alarming series based fire detection system is presented. The proper inter-connectivity mapping between processing elements of imagery based on classification factor for temperature monitoring and multilevel intelligent alarm sequence is introduced by abstractive canonical approach. The flow of image processing components between core implementation of intelligent alarming system with temperature wise area segmentation as well as boundary detection technique is not yet fully explored in the present era of thermal imaging. In the light of analytical perspective of convolutive functionalism in thermal imaging, the abstract algebra based inter-mapping model between event-calculus supported DAGSVM classification for step-by-step generation of alarm series with gradual monitoring technique and segmentation of regions with its affected boundaries in thermographic image of coal with respect to temperature distinctions is discussed. The connectedness of the multifunctional operations of image processing based compatible fire protection system with proper monitoring sequence is presently investigated here. The mathematical models representing the relation between the temperature affected areas and its boundary in the obtained thermal image defined in partial derivative fashion is the core contribution of this study. The thermal image of coal sample is obtained in real-life scenario by self-assembled thermographic camera in this study. The amalgamation between area segmentation, boundary detection and alarm series are described in abstract algebra. The principal objective of this paper is to understand the dependency pattern and the principles of working of image processing components and structure an inter-connected modelling technique also for those components with the help of mathematical foundation.
Performance analysis on free-piston Stirling cryocooler based on an idealized mathematical model
Guo, Y. X.; Chao, Y. J.; Gan, Z. H.; Li, S. Z.; Wang, B.
2017-12-01
Free-piston Stirling cryocoolers have extensive applications for its simplicity in structure and decrease in mass. However, the elimination of the motor and the crankshaft has made its thermodynamic characteristic different from that of Stirling cryocoolers with displacer driving mechanism. Therefore, an idealized mathematical model has been established, and with this model, an attempt has been made to analyse the thermodynamic characteristic and the performance of free-piston Stirling cryocooler. To certify this mathematical model, a comparison has been made between the model and a numerical model. This study reveals that due to the displacer damping force necessary for the production of cooling capacity, the free-piston Stirling cryocooler is inherently less efficient than Stirling cryocooler with displacer driving mechanism. Viscous flow resistance and incomplete heat transfer in the regenerator are the two major causes of the discrepancy between the results of the idealized mathematical model and the numerical model.
A mathematical model for transporting the biomass to biomass based power plant
Energy Technology Data Exchange (ETDEWEB)
Singh, Jagtar [Mechanical Engineering Department, SLIET Longowal, District Sangrur, Punjab (India); Panesar, B.S. [Project Professional, SCS Engineers, 11260 Roger Bacon Drive, 300, Virginia 20190 (United States); Sharma, S.K. [Mechanical Engineering Department, NIT Kurukshetra, Haryana (India)
2010-04-15
In Punjab, million of tons of agricultural biomass are being generated every year, but it is spatially scattered. The spatial distribution of this resource and the associated costs on collection and transportation are the major bottleneck in the success of biomass energy-conversion facilities. This paper deals with the mathematical model for collection and transporting the biomass from fields to biomass based power plant. The unit transport cost was calculated by using this model. Four systems of transport were conceptualized for two transport modes (tractor with wagon and truck). Three types of agricultural biomass (loose, baled and briquetted) were considered for transport analysis. For all modes of transport, it was observed that unit cost of transport decreases with increase in distance. The transport cost was least for briquetted biomass as compared to loose and baled biomass. (author)
Authenticity of Mathematical Modeling
Tran, Dung; Dougherty, Barbara J.
2014-01-01
Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…
Richardson, mathematical modeller
Vreugdenhil, C. B.
1994-03-01
On the occasion of the 70th anniversary of Richardson's book Weather Prediction by Numerical Process (Cambridge University Press, Cambridge), a review is given of Richardson's scientific work. He made lasting contributions to very diverse fields of interest, such as finite-difference methods and related numerical methods, weather forecasting by computer, turbulence, international relations, and fractals. Although he was an original experimenter, the main present-day interest is in his mathematical modelling work.
Mathematical modeling of high-rate Anammox UASB reactor based on granular packing patterns
International Nuclear Information System (INIS)
Tang, Chong-Jian; He, Rui; Zheng, Ping; Chai, Li-Yuan; Min, Xiao-Bo
2013-01-01
Highlights: ► A novel model was conducted to estimate volumetric nitrogen conversion rates. ► The packing patterns of the granules in Anammox reactor are investigated. ► The simple cubic packing pattern was simulated in high-rate Anammox UASB reactor. ► Operational strategies concerning sludge concentration were proposed by the modeling. -- Abstract: A novel mathematical model was developed to estimate the volumetric nitrogen conversion rates of a high-rate Anammox UASB reactor based on the packing patterns of granular sludge. A series of relationships among granular packing density, sludge concentration, hydraulic retention time and volumetric conversion rate were constructed to correlate Anammox reactor performance with granular packing patterns. It was suggested that the Anammox granules packed as the equivalent simple cubic pattern in high-rate UASB reactor with packing density of 50–55%, which not only accommodated a high concentration of sludge inside the reactor, but also provided large pore volume, thus prolonging the actual substrate conversion time. Results also indicated that it was necessary to improve Anammox reactor performance by enhancing substrate loading when sludge concentration was higher than 37.8 gVSS/L. The established model was carefully calibrated and verified, and it well simulated the performance of granule-based high-rate Anammox UASB reactor
Mathematical modeling of high-rate Anammox UASB reactor based on granular packing patterns
Energy Technology Data Exchange (ETDEWEB)
Tang, Chong-Jian, E-mail: chjtangzju@yahoo.com.cn [Department of Environmental Engineering, School of Metallurgical Science and Engineering, Central South University, Changsha 410083 (China); National Engineering Research Center for Control and Treatment of Heavy Metal Pollution, Changsha 410083 (China); He, Rui; Zheng, Ping [Department of Environmental Engineering, Zhejiang University, Zijingang Campus, Hangzhou 310058 (China); Chai, Li-Yuan; Min, Xiao-Bo [Department of Environmental Engineering, School of Metallurgical Science and Engineering, Central South University, Changsha 410083 (China); National Engineering Research Center for Control and Treatment of Heavy Metal Pollution, Changsha 410083 (China)
2013-04-15
Highlights: ► A novel model was conducted to estimate volumetric nitrogen conversion rates. ► The packing patterns of the granules in Anammox reactor are investigated. ► The simple cubic packing pattern was simulated in high-rate Anammox UASB reactor. ► Operational strategies concerning sludge concentration were proposed by the modeling. -- Abstract: A novel mathematical model was developed to estimate the volumetric nitrogen conversion rates of a high-rate Anammox UASB reactor based on the packing patterns of granular sludge. A series of relationships among granular packing density, sludge concentration, hydraulic retention time and volumetric conversion rate were constructed to correlate Anammox reactor performance with granular packing patterns. It was suggested that the Anammox granules packed as the equivalent simple cubic pattern in high-rate UASB reactor with packing density of 50–55%, which not only accommodated a high concentration of sludge inside the reactor, but also provided large pore volume, thus prolonging the actual substrate conversion time. Results also indicated that it was necessary to improve Anammox reactor performance by enhancing substrate loading when sludge concentration was higher than 37.8 gVSS/L. The established model was carefully calibrated and verified, and it well simulated the performance of granule-based high-rate Anammox UASB reactor.
Directory of Open Access Journals (Sweden)
Longxiang Wang
2016-07-01
Full Text Available Deduplication is an efficient data reduction technique, and it is used to mitigate the problem of huge data volume in big data storage systems. Content defined chunking (CDC is the most widely used algorithm in deduplication systems. The expected chunk size is an important parameter of CDC, and it influences the duplicate elimination ratio (DER significantly. We collected two realistic datasets to perform an experiment. The experimental results showed that the current approach of setting the expected chunk size to 4 KB or 8 KB empirically cannot optimize DER. Therefore, we present a logistic based mathematical model to reveal the hidden relationship between the expected chunk size and the DER. This model provides a theoretical basis for optimizing DER by setting the expected chunk size reasonably. We used the collected datasets to verify this model. The experimental results showed that the R2 values, which describe the goodness of fit, are above 0.9, validating the correctness of this mathematic model. Based on the DER model, we discussed how to make DER close to the optimum by setting the expected chunk size reasonably.
Helming, J.F.M.
2005-01-01
The purpose of this thesis is to describe the current state-of-the-art of the Dutch Regionalized Agricultural Model (DRAM). DRAM can be defined as a comparative static, partial equilibrium, mathematical programming and regionalized model of the Dutch agricultural sector with environmental aspects.
Mathematical modeling of plant allelopathic hormesis based on ecological-limiting-factor models.
Liu, Yinghu; Chen, Xiaoqiu; Duan, Shunshan; Feng, Yuanjiao; An, Min
2010-05-28
Allelopathy arises from the release of chemicals by one plant species that affect other species in its vicinity, usually to their detriment. Allelopathic effects have been demonstrated to be limiting factors for species distributions and ecological processes in some natural or agricultural communities. Based on the biphasic hormetic responses of plants to allelochemicals, ecological-limiting-factor models were introduced into the An-Johnson-Lovett hormesis model to improve modelling the phenomenon of allelopathic hormesis and to better reflect the nature of allelopathy as a limiting factor in ecological processes. Outcomes of the models have been compared for several sets of experimental data from the literature and good agreement between the models and data was observed, which indicates that the new models give some insight into the ecological mechanisms involved and may provide more options for modelling the allelopathic phenomenon as well as platforms for further research on plant allelopathic hormesis.
Dielectric Relaxation of Lanthanide-Based Ternary Oxides: Physical and Mathematical Models
Directory of Open Access Journals (Sweden)
Chun Zhao
2012-01-01
Full Text Available Cerium-doped hafnium oxides (CexHf1−xO2 and lanthanum-doped zirconium oxides (LaxZr1−xO2 were investigated. The highest dielectric constants, k, were obtained from lightly doped oxides with an La content of x=0.09 and a Ce content of x=0.1, for which k-values of 33~40 were obtained. The dielectric relaxation appears to be related to the size of crystal grains formed during annealing, which was dependent on the doping level. The physical and mathematical models were used to analyze the relationship between k-values and frequencies. The variations in the k-values up to megahertz frequencies for both CexHf1−xO2 and LaxZr1−xO2 are simulated based on the Curie-von Schweidler (CS or Havriliak-Negami (HN relationships. Concerning the lightly doped CexHf1−xO2 and LaxZr1−xO2, the data extracted are best modeled by the HN law, while LaxZr1−xO2 with doping level from x=0.22 to 0.63 are best modelled based on the CS law.
International Nuclear Information System (INIS)
Elfelsoufi, Z.; Azrar, L.
2016-01-01
In this paper, a mathematical modeling of flutter and divergence analyses of fluid conveying pipes based on integral equation formulations is presented. Dynamic stability problems related to fluid pressure, velocity, tension, topography slope and viscoelastic supports and foundations are formulated. A methodological approach is presented and the required matrices, associated to the influencing fluid and pipe parameters, are explicitly given. Internal discretizations are used allowing to investigate the deformation, the bending moment, slope and shear force at internal points. Velocity–frequency, pressure-frequency and tension-frequency curves are analyzed for various fluid parameters and internal elastic supports. Critical values of divergence and flutter behaviors with respect to various fluid parameters are investigated. This model is general and allows the study of dynamic stability of tubes crossed by stationary and instationary fluid on various types of supports. Accurate predictions can be obtained and are of particular interest for a better performance and for an optimal safety of piping system installations. - Highlights: • Modeling the flutter and divergence of fluid conveying pipes based on RBF. • Dynamic analysis of a fluid conveying pipe with generalized boundary conditions. • Considered parameters fluid are the pressure, tension, slopes topography, velocity. • Internal support increase the critical velocity value. • This methodologies determine the fluid parameters effects.
Ataei, Sh; Mahmud, Z.; Khalid, M. N.
2014-04-01
The students learning outcomes clarify what students should know and be able to demonstrate after completing their course. So, one of the issues on the process of teaching and learning is how to assess students' learning. This paper describes an application of the dichotomous Rasch measurement model in measuring the cognitive process of engineering students' learning of mathematics. This study provides insights into the perspective of 54 engineering students' cognitive ability in learning Calculus III based on Bloom's Taxonomy on 31 items. The results denote that some of the examination questions are either too difficult or too easy for the majority of the students. This analysis yields FIT statistics which are able to identify if there is data departure from the Rasch theoretical model. The study has identified some potential misfit items based on the measurement of ZSTD where the removal misfit item was accomplished based on the MNSQ outfit of above 1.3 or less than 0.7 logit. Therefore, it is recommended that these items be reviewed or revised to better match the range of students' ability in the respective course.
International Nuclear Information System (INIS)
Ataei, Sh; Mahmud, Z; Khalid, M N
2014-01-01
The students learning outcomes clarify what students should know and be able to demonstrate after completing their course. So, one of the issues on the process of teaching and learning is how to assess students' learning. This paper describes an application of the dichotomous Rasch measurement model in measuring the cognitive process of engineering students' learning of mathematics. This study provides insights into the perspective of 54 engineering students' cognitive ability in learning Calculus III based on Bloom's Taxonomy on 31 items. The results denote that some of the examination questions are either too difficult or too easy for the majority of the students. This analysis yields FIT statistics which are able to identify if there is data departure from the Rasch theoretical model. The study has identified some potential misfit items based on the measurement of ZSTD where the removal misfit item was accomplished based on the MNSQ outfit of above 1.3 or less than 0.7 logit. Therefore, it is recommended that these items be reviewed or revised to better match the range of students' ability in the respective course.
International Nuclear Information System (INIS)
Gladchenkov, E V; Kolyubin, V A; Nedosekin, P G; Zaharchenko, K V; Ibragimov, R F; Kadilin, V V; Tyurin, E M
2017-01-01
Were conducted a series of experiments, the purpose of which had to verify the mathematical model of the radiation environment sensor. Theoretical values of the beta particles count rate from 90 Sr - 90 Y source registered by radiation environment sensor was compared with the experimental one. Theoretical (calculated) count rate of beta particles was found with using the developed mathematical model of the radiation environment sensor. Deviation of the calculated values of the beta particle count rate does not exceed 10% from the experimental. (paper)
A Primer for Mathematical Modeling
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…
Directory of Open Access Journals (Sweden)
Abhishek Subramanian
2015-09-01
Full Text Available Understanding the transmission and control of visceral leishmaniasis, a neglected tropical disease that manifests in human and animals, still remains a challenging problem globally. To study the nature of disease spread, we have developed a compartment-based mathematical model of zoonotic visceral leishmaniasis transmission among three different populations—human, animal and sandfly; dividing the human class into asymptomatic, symptomatic, post-kala-azar dermal leishmaniasis and transiently infected. We analyzed this large model for positivity, boundedness and stability around steady states in different diseased and disease-free scenarios and derived the analytical expression for basic reproduction number (R0. Sensitive parameters for each infected population were identified and varied to observe their effects on the steady state. Epidemic threshold R0 was calculated for every parameter variation. Animal population was identified to play a protective role in absorbing infection, thereby controlling the disease spread in human. To test the predictive ability of the model, seasonal fluctuation was incorporated in the birth rate of the sandflies to compare the model predictions with real data. Control scenarios on this real population data were created to predict the degree of control that can be exerted on the sensitive parameters so as to effectively reduce the infected populations.
Mathematical Model of the One-stage Magneto-optical Sensor Based on Faraday Effect
Babaev, O. G.; Paranin, V. D.; Sinitsin, L. I.
2018-01-01
The aim of this work is to refine a model of magneto-optical sensors based on Faraday’s longitudinal magneto-optical effect. The tasks of the study include computer modeling and analysis of the transfer characteristic of a single-stage magneto-optical sensor for various polarization of the input beam and non-ideal optical components. The proposed mathematical model and software make it possible to take into account the non-ideal characteristics of film polaroids observed in operation in the near infrared region and at increased temperatures. On the basis of the results of the model analysis it was found that the dependence of normalized transmission T(γ2) has periodic nature. Choosing the angle (γ 2-γ 1) makes it possible to shift the initial operation point and change the sensitivity dT/dγ 2. The influence of the input beam polarization increases with the increase of polaroid parameter deviation from ideal and shows itself as reduction of modulation depth and angular shift of the sensor conversion response.
Mathematical Model Based on Newton’s Laws and in First Thermodynamic Law of a Gas Turbine
Ottmar Rafael Uriza Gosebruch; Carlos Alexander Nuñez Martin; Eloy Edmundo Rodríguez Vázquez; Eduardo Campos Mercado
2017-01-01
The present article explains the modeling of a Gas Turbine system; the mathematical modeling is based on fluid mechanics applying the principal energy laws such as Euler’s Law, Newton’s second Law and the first thermodynamic law to obtain the equations for mass, momentum and energy conservation; expressed as the continuity equation, the Navier-Stokes equation and the energy conservation using Fourier’s Law. The purpose of this article is to establish a precise mathematical model to be applied...
Mathematical Model Based on Newton’s Laws and in First Thermodynamic Law of a Gas Turbine
Directory of Open Access Journals (Sweden)
Ottmar Rafael Uriza Gosebruch
2017-09-01
Full Text Available The present article explains the modeling of a Gas Turbine system; the mathematical modeling is based on fluid mechanics applying the principal energy laws such as Euler’s Law, Newton’s second Law and the first thermodynamic law to obtain the equations for mass, momentum and energy conservation; expressed as the continuity equation, the Navier-Stokes equation and the energy conservation using Fourier’s Law. The purpose of this article is to establish a precise mathematical model to be applied in control applications, for future works, within industry applications.
Mathematical modeling of high-rate Anammox UASB reactor based on granular packing patterns.
Tang, Chong-Jian; He, Rui; Zheng, Ping; Chai, Li-Yuan; Min, Xiao-Bo
2013-04-15
A novel mathematical model was developed to estimate the volumetric nitrogen conversion rates of a high-rate Anammox UASB reactor based on the packing patterns of granular sludge. A series of relationships among granular packing density, sludge concentration, hydraulic retention time and volumetric conversion rate were constructed to correlate Anammox reactor performance with granular packing patterns. It was suggested that the Anammox granules packed as the equivalent simple cubic pattern in high-rate UASB reactor with packing density of 50-55%, which not only accommodated a high concentration of sludge inside the reactor, but also provided large pore volume, thus prolonging the actual substrate conversion time. Results also indicated that it was necessary to improve Anammox reactor performance by enhancing substrate loading when sludge concentration was higher than 37.8 gVSS/L. The established model was carefully calibrated and verified, and it well simulated the performance of granule-based high-rate Anammox UASB reactor. Copyright © 2013 Elsevier B.V. All rights reserved.
A mathematical model for pressure-based organs behaving as biological pressure vessels.
Casha, Aaron R; Camilleri, Liberato; Gauci, Marilyn; Gatt, Ruben; Sladden, David; Chetcuti, Stanley; Grima, Joseph N
2018-04-26
We introduce a mathematical model that describes the allometry of physical characteristics of hollow organs behaving as pressure vessels based on the physics of ideal pressure vessels. The model was validated by studying parameters such as body and organ mass, systolic and diastolic pressures, internal and external dimensions, pressurization energy and organ energy output measurements of pressure-based organs in a wide range of mammals and birds. Seven rules were derived that govern amongst others, lack of size efficiency on scaling to larger organ sizes, matching organ size in the same species, equal relative efficiency in pressurization energy across species and direct size matching between organ mass and mass of contents. The lung, heart and bladder follow these predicted theoretical relationships with a similar relative efficiency across various mammalian and avian species; an exception is cardiac output in mammals with a mass exceeding 10kg. This may limit massive body size in mammals, breaking Cope's rule that populations evolve to increase in body size over time. Such a limit was not found in large flightless birds exceeding 100kg, leading to speculation about unlimited dinosaur size should dinosaurs carry avian-like cardiac characteristics. Copyright © 2018. Published by Elsevier Ltd.
International Nuclear Information System (INIS)
Castillo M, J.A.; Pimentel P, A.E.
2000-01-01
This work presents the results to define the adult egg viability behavior (VHA) of two species, Drosophila melanogaster and D. simulans obtained with the mathematical model proposed, as well as the respective curves. The data are the VHA result of both species coming from the vicinity of the Laguna Verde Nuclear Power plant (CNLV) comprise a 10 years collect period starting from 1987 until 1997. Each collect includes four series of data which are the VHA result obtained after treatment with 0, 4, 6 and 8 Gy of gamma rays. (Author)
DEFF Research Database (Denmark)
Palla, Mirko; Bosco, Filippo Giacomo; Yang, Jaeyoung
2015-01-01
This paper presents the development of a novel statistical method for quantifying trace amounts of biomolecules by surface-enhanced Raman spectroscopy (SERS) using a rigorous, single molecule (SM) theory based mathematical derivation. Our quantification framework could be generalized for planar...
Modeling Zombie Outbreaks: A Problem-Based Approach to Improving Mathematics One Brain at a Time
Lewis, Matthew; Powell, James A.
2016-01-01
A great deal of educational literature has focused on problem-based learning (PBL) in mathematics at the primary and secondary level, but arguably there is an even greater need for PBL in college math courses. We present a project centered around the Humans versus Zombies moderated tag game played on the Utah State University campus. We discuss…
Chandrasekaran, Sivapragasam; Sankararajan, Vanitha; Neelakandhan, Nampoothiri; Ram Kumar, Mahalakshmi
2017-11-04
This study, through extensive experiments and mathematical modeling, reveals that other than retention time and wastewater temperature (T w ), atmospheric parameters also play important role in the effective functioning of aquatic macrophyte-based treatment system. Duckweed species Lemna minor is considered in this study. It is observed that the combined effect of atmospheric temperature (T atm ), wind speed (U w ), and relative humidity (RH) can be reflected through one parameter, namely the "apparent temperature" (T a ). A total of eight different models are considered based on the combination of input parameters and the best mathematical model is arrived at which is validated through a new experimental set-up outside the modeling period. The validation results are highly encouraging. Genetic programming (GP)-based models are found to reveal deeper understandings of the wetland process.
Mathematical models of human retina.
Tălu, Stefan
2011-01-01
To describe the human retina, due the absence of complete topographical data, mathematical models are required. The mathematical formula permits a relatively simple representation to explore the physical and optical characteristics of the retina, with particular parameters. Advanced mathematical models are applied for human vision studies, solid modelling and biomechanical behavior of the retina. The accurate modelling of the retina is important in the development of visual prostheses. The objective of this paper is to present an overview of researches for human retina modelling using mathematical models.
Mathematical modelling in solid mechanics
Sofonea, Mircea; Steigmann, David
2017-01-01
This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling a...
Mathematical modeling with multidisciplinary applications
Yang, Xin-She
2013-01-01
Features mathematical modeling techniques and real-world processes with applications in diverse fields Mathematical Modeling with Multidisciplinary Applications details the interdisciplinary nature of mathematical modeling and numerical algorithms. The book combines a variety of applications from diverse fields to illustrate how the methods can be used to model physical processes, design new products, find solutions to challenging problems, and increase competitiveness in international markets. Written by leading scholars and international experts in the field, the
Mathematical modeling of a radio-frequency path for IEEE 802.11ah based wireless sensor networks
Tyshchenko, Igor; Cherepanov, Alexander; Dmitrii, Vakhnin; Popova, Mariia
2017-09-01
This article discusses the process of creating the mathematical model of a radio-frequency path for an IEEE 802.11ah based wireless sensor networks using M atLab Simulink CAD tools. In addition, it describes occurring perturbing effects and determining the presence of a useful signal in the received mixture.
An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers
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 Modeling in Mathematics Education: Basic Concepts and Approaches
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…
A QFD-Based Mathematical Model for New Product Development Considering the Target Market Segment
Chen, Liang-Hsuan; Chen, Cheng-Nien
2014-01-01
Responding to customer needs is important for business success. Quality function deployment provides systematic procedures for converting customer needs into technical requirements to ensure maximum customer satisfaction. The existing literature mainly focuses on the achievement of maximum customer satisfaction under a budgetary limit via mathematical models. The market goal of the new product for the target market segment is usually ignored. In this study, the proposed approach thus consider...
Mathematical Model and Stability Analysis of Inverter-Based Distributed Generator
Directory of Open Access Journals (Sweden)
Alireza Khadem Abbasi
2013-01-01
Full Text Available This paper presents a mathematical (small-signal model of an electronically interfaced distributed generator (DG by considering the effect of voltage and frequency variations of the prime source. Dynamic equations are found by linearization about an operating point. In this study, the dynamic of DC part of the interface is included in the model. The stability analysis shows with proper selection of system parameters; the system is stable during steady-state and dynamic situations, and oscillatory modes are well damped. The proposed model is useful to study stability analysis of a standalone DG or a Microgrid.
Conceptualising inquiry based education in mathematics
DEFF Research Database (Denmark)
Blomhøj, Morten; Artigue, Michéle
2013-01-01
The terms inquiry-based learning (IBL) and inquiry-based education (IBE) have appeared with increasing frequency in educational policy and curriculum documents related to mathematics and science education over the past decade, indicating a major educational trend. We go back to the origin...... frameworks in mathematics education. Six such frameworks are analysed from the perspective of inquiry: the problem-solving tradition, the Theory of Didactical Situations, the Realistic Mathematics Education programme, the mathematical modelling perspective, the Anthropological Theory of Didactics...... of inquiry as a pedagogical concept in the work of Dewey (e.g. 1916, 1938) to analyse and discuss its migration to science and mathematics education. For conceptualizing inquiry-based mathematics education (IBME) it is important to analyse how this concept resonates with already well-established theoretical...
Mathematical problems in meteorological modelling
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 Computational Thinking
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…
Explorations in Elementary Mathematical Modeling
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…
Kadakia, Ekta; Shah, Lipa; Amiji, Mansoor M
2017-07-01
Nanoemulsions have shown potential in delivering drug across epithelial and endothelial cell barriers, which express efflux transporters. However, their transport mechanisms are not entirely understood. Our goal was to investigate the cellular permeability of nanoemulsion-encapsulated drugs and apply mathematical modeling to elucidate transport mechanisms and sensitive nanoemulsion attributes. Transport studies were performed in Caco-2 cells, using fish oil nanoemulsions and a model substrate, rhodamine-123. Permeability data was modeled using a semi-mechanistic approach, capturing the following cellular processes: endocytotic uptake of the nanoemulsion, release of rhodamine-123 from the nanoemulsion, efflux and passive permeability of rhodamine-123 in aqueous solution. Nanoemulsions not only improved the permeability of rhodamine-123, but were also less sensitive to efflux transporters. The model captured bidirectional permeability results and identified sensitive processes, such as the release of the nanoemulsion-encapsulated drug and cellular uptake of the nanoemulsion. Mathematical description of cellular processes, improved our understanding of transport mechanisms, such as nanoemulsions don't inhibit efflux to improve drug permeability. Instead, their endocytotic uptake, results in higher intracellular drug concentrations, thereby increasing the concentration gradient and transcellular permeability across biological barriers. Modeling results indicated optimizing nanoemulsion attributes like the droplet size and intracellular drug release rate, may further improve drug permeability.
Risnawati; Khairinnisa, S.; Darwis, A. H.
2018-01-01
The purpose of this study was to develop a CORE model-based worksheet with recitation task that were valid and practical and could facilitate students’ communication skills in Linear Algebra course. This study was conducted in mathematics education department of one public university in Riau, Indonesia. Participants of the study were media and subject matter experts as validators as well as students from mathematics education department. The objects of this study are students’ worksheet and students’ mathematical communication skills. The results of study showed that: (1) based on validation of the experts, the developed students’ worksheet was valid and could be applied for students in Linear Algebra courses; (2) based on the group trial, the practicality percentage was 92.14% in small group and 90.19% in large group, so the worksheet was very practical and could attract students to learn; and (3) based on the post test, the average percentage of ideals was 87.83%. In addition, the results showed that the students’ worksheet was able to facilitate students’ mathematical communication skills in linear algebra course.
Directory of Open Access Journals (Sweden)
Uaychai Sukanalam
2017-09-01
Full Text Available This research study aimed to: 1 investigate problems and needs for the learning management that helps increase capacities of mathematics teachers at the lower-secondary level, 2 develop a teacher competency enhancement model based on the coaching processes to enhance mathematical reasoning abilities of lower-secondary students, 3 find out the educational supervisors’ opinions on the model designed. The samples of the study comprised 212 mathematics teachers at the lower-secondary level from 60 schools under jurisdiction of the Office of Secondary Educational Service Area 27, who were selected through the simple random sampling technique ; and 201 educational supervisors in charge of the mathematics learning strand from 42 educational service areas, who were selected through the purposive sampling technique. This study was conducted in the academic year 2015. The research instruments included: 1 a teacher competency enhancement manual that illustrated the steps and procedures for increasing the teacher’s capacities based on the coaching processes in order to enhance mathematical reasoning abilities of lower-secondary students, 2 a survey on problems and needs for the learning management to enhance capacities of mathematics teachers at the lower-secondary level, 3 A questionnaire concerning the educational supervisor’s opinion on the model designed. The statistics used included percentage, mean, and standard deviation. The study results showed that: 1. According to the study and analysis of basic data, problems and needs, it was found that the needs for increasing capacities of mathematics teachers at the lower-secondary level was overall at the high level. In terms of identifying behaviors as “mathematical competencies”, there were some problems associated with thinking and reasoning abilities of the teachers, and their needs in developing the learning management were at the highest level. To solve such problems, it is suggested that
Mathematical modeling based on ordinary differential equations: A promising approach to vaccinology.
Bonin, Carla Rezende Barbosa; Fernandes, Guilherme Cortes; Dos Santos, Rodrigo Weber; Lobosco, Marcelo
2017-02-01
New contributions that aim to accelerate the development or to improve the efficacy and safety of vaccines arise from many different areas of research and technology. One of these areas is computational science, which traditionally participates in the initial steps, such as the pre-screening of active substances that have the potential to become a vaccine antigen. In this work, we present another promising way to use computational science in vaccinology: mathematical and computational models of important cell and protein dynamics of the immune system. A system of Ordinary Differential Equations represents different immune system populations, such as B cells and T cells, antigen presenting cells and antibodies. In this way, it is possible to simulate, in silico, the immune response to vaccines under development or under study. Distinct scenarios can be simulated by varying parameters of the mathematical model. As a proof of concept, we developed a model of the immune response to vaccination against the yellow fever. Our simulations have shown consistent results when compared with experimental data available in the literature. The model is generic enough to represent the action of other diseases or vaccines in the human immune system, such as dengue and Zika virus.
Mathematical Modeling of Circadian/Performance Countermeasures
National Aeronautics and Space Administration — We developed and refined our current mathematical model of circadian rhythms to incorporate melatonin as a marker rhythm. We used an existing physiologically based...
Mathematical model for gyroscope effects
Usubamatov, Ryspek
2015-05-01
Gyroscope effects are used in many engineering calculations of rotating parts, and a gyroscope is the basic unit of numerous devices and instruments used in aviation, space, marine and other industries. The primary attribute of a gyroscope is a spinning rotor that persists in maintaining its plane of rotation, creating gyroscope effects. Numerous publications represent the gyroscope theory using mathematical models based on the law of kinetic energy conservation and the rate of change in angular momentum of a spinning rotor. Gyroscope theory still attracts many researchers who continue to discover new properties of gyroscopic devices. In reality, gyroscope effects are more complex and known mathematical models do not accurately reflect the actual motions. Analysis of forces acting on a gyroscope shows that four dynamic components act simultaneously: the centrifugal, inertial and Coriolis forces and the rate of change in angular momentum of the spinning rotor. The spinning rotor generates a rotating plane of centrifugal and Coriols forces that resist the twisting of the spinning rotor with external torque applied. The forced inclination of the spinning rotor generates inertial forces, resulting in precession torque of a gyroscope. The rate of change of the angular momentum creates resisting and precession torques which are not primary one in gyroscope effects. The new mathematical model for the gyroscope motions under the action of the external torque applied can be as base for new gyroscope theory. At the request of the author of the paper, this corrigendum was issued on 24 May 2016 to correct an incomplete Table 1 and errors in Eq. (47) and Eq. (48).
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 Modeling of Diverse Phenomena
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.
Makino, Nobuo; Mise, Takeshi; Sagara, Jun-Ichi
2008-06-01
Oxidative stress is implicated in a variety of disorders including neurodegenerative diseases, and H(2)O(2) is important in the generation of reactive oxygen and oxidative stress. In this study, we have examined the rate of extracellular H(2)O(2) elimination and relevant enzyme activities in cultured astrocytes and C6 glioma cells and have analyzed the results based on a mathematical model. As compared with other types of cultured cells, astrocytes showed higher activity of glutathione peroxidase (GPx) but lower activities for GSH recycling. C6 cells showed relatively low GPx activity, and treatment of C6 cells with dibutyryl-cAMP, which induces astrocytic differentiation, increased catalase activity and H(2)O(2) permeation rate but exerted little effect on other enzyme activities. A mathematical model [N. Makino, K. Sasaki, N. Hashida, Y. Sakakura, A metabolic model describing the H(2)O(2) elimination by mammalian cells including H(2)O(2) permeation through cytoplasmic and peroxisomal membranes: comparison with experimental data, Biochim. Biophys. Acta 1673 (2004) 149-159.], which includes relevant enzymes and H(2)O(2) permeation through membranes, was found to be fitted well to the H(2)O(2) concentration dependences of removal reaction with the permeation rate constants as variable parameters. As compared with PC12 cells as a culture model for neuron, H(2)O(2) removal activity of astrocytes was considerably higher at physiological H(2)O(2) concentrations. The details of the mathematical model are presented in Appendix.
Mathematical models of behavior of individual animals.
Tsibulsky, Vladimir L; Norman, Andrew B
2007-01-01
This review is focused on mathematical modeling of behaviors of a whole organism with special emphasis on models with a clearly scientific approach to the problem that helps to understand the mechanisms underlying behavior. The aim is to provide an overview of old and contemporary mathematical models without complex mathematical details. Only deterministic and stochastic, but not statistical models are reviewed. All mathematical models of behavior can be divided into two main classes. First, models that are based on the principle of teleological determinism assume that subjects choose the behavior that will lead them to a better payoff in the future. Examples are game theories and operant behavior models both of which are based on the matching law. The second class of models are based on the principle of causal determinism, which assume that subjects do not choose from a set of possibilities but rather are compelled to perform a predetermined behavior in response to specific stimuli. Examples are perception and discrimination models, drug effects models and individual-based population models. A brief overview of the utility of each mathematical model is provided for each section.
A QFD-Based Mathematical Model for New Product Development Considering the Target Market Segment
Directory of Open Access Journals (Sweden)
Liang-Hsuan Chen
2014-01-01
Full Text Available Responding to customer needs is important for business success. Quality function deployment provides systematic procedures for converting customer needs into technical requirements to ensure maximum customer satisfaction. The existing literature mainly focuses on the achievement of maximum customer satisfaction under a budgetary limit via mathematical models. The market goal of the new product for the target market segment is usually ignored. In this study, the proposed approach thus considers the target customer satisfaction degree for the target market segment in the model by formulating the overall customer satisfaction as a function of the quality level. In addition, the proposed approach emphasizes the cost-effectiveness concept in the design stage via the achievement of the target customer satisfaction degree using the minimal total cost. A numerical example is used to demonstrate the applicability of the proposed approach and its characteristics are discussed.
Mathematical modeling based evaluation and simulation of boron removal in bioelectrochemical systems
Energy Technology Data Exchange (ETDEWEB)
Ping, Qingyun [Department of Civil and Environmental Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061 (United States); Abu-Reesh, Ibrahim M. [Department of Chemical Engineering, College of Engineering, Qatar University, P.O. Box 2713, Doha (Qatar); He, Zhen, E-mail: zhenhe@vt.edu [Department of Civil and Environmental Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061 (United States)
2016-11-01
Boron removal is an arising issue in desalination plants due to boron's toxicity. As an emerging treatment concept, bioelectrochemical systems (BES) can achieve potentially cost-effective boron removal by taking advantage of cathodic-produced alkali. Prior studies have demonstrated successful removal of boron in microbial desalination cells (MDCs) and microbial fuel cells (MFCs), both of which are representative BES. Herein, mathematical models were developed to further evaluate boron removal by different BES and understand the key operating factors. The models delivered very good prediction of the boron concentration in the MDC integrated with Donnan Dialysis (DD) system with the lowest relative root-mean-square error (RMSE) of 0.00%; the predication of the MFC performance generated the highest RMSE of 18.55%. The model results of salt concentration, solution pH, and current generation were well fitted with experimental data for RMSE values mostly below 10%. The long term simulation of the MDC-DD system suggests that the accumulation of salt in the catholyte/stripping solution could have a positive impact on the removal of boron due to osmosis-driven convection. The current generation in the MDC may have little influence on the boron removal, while in the MFC the current-driven electromigration can contribute up to 40% of boron removal. Osmosis-induced convection transport of boron could be the major driving force for boron removal to a low level < 2 mg L{sup −} {sup 1}. The ratio between the anolyte and the catholyte flow rates should be kept > 22.2 in order to avoid boron accumulation in the anolyte effluent. - Highlights: • Mathematical models are developed to understand boron removal in BES. • Boron removal can be driven by electromigration induced by current generation. • Diffusion induced by a salt concentration gradient also contributes to boron removal. • Osmosis and current driven convection transport play diverse roles in different BES.
Mathematical modelling of cucumber (cucumis sativus) drying
Shahari, N.; Hussein, S. M.; Nursabrina, M.; Hibberd, S.
2014-07-01
This paper investigates the applicability of using an experiment based mathematical model (empirical model) and a single phase mathematical model with shrinkage to describe the drying curve of cucumis sativus (cucumber). Drying experiments were conducted using conventional air drying and data obtained from these experiments were fitted to seven empirical models using non-linear least square regression based on the Levenberg Marquardt algorithm. The empirical models were compared according to their root mean square error (RMSE), sum of square error (SSE) and coefficient of determination (R2). A logarithmic model was found to be the best empirical model to describe the drying curve of cucumber. The numerical result of a single phase mathematical model with shrinkage was also compared with experiment data for cucumber drying. A good agreement was obtained between the model predictions and the experimental data.
Reflexion and control mathematical models
Novikov, Dmitry A
2014-01-01
This book is dedicated to modern approaches to mathematical modeling of reflexive processes in control. The authors consider reflexive games that describe the gametheoretical interaction of agents making decisions based on a hierarchy of beliefs regarding (1) essential parameters (informational reflexion), (2) decision principles used by opponents (strategic reflexion), (3) beliefs about beliefs, and so on. Informational and reflexive equilibria in reflexive games generalize a series of well-known equilibrium concepts in noncooperative games and models of collective behavior. These models allow posing and solving the problems of informational and reflexive control in organizational, economic, social and other systems, in military applications, etc. (the interested reader will find in the book over 30 examples of possible applications in these fields) and describing uniformly many psychological/sociological phenomena connected with reflexion, viz., implicit control, informational control via the mass media, re...
Directory of Open Access Journals (Sweden)
Cecilia Suarez
Full Text Available Gliomas are the most common primary brain tumors and yet almost incurable due mainly to their great invasion capability. This represents a challenge to present clinical oncology. Here, we introduce a mathematical model aiming to improve tumor spreading capability definition. The model consists in a time dependent reaction-diffusion equation in a three-dimensional spatial domain that distinguishes between different brain topological structures. The model uses a series of digitized images from brain slices covering the whole human brain. The Talairach atlas included in the model describes brain structures at different levels. Also, the inclusion of the Brodmann areas allows prediction of the brain functions affected during tumor evolution and the estimation of correlated symptoms. The model is solved numerically using patient-specific parametrization and finite differences. Simulations consider an initial state with cellular proliferation alone (benign tumor, and an advanced state when infiltration starts (malign tumor. Survival time is estimated on the basis of tumor size and location. The model is used to predict tumor evolution in two clinical cases. In the first case, predictions show that real infiltrative areas are underestimated by current diagnostic imaging. In the second case, tumor spreading predictions were shown to be more accurate than those derived from previous models in the literature. Our results suggest that the inclusion of differential migration in glioma growth models constitutes another step towards a better prediction of tumor infiltration at the moment of surgical or radiosurgical target definition. Also, the addition of physiological/psychological considerations to classical anatomical models will provide a better and integral understanding of the patient disease at the moment of deciding therapeutic options, taking into account not only survival but also life quality.
Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.
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 new mathematical modelling based shape extraction technique for Forensic Odontology.
G, Jaffino; A, Banumathi; Gurunathan, Ulaganathan; B, Vijayakumari; J, Prabin Jose
2017-04-01
Forensic Odontology is a specific means for identifying a person in which deceased, and particularly in fatality incidents. The algorithm can be proposed to identify a person by comparing both postmortem (PM) and antemortem (AM) dental radiographs and photographs. This work aims to introduce a new mathematical algorithm for photographs in addition with radiographs. Isoperimetric graph partitioning method is used to extract the shape of dental images in forensic identification. Shape matching is done by comparing AM and PM dental images using both similarity and distance measures. Experimental results prove that the higher matching distance is observed by distance metric rather than similarity measures. The results of this algorithm show that a high hit rate is observed for distance based performance measures and it is well suited for forensic odontologist to identify a person. Copyright © 2017 Elsevier Ltd and Faculty of Forensic and Legal Medicine. All rights reserved.
Teaching mathematical modelling through project work
DEFF Research Database (Denmark)
Blomhøj, Morten; Kjeldsen, Tinne Hoff
2006-01-01
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...
The Spectrum of Mathematical Models.
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…
Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics
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…
A Mathematical Spline-Based Model of Cardiac Left Ventricle Anatomy and Morphology
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Sergei Pravdin
2016-10-01
Full Text Available Computer simulation of normal and diseased human heart activity requires a 3D anatomical model of the myocardium, including myofibers. For clinical applications, such a model has to be constructed based on routine methods of cardiac visualization, such as sonography. Symmetrical models are shown to be too rigid, so an analytical non-symmetrical model with enough flexibility is necessary. Based on previously-made anatomical models of the left ventricle, we propose a new, much more flexible spline-based analytical model. The model is fully described and verified against DT-MRI data. We show a way to construct it on the basis of sonography data. To use this model in further physiological simulations, we propose a numerical method to utilize finite differences in solving the reaction-diffusion problem together with an example of scroll wave dynamics simulation.
Directory of Open Access Journals (Sweden)
Fitria Habsah
2017-05-01
Full Text Available This research aims to produce mathematics textbook for grade VII junior high school students based on realistic mathematics and oriented to the mathematical reasoning and mathematical communication. The quality is determined based on Nieveen criteria, including validity, practicality, and effectiveness.This study was a research and development and used Borg & Gall model. The subject of this research were the students of SMPN 2 Pujon-Kabupaten Malang, that is 30 students in an experimental class (using the developed textbook and 29 students in a control class (using BSE book from the government. The teaching material was categorized valid if the expert's judgment at least is categorized as “good”. The teaching material was categorized practical if both of teachers and students assessment at least categorized as “good”. The teaching material was categorized effectively if minimum 75% of student scores at least is categorized as “good” for the mathematical reasoning test and mathematical communication test. This research resulted in a valid, practical, and effective teaching material. The resulted of the validation show that material teaching is valid. The resulted of teachers and students assessment show that the product is practical. The tests scores show that the product is effective. Percentage of students who categorized at least as “good” is 83,33% for the mathematical reasoning and 86,67% for the mathematical communication. The resulted of statistic test shows that the product more effective than the BSE book from the government in terms of mathematical reasoning and mathematical communication.
Mechanism-Based Mathematical Model for Gating of Ionotropic Glutamate Receptors.
Dai, Jian; Wollmuth, Lonnie P; Zhou, Huan-Xiang
2015-08-27
We present a mathematical model for ionotropic glutamate receptors (iGluR's) that is built on mechanistic understanding and yields a number of thermodynamic and kinetic properties of channel gating. iGluR's are ligand-gated ion channels responsible for the vast majority of fast excitatory neurotransmission in the central nervous system. The effects of agonist-induced closure of the ligand-binding domain (LBD) are transmitted to the transmembrane channel (TMC) via interdomain linkers. Our model demonstrates that, relative to full agonists, partial agonists may reduce either the degree of LBD closure or the curvature of the LBD free energy basin, leading to less stabilization of the channel open state and hence lower channel open probability. A rigorous relation is derived between the channel closed-to-open free energy difference and the tension within the linker. Finally, by treating LBD closure and TMC opening as diffusive motions, we obtain gating trajectories that resemble stochastic current traces from single-channel recordings and calculate the rate constants for transitions between the channel open and closed states. Our model can be implemented by molecular dynamics simulations to realistically depict iGluR gating and may guide functional experiments in gaining deeper insight into this essential family of channel proteins.
Street, Garrett M.; Laubach, Timothy A.
2013-01-01
We provide a 5E structured-inquiry lesson so that students can learn more of the mathematics behind the logistic model of population biology. By using models and mathematics, students understand how population dynamics can be influenced by relatively simple changes in the environment.
Directory of Open Access Journals (Sweden)
Natalia Junakova
2017-12-01
Full Text Available Soil erosion, as a significant contributor to nonpoint-source pollution, is ranked top of sediment sources, pollutants attached to sediment, and pollutants in the solution in surface water. This paper is focused on the design of mathematical model intended to predict the total content of nitrogen (N, phosphorus (P, and potassium (K in bottom sediments in small water reservoirs depending on water erosion processes, together with its application and validation in small agricultural watershed of the Tisovec River, Slovakia. The designed model takes into account the calculation of total N, P, and K content adsorbed on detached and transported soil particles, which consists of supplementing the soil loss calculation with a determination of the average nutrient content in topsoils. The dissolved forms of these elements are neglected in this model. Validation of the model was carried out by statistical assessment of calculated concentrations and measured concentrations in Kľušov, a small water reservoir (Slovakia, using the t-test and F-test, at a 0.05 significance level. Calculated concentrations of total N, P, and K in reservoir sediments were in the range from 0.188 to 0.236 for total N, from 0.065 to 0.078 for total P, and from 1.94 to 2.47 for total K. Measured nutrient concentrations in composite sediment samples ranged from 0.16 to 0.26% for total N, from 0.049 to 0.113% for total P, and from 1.71 to 2.42% for total K. The statistical assessment indicates the applicability of the model in predicting the reservoir’s sediment quality detached through erosion processes in the catchment.
Sensor-Augmented Pump-Based Customized Mathematical Model for Type 1 Diabetes.
Grosman, Benyamin; Wu, Di; Miller, Diana; Lintereur, Louis; Roy, Anirban; Parikh, Neha; Kaufman, Francine R
2018-03-01
Simulations using mathematical models are important for studying, developing, and improving therapies for people with type 1 diabetes. The Medtronic CareLink ® database was used to create virtual patients with a variety of inter-insulin sensitivities, meal absorption rates, pharmacokinetics, age, and gender. In addition, intra-insulin sensitivities of the virtual patients change over a 24-h cycle. A total of 2087 virtual patients were developed. The time percentage between 70 and 180 mg/dL of the CareLink uploads and the simulated virtual patients was 72.4% (18.6) and 74.1% (16.9), respectively. The time percentage 18 years) and 90 adult (>28 years) virtual patients, respectively. The Medtronic CareLink database was utilized to generate a large number of virtual patients with a variety of insulin sensitivities, pharmacokinetics, and meal absorption rates. This new simulation model can be potentially used to evaluate and prognosticate the outcomes of studies of artificial pancreas algorithms and systems.
Energy and exergy analysis of an indirect solar cabinet dryer based on mathematical modeling results
International Nuclear Information System (INIS)
Sami, Samaneh; Etesami, Nasrin; Rahimi, Amir
2011-01-01
In the present study, using a previously developed dynamic mathematical model for performance analysis of an indirect cabinet solar dryer , a microscopic energy and exergy analysis for an indirect solar cabinet dryer is carried out. To this end, appropriate energy and exergy models are developed and using the predicted values for temperature and enthalpy of gas stream and the temperature, enthalpy and moisture content of the drying solid, the energy and exergy efficiencies are estimated. The validity of the model for predicting variations in gas and solid characteristics along the time and the length of the solar collector and/or dryer length was examined against some existing experimental data. The results show that in spite of high energy efficiency, the indirect solar cabinet dryer has relatively low exergy efficiency. Results show that the maximum exergy losses are in midday. Also the minimums of total exergy efficiency are 32.3% and 47.2% on the first and second days, respectively. Furthermore, the effect of some operating parameters, including length of the collector, its surface, and air flow rate was investigated on the exergy destruction and efficiency. -- Highlights: → In the literature, there are few studies on the energy and exergy analysis of solar cabinet dryers. → In the present study a microscopic energy and exergy analysis for an indirect solar cabinet dryer is carried out. → Effect of operating parameters, including collector length, and air flow rate was investigated on the exergy destruction and efficiency. → For collector section, the maximum values for outlet air temperature, outlet exergy and energy are 69 o C, 2.5 kW and 1.12 kW, respectively. → Increasing the air flow rate decreases the exergy efficiency of solar collector.
Ping, Qingyun; Abu-Reesh, Ibrahim M; He, Zhen
2016-11-01
Boron removal is an arising issue in desalination plants due to boron's toxicity. As an emerging treatment concept, bioelectrochemical systems (BES) can achieve potentially cost-effective boron removal by taking advantage of cathodic-produced alkali. Prior studies have demonstrated successful removal of boron in microbial desalination cells (MDCs) and microbial fuel cells (MFCs), both of which are representative BES. Herein, mathematical models were developed to further evaluate boron removal by different BES and understand the key operating factors. The models delivered very good prediction of the boron concentration in the MDC integrated with Donnan Dialysis (DD) system with the lowest relative root-mean-square error (RMSE) of 0.00%; the predication of the MFC performance generated the highest RMSE of 18.55%. The model results of salt concentration, solution pH, and current generation were well fitted with experimental data for RMSE values mostly below 10%. The long term simulation of the MDC-DD system suggests that the accumulation of salt in the catholyte/stripping solution could have a positive impact on the removal of boron due to osmosis-driven convection. The current generation in the MDC may have little influence on the boron removal, while in the MFC the current-driven electromigration can contribute up to 40% of boron removal. Osmosis-induced convection transport of boron could be the major driving force for boron removal to a low level 22.2 in order to avoid boron accumulation in the anolyte effluent. Copyright © 2016 Elsevier B.V. All rights reserved.
Mathematical Models of Gene Regulation
Mackey, Michael C.
2004-03-01
This talk will focus on examples of mathematical models for the regulation of repressible operons (e.g. the tryptophan operon), inducible operons (e.g. the lactose operon), and the lysis/lysogeny switch in phage λ. These ``simple" gene regulatory elements can display characteristics experimentally of rapid response to perturbations and bistability, and biologically accurate mathematical models capture these aspects of the dynamics. The models, if realistic, are always nonlinear and contain significant time delays due to transcriptional and translational delays that pose substantial problems for the analysis of the possible ranges of dynamics.
Directory of Open Access Journals (Sweden)
Michael J. Panza
2015-01-01
Full Text Available This paper presents another application of an images group model for a special enclosure geometry and source orientation. A previous work outlined the concept via application to a special tight-fitting enclosure. Application of the concept to a fan plenum requires different mathematical descriptions for the image groups. This paper describes the sound reverberation inside a sound enclosure with mostly open sides where the primary noise sources are the air inlets and exhausts of axial type fans located at the top of the enclosure, the sound transmission through the air inlet openings, and the radiation to wayside positions. The main reverberation between the floor and ceiling is determined with an image based mathematical model. The model considers how the main reverberant part image group is amplified by its images from two parallel bulkheads and any side wall frame members. The method of images approach allows the hard surfaces of an untreated plenum to be represented by perfectly reflecting surfaces with zero sound absorption coefficients, thus not requiring any estimate or measurement for these surfaces. Numerical results show excellent comparison to experimental results for an actual plenum. The image model is also shown to be significantly more accurate than the standard large room diffuse field reverberant model.
Using Covariation Reasoning to Support Mathematical Modeling
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…
Mathematical modeling of drug dissolution.
Siepmann, J; Siepmann, F
2013-08-30
The dissolution of a drug administered in the solid state is a pre-requisite for efficient subsequent transport within the human body. This is because only dissolved drug molecules/ions/atoms are able to diffuse, e.g. through living tissue. Thus, generally major barriers, including the mucosa of the gastro intestinal tract, can only be crossed after dissolution. Consequently, the process of dissolution is of fundamental importance for the bioavailability and, hence, therapeutic efficacy of various pharmaco-treatments. Poor aqueous solubility and/or very low dissolution rates potentially lead to insufficient availability at the site of action and, hence, failure of the treatment in vivo, despite a potentially ideal chemical structure of the drug to interact with its target site. Different physical phenomena are involved in the process of drug dissolution in an aqueous body fluid, namely the wetting of the particle's surface, breakdown of solid state bonds, solvation, diffusion through the liquid unstirred boundary layer surrounding the particle as well as convection in the surrounding bulk fluid. Appropriate mathematical equations can be used to quantify these mass transport steps, and more or less complex theories can be developed to describe the resulting drug dissolution kinetics. This article gives an overview on the current state of the art of modeling drug dissolution and points out the assumptions the different theories are based on. Various practical examples are given in order to illustrate the benefits of such models. This review is not restricted to mathematical theories considering drugs exhibiting poor aqueous solubility and/or low dissolution rates, but also addresses models quantifying drug release from controlled release dosage forms, in which the process of drug dissolution plays a major role. Copyright © 2013 Elsevier B.V. All rights reserved.
Wijayanti, R.; Waluya, S. B.; Masrukan
2018-03-01
The purpose of this research are (1) to analyze the learning quality of MEAs with MURDER strategy, (2) to analyze students’ mathematical literacy ability based on goal orientation in MEAs learning with MURDER strategy. This research is a mixed method research of concurrent embedded type where qualitative method as the primary method. The data were obtained using the methods of scale, observation, test and interviews. The results showed that (1) MEAs Learning with MURDER strategy on students' mathematical literacy ability is qualified, (2) Students who have mastery goal characteristics are able to master the seven components of mathematical literacy process although there are still two components that the solution is less than the maximum. Students who have performance goal characteristics have not mastered the components of mathematical literacy process with the maximum, they are only able to master the ability of using mathematics tool and the other components of mathematical literacy process is quite good.
Mathematical model for bone mineralization
Directory of Open Access Journals (Sweden)
Svetlana V Komarova
2015-08-01
Full Text Available Defective bone mineralization has serious clinical manifestations, including deformities and fractures, but the regulation of this extracellular process is not fully understood. We have developed a mathematical model consisting of ordinary differential equations that describe collagen maturation, production and degradation of inhibitors, and mineral nucleation and growth. We examined the roles of individual processes in generating normal and abnormal mineralization patterns characterized using two outcome measures: mineralization lag time and degree of mineralization. Model parameters describing the formation of hydroxyapatite mineral on the nucleating centers most potently affected the degree of mineralization, while the parameters describing inhibitor homeostasis most effectively changed the mineralization lag time. Of interest, a parameter describing the rate of matrix maturation emerged as being capable of counter-intuitively increasing both the mineralization lag time and the degree of mineralization. We validated the accuracy of model predictions using known diseases of bone mineralization such as osteogenesis imperfecta and X-linked hypophosphatemia. The model successfully describes the highly non-linear mineralization dynamics, which includes an initial lag phase when osteoid is present but no mineralization is evident, then fast primary mineralization, followed by secondary mineralization characterized by a continuous slow increase in bone mineral content. The developed model can potentially predict the function for a mutated protein based on the histology of pathologic bone samples from mineralization disorders of unknown etiology.
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...... and the rejection coefficient. The second model is a stationary model for the flux of solvent and solute in a hollow fibre membrane. In the model we solve the time independent equations for transport of solvent and solute within the hollow fibre. Furthermore, the flux of solute and solvent through the membrane...
The 24-Hour Mathematical Modeling Challenge
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 Modeling: A Bridge to STEM Education
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…
Lee, Taek-Soo; Frey, Eric C.; Tsui, Benjamin M. W.
2015-04-01
This paper presents two 4D mathematical observer models for the detection of motion defects in 4D gated medical images. Their performance was compared with results from human observers in detecting a regional motion abnormality in simulated 4D gated myocardial perfusion (MP) SPECT images. The first 4D mathematical observer model extends the conventional channelized Hotelling observer (CHO) based on a set of 2D spatial channels and the second is a proposed model that uses a set of 4D space-time channels. Simulated projection data were generated using the 4D NURBS-based cardiac-torso (NCAT) phantom with 16 gates/cardiac cycle. The activity distribution modelled uptake of 99mTc MIBI with normal perfusion and a regional wall motion defect. An analytical projector was used in the simulation and the filtered backprojection (FBP) algorithm was used in image reconstruction followed by spatial and temporal low-pass filtering with various cut-off frequencies. Then, we extracted 2D image slices from each time frame and reorganized them into a set of cine images. For the first model, we applied 2D spatial channels to the cine images and generated a set of feature vectors that were stacked for the images from different slices of the heart. The process was repeated for each of the 1,024 noise realizations, and CHO and receiver operating characteristics (ROC) analysis methodologies were applied to the ensemble of the feature vectors to compute areas under the ROC curves (AUCs). For the second model, a set of 4D space-time channels was developed and applied to the sets of cine images to produce space-time feature vectors to which the CHO methodology was applied. The AUC values of the second model showed better agreement (Spearman’s rank correlation (SRC) coefficient = 0.8) to human observer results than those from the first model (SRC coefficient = 0.4). The agreement with human observers indicates the proposed 4D mathematical observer model provides a good predictor of the
International Nuclear Information System (INIS)
Lee, Taek-Soo; Frey, Eric C; Tsui, Benjamin M W
2015-01-01
This paper presents two 4D mathematical observer models for the detection of motion defects in 4D gated medical images. Their performance was compared with results from human observers in detecting a regional motion abnormality in simulated 4D gated myocardial perfusion (MP) SPECT images. The first 4D mathematical observer model extends the conventional channelized Hotelling observer (CHO) based on a set of 2D spatial channels and the second is a proposed model that uses a set of 4D space-time channels. Simulated projection data were generated using the 4D NURBS-based cardiac-torso (NCAT) phantom with 16 gates/cardiac cycle. The activity distribution modelled uptake of 99m Tc MIBI with normal perfusion and a regional wall motion defect. An analytical projector was used in the simulation and the filtered backprojection (FBP) algorithm was used in image reconstruction followed by spatial and temporal low-pass filtering with various cut-off frequencies. Then, we extracted 2D image slices from each time frame and reorganized them into a set of cine images. For the first model, we applied 2D spatial channels to the cine images and generated a set of feature vectors that were stacked for the images from different slices of the heart. The process was repeated for each of the 1,024 noise realizations, and CHO and receiver operating characteristics (ROC) analysis methodologies were applied to the ensemble of the feature vectors to compute areas under the ROC curves (AUCs). For the second model, a set of 4D space-time channels was developed and applied to the sets of cine images to produce space-time feature vectors to which the CHO methodology was applied. The AUC values of the second model showed better agreement (Spearman’s rank correlation (SRC) coefficient = 0.8) to human observer results than those from the first model (SRC coefficient = 0.4). The agreement with human observers indicates the proposed 4D mathematical observer model provides a good predictor of the
Mathematical models in biology bringing mathematics to life
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...
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...... 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...
A mathematical model of embodied consciousness
Rudrauf, D.; Bennequin, D.; Granic, I.; Landini, G.; Friston, K.; Williford, K.
2017-01-01
We introduce a mathematical model of embodied consciousness, the Projective Consciousness Model (PCM), which is based on the hypothesis that the spatial field of consciousness (FoC) is structured by a projective geometry and under the control of a process of active inference. The FoC in the PCM
Mathematical model of the reactor coolant pump
International Nuclear Information System (INIS)
Kozuh, M.
1989-01-01
The mathematical model of reactor coolant pump is described in this paper. It is based on correlations for centrifugal reactor coolant pumps. This code is one of the elements needed for the simulation of the whole NPP primary system. In subroutine developed according to this model we tried in every possible detail to incorporate plant specific data for Krsko NPP. (author)
A mathematical model of forgetting and amnesia
Murre, J.M.J.; Chessa, A.G.; Meeter, M.
2013-01-01
We describe a mathematical model of learning and memory and apply it to the dynamics of forgetting and amnesia. The model is based on the hypothesis that the neural systems involved in memory at different time scales share two fundamental properties: (1) representations in a store decline in
International Nuclear Information System (INIS)
Ginevan, M.E.; Collins, J.J.; Brown, C.D.; Carnes, B.A.; Curtiss, J.B.; Devine, N.
1981-01-01
The present research develops new statistical methodology, mathematical models, and data bases of relevance to the assessment of health impacts of energy technologies, and uses these to identify, quantify, and pedict adverse health effects of energy related pollutants. Efforts are in five related areas including: (1) evaluation and development of statistical procedures for the analysis of death rate data, disease incidence data, and large scale data sets; (2) development of dose response and demographic models useful in the prediction of the health effects of energy technologies; (3) application of our method and models to analyses of the health risks of energy production; (4) a reanalysis of the Tri-State leukemia survey data, focusing on the relationship between myelogenous leukemia risk and diagnostic x-ray exposure; and (5) investigation of human birth weights as a possible early warning system for the effects of environmental pollution
Mathematical modeling of aeroelastic systems
Velmisov, Petr A.; Ankilov, Andrey V.; Semenova, Elizaveta P.
2017-12-01
In the paper, the stability of elastic elements of a class of designs that are in interaction with a gas or liquid flow is investigated. The definition of the stability of an elastic body corresponds to the concept of stability of dynamical systems by Lyapunov. As examples the mathematical models of flowing channels (models of vibration devices) at a subsonic flow and the mathematical models of protective surface at a supersonic flow are considered. Models are described by the related systems of the partial differential equations. An analytic investigation of stability is carried out on the basis of the construction of Lyapunov-type functionals, a numerical investigation is carried out on the basis of the Galerkin method. The various models of the gas-liquid environment (compressed, incompressible) and the various models of a deformable body (elastic linear and elastic nonlinear) are considered.
DEFF Research Database (Denmark)
Tajsoleiman, Tannaz; J. Abdekhodaie, Mohammad; Gernaey, Krist
2016-01-01
are the main bottlenecks in this type of processes. In this regard, mathematical modelling and computational fluid dynamics simulation (CFD) are powerful tools to identify an efficient and optimized design by providing reliable insights of the process. This study presents a mathematical model and CFD...... an optimized design of the scaffold within a new mathematical optimization algorithm that is proposed. The main concept of this optimization routine isto maintain a large effective surface while simultaneously keeping the shear stress levelin an operating range that is expected to be supporting growth....... Therewith, it should bepossible to gradually reach improved culture efficiency as defined in the objective function....
Mathematical modeling of inhalation exposure
Fiserova-Bergerova, V.
1976-01-01
The paper presents a mathematical model of inhalation exposure in which uptake, distribution and excretion are described by exponential functions, while rate constants are determined by tissue volumes, blood perfusion and by the solubility of vapors (partition coefficients). In the model, tissues are grouped into four pharmokinetic compartments. The model is used to study continuous and interrupted chronic exposures and is applied to the inhalation of Forane and methylene chloride.
Mathematical model on Alzheimer's disease.
Hao, Wenrui; Friedman, Avner
2016-11-18
Alzheimer disease (AD) is a progressive neurodegenerative disease that destroys memory and cognitive skills. AD is characterized by the presence of two types of neuropathological hallmarks: extracellular plaques consisting of amyloid β-peptides and intracellular neurofibrillary tangles of hyperphosphorylated tau proteins. The disease affects 5 million people in the United States and 44 million world-wide. Currently there is no drug that can cure, stop or even slow the progression of the disease. If no cure is found, by 2050 the number of alzheimer's patients in the U.S. will reach 15 million and the cost of caring for them will exceed $ 1 trillion annually. The present paper develops a mathematical model of AD that includes neurons, astrocytes, microglias and peripheral macrophages, as well as amyloid β aggregation and hyperphosphorylated tau proteins. The model is represented by a system of partial differential equations. The model is used to simulate the effect of drugs that either failed in clinical trials, or are currently in clinical trials. Based on these simulations it is suggested that combined therapy with TNF- α inhibitor and anti amyloid β could yield significant efficacy in slowing the progression of AD.
Teachers' Conceptions of Mathematical Modeling
Gould, Heather
2013-01-01
The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…
Mathematical Modeling in the Undergraduate Curriculum
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…
Exploring optimal air ambulance base locations in Norway using advanced mathematical modelling.
Røislien, Jo; van den Berg, Pieter L; Lindner, Thomas; Zakariassen, Erik; Aardal, Karen; van Essen, J Theresia
2017-02-01
Helicopter emergency medical services are an important part of many healthcare systems. Norway has a nationwide physician staffed air ambulance service with 12 bases servicing a country with large geographical variations in population density. The aim of the study was to estimate optimal air ambulance base locations. We used high resolution population data for Norway from 2015, dividing Norway into >300 000 1 km×1 km cells. Inhabited cells had a median (5-95 percentile) of 13 (1-391) inhabitants. Optimal helicopter base locations were estimated using the maximal covering location problem facility location optimisation model, exploring the number of bases needed to cover various fractions of the population for time thresholds 30 and 45 min, both in green field scenarios and conditioning on the current base structure. We reanalysed on municipality level data to explore the potential information loss using coarser population data. For a 45 min threshold, 90% of the population could be covered using four bases, and 100% using nine bases. Given the existing bases, the calculations imply the need for two more bases to achieve full coverage. Decreasing the threshold to 30 min approximately doubles the number of bases needed. Results using municipality level data were remarkably similar to those using fine grid information. The whole population could be reached in 45 min or less using nine optimally placed bases. The current base structure could be improved by moving or adding one or two select bases. Municipality level data appears sufficient for proper analysis. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/.
Mathematical model for bone mineralization
Komarova, Svetlana V.; Safranek, Lee; Gopalakrishnan, Jay; Ou, Miao-jung Yvonne; McKee, Marc D.; Murshed, Monzur; Rauch, Frank; Zuhr, Erica
2015-01-01
Defective bone mineralization has serious clinical manifestations, including deformities and fractures, but the regulation of this extracellular process is not fully understood. We have developed a mathematical model consisting of ordinary differential equations that describe collagen maturation, production and degradation of inhibitors, and mineral nucleation and growth. We examined the roles of individual processes in generating normal and abnormal mineralization patterns characterized usin...
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.
Film dosimetry: a mathematical model
International Nuclear Information System (INIS)
Mafra Neto, F.
1993-01-01
A mathematical model for electromagnetic radiation dosimetry using photosensitive emulsions is presented. A Kodak odontological radiographic film was used for that purpose. Some properties such as energy dependence, reproductiveness and the characteristic curve were studied. A linear and energy-independent dosimeter for beams above 50 KeV was obtained by adding 1 mm lead filters. 4 refs, 8 figs, 2 tabs
Mathematical modeling and optimization of complex structures
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...
Mathematical modeling of biological processes
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.
Category Theory as a Formal Mathematical Foundation for Model-Based Systems Engineering
Mabrok, Mohamed
2017-01-09
In this paper, we introduce Category Theory as a formal foundation for model-based systems engineering. A generalised view of the system based on category theory is presented, where any system can be considered as a category. The objects of the category represent all the elements and components of the system and the arrows represent the relations between these components (objects). The relationship between these objects are the arrows or the morphisms in the category. The Olog is introduced as a formal language to describe a given real-world situation description and requirement writing. A simple example is provided.
Klamt, Steffen; Müller, Stefan; Regensburger, Georg; Zanghellini, Jürgen
2018-02-07
The optimization of metabolic rates (as linear objective functions) represents the methodical core of flux-balance analysis techniques which have become a standard tool for the study of genome-scale metabolic models. Besides (growth and synthesis) rates, metabolic yields are key parameters for the characterization of biochemical transformation processes, especially in the context of biotechnological applications. However, yields are ratios of rates, and hence the optimization of yields (as nonlinear objective functions) under arbitrary linear constraints is not possible with current flux-balance analysis techniques. Despite the fundamental importance of yields in constraint-based modeling, a comprehensive mathematical framework for yield optimization is still missing. We present a mathematical theory that allows one to systematically compute and analyze yield-optimal solutions of metabolic models under arbitrary linear constraints. In particular, we formulate yield optimization as a linear-fractional program. For practical computations, we transform the linear-fractional yield optimization problem to a (higher-dimensional) linear problem. Its solutions determine the solutions of the original problem and can be used to predict yield-optimal flux distributions in genome-scale metabolic models. For the theoretical analysis, we consider the linear-fractional problem directly. Most importantly, we show that the yield-optimal solution set (like the rate-optimal solution set) is determined by (yield-optimal) elementary flux vectors of the underlying metabolic model. However, yield- and rate-optimal solutions may differ from each other, and hence optimal (biomass or product) yields are not necessarily obtained at solutions with optimal (growth or synthesis) rates. Moreover, we discuss phase planes/production envelopes and yield spaces, in particular, we prove that yield spaces are convex and provide algorithms for their computation. We illustrate our findings by a small
Directory of Open Access Journals (Sweden)
Eva Anglada
2017-01-01
Full Text Available The correlation of the thermal mathematical models (TMMs of spacecrafts with the results of the thermal test is a demanding task in terms of time and effort. Theoretically, it can be automatized by means of optimization techniques, although this is a challenging task. Previous studies have shown the ability of genetic algorithms to perform this task in several cases, although some limitations have been detected. In addition, gradient-based methods, although also presenting some limitations, have provided good solutions in other technical fields. For this reason, the performance of genetic algorithms and gradient-based methods in the correlation of TMMs is discussed in this paper to compare the pros and cons of them. The case of study used in the comparison is a real space instrument flown aboard the International Space Station.
Directory of Open Access Journals (Sweden)
A H Sabry
Full Text Available The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system's modeling equations based on the Bode plot equations and the vector fitting (VF algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model.
W. Hasan, W. Z.
2018-01-01
The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system’s modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model. PMID:29351554
Sabry, A H; W Hasan, W Z; Ab Kadir, M Z A; Radzi, M A M; Shafie, S
2018-01-01
The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system's modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model.
Mathematical models in genetics.
Traykov, M; Trenchev, Iv
2016-09-01
In this study, we present some of the basic ideas of population genetics. The founders of population genetics are R.A. Fisher, S. Wright, and J. B.S. Haldane. They, not only developed almost all the basic theory associated with genetics, but they also initiated multiple experiments in support of their theories. One of the first significant insights, which are a result of the Hardy–Weinberg law, is Mendelian inheritance preserves genetic variation on which the natural selection acts. We will limit to simple models formulated in terms of differential equations. Some of those differential equations are nonlinear and thus emphasize issues such as the stability of the fixed points and time scales on which those equations operate. First, we consider the classic case when selection acts on diploid locus at which wу can get arbitrary number of alleles. Then, we consider summaries that include recombination and selection at multiple loci. Also, we discuss the evolution of quantitative traits. In this case, the theory is formulated in respect of directly measurable quantities. Special cases of this theory have been successfully used for many decades in plants and animals breeding.
Mathematical Modeling and Simulation of SWRO Process Based on Simultaneous Method
Directory of Open Access Journals (Sweden)
Aipeng Jiang
2014-01-01
Full Text Available Reverse osmosis (RO technique is one of the most efficient ways for seawater desalination to solve the shortage of freshwater. For prediction and analysis of the performance of seawater reverse osmosis (SWRO process, an accurate and detailed model based on the solution-diffusion and mass transfer theory is established. Since the accurate formulation of the model includes many differential equations and strong nonlinear equations (differential and algebraic equations, DAEs, to solve the problem efficiently, the simultaneous method through orthogonal collocation on finite elements and large scale solver were used to obtain the solutions. The model was fully discretized into NLP (nonlinear programming with large scale variables and equations, and then the NLP was solved by large scale solver of IPOPT. Validation of the formulated model and solution method is verified by case study on a SWRO plant. Then simulation and analysis are carried out to demonstrate the performance of reverse osmosis process; operational conditions such as feed pressure and feed flow rate as well as feed temperature are also analyzed. This work is of significant meaning for the detailed understanding of RO process and future energy saving through operational optimization.
Mathematical Modeling Projects: Success for All Students
Shelton, Therese
2018-01-01
Mathematical modeling allows flexibility for a project-based experience. We share details of our regular capstone course, successful for virtually 100% of our math majors for almost two decades. Our research-like approach in this course accommodates a variety of student backgrounds and interests, and has produced some award-winning student…
Exploring Yellowstone National Park with Mathematical Modeling
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…
Strategies to Support Students' Mathematical Modeling
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…
Mathematical Modeling in the High School Curriculum
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 model of subscriber extension line
Petříková, Iva; Diviš, Zdeněk; Tesař, Zdeněk
2012-01-01
The paper focuses on measurement properties of metallic subscriber extension lines to build regression mathematical model for a symmetric pair cable. The regression model is compared with an analytical model based on a theoretical description of transfer parameters for this type of line. The output of the paper should demonstrate the impact of electromagnetic interference on the symmetric pair. The paper also describes the method to identify the interference sources and ...
ANALYSIS OF MATHEMATICS LITERACY BASED ON MATHEMATICAL ABILITY
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Andes Safarandes Asmara
2017-05-01
Full Text Available This research was conducted to determine the literacy skills students of class X on their math skill. This study used a qualitative approach, the approach that drives meaningful results. To determine the ability of mathematical literacy class X, there were study subjects of 3 people who were selected based on their level of math skills. The determination was based on the categories of low, medium and high. Each subject was given a test and interview questions to determine the literacy skills. The results revealed that subjects with low category were in the second level of mathematics literacy, and subjects with high category were in the third level of mathematical literacy skills. Based on these results, it is necessary to seek strategies in the learning process of mathematics, which allows the improvement of mathematics literacy skills.
An, Guohua; Widness, John A; Mock, Donald M; Veng-Pedersen, Peter
2016-09-01
Direct measurement of red blood cell (RBC) survival in humans has improved from the original accurate but limited differential agglutination technique to the current reliable, safe, and accurate biotin method. Despite this, all of these methods are time consuming and require blood sampling over several months to determine the RBC lifespan. For situations in which RBC survival information must be obtained quickly, these methods are not suitable. With the exception of adults and infants, RBC survival has not been extensively investigated in other age groups. To address this need, we developed a novel, physiology-based mathematical model that quickly estimates RBC lifespan in healthy individuals at any age. The model is based on the assumption that the total number of RBC recirculations during the lifespan of each RBC (denoted by N max) is relatively constant for all age groups. The model was initially validated using the data from our prior infant and adult biotin-labeled red blood cell studies and then extended to the other age groups. The model generated the following estimated RBC lifespans in 2-year-old, 5-year-old, 8-year-old, and 10-year-old children: 62, 74, 82, and 86 days, respectively. We speculate that this model has useful clinical applications. For example, HbA1c testing is not reliable in identifying children with diabetes because HbA1c is directly affected by RBC lifespan. Because our model can estimate RBC lifespan in children at any age, corrections to HbA1c values based on the model-generated RBC lifespan could improve diabetes diagnosis as well as therapy in children.
Mathematical modeling of drug delivery.
Siepmann, J; Siepmann, F
2008-12-08
Due to the significant advances in information technology mathematical modeling of drug delivery is a field of steadily increasing academic and industrial importance with an enormous future potential. The in silico optimization of novel drug delivery systems can be expected to significantly increase in accuracy and easiness of application. Analogous to other scientific disciplines, computer simulations are likely to become an integral part of future research and development in pharmaceutical technology. Mathematical programs can be expected to be routinely used to help optimizing the design of novel dosage forms. Good estimates for the required composition, geometry, dimensions and preparation procedure of various types of delivery systems will be available, taking into account the desired administration route, drug dose and release profile. Thus, the number of required experimental studies during product development can be significantly reduced, saving time and reducing costs. In addition, the quantitative analysis of the physical, chemical and potentially biological phenomena, which are involved in the control of drug release, offers another fundamental advantage: The underlying drug release mechanisms can be elucidated, which is not only of academic interest, but a pre-requisite for an efficient improvement of the safety of the pharmaco-treatments and for effective trouble-shooting during production. This article gives an overview on the current state of the art of mathematical modeling of drug delivery, including empirical/semi-empirical and mechanistic realistic models. Analytical as well as numerical solutions are described and various practical examples are given. One of the major challenges to be addressed in the future is the combination of mechanistic theories describing drug release out of the delivery systems with mathematical models quantifying the subsequent drug transport within the human body in a realistic way. Ideally, the effects of the design
Mathematical Model of Age Aggression
Golovinski, P. A.
2013-01-01
We formulate a mathematical model of competition for resources between representatives of different age groups. A nonlinear kinetic integral-differential equation of the age aggression describes the process of redistribution of resources. It is shown that the equation of the age aggression has a stationary solution, in the absence of age-dependency in the interaction of different age groups. A numerical simulation of the evolution of resources for different initial distributions has done. It ...
Yan, Lincan; Zhou, Chenming; Reyes, Miguel; Whisner, Bruce; Damiano, Nicholas
2017-06-01
There are two types of through-the-earth (TTE) wireless communication in the mining industry: magnetic loop TTE and electrode-based (or linear) TTE. While the magnetic loop systems send signal through magnetic fields, the transmitter of an electrode-based TTE system sends signal directly through the mine overburden by driving an extremely low frequency (ELF) or ultralow frequency (ULF) AC current into the earth. The receiver at the other end (underground or surface) detects the resultant current and receives it as a voltage. A wireless communication link between surface and underground is then established. For electrode-based TTE communications, the signal is transmitted through the established electric field and is received as a voltage detected at the receiver. It is important to understand the electric field distribution within the mine overburden for the purpose of designing and improving the performance of the electrode-based TTE systems. In this paper, a complete explicit solution for all three electric field components for the electrode-based TTE communication was developed. An experiment was conducted using a prototype electrode-based TTE system developed by National Institute for Occupational Safety and Health. The mathematical model was then compared and validated with test data. A reasonable agreement was found between them.
Antonopoulos, Markos; Stamatakos, Georgios
2015-01-01
Intensive glioma tumor infiltration into the surrounding normal brain tissues is one of the most critical causes of glioma treatment failure. To quantitatively understand and mathematically simulate this phenomenon, several diffusion-based mathematical models have appeared in the literature. The majority of them ignore the anisotropic character of diffusion of glioma cells since availability of pertinent truly exploitable tomographic imaging data is limited. Aiming at enriching the anisotropy-enhanced glioma model weaponry so as to increase the potential of exploiting available tomographic imaging data, we propose a Brownian motion-based mathematical analysis that could serve as the basis for a simulation model estimating the infiltration of glioblastoma cells into the surrounding brain tissue. The analysis is based on clinical observations and exploits diffusion tensor imaging (DTI) data. Numerical simulations and suggestions for further elaboration are provided. PMID:26309390
Apipah, S.; Kartono; Isnarto
2018-03-01
This research aims to analyze the quality of VAK learning with self-assessment toward the ability of mathematical connection performed by students and to analyze students’ mathematical connection ability based on learning styles in VAK learning model with self-assessment. This research applies mixed method type with concurrent embedded design. The subject of this research consists of VIII grade students from State Junior High School 9 Semarang who apply visual learning style, auditory learning style, and kinesthetic learning style. The data of learning style is collected by using questionnaires, the data of mathematical connection ability is collected by performing tests, and the data of self-assessment is collected by using assessment sheets. The quality of learning is qualitatively valued from planning stage, realization stage, and valuation stage. The result of mathematical connection ability test is analyzed quantitatively by mean test, conducting completeness test, mean differentiation test, and mean proportional differentiation test. The result of the research shows that VAK learning model results in well-qualified learning regarded from qualitative and quantitative sides. Students with visual learning style perform the highest mathematical connection ability, students with kinesthetic learning style perform average mathematical connection ability, and students with auditory learning style perform the lowest mathematical connection ability.
Summer Camp of Mathematical Modeling in China
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…
Continuum mechanics the birthplace of mathematical models
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
International Nuclear Information System (INIS)
Rettig, Ralf
2010-01-01
A new model has been developed in this work which is capable of simulating the precipitation kinetics of brittle phases, especially TCP-phases (topologically close packed phases) in ruthenium containing superalloys. The model simultaneously simulates the nucleation and the growth stage of precipitation for any number of precipitating phases. The CALPHAD method (Calculation of Phase Diagrams) is employed to calculate thermodynamic properties, such as the driving force or phase compositions in equilibrium. For calculation of diffusion coefficients, kinetic mobility databases which are also based on the CALPHAD-method are used. The model is fully capable of handling multicomponent effects, which are common in complex superalloys. Metastable phases can be treated and will automatically be dissolved if they get unstable. As the model is based on the general CALPHAD method, it can be applied to a broad range of precipitation processes in different alloys as long as the relevant thermodynamic and kinetic databases are available. The developed model proves that the TCP-phases precipitate in a sequence of phases. The first phase that is often formed is the metastable σ-phase because it has the lowest interface energy due to low-energy planes at the interface between matrix and precipitate. After several hundred hours the stable μ- and P-phases start to precipitate by nucleating at the σ-phase which is energetically favourable. During the growth of these stable phases the sigma-phase is continuously dissolved. It can be shown by thermodynamic CALPHAD calculations that the sigma-phase has a lower Gibbs free enthalpy than the μ- and P-phase. All required parameters of the model, such as interface energy and nucleate densities, have been estimated. The mechanisms of suppression of TCP-phase precipitation in the presence of ruthenium in superalloys were investigated with the newly developed model. It is shown by the simulations that ruthenium mostly affects the nucleation
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
Directory of Open Access Journals (Sweden)
Amir R. Ali
2017-01-01
Full Text Available This paper presents and verifies the mathematical model of an electric field senor based on the whispering gallery mode (WGM. The sensing element is a dielectric microsphere, where the light is used to tune the optical modes of the microsphere. The light undergoes total internal reflection along the circumference of the sphere; then it experiences optical resonance. The WGM are monitored as sharp dips on the transmission spectrum. These modes are very sensitive to morphology changes of the sphere, such that, for every minute change in the sphere’s morphology, a shift in the transmission spectrum will happen and that is known as WGM shifts. Due to the electrostriction effect, the applied electric field will induce forces acting on the surface of the dielectric sphere. In turn, these forces will deform the sphere causing shifts in its WGM spectrum. The applied electric field can be obtained by calculating these shifts. Navier’s equation for linear elasticity is used to model the deformation of the sphere to find the WGM shift. The finite element numerical studies are performed to verify the introduced model and to study the behavior of the sensor at different values of microspheres’ Young’s modulus and dielectric constant. Furthermore, the sensitivity and resolution of the developed WGM electric filed sensor model will be presented in this paper.
Mathematical Modeling in Combustion Science
Takeno, Tadao
1988-01-01
An important new area of current research in combustion science is reviewed in the contributions to this volume. The complicated phenomena of combustion, such as chemical reactions, heat and mass transfer, and gaseous flows, have so far been studied predominantly by experiment and by phenomenological approaches. But asymptotic analysis and other recent developments are rapidly changing this situation. The contributions in this volume are devoted to mathematical modeling in three areas: high Mach number combustion, complex chemistry and physics, and flame modeling in small scale turbulent flow combustion.
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 Modeling of Loop Heat Pipes
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 models of skin permeability: an overview.
Mitragotri, Samir; Anissimov, Yuri G; Bunge, Annette L; Frasch, H Frederick; Guy, Richard H; Hadgraft, Jonathan; Kasting, Gerald B; Lane, Majella E; Roberts, Michael S
2011-10-10
Mathematical models of skin permeability play an important role in various fields including prediction of transdermal drug delivery and assessment of dermal exposure to industrial chemicals. Extensive research has been performed over the last several decades to yield predictions of skin permeability to various molecules. These efforts include the development of empirical approaches such as quantitative structure-permeability relationships and porous pathway theories as well as the establishment of rigorous structure-based models. In addition to establishing the necessary mathematical framework to describe these models, efforts have also been dedicated to determining the key parameters that are required to use these models. This article provides an overview of various modeling approaches with respect to their advantages, limitations and future prospects. Copyright © 2011 Elsevier B.V. All rights reserved.
Mathematical models of bipolar disorder
Daugherty, Darryl; Roque-Urrea, Tairi; Urrea-Roque, John; Troyer, Jessica; Wirkus, Stephen; Porter, Mason A.
2009-07-01
We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.
Directory of Open Access Journals (Sweden)
Rita Peñabaena-Niebles
2017-01-01
Full Text Available Signal plan transition is the process of changing from one timing plan to another. It begins when the first intersection starts adjusting signal timing plans and ends when the last intersection completes adjusting signal timing plans. The transition between signal timing plans is required because traffic patterns change during the day. Therefore, it is necessary to modify signal timing parameters offset, phase split, and cycle length for different expectations of traffic volume. This paper presents an alternative and new mathematical model to enhance the performance of traffic signals coordination at intersections during the transition phase. This model is oriented to describe the transition regarding coordination parameters in all intersections of an arterial road for minimizing the social cost during the transition phase expressed in function of costs due to delays, fuel consumption, and air emissions. An ant colony algorithm was designed, coded, and simulated to find the optimal transition parameters using available data. The model was evaluated based on its ability to minimize social costs during the transition period. Results showed that the proposed method performs better than traditional ones.
Mathematical models for therapeutic approaches to control HIV disease transmission
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...
Identification of the noise using mathematical modelling
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Dobeš Josef
2016-01-01
Full Text Available In engineering applications the noisiness of a component or the whole device is a common problem. Currently, a lot of effort is put to eliminate noise of the already produced devices, to prevent generation of acoustic waves during the design of new components, or to specify the operating problems based on noisiness change. The experimental method and the mathematical modelling method belong to these identification methods. With the power of today’s computers the ability to identify the sources of the noise on the mathematical modelling level is a very appreciated tool for engineers. For example, the noise itself may be generated by the vibration of the solid object, combustion, shock, fluid flow around an object or cavitation at the fluid flow in an object. For the given task generating the noise using fluid flow on the selected geometry and propagation of the acoustic waves and their subsequent identification are solved and evaluated. In this paper the principle of measurement of variables describing the fluid flow field and acoustic field are described. For the solution of fluid flow a mathematical model implemented into the CFD code is used. The mathematical modelling evaluation of the flow field is compared to the experimental data.
Inquiry-Based Mathematics Curriculum Design for Young Children-Teaching Experiment and Reflection
Wu, Su-Chiao; Lin, Fou-Lai
2016-01-01
A group of teacher educators and practitioners in mathematics education and early childhood education generalized a set of inquiry-based mathematics models for Taiwanese young children of ages 3-6 and designed a series of inquiry-based mathematics curriculum tasks in cultivate the children's diverse mathematical concepts and mathematical power. In…
Mathematical Modelling Plant Signalling Networks
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.
Warsito; Darhim; Herman, T.
2018-01-01
This study aims to determine the differences in the improving of mathematical representation ability based on progressive mathematization with realistic mathematics education (PMR-MP) with conventional learning approach (PB). The method of research is quasi-experiments with non-equivalent control group designs. The study population is all students of class VIII SMPN 2 Tangerang consisting of 6 classes, while the sample was taken two classes with purposive sampling technique. The experimental class is treated with PMR-MP while the control class is treated with PB. The instruments used are test of mathematical representation ability. Data analysis was done by t-test, ANOVA test, post hoc test, and descriptive analysis. The result of analysis can be concluded that: 1) there are differences of mathematical representation ability improvement between students treated by PMR-MP and PB, 2) no interaction between learning approach (PMR-MP, PB) and prior mathematics knowledge (PAM) to improve students’ mathematical representation; 3) Students’ mathematical representation improvement in the level of higher PAM is better than medium, and low PAM students. Thus, based on the process of mathematization, it is very important when the learning direction of PMR-MP emphasizes on the process of building mathematics through a mathematical model.
Harmonic Analyzing of the Double PWM Converter in DFIG Based on Mathematical Model
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Jing Liu
2017-12-01
Full Text Available Harmonic pollution of double fed induction generators (DFIGs has become a vital concern for its undesirable effects on power quality issues of wind generation systems and grid-connected system, and the double pulse width modulation (PWMconverter is one of the main harmonic sources in DFIGs. Thus the harmonic analysis of the converter in DFIGs is a necessary step to evaluate their harmonic pollution of DFIGs. This paper proposes a detailed harmonic modeling method to discuss the main harmonic components in a converter. In general the harmonic modeling could be divided into the low-order harmonic part (up to 30th order and the high-order harmonic part (greater than order 30 parts in general. The low-order harmonics are produced by the circuit topology and control algorithm, and the harmonic component will be different if the control strategy changes. The high-order harmonics are produced by the modulation of the switching function to the dc variable. In this paper, the low-order harmonic modeling is established according to the directions of power flow under the vector control (VC, and the high-order harmonic modeling is established by the switching function of space vector PWM and dc currents. Meanwhile, the simulations of harmonic a components in a converter are accomplished in a real time digital simulation system. The results indicate that the proposed modeling could effectively show the harmonics distribution of the converter in DFIGs.
Mathematical model of integrated thermal apparatus
Directory of Open Access Journals (Sweden)
Katarína Mikulová Polčová
2010-03-01
Full Text Available Mathematical model for the integrated thermal apparatus was developed. It consists of program modules from which individualfurnace model can be generated. For the model generation elementary balance method was used. Generation of the individual modelincludes model formulation and parameters determination. Model formulation is based on first principles, heuristics and empirical results.Parameters determination is generally based on priory information, but it has to take into account specific conditions. The developed modelwas adapted for real time applications. For quantitative application developed model has to be calibrated. For the calibration theoperational furnace can be used. For model calibration of not existing furnace the priory knowledge and physical model can be used.Presented model was calibrated on experimental furnace. The results were gained by simulations.
Paterson, Judy; Sneddon, Jamie
2011-01-01
This article reports on the learning conversations between a mathematician and a mathematics educator as they worked together to change the delivery model of a third year discrete mathematics course from a traditional lecture mode to team-based learning (TBL). This change prompted the mathematician to create team tasks which increasingly focused…
Directory of Open Access Journals (Sweden)
Liu Cong
2011-12-01
Full Text Available Abstract Background Elucidating the effects of drugs on solid tumours is a highly challenging multi-level problem, since this involves many complexities associated with transport and cellular response, which in turn is characterized by highly non-linear chemical signal transduction. Appropriate systems frameworks are needed to seriously address the sources of these complexities, especially from the cellular side. Results We develop a skeletal modelling framework incorporating interstitial drug transport, intracellular signal processing and cell population descriptions. The descriptions aim to appropriately capture the nature of information flow. The model is deliberately formulated to start with simple intracellular descriptions so that additional features can be incorporated in a modular fashion. Two kinds of intracellular signalling modules which describe the drug effect were considered, one a monostable switch and the other a bistable switch. Analysis of our model revealed how different drug stimuli can lead to cell killing in the tumour. Interestingly both modules considered exhibited similar trends. The effects of important parameters were also studied. Conclusions We have created a predictive systems platform integrating drug transport and cellular response which can be systematically augmented to include additional layers of cellular complexity. Our results indicate that intracellular signalling models which are qualitatively different can give rise to similar behaviour to simple (and typical stimuli, and that validating intracellular descriptions must be performed with care by considering a variety of drug stimuli.
Mathematical modeling of microbial growth in milk
Directory of Open Access Journals (Sweden)
Jhony Tiago Teleken
2011-12-01
Full Text Available A mathematical model to predict microbial growth in milk was developed and analyzed. The model consists of a system of two differential equations of first order. The equations are based on physical hypotheses of population growth. The model was applied to five different sets of data of microbial growth in dairy products selected from Combase, which is the most important database in the area with thousands of datasets from around the world, and the results showed a good fit. In addition, the model provides equations for the evaluation of the maximum specific growth rate and the duration of the lag phase which may provide useful information about microbial growth.
Mathematical models in biological discovery
Walter, Charles
1977-01-01
When I was asked to help organize an American Association for the Advancement of Science symposium about how mathematical models have con tributed to biology, I agreed immediately. The subject is of immense importance and wide-spread interest. However, too often it is discussed in biologically sterile environments by "mutual admiration society" groups of "theoreticians", many of whom have never seen, and most of whom have never done, an original scientific experiment with the biolog ical materials they attempt to describe in abstract (and often prejudiced) terms. The opportunity to address the topic during an annual meeting of the AAAS was irresistable. In order to try to maintain the integrity ;,f the original intent of the symposium, it was entitled, "Contributions of Mathematical Models to Biological Discovery". This symposium was organized by Daniel Solomon and myself, held during the 141st annual meeting of the AAAS in New York during January, 1975, sponsored by sections G and N (Biological and Medic...
Mathematical models of viscous friction
Buttà, Paolo; Marchioro, Carlo
2015-01-01
In this monograph we present a review of a number of recent results on the motion of a classical body immersed in an infinitely extended medium and subjected to the action of an external force. We investigate this topic in the framework of mathematical physics by focusing mainly on the class of purely Hamiltonian systems, for which very few results are available. We discuss two cases: when the medium is a gas and when it is a fluid. In the first case, the aim is to obtain microscopic models of viscous friction. In the second, we seek to underline some non-trivial features of the motion. Far from giving a general survey on the subject, which is very rich and complex from both a phenomenological and theoretical point of view, we focus on some fairly simple models that can be studied rigorously, thus providing a first step towards a mathematical description of viscous friction. In some cases, we restrict ourselves to studying the problem at a heuristic level, or we present the main ideas, discussing only some as...
On Fences, Forms and Mathematical Modeling
Lege, Jerry
2009-01-01
The white picket fence is an integral component of the iconic American townscape. But, for mathematics students, it can be a mathematical challenge. Picket fences in a variety of styles serve as excellent sources to model constant, step, absolute value, and sinusoidal functions. "Principles and Standards for School Mathematics" (NCTM 2000)…
Mathematical model for classification of EEG signals
Ortiz, Victor H.; Tapia, Juan J.
2015-09-01
A mathematical model to filter and classify brain signals from a brain machine interface is developed. The mathematical model classifies the signals from the different lobes of the brain to differentiate the signals: alpha, beta, gamma and theta, besides the signals from vision, speech, and orientation. The model to develop further eliminates noise signals that occur in the process of signal acquisition. This mathematical model can be used on different platforms interfaces for rehabilitation of physically handicapped persons.
Directory of Open Access Journals (Sweden)
Maslov A. A.
2016-12-01
Full Text Available Definition of preparatory parameters for sterilization regime of canned "Natural Atlantic Mackerel with Oil" is the aim of current study. PRSC software developed at the department of automation and computer engineering is used for preparatory selection. To determine the parameters of process model, in laboratory autoclave AVK-30M the pre-trial process of sterilization and cooling in water with backpressure of canned "Natural Atlantic Mackerel with Oil" in can N 3 has been performed. Gathering information about the temperature in the autoclave sterilization chamber and the can with product has been carried out using Ellab TrackSense PRO loggers. Due to the obtained information three transfer functions for the product model have been identified: in the least heated area of autoclave, the average heated and the most heated. In PRSC programme temporary temperature dependences in the sterilization chamber have been built using this information. The model of sterilization process of canned "Natural Atlantic Mackerel with Oil" has been received after the pre-trial process. Then in the automatic mode the sterilization regime of canned "Natural Atlantic Mackerel with Oil" has been selected using the value of actual effect close to normative sterilizing effect (5.9 conditional minutes. Furthermore, in this study step-mode sterilization of canned "Natural Atlantic Mackerel with Oil" has been selected. Utilization of step-mode sterilization with the maximum temperature equal to 125 °C in the sterilization chamber allows reduce process duration by 10 %. However, the application of this regime in practice requires additional research. Using the described approach based on the developed mathematical models of the process allows receive optimal step and variable canned food sterilization regimes with high energy efficiency and product quality.
Afenya, Evans K; Ouifki, Rachid; Camara, Baba I; Mundle, Suneel D
2016-04-01
Stemming from current emerging paradigms related to the cancer stem cell hypothesis, an existing mathematical model is expanded and used to study cell interaction dynamics in the bone marrow and peripheral blood. The proposed mathematical model is described by a system of nonlinear differential equations with delay, to quantify the dynamics in abnormal hematopoiesis. The steady states of the model are analytically and numerically obtained. Some conditions for the local asymptotic stability of such states are investigated. Model analyses suggest that malignancy may be irreversible once it evolves from a nonmalignant state into a malignant one and no intervention takes place. This leads to the proposition that a great deal of emphasis be placed on cancer prevention. Nevertheless, should malignancy arise, treatment programs for its containment or curtailment may have to include a maximum and extensive level of effort to protect normal cells from eventual destruction. Further model analyses and simulations predict that in the untreated disease state, there is an evolution towards a situation in which malignant cells dominate the entire bone marrow - peripheral blood system. Arguments are then advanced regarding requirements for quantitatively understanding cancer stem cell behavior. Among the suggested requirements are, mathematical frameworks for describing the dynamics of cancer initiation and progression, the response to treatment, the evolution of resistance, and malignancy prevention dynamics within the bone marrow - peripheral blood architecture. Copyright © 2016 Elsevier Inc. All rights reserved.
Using Mathematical Modeling and Set-Based Design Principles to Recommend an Existing CVL Design
2017-09-01
searching existing data sources , gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments...can be used to produce the ideal CVL design for a future maritime conflict scenario. The scenario is based on the Naval Postgraduate School’s...vulnerability in future maritime conflict . Using smaller aircraft carriers will reduce the risk to grand strategy as well as life cycle and operating costs
Siregar, K.; Siregar, S. F.
2018-02-01
This research is design employee performance assessment by considering work result of employee based on competency. Relevant competencies are identified according to Spencer’s competence of employees that subsequently processed by Analytical Hierarchy Process (AHP) method. The results of weighting AHP indicate the highest priority order of criteria, there are; concern of customer satisfaction (0.1325), group work (0.1324) and technical expertise (0.0826). The weight of the criteria is used to design the Work Performance Value (WPV) to be used as the basis for calculating the incentive index. The higher incentive index of an employee, the greater amount of incentives was earned. The calculation of incentives is made to four employees of chopsticks production. From employee incentives A, B, C and D, employee D has the highest incentive index and increment of IDR 2,700,675 compared to previous incentive system. The incentive division system based on the Work Performance Values (WPV) of this proposal reflects a real incentive so that the incapacity of incentive can be reduced.
Mathematical models for centrifugal pumps. Pt. 1
Energy Technology Data Exchange (ETDEWEB)
Hastrup, J.
1984-01-01
This report is primary concerned with mathematical models of the volute and impeller in centrifugal pumps. The pressure distribution in the volute is calculated. The results are compared to experimental results, and show a good qualitative agreement. Furthermore, the mass flow in the impeller is calculated, based on the pressure distribution in the volute. The mathematical model of the impeller is used to calculate the velocity and pressure distribution in the blade-to-blade plane of the impeller, including the effect of the shear stress in the boundary layers. Based on these calculations, the velocity distribution in the hub-to-shroud plane is calculated along a line in the middle of the blade-to-blade plane, giving all in all a quasi-three-dimensional description. The volute and impeller models are combined with simple mathematical models of the disc- friction and leakage losses, thereby giving the all-over efficiency of a centrifugal pump. The comparison with experimental results shows the need for a more accurate description of the entrance losses and disc-friction losses.
Mathematical models for centrifugal pumps. Pt. 2
Energy Technology Data Exchange (ETDEWEB)
Hastrup, J.
1984-01-01
This report is primarily concerned with mathematical models of the volute and impeller in centrifugal pumps. The pressure distribution in the volute is calculated. The results are compared to experimental results, and show a good qualitative agreement. Furthermore, the mass flow in the impeller is calculated, based on the pressure distribution in the volute. The mathematical model of the impeller is used to calculate the velocity and pressure distribution in the blade-to-blade plane of the impeller, including the effect of the shear stress in the boundary layers. Based on these calculations, the velocity distribution in the hub-to-shroud plane is calculated along a line in the middle of the blade-to-blade plane, giving all in all a quasi-three-dimensional description. The volute and impeller models are combined with simple mathematical models of the disc-friction and leakage losses, thereby giving the all- over efficiency of a centrifugal pump. The comparison with experimental results shows the need for a more accurate description of the entrance losses and disc-friction losses.
Mathematical models for centrifugal pumps. Pt. 3
Energy Technology Data Exchange (ETDEWEB)
Hastrup, J.
1984-01-01
This report is primary concerned with mathematical models of the volute and impeller in centrifugal pumps. The pressure distribution in the volute is calculated. The results are compared to experimental results, and show a good qualitative agreement. Furthermore, the mass flow in the impeller is calculated, based on the pressure distribution in the volute. The mathematical model of the impeller is used to calculate the velocity and pressure distribution in the blade-to-blade plane of the impeller, including the effect of the shear stress in the boundary layers. Based on these calculations, the velocity distribution in the hub-to-shroud plane is calculated along a line in the middle of the blade-to-blade plane, giving all in all a quasi-three-dimensional description. The volute and impeller models are combined with simple mathematical models of the disc-friction and leakage losses, thereby giving the all-over efficiency of a centrifugal pump. The comparison with experimental results shows the need for a more accurate description of the entrance losses and disc-friction losses.
Mathematical rainfall model for hydrographic demarcation of Manabi ...
African Journals Online (AJOL)
... systems (GIS), a mathematical model to estimate very accurately the values of rainfall based only on the geographical coordinates. To achieve this objective, the basins of the Hydrographic Demarcation of Manabí have been chosen to develop the indicated mathematical model, which can be applied to other basins in the ...
Mathematical Modelling Research in Turkey: A Content Analysis Study
Çelik, H. Coskun
2017-01-01
The aim of the present study was to examine the mathematical modelling studies done between 2004 and 2015 in Turkey and to reveal their tendencies. Forty-nine studies were selected using purposeful sampling based on the term, "mathematical modelling" with Higher Education Academic Search Engine. They were analyzed with content analysis.…
DEFF Research Database (Denmark)
Carugati, Andrea
to observe and analyze the workings of a development project. I have been working as part of the team assembled for the development of the information system based on AMM for a period of three years. My active participation in the development project granted me access to all the actors involved. In my role I...... through negotiation and democratic decision making will it be possible for the team members to have their current weltanschauung represented in decision making. Thirdly, geographical distribution and loose coupling foster individualist rather than group behavior. The more the social tissue is disconnected...... of the technology, the development team was formed by individuals from both universities and the private sector. The organization of the development team was geographically distributed and loosely coupled. The development of information systems has always been a difficult activity and the records show a remarkable...
International Nuclear Information System (INIS)
Zhang, Zili; Gao, Chao; Liu, Yuxin; Qian, Tao
2014-01-01
Ant colony optimization (ACO) algorithms often fall into the local optimal solution and have lower search efficiency for solving the travelling salesman problem (TSP). According to these shortcomings, this paper proposes a universal optimization strategy for updating the pheromone matrix in the ACO algorithms. The new optimization strategy takes advantages of the unique feature of critical paths reserved in the process of evolving adaptive networks of the Physarum-inspired mathematical model (PMM). The optimized algorithms, denoted as PMACO algorithms, can enhance the amount of pheromone in the critical paths and promote the exploitation of the optimal solution. Experimental results in synthetic and real networks show that the PMACO algorithms are more efficient and robust than the traditional ACO algorithms, which are adaptable to solve the TSP with single or multiple objectives. Meanwhile, we further analyse the influence of parameters on the performance of the PMACO algorithms. Based on these analyses, the best values of these parameters are worked out for the TSP. (paper)
Arepyeva, M A; Kolbin, A S; Sidorenko, S V; Lawson, R; Kurylev, A A; Balykina, Yu E; Mukhina, N V; Spiridonova, A A
2017-03-01
Infections that are inadequately treated owing to acquired bacterial resistance are a leading cause of mortality. Rates of multidrug-resistant bacteria are rising, resulting in increased antibiotic failures and worsening patient outcomes. Mathematical modelling makes it possible to predict the future spread of bacterial antimicrobial resistance. The aim of this study was to construct a mathematical model that can describe the dependency between the level of antimicrobial resistance and the amount of antibiotic usage. After reviewing existing mathematical models, a cross-sectional, retrospective study was carried out to collect clinical and microbiological data across 3000 patients for the construction of the mathematical model. Based on these data, a model was developed and tested to determine the dependency between antibiotic usage and resistance. Consumption of inhibitor/cephalosporins and fluoroquinolones increases inhibitor/penicillin resistance. Consumption of inhibitor/penicillins increases cephalosporin resistance. Consumption of inhibitor/penicillins increases inhibitor/cephalosporin resistance. It was demonstrated that in some antibiotic-micro-organism pairs, the level of antibiotic usage significantly influences the level of resistance. The model makes it possible to predict the change in resistance and also shows the quantitative effect of antibiotic consumption on the level of bacterial resistance. Copyright © 2017 International Society for Chemotherapy of Infection and Cancer. Published by Elsevier Ltd. All rights reserved.
Mathematical models for plant-herbivore interactions
Feng, Zhilan; DeAngelis, Donald L.
2017-01-01
Mathematical Models of Plant-Herbivore Interactions addresses mathematical models in the study of practical questions in ecology, particularly factors that affect herbivory, including plant defense, herbivore natural enemies, and adaptive herbivory, as well as the effects of these on plant community dynamics. The result of extensive research on the use of mathematical modeling to investigate the effects of plant defenses on plant-herbivore dynamics, this book describes a toxin-determined functional response model (TDFRM) that helps explains field observations of these interactions. This book is intended for graduate students and researchers interested in mathematical biology and ecology.
Mathematical models of human behavior
DEFF Research Database (Denmark)
Møllgaard, Anders Edsberg
During the last 15 years there has been an explosion in human behavioral data caused by the emergence of cheap electronics and online platforms. This has spawned a whole new research field called computational social science, which has a quantitative approach to the study of human behavior. Most...... studies have considered data sets with just one behavioral variable such as email communication. The Social Fabric interdisciplinary research project is an attempt to collect a more complete data set on human behavior by providing 1000 smartphones with pre-installed data collection software to students...... data set, along with work on other behavioral data. The overall goal is to contribute to a quantitative understanding of human behavior using big data and mathematical models. Central to the thesis is the determination of the predictability of different human activities. Upper limits are derived...
Surface EXAFS - A mathematical model
International Nuclear Information System (INIS)
Bateman, J.E.
2002-01-01
Extended X-ray absorption fine structure (EXAFS) studies are a powerful technique for studying the chemical environment of specific atoms in a molecular or solid matrix. The study of the surface layers of 'thick' materials introduces special problems due to the different escape depths of the various primary and secondary emission products which follow X-ray absorption. The processes are governed by the properties of the emitted fluorescent photons or electrons and of the material. Their interactions can easily destroy the linear relation between the detected signal and the absorption cross-section. Also affected are the probe depth within the surface and the background superimposed on the detected emission signal. A general mathematical model of the escape processes is developed which permits the optimisation of the detection modality (X-rays or electrons) and the experimental variables to suit the composition of any given surface under study
The Activity System of School-Teaching Mathematics and Mathematical Modelling.
Julie, Cyril
2002-01-01
Focuses on the activity system of school-teaching mathematics and the impact of mathematical modeling. Describes the Applications of and Modeling in School Mathematics Project (AMSMAP) which investigates teachers' mathematical modeling and its relationship to a hypothesized school mathematical modeling activity system. Discusses the notion of an…
Mathematical modeling of deformation during hot rolling
Energy Technology Data Exchange (ETDEWEB)
Jin, D.; Stachowiak, R.G.; Samarasekera, I.V.; Brimacombe, J.K. [Univ. of British Columbia, Vancouver, British Columbia (Canada). Centre for Metallurgical Processing Engineering
1994-12-31
The deformation that occurs in the roll bite during the hot rolling of steel, particularly the strain-rate and strain distribution, has been mathematically modeled using finite-element analysis. In this paper three different finite-element models are compared with one another and with industrial measurements. The first model is an Eulerian analysis based on the flow formulation method, while the second utilizes an Updated Lagrangian approach. The third model is based on a commercially available program DEFORM which also utilizes a Lagrangian reference frame. Model predictions of strain and strain-rate distribution, particularly near the surface of the slab, are strongly influenced by the treatment of friction at the boundary and the magnitude of the friction coefficient or shear factor. Roll forces predicted by the model have been compared with industrial rolling loads from a seven-stand hot-strip mill.
Directory of Open Access Journals (Sweden)
Eva Jager
Full Text Available Gemtuzumab ozogamicin (GO is a chemotherapy-conjugated anti-CD33 monoclonal antibody effective in some patients with acute myeloid leukemia (AML. The optimal treatment schedule and optimal timing of GO administration relative to other agents remains unknown. Conventional pharmacokinetic analysis has been of limited insight for the schedule optimization. We developed a mechanism-based mathematical model and employed it to analyze the time-course of free and GO-bound CD33 molecules on the lekemic blasts in individual AML patients treated with GO. We calculated expected intravascular drug exposure (I-AUC as a surrogate marker for the response to the drug. A high CD33 production rate and low drug efflux were the most important determinants of high I-AUC, characterizing patients with favorable pharmacokinetic profile and, hence, improved response. I-AUC was insensitive to other studied parameters within biologically relevant ranges, including internalization rate and dissociation constant. Our computations suggested that even moderate blast burden reduction prior to drug administration enables lowering of GO doses without significantly compromising intracellular drug exposure. These findings indicate that GO may optimally be used after cyto-reductive chemotherapy, rather than before, or concomitantly with it, and that GO efficacy can be maintained by dose reduction to 6 mg/m(2 and a dosing interval of 7 days. Model predictions are validated by comparison with the results of EORTC-GIMEMA AML19 clinical trial, where two different GO schedules were administered. We suggest that incorporation of our results in clinical practice can serve identification of the subpopulation of elderly patients who can benefit most of the GO treatment and enable return of the currently suspended drug to clinic.
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...... Modeling on 6th semester being the latest addition. Some of the reasoning behind curriculum development, lessons learned and remaining issues are presented and discussed. ...
Economic-mathematical methods and models under uncertainty
Aliyev, A G
2013-01-01
Brief Information on Finite-Dimensional Vector Space and its Application in EconomicsBases of Piecewise-Linear Economic-Mathematical Models with Regard to Influence of Unaccounted Factors in Finite-Dimensional Vector SpacePiecewise Linear Economic-Mathematical Models with Regard to Unaccounted Factors Influence in Three-Dimensional Vector SpacePiecewise-Linear Economic-Mathematical Models with Regard to Unaccounted Factors Influence on a PlaneBases of Software for Computer Simulation and Multivariant Prediction of Economic Even at Uncertainty Conditions on the Base of N-Comp
Inquiry-based Learning in Mathematics Education
DEFF Research Database (Denmark)
Dreyøe, Jonas; Larsen, Dorte Moeskær; Hjelmborg, Mette Dreier
From a grading list of 28 of the highest ranked mathematics education journals, the six highest ranked journals were chosen, and a systematic search for inquiry-based mathematics education and related keywords was conducted. This led to five important theme/issues for inquiry-based learning...... developed to determine which implications were important for the didactical intervention of the design in the Quality in the subjects Danish and Mathematics (KiDM) project....
Dermol, Janja; Miklavčič, Damijan
2014-12-01
High voltage electric pulses cause electroporation of the cell membrane. Consequently, flow of the molecules across the membrane increases. In our study we investigated possibility to predict the percentage of the electroporated cells in an inhomogeneous electric field on the basis of the experimental results obtained when cells were exposed to a homogeneous electric field. We compared and evaluated different mathematical models previously suggested by other authors for interpolation of the results (symmetric sigmoid, asymmetric sigmoid, hyperbolic tangent and Gompertz curve). We investigated the density of the cells and observed that it has the most significant effect on the electroporation of the cells while all four of the mathematical models yielded similar results. We were able to predict electroporation of cells exposed to an inhomogeneous electric field based on mathematical modeling and using mathematical formulations of electroporation probability obtained experimentally using exposure to the homogeneous field of the same density of cells. Models describing cell electroporation probability can be useful for development and presentation of treatment planning for electrochemotherapy and non-thermal irreversible electroporation. Copyright © 2014 Elsevier B.V. All rights reserved.
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...... to predict or decode experimentally defined cognitive states based on brain scans. The topics covered in the dissertation are divided into two broad parts: The first part investigates the relative importance of model selection on the brain patterns extracted form analysis models. Typical neuroimaging data...... for extracting a global summary map from a trained model. Such summary maps provides the investigator with an overview of brain locations of importance to the model’s predictions. The sensitivity map proves as a versatile technique for model visualization. Furthermore, we perform a preliminary investigation...
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...... attempt to predict or decode experimentally defined cognitive states based on brain scans. The topics covered in the dissertation are divided into two broad parts: The first part investigates the relative importance of model selection on the brain patterns extracted form analysis models. Typical...... for extracting a global summary map from a trained model. Such summary maps provides the investigator with an overview of brain locations of importance to the model’s predictions. The sensitivity map proves as a versatile technique for model visualization. Furthermore, we perform a preliminary investigation...
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...
Leading Undergraduate Research Projects in Mathematical Modeling
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…
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...... 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....
Yilmaz, L Safak; Parnerkar, Shreyas; Noguera, Daniel R
2011-02-01
Mathematical models of RNA-targeted fluorescence in situ hybridization (FISH) for perfectly matched and mismatched probe/target pairs are organized and automated in web-based mathFISH (http://mathfish.cee.wisc.edu). Offering the users up-to-date knowledge of hybridization thermodynamics within a theoretical framework, mathFISH is expected to maximize the probability of success during oligonucleotide probe design.
Syahputra, Edi; Surya, Edy
2017-01-01
This paper is a summary study of team Postgraduate on 11th grade. The objective of this study is to develop a learning model based on problem solving which can construct high-order thinking on the learning mathematics in SMA/MA. The subject of dissemination consists of Students of 11th grade in SMA/MA in 3 kabupaten/kota in North Sumatera, namely:…
MATHEMATICAL MODEL OF GRAIN MICRONIZATION
Directory of Open Access Journals (Sweden)
V. A. Afanas’ev
2014-01-01
Full Text Available Summary. During micronisation grain moisture evaporates mainly in decreasing drying rate period. Grain layer located on the surface of the conveyor micronisers will be regarded as horizontal plate. Due to the fact that the micronisation process the surface of the grain evaporates little moisture (within 2-7 % is assumed constant plate thickness. Because in the process of micronization grain structure is changing, in order to achieve an exact solution of the equations necessary to take into account changes thermophysical, optical and others. Equation of heat transfer is necessary to add a term that is responsible for the infrared heating. Because of the small thickness of the grain, neglecting the processes occurring at the edge of the grain, that is actually consider the problem of an infinite plate. To check the adequacy of the mathematical model of the process of micronisation of wheat grain moisture content must be comparable to the function of time, obtained by solving the system of equations with the measured experimental data of experience. Numerical solution of a system of equations for the period of decreasing drying rate is feasible with the help of the Maple 14, substituting the values of the constants in the system. Calculation of the average relative error does not exceed 7- 10 %, and shows a good agreement between the calculated data and the experimental values.
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
A Seminar in Mathematical Model-Building.
Smith, David A.
1979-01-01
A course in mathematical model-building is described. Suggested modeling projects include: urban problems, biology and ecology, economics, psychology, games and gaming, cosmology, medicine, history, computer science, energy, and music. (MK)
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…
The Effect of Teacher Beliefs on Student Competence in Mathematical Modeling--An Intervention Study
Mischo, Christoph; Maaß, Katja
2013-01-01
This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and…
Methods and models in mathematical biology deterministic and stochastic approaches
Müller, Johannes
2015-01-01
This book developed from classes in mathematical biology taught by the authors over several years at the Technische Universität München. The main themes are modeling principles, mathematical principles for the analysis of these models, and model-based analysis of data. The key topics of modern biomathematics are covered: ecology, epidemiology, biochemistry, regulatory networks, neuronal networks, and population genetics. A variety of mathematical methods are introduced, ranging from ordinary and partial differential equations to stochastic graph theory and branching processes. A special emphasis is placed on the interplay between stochastic and deterministic models.
A mathematical model of Chagas disease transmission
Hidayat, Dayat; Nugraha, Edwin Setiawan; Nuraini, Nuning
2018-03-01
Chagas disease is a parasitic infection caused by protozoan Trypanosoma cruzi which is transmitted to human by insects of the subfamily Triatominae, including Rhodnius prolixus. This disease is a major problem in several countries of Latin America. A mathematical model of Chagas disease with separate vector reservoir and a neighboring human resident is constructed. The basic reproductive ratio is obtained and stability analysis of the equilibria is shown. We also performed sensitivity populations dynamics of infected humans and infected insects based on migration rate, carrying capacity, and infection rate parameters. Our findings showed that the dynamics of the infected human and insect is mostly affected by carrying capacity insect in the settlement.
Computer-Game-Based Tutoring of Mathematics
Ke, Fengfeng
2013-01-01
This in-situ, descriptive case study examined the potential of implementing computer mathematics games as an anchor for tutoring of mathematics. Data were collected from middle school students at a rural pueblo school and an urban Hispanic-serving school, through in-field observation, content analysis of game-based tutoring-learning interactions,…
Junakova, N.; Balintova, M.; Junak, J.
2017-10-01
The aim of this paper is to propose a mathematical model for determining of total nitrogen (N) and phosphorus (P) content in eroded soil particles with emphasis on prediction of bottom sediment quality in reservoirs. The adsorbed nutrient concentrations are calculated using the Universal Soil Loss Equation (USLE) extended by the determination of the average soil nutrient concentration in top soils. The average annual vegetation and management factor is divided into five periods of the cropping cycle. For selected plants, the average plant nutrient uptake divided into five cropping periods is also proposed. The average nutrient concentrations in eroded soil particles in adsorbed form are modified by sediment enrichment ratio to obtain the total nutrient content in transported soil particles. The model was designed for the conditions of north-eastern Slovakia. The study was carried out in the agricultural basin of the small water reservoir Klusov.
Directory of Open Access Journals (Sweden)
Katelyn C. Corey
2016-09-01
Full Text Available Using a mathematical model with realistic demography, we analyze a large outbreak of measles in Muyinga sector in rural Burundi in 1988–1989. We generate simulated epidemic curves and age × time epidemic surfaces, which we qualitatively and quantitatively compare with the data. Our findings suggest that supplementary immunization activities (SIAs should be used in places where routine vaccination cannot keep up with the increasing numbers of susceptible individuals resulting from population growth or from logistical problems such as cold chain maintenance. We use the model to characterize the relationship between SIA frequency and SIA age range necessary to suppress measles outbreaks. If SIAs are less frequent, they must expand their target age range.
a Discrete Mathematical Model to Simulate Malware Spreading
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.
Mathematical modeling and computational intelligence in engineering applications
Silva Neto, Antônio José da; Silva, Geraldo Nunes
2016-01-01
This book brings together a rich selection of studies in mathematical modeling and computational intelligence, with application in several fields of engineering, like automation, biomedical, chemical, civil, electrical, electronic, geophysical and mechanical engineering, on a multidisciplinary approach. Authors from five countries and 16 different research centers contribute with their expertise in both the fundamentals and real problems applications based upon their strong background on modeling and computational intelligence. The reader will find a wide variety of applications, mathematical and computational tools and original results, all presented with rigorous mathematical procedures. This work is intended for use in graduate courses of engineering, applied mathematics and applied computation where tools as mathematical and computational modeling, numerical methods and computational intelligence are applied to the solution of real problems.
Mathematical modeling a chemical engineer's perspective
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
Directory of Open Access Journals (Sweden)
Frivaldsky Michal
2017-06-01
Full Text Available The main purpose of the paper is the proposal of multi-level simulation, suited for the evaluation of the lifetime of critical electronic devices (electrolytic capacitors. The aim of this issue is to imagine about the expected operation of complex and expensive power electronic systems, when the failure of the most critical component occurs. For that reason, various operational conditions and various physical influences must be considered (e.g. mechanical, humidity, electrical, heat stress, where nonlinearities are naturally introduced. Verification of the proposal is given, whereby the life-time estimation of an electrolytic capacitor operated in a DC-DC converter during various operational conditions is shown. At this point electrical and heat stress is considered for lifetime influence. First, the current state in the field of mathematical modeling of the lifetime for electrolytic capacitors, considering main phenomena is introduced. Next, individual sub-models for multi-level simulation purposes are developed, including a thermal simulation model and electrical simulation model. Several complexities of individual models are mutually compared in order to evaluate their accuracy and suitability for further use. Proper simulation tools have been mutually linked and data transfer was secured, in order to have the possibility of investigation of a lifetime depend on the changes of various variables.
Andreu, Yolanda; Baldini, Francesco; Giannetti, Ambra; Mencaglia, Andrea
2005-01-30
This paper introduces a mathematical model which makes it possible both to determine the concentration of photosynthetic herbicides and to obtain a quantitative parameter in order to compare their activity using a previously described sensing system. The working principle involves the changes in absorption properties at 860nm of the reaction centre (RC) isolated from the bacteria Rhodobacter sphaeroides when photosynthetic herbicides are present. The method has been used for the determination and activity comparison of five photosynthetic herbicides: diuron, atrazine, terbutryn, terbuthylazine and simazine. Detection limits obtained were 2.2, 0.75, 0.046, 0.25, and 1.4muM, respectively. The resulting order for the different herbicides according to their action on RC was: terbutryn > terbuthylazine > atrazine > simazine > diuron.
Mathematical Manipulative Models: In Defense of “Beanbag Biology”
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. PMID:20810952
Mathematical modeling in biomedical imaging
2009-01-01
This volume gives an introduction to a fascinating research area to applied mathematicians. It is devoted to providing the exposition of promising analytical and numerical techniques for solving challenging biomedical imaging problems, which trigger the investigation of interesting issues in various branches of mathematics.
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 models for quantum point contact spectroscopy
International Nuclear Information System (INIS)
Exner, P.; Seba, P.
1986-01-01
Two mathematical models intended to describe the point contact spectroscopical experiments are constructed. It adds a new item to the list of recently discovered applications of the self-adjoint extension theory
Mathematical Modelling as Problem Solving for Children in the Singapore Mathematics Classrooms
Eric, Chan Chun Ming
2009-01-01
The newly revised mathematics curriculum in Singapore has recently factored Applications and Modelling to be part of the teaching and learning of mathematics. Its implication is that even children should now be involved in works of mathematical modelling. However, to be able to implement modelling activities in the primary mathematics classroom,…
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 modeling of a V-stack piezoelectric aileron actuation
Directory of Open Access Journals (Sweden)
Ioan URSU
2016-12-01
Full Text Available The article presents a mathematical modeling of aileron actuation that uses piezo V-shaped stacks. The aim of the actuation is the increasing of flutter speed in the context of a control law, in order to widen the flight envelope. In this way the main advantage of such a piezo actuator, the bandwidth is exploited. The mathematical model is obtained based on free body diagrams, and the numerical simulations allow a preliminary sizing of the actuator.
SECURE MATHEMATICALLY- ASSURED COMPOSITION OF CONTROL MODELS
2017-09-27
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Pokhilko, Alexandra
2017-11-21
E. coli can be used as bacterial cell factories for production of biofuels and other useful compounds. The efficient production of the desired products requires careful monitoring of growth conditions and the optimization of metabolic fluxes. To avoid nutrient depletion and maximize product yields we suggest using a natural mechanism for sensing nutrient limitation, related to biosynthesis of an intracellular messenger - guanosine tetraphosphate (ppGpp). We propose a design for a biosensor, which monitors changes in the intracellular concentration of ppGpp by coupling it to a fluorescent output. We used mathematical modelling to analyse the intracellular dynamics of ppGpp, its fluorescent reporter, and cell growth in normal and fatty acid-producing E. coli lines. The model integrates existing mechanisms of ppGpp regulation and predicts the biosensor response to changes in nutrient state. In particular, the model predicts that excessive stimulation of fatty acid production depletes fatty acid intermediates, downregulates growth and increases the levels of ppGpp-related fluorescence. Our analysis demonstrates that the ppGpp sensor can be used for early detection of nutrient limitation during cell growth and for testing productivity of engineered lines.
A practical course in differential equations and mathematical modeling
Ibragimov , Nail H
2009-01-01
A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book which aims to present new mathematical curricula based on symmetry and invariance principles is tailored to develop analytic skills and working knowledge in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundame
Mathematical Modeling of Hybrid Electrical Engineering Systems
Directory of Open Access Journals (Sweden)
A. A. Lobaty
2016-01-01
Full Text Available A large class of systems that have found application in various industries and households, electrified transportation facilities and energy sector has been classified as electrical engineering systems. Their characteristic feature is a combination of continuous and discontinuous modes of operation, which is reflected in the appearance of a relatively new term “hybrid systems”. A wide class of hybrid systems is pulsed DC converters operating in a pulse width modulation, which are non-linear systems with variable structure. Using various methods for linearization it is possible to obtain linear mathematical models that rather accurately simulate behavior of such systems. However, the presence in the mathematical models of exponential nonlinearities creates considerable difficulties in the implementation of digital hardware. The solution can be found while using an approximation of exponential functions by polynomials of the first order, that, however, violates the rigor accordance of the analytical model with characteristics of a real object. There are two practical approaches to synthesize algorithms for control of hybrid systems. The first approach is based on the representation of the whole system by a discrete model which is described by difference equations that makes it possible to synthesize discrete algorithms. The second approach is based on description of the system by differential equations. The equations describe synthesis of continuous algorithms and their further implementation in a digital computer included in the control loop system. The paper considers modeling of a hybrid electrical engineering system using differential equations. Neglecting the pulse duration, it has been proposed to describe behavior of vector components in phase coordinates of the hybrid system by stochastic differential equations containing generally non-linear differentiable random functions. A stochastic vector-matrix equation describing dynamics of the
Mathematical modelling of the MAP kinase pathway using proteomic datasets.
Tian, Tianhai; Song, Jiangning
2012-01-01
The advances in proteomics technologies offer an unprecedented opportunity and valuable resources to understand how living organisms execute necessary functions at systems levels. However, little work has been done up to date to utilize the highly accurate spatio-temporal dynamic proteome data generated by phosphoprotemics for mathematical modeling of complex cell signaling pathways. This work proposed a novel computational framework to develop mathematical models based on proteomic datasets. Using the MAP kinase pathway as the test system, we developed a mathematical model including the cytosolic and nuclear subsystems; and applied the genetic algorithm to infer unknown model parameters. Robustness property of the mathematical model was used as a criterion to select the appropriate rate constants from the estimated candidates. Quantitative information regarding the absolute protein concentrations was used to refine the mathematical model. We have demonstrated that the incorporation of more experimental data could significantly enhance both the simulation accuracy and robustness property of the proposed model. In addition, we used the MAP kinase pathway inhibited by phosphatases with different concentrations to predict the signal output influenced by different cellular conditions. Our predictions are in good agreement with the experimental observations when the MAP kinase pathway was inhibited by phosphatase PP2A and MKP3. The successful application of the proposed modeling framework to the MAP kinase pathway suggests that our method is very promising for developing accurate mathematical models and yielding insights into the regulatory mechanisms of complex cell signaling pathways.
Analysis of mathematical modelling on potentiometric biosensors.
Mehala, N; Rajendran, L
2014-01-01
A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.
Laser interaction with biological material mathematical modeling
Kulikov, Kirill
2014-01-01
This book covers the principles of laser interaction with biological cells and tissues of varying degrees of organization. The problems of biomedical diagnostics are considered. Scattering of laser irradiation of blood cells is modeled for biological structures (dermis, epidermis, vascular plexus). An analytic theory is provided which is based on solving the wave equation for the electromagnetic field. It allows the accurate analysis of interference effects arising from the partial superposition of scattered waves. Treated topics of mathematical modeling are: optical characterization of biological tissue with large-scale and small-scale inhomogeneities in the layers, heating blood vessel under laser irradiation incident on the outer surface of the skin and thermo-chemical denaturation of biological structures at the example of human skin.
Pieters, Stefanie; Roeyers, Herbert; Rosseel, Yves; Van Waelvelde, Hilde; Desoete, Annemie
2015-01-01
A relationship between motor and mathematical skills has been shown by previous research. However, the question of whether subtypes can be differentiated within developmental coordination disorder (DCD) and/or mathematical learning disability (MLD) remains unresolved. In a sample of children with and without DCD and/or MLD, a data-driven…
Modellus: Learning Physics with Mathematical Modelling
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 biology modules based on modern molecular biology and modern discrete mathematics.
Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander
2010-01-01
We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.
Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics
Davies, Robin; Hodge, Terrell; Enyedi, Alexander
2010-01-01
We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955
The possibilities of a modelling perspective for school mathematics
Directory of Open Access Journals (Sweden)
Dirk Wessels
2009-09-01
complex teaching methodology requires in-depth thinking about the role of the teacher, the role of the learner, the nature of the classroom culture, the nature of the negotiation of meaning between the teacher and individuals or groups, the nature of selected problems and material, as well as the kind of integrative assessment used in the mathematics classroom. Modelling is closely related to the problem-centred teaching approach, but it also smoothly relates to bigger and longer mathematical tasks. This article gives a theoretical exposition of the scope and depth of mathematical modelling. It is possible to introduce modelling at every school phase in our educational sytem. Modelling in school mathematics seems to make the learning of mathematics more effective. The mastering of problem solving and modelling strategies has deﬁnitely changed the orientation, the competencies and performances of learners at each school level. It would appear from research that learners like the application side of mathematics and that they want to see it in action. Genuine real life problems should be selected, which is why a modelling perspective is so important for the teaching and mastering of mathematics. Modelling should be integrated into the present curriculum because learners will then get full access to involvement in the classroom, to mathematisation, to doing problems, to criticising arguments, to ﬁnding proofs, to recognising concepts and to obtaining the ability to abstract these from the realistic situation. Modelling should be given a full opportunity in mathematics teacher education so that our learners can get the full beneﬁt of it. This will put the mathematical performances of learners in our country on a more solid base, which will make our learners more competitive at all levels in the future.
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…
Introduction to mathematical modeling and chaotic dynamics
Upadhyay, Ranjit Kumar
2013-01-01
""The presentation is so clear that anyone with even a basic mathematical background can study it and get a clear picture. … Unlike many other similar textbooks, a rich reference section is given at the end of each chapter. The cautious selection of worked out examples and exercises throughout the book is superb. For anyone with previous experience of having run into books in mathematical modeling and chaotic dynamics that rapidly move into advanced mathematical content, the book offers a pleasant recourse at an introductory level and therefore can be very inspirational.""-MAA Reviews, Decembe
MATHEMATICAL MODEL FOR RIVERBOAT DYNAMICS
Directory of Open Access Journals (Sweden)
Aleksander Grm
2017-01-01
Full Text Available Present work describes a simple dynamical model for riverboat motion based on the square drag law. Air and water interactions with the boat are determined from aerodynamic coefficients. CFX simulations were performed with fully developed turbulent flow to determine boat aerodynamic coefficients for an arbitrary angle of attack for the air and water portions separately. The effect of wave resistance is negligible compared to other forces. Boat movement analysis considers only two-dimensional motion, therefore only six aerodynamics coefficients are required. The proposed model is solved and used to determine the critical environmental parameters (wind and current under which river navigation can be conducted safely. Boat simulator was tested in a single area on the Ljubljanica river and estimated critical wind velocity.
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…
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…
Principle-Based Mathematics: An Exploratory Study
Poon, Rebecca Chung-Yan
2014-01-01
Although educators and policymakers are becoming increasingly aware of the need for professional development that is content specific (Kennedy, 1999) and focuses on deepening and broadening teachers' knowledge of content for teaching (American Federation of Teachers, 2002; National Academy of Education, 2009), little attention has been given to supporting teachers' development of content knowledge as defined by Shulman (1986). Principle-Based Mathematics (PBM), a presentation of K-12 mathemat...
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 ...
On the mathematical modeling of aeolian saltation
DEFF Research Database (Denmark)
Jensen, Jens Ledet; Sørensen, Michael
1983-01-01
The development of a mathematical model for aeolian saltation is a promising way of obtaining further progress in the field of wind-blown sand. Interesting quantities can be calculated from a model defined in general terms, and a specific model is defined and compared to previously published data...
Mathematical Model of Evolution of Brain Parcellation.
Ferrante, Daniel D; Wei, Yi; Koulakov, Alexei A
2016-01-01
We study the distribution of brain and cortical area sizes [parcellation units (PUs)] obtained for three species: mouse, macaque, and human. We find that the distribution of PU sizes is close to lognormal. We propose the mathematical model of evolution of brain parcellation based on iterative fragmentation and specialization. In this model, each existing PU has a probability to be split that depends on PU size only. This model suggests that the same evolutionary process may have led to brain parcellation in these three species. Within our model, region-to-region (macro) connectivity is given by the outer product form. We show that most experimental data on non-zero macaque cortex macroscopic-level connections can be explained by the outer product power-law form suggested by our model (62% for area V1). We propose a multiplicative Hebbian learning rule for the macroconnectome that could yield the correct scaling of connection strengths between areas. We thus propose an evolutionary model that may have contributed to both brain parcellation and mesoscopic level connectivity in mammals.
Mathematical modeling and applications in nonlinear dynamics
Merdan, Hüseyin
2016-01-01
The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...
Mathematical 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.
Interfacial Fluid Mechanics A Mathematical Modeling Approach
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 and methods for planet Earth
Locatelli, Ugo; Ruggeri, Tommaso; Strickland, Elisabetta
2014-01-01
In 2013 several scientific activities have been devoted to mathematical researches for the study of planet Earth. The current volume presents a selection of the highly topical issues presented at the workshop “Mathematical Models and Methods for Planet Earth”, held in Roma (Italy), in May 2013. The fields of interest span from impacts of dangerous asteroids to the safeguard from space debris, from climatic changes to monitoring geological events, from the study of tumor growth to sociological problems. In all these fields the mathematical studies play a relevant role as a tool for the analysis of specific topics and as an ingredient of multidisciplinary problems. To investigate these problems we will see many different mathematical tools at work: just to mention some, stochastic processes, PDE, normal forms, chaos theory.
Mathematical 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.
Gurarie, David; Karl, Stephan; Zimmerman, Peter A; King, Charles H; St Pierre, Timothy G; Davis, Timothy M E
2012-01-01
Agent-based modeling of Plasmodium falciparum infection offers an attractive alternative to the conventional Ross-Macdonald methodology, as it allows simulation of heterogeneous communities subjected to realistic transmission (inoculation patterns). We developed a new, agent based model that accounts for the essential in-host processes: parasite replication and its regulation by innate and adaptive immunity. The model also incorporates a simplified version of antigenic variation by Plasmodium falciparum. We calibrated the model using data from malaria-therapy (MT) studies, and developed a novel calibration procedure that accounts for a deterministic and a pseudo-random component in the observed parasite density patterns. Using the parasite density patterns of 122 MT patients, we generated a large number of calibrated parameters. The resulting data set served as a basis for constructing and simulating heterogeneous agent-based (AB) communities of MT-like hosts. We conducted several numerical experiments subjecting AB communities to realistic inoculation patterns reported from previous field studies, and compared the model output to the observed malaria prevalence in the field. There was overall consistency, supporting the potential of this agent-based methodology to represent transmission in realistic communities. Our approach represents a novel, convenient and versatile method to model Plasmodium falciparum infection.
Directory of Open Access Journals (Sweden)
David Gurarie
Full Text Available BACKGROUND: Agent-based modeling of Plasmodium falciparum infection offers an attractive alternative to the conventional Ross-Macdonald methodology, as it allows simulation of heterogeneous communities subjected to realistic transmission (inoculation patterns. METHODOLOGY/PRINCIPAL FINDINGS: We developed a new, agent based model that accounts for the essential in-host processes: parasite replication and its regulation by innate and adaptive immunity. The model also incorporates a simplified version of antigenic variation by Plasmodium falciparum. We calibrated the model using data from malaria-therapy (MT studies, and developed a novel calibration procedure that accounts for a deterministic and a pseudo-random component in the observed parasite density patterns. Using the parasite density patterns of 122 MT patients, we generated a large number of calibrated parameters. The resulting data set served as a basis for constructing and simulating heterogeneous agent-based (AB communities of MT-like hosts. We conducted several numerical experiments subjecting AB communities to realistic inoculation patterns reported from previous field studies, and compared the model output to the observed malaria prevalence in the field. There was overall consistency, supporting the potential of this agent-based methodology to represent transmission in realistic communities. CONCLUSIONS/SIGNIFICANCE: Our approach represents a novel, convenient and versatile method to model Plasmodium falciparum infection.
Mathematical modeling of diphtheria transmission in Thailand.
Sornbundit, Kan; Triampo, Wannapong; Modchang, Charin
2017-08-01
In this work, a mathematical model for describing diphtheria transmission in Thailand is proposed. Based on the course of diphtheria infection, the population is divided into 8 epidemiological classes, namely, susceptible, symptomatic infectious, asymptomatic infectious, carrier with full natural-acquired immunity, carrier with partial natural-acquired immunity, individual with full vaccine-induced immunity, and individual with partial vaccine-induced immunity. Parameter values in the model were either directly obtained from the literature, estimated from available data, or estimated by means of sensitivity analysis. Numerical solutions show that our model can correctly describe the decreasing trend of diphtheria cases in Thailand during the years 1977-2014. Furthermore, despite Thailand having high DTP vaccine coverage, our model predicts that there will be diphtheria outbreaks after the year 2014 due to waning immunity. Our model also suggests that providing booster doses to some susceptible individuals and those with partial immunity every 10 years is a potential way to inhibit future diphtheria outbreaks. Copyright © 2017 Elsevier Ltd. All rights reserved.
Mathematical human body modelling for impact loading
Happee, R.; Morsink, P.L.J.; Wismans, J.S.H.M.
1999-01-01
Mathematical modelling of the human body is widely used for automotive crash safety research and design. Simulations have contributed to a reduction of injury numbers by optimisation of vehicle structures and restraint systems. Currently such simulations are largely performed using occupant models
Building Mathematical Models Of Solid Objects
Randall, Donald P.; Jones, Kennie H.; Von Ofenheim, William H.; Gates, Raymond L.; Matthews, Christine G.
1989-01-01
Solid Modeling Program (SMP) version 2.0 provides capability to model complex solid objects mathematically through aggregation of geometric primitives (parts). System provides designer with basic set of primitive parts and capability to define new primitives. Six primitives included in present version: boxes, cones, spheres, paraboloids, tori, and trusses. Written in VAX/VMS FORTRAN 77.
About a mathematical model of market
Kulikov, D. A.
2017-01-01
In the paper a famous mathematical model of macroeconomics, which is called “market model” was considered. Traditional versions of this model have no periodic solutions and, therefore, they cannot describe a cyclic recurrence of the market economy. In the paper for the corresponding equation a delay was added. It allows obtaining sufficient conditions for existence of the stable cycles.
Uncertainty and Complexity in Mathematical Modeling
Cannon, Susan O.; Sanders, Mark
2017-01-01
Modeling is an effective tool to help students access mathematical concepts. Finding a math teacher who has not drawn a fraction bar or pie chart on the board would be difficult, as would finding students who have not been asked to draw models and represent numbers in different ways. In this article, the authors will discuss: (1) the properties of…
Mathematical Modeling: Are Prior Experiences Important?
Czocher, Jennifer A.; Moss, Diana L.
2017-01-01
Why are math modeling problems the source of such frustration for students and teachers? The conceptual understanding that students have when engaging with a math modeling problem varies greatly. They need opportunities to make their own assumptions and design the mathematics to fit these assumptions (CCSSI 2010). Making these assumptions is part…
Mathematical modeling and analysis of WEDM machining ...
Indian Academy of Sciences (India)
Home; Journals; Sadhana; Volume 42; Issue 6. Mathematical modeling and analysis ... The present work is mainly focused on the analysis and optimization of the WEDM process parameters of Inconel 625. The four machining ... Response surface methodology was used to develop the experimental models. The parametric ...
Mathematical Properties Relevant to Geomagnetic Field Modeling
DEFF Research Database (Denmark)
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2010-01-01
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...... 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...
Developing Mathematics Problems Based on Pisa Level
Directory of Open Access Journals (Sweden)
Shahibul Ahyan
2014-01-01
Full Text Available This research aims to produce mathematics problems based on PISA level with valid and practical content of change and relationships and has potential effect for Junior High School students. A development research method developed by Akker, Gravemeijer, McKenney and Nieveen is used this research. In the first stage, the researcher analyzed students, algebra material in school-based curricula (KTSP and mathematics problems of PISA 2003 of change and relationships content. The second stage, the researcher designed 13 problems with content of change and relationships. The last, the researcher used formative evaluation design developed by Tessmer which includes self evaluation, one-to-one, expert review, small group, and field test. The data collect by walk through, interview, and questionnaire. The result of this research indicated that 12 mathematical problems based on PISA level of change and relationships content that developed have validity, practically, and potential effects for Junior High School students.
Mathematical model comparing of the multi-level economics systems
Brykalov, S. M.; Kryanev, A. V.
2017-12-01
The mathematical model (scheme) of a multi-level comparison of the economic system, characterized by the system of indices, is worked out. In the mathematical model of the multi-level comparison of the economic systems, the indicators of peer review and forecasting of the economic system under consideration can be used. The model can take into account the uncertainty in the estimated values of the parameters or expert estimations. The model uses the multi-criteria approach based on the Pareto solutions.
Manual on mathematical models in isotope hydrogeology
International Nuclear Information System (INIS)
1996-10-01
Methodologies based on the use of naturally occurring isotopes are, at present, an integral part of studies being undertaken for water resources assessment and management. Quantitative evaluations based on the temporal and/or spatial distribution of different isotopic species in hydrological systems require conceptual mathematical formulations. Different types of model can be employed depending on the nature of the hydrological system under investigation, the amount and type of data available, and the required accuracy of the parameter to be estimated. This manual provides an overview of the basic concepts of existing modelling approaches, procedures for their application to different hydrological systems, their limitations and data requirements. Guidance in their practical applications, illustrative case studies and information on existing PC software are also included. While the subject matter of isotope transport modelling and improved quantitative evaluations through natural isotopes in water sciences is still at the development stage, this manual summarizes the methodologies available at present, to assist the practitioner in the proper use within the framework of ongoing isotope hydrological field studies. In view of the widespread use of isotope methods in groundwater hydrology, the methodologies covered in the manual are directed towards hydrogeological applications, although most of the conceptual formulations presented would generally be valid. Refs, figs, tabs
Piantadosi, Steven
2017-01-01
This paper presents an approach to describing the three dimensional shape of a violin plate in mathematical form. The shape description begins with standard contour lines and ends with an equation for a surface in three dimensional space. The traditional specification of cross sectional arching is unnecessary. Advantages of this approach are that it employs simple and universal description of plate geometry and yields a complete, smoothed, precise mathematical equation of the plate that is suitable for modern three dimensional production. It is quite general and suitable for both exterior and interior plate surfaces, yielding the ability to control thicknesses along with shape. This method can produce mathematical descriptions with tolerances easily less than 0.001 millimeters suitable for modern computerized numerical control carving and hand finishing.
A mathematical model of glutathione metabolism
Directory of Open Access Journals (Sweden)
James S Jill
2008-04-01
Full Text Available Abstract Background Glutathione (GSH plays an important role in anti-oxidant defense and detoxification reactions. It is primarily synthesized in the liver by the transsulfuration pathway and exported to provide precursors for in situ GSH synthesis by other tissues. Deficits in glutathione have been implicated in aging and a host of diseases including Alzheimer's disease, Parkinson's disease, cardiovascular disease, cancer, Down syndrome and autism. Approach We explore the properties of glutathione metabolism in the liver by experimenting with a mathematical model of one-carbon metabolism, the transsulfuration pathway, and glutathione synthesis, transport, and breakdown. The model is based on known properties of the enzymes and the regulation of those enzymes by oxidative stress. We explore the half-life of glutathione, the regulation of glutathione synthesis, and its sensitivity to fluctuations in amino acid input. We use the model to simulate the metabolic profiles previously observed in Down syndrome and autism and compare the model results to clinical data. Conclusion We show that the glutathione pools in hepatic cells and in the blood are quite insensitive to fluctuations in amino acid input and offer an explanation based on model predictions. In contrast, we show that hepatic glutathione pools are highly sensitive to the level of oxidative stress. The model shows that overexpression of genes on chromosome 21 and an increase in oxidative stress can explain the metabolic profile of Down syndrome. The model also correctly simulates the metabolic profile of autism when oxidative stress is substantially increased and the adenosine concentration is raised. Finally, we discuss how individual variation arises and its consequences for one-carbon and glutathione metabolism.
On the mathematical modeling of memristors
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.
Cocaine addiction and personality: a mathematical model.
Caselles, Antonio; Micó, Joan C; Amigó, Salvador
2010-05-01
The existence of a close relation between personality and drug consumption is recognized, but the corresponding causal connection is not well known. Neither is it well known whether personality exercises an influence predominantly at the beginning and development of addiction, nor whether drug consumption produces changes in personality. This paper presents a dynamic mathematical model of personality and addiction based on the unique personality trait theory (UPTT) and the general modelling methodology. This model attempts to integrate personality, the acute effect of drugs, and addiction. The UPTT states the existence of a unique trait of personality called extraversion, understood as a dimension that ranges from impulsive behaviour and sensation-seeking (extravert pole) to fearful and anxious behaviour (introvert pole). As a consequence of drug consumption, the model provides the main patterns of extraversion dynamics through a system of five coupled differential equations. It combines genetic extraversion, as a steady state, and dynamic extraversion in a unique variable measured on the hedonic scale. The dynamics of this variable describes the effects of stimulant drugs on a short-term time scale (typical of the acute effect); while its mean time value describes the effects of stimulant drugs on a long-term time scale (typical of the addiction effect). This understanding may help to develop programmes of prevention and intervention in drug misuse.
Dynamics of mathematical models in biology bringing mathematics to life
Zazzu, Valeria; Guarracino, Mario
2016-01-01
This volume focuses on contributions from both the mathematics and life science community surrounding the concepts of time and dynamicity of nature, two significant elements which are often overlooked in modeling process to avoid exponential computations. The book is divided into three distinct parts: dynamics of genomes and genetic variation, dynamics of motifs, and dynamics of biological networks. Chapters included in dynamics of genomes and genetic variation analyze the molecular mechanisms and evolutionary processes that shape the structure and function of genomes and those that govern genome dynamics. The dynamics of motifs portion of the volume provides an overview of current methods for motif searching in DNA, RNA and proteins, a key process to discover emergent properties of cells, tissues, and organisms. The part devoted to the dynamics of biological networks covers networks aptly discusses networks in complex biological functions and activities that interpret processes in cells. Moreover, chapters i...
Mathematical modelling as basis for efficient enterprise management
Directory of Open Access Journals (Sweden)
Kalmykova Svetlana
2017-01-01
Full Text Available The choice of the most effective HR- management style at the enterprise is based on modeling various socio-economic situations. The article describes the formalization of the managing processes aimed at the interaction between the allocated management subsystems. The mathematical modelling tools are used to determine the time spent on recruiting personnel for key positions in the management hierarchy selection.
Mathematical Model for Direct Evaporative Space Cooling Systems ...
African Journals Online (AJOL)
This paper deals with the development of a simple mathematical model for experimental validation of the performance of a small evaporative cooling system in a tropical climate. It also presents the coefficient of convective heat transfer of wide range of temperatures based on existing model. Extensive experiments have ...
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)
Long-term development of how students interpret a model; Complementarity of contexts and mathematics
Vos, Pauline; Roorda, Gerrit; Stillman, Gloria Ann; Blum, Werner; Kaiser, Gabriele
2017-01-01
When students engage in rich mathematical modelling tasks, they have to handle real-world contexts and mathematics in chorus. This is not easy. In this chapter, contexts and mathematics are perceived as complementary, which means they can be integrated. Based on four types of approaches to modelling
Genetic demographic networks: Mathematical model and applications.
Kimmel, Marek; Wojdyła, Tomasz
2016-10-01
Recent improvement in the quality of genetic data obtained from extinct human populations and their ancestors encourages searching for answers to basic questions regarding human population history. The most common and successful are model-based approaches, in which genetic data are compared to the data obtained from the assumed demography model. Using such approach, it is possible to either validate or adjust assumed demography. Model fit to data can be obtained based on reverse-time coalescent simulations or forward-time simulations. In this paper we introduce a computational method based on mathematical equation that allows obtaining joint distributions of pairs of individuals under a specified demography model, each of them characterized by a genetic variant at a chosen locus. The two individuals are randomly sampled from either the same or two different populations. The model assumes three types of demographic events (split, merge and migration). Populations evolve according to the time-continuous Moran model with drift and Markov-process mutation. This latter process is described by the Lyapunov-type equation introduced by O'Brien and generalized in our previous works. Application of this equation constitutes an original contribution. In the result section of the paper we present sample applications of our model to both simulated and literature-based demographies. Among other we include a study of the Slavs-Balts-Finns genetic relationship, in which we model split and migrations between the Balts and Slavs. We also include another example that involves the migration rates between farmers and hunters-gatherers, based on modern and ancient DNA samples. This latter process was previously studied using coalescent simulations. Our results are in general agreement with the previous method, which provides validation of our approach. Although our model is not an alternative to simulation methods in the practical sense, it provides an algorithm to compute pairwise
Applied Mathematics, Modelling and Computational Science
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 ...
Mathematical modeling plasma transport in tokamaks
International Nuclear Information System (INIS)
Quiang, Ji
1995-01-01
In this work, the author applied a systematic calibration, validation and application procedure based on the methodology of mathematical modeling to international thermonuclear experimental reactor (ITER) ignition studies. The multi-mode plasma transport model used here includes a linear combination of drift wave branch and ballooning branch instabilities with two a priori uncertain constants to account for anomalous plasma transport in tokamaks. A Bayesian parameter estimation method is used including experimental calibration error/model offsets and error bar rescaling factors to determine the two uncertain constants in the transport model with quantitative confidence level estimates for the calibrated parameters, which gives two saturation levels of instabilities. This method is first tested using a gyroBohm multi-mode transport model with a pair of DIII-D discharge experimental data, and then applied to calibrating a nominal multi-mode transport model against a broad database using twelve discharges from seven different tokamaks. The calibrated transport model is then validated on five discharges from JT-60 with no adjustable constants. The results are in a good agreement with experimental data. Finally, the resulting class of multi-mode tokamak plasma transport models is applied to the transport analysis of the ignition probability in a next generation machine, ITER. A reference simulation of basic ITER engineering design activity (EDA) parameters shows that a self-sustained thermonuclear burn with 1.5 GW output power can be achieved provided that impurity control makes radiative losses sufficiently small at an average plasma density of 1.2 X 10 20 /m 3 with 50 MW auxiliary heating. The ignition probability of ITER for the EDA parameters, can be formally as high as 99.9% in the present context. The same probability for concept design activity (CDA) parameters of ITER, which has smaller size and lower current, is only 62.6%
Dog Mathematics: Exploring Base-4
Kurz, Terri L.; Yanik, H. Bahadir; Lee, Mi Yeon
2016-01-01
Using a dog's paw as a basis for numerical representation, sixth grade students explored how to count and regroup using the dog's four digital pads. Teachers can connect these base-4 explorations to the conceptual meaning of place value and regrouping using base-10.
Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling
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…
Wheels, Cranks, and Cams: An Animated Spreadsheet-Based Mathematical Model of a Four-Stroke Engine.
Callender, J. T.; Jackson, R.
1998-01-01
Analyzes the mathematics of rotational and translational motion and how one can influence the other in the context of cams and cranks. Describes how the individual components can be brought together to simulate a four-stroke engine and how the engine animates again using the same simple macro. (Author/ASK)
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.
The (Mathematical) Modeling Process in Biosciences.
Torres, Nestor V; Santos, Guido
2015-01-01
In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology.
Mathematical modeling of renal hemodynamics in physiology and pathophysiology.
Sgouralis, Ioannis; Layton, Anita T
2015-06-01
In addition to the excretion of metabolic waste and toxin, the kidney plays an indispensable role in regulating the balance of water, electrolyte, acid-base, and blood pressure. For the kidney to maintain proper functions, hemodynamic control is crucial. In this review, we describe representative mathematical models that have been developed to better understand the kidney's autoregulatory processes. We consider mathematical models that simulate glomerular filtration, and renal blood flow regulation by means of the myogenic response and tubuloglomerular feedback. We discuss the extent to which these modeling efforts have expanded the understanding of renal functions in health and disease. Copyright © 2015 Elsevier Inc. All rights reserved.
Mathematical model of concentrating solar cooker
Avilés, Mauricio González; Avilés, José Juan González
2013-01-01
The main purpose of this work is to obtain a mathematical model consistent with the thermal behavior of concentrating solar cookers, such as Jorhejpataranskua. We also want to simulate different conditions respect to the parameters involved of several materials for its construction and efficiency. The model is expressed in terms of a coupled nonlinear system of differential equations which are solved using Mathematica 8. The results obtained by our model are compared with measurements of sola...
Mathematical model of self-cycling fermentation
Energy Technology Data Exchange (ETDEWEB)
Wincure, B.M.; Cooper, D.G.; Rey, A. [McGill Univ., Montreal, Quebec (Canada). Dept. of Chemical Engineering
1995-04-20
This article presents a mathematical model for biomass, limiting substrate, and dissolved oxygen concentrations during stable operation of self-cycling fermentation (SCF). Laboratory experiments using the bacterium Acinetobacter calcoaceticus RAG-1 and ethanol as the limiting substrate were performed to validate the model. A computer simulation developed from the model successfully matched experimental SCF intracycle trends and end-of-cycle results and, most importantly, settled into an unimposed periodicity characteristic of stable SCF operation.
On Mathematical Modeling Of Quantum Systems
Achuthan, P.; Narayanankutty, Karuppath
2009-07-01
The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.
Mathematical Models of Cardiac Pacemaking Function
Directory of Open Access Journals (Sweden)
Pan eLi
2013-10-01
Full Text Available Over the past half century, there has been intense and fruitful interaction between experimental and computational investigations of cardiac function. This interaction has, for example, led to deep understanding of cardiac excitation-contraction coupling; how it works, as well as how it fails. However, many lines of inquiry remain unresolved, among them the initiation of each heartbeat. The sinoatrial node, a cluster of specialized pacemaking cells in the right atrium of the heart, spontaneously generates an electro-chemical wave that spreads through the atria and through the cardiac conduction system to the ventricles, initiating the contraction of cardiac muscle essential for pumping blood to the body. Despite the fundamental importance of this primary pacemaker, this process is still not fully understood, and ionic mechanisms underlying cardiac pacemaking function are currently under heated debate. Several mathematical models of sinoatrial node cell membrane electrophysiology have been constructed as based on different experimental data sets and hypotheses. As could be expected, these differing models offer diverse predictions about cardiac pacemaking activities. This paper aims to present the current state of debate over the origins of the pacemaking function of the sinoatrial node. Here, we will specifically review the state-of-the-art of cardiac pacemaker modeling, with a special emphasis on current discrepancies, limitations, and future challenges.
Mathematical model of two-phase flow in accelerator channel
Directory of Open Access Journals (Sweden)
О.Ф. Нікулін
2010-01-01
Full Text Available The problem of two-phase flow composed of energy-carrier phase (Newtonian liquid and solid fine-dispersed phase (particles in counter jet mill accelerator channel is considered. The mathematical model bases goes on the supposition that the phases interact with each other like independent substances by means of aerodynamics’ forces in conditions of adiabatic flow. The mathematical model in the form of system of differential equations of order 11 is represented. Derivations of equations by base physical principles for cross-section-averaged quantity are produced. The mathematical model can be used for estimation of any kinematic and thermodynamic flow characteristics for purposely parameters optimization problem solving and transfer functions determination, that take place in counter jet mill accelerator channel design.
Mathematical Modelling of Intraretinal Oxygen Partial Pressure
African Journals Online (AJOL)
Erah
pressure distribution under adapted conditions of light and darkness.. Method: A simple eight-layered mathematical model for intraretinal oxygen partial pressure distribution was developed using Fick's law of diffusion, Michaelis-Menten kinetics, and oxygen delivery in the inner retina. The system of non-linear differential ...
Description of a comprehensive mathematical model
DEFF Research Database (Denmark)
Li, Xiyan; Yin, Chungen
2017-01-01
Biomass gasification is still a promising technology after over 30 years’ research and development and has success only in a few niche markets. In this paper, a comprehensive mathematical model for biomass particle gasification is developed within a generic particle framework, assuming the feed i...
Mathematical Modelling of Intraretinal Oxygen Partial Pressure
African Journals Online (AJOL)
Erah
This minimum pressure may fall below the critical level of oxygen partial pressure and affect the retinal function. In order to restore normal retinal function, extreme hyperoxia may assist to make the choroid capable of supplying oxygen to the whole retina during total retinal artery occlusion. Keywords: Mathematical modeling ...
Mathematical modelling of the calcination process | Olayiwola ...
African Journals Online (AJOL)
High quality lime is an essential raw material for Electric Arc Furnaces and Basic Oxygen Furnaces, steelmaking, alumina production etc. Decrease in fuel consumption in metallurgical furnaces is a tremendous opportunity for reduction of greenhouse gas emissions into the atmosphere. In this paper, a mathematical model ...
Mathematical modeling of fructose production by immobilised ...
African Journals Online (AJOL)
Production of fructose from glucose isomerisation process using commercial immobilized glucose isomerase (IGI) was conducted in a batch type of stirred tank bioreactor. A mathematical model was developed to describe the effect of temperature and pH on the kinetic parameters of fructose production. Modified Santos ...
ECONOMIC AND MATHEMATICAL MODELING INNOVATION SYSTEMS
Directory of Open Access Journals (Sweden)
D.V. Makarov
2014-06-01
Full Text Available The paper presents one of the mathematical tools for modeling innovation processes. With the help of Kondratieff long waves can define innovation cycles. However, complexity of the innovation system implies a qualitative description. The article describes the problems of this area of research.
A Model for Community Partnerships in Mathematics
Forrest, Bradley; Kosick, Pamela; Vogel, Judith; Wu, Chia-Lin
2012-01-01
This article describes a partnership involving a college and its surrounding public high schools in order to offer a model for transforming professional development initiatives into collaborative, reciprocal community engagement opportunities. This ongoing partnership addresses the shared goal of improving the mathematical college readiness of…
Mathematical Properties Relevant to Geomagnetic Field Modeling
DEFF Research Database (Denmark)
Sabaka, Terence J.; Hulot, Gauthier; Olsen, Nils
2014-01-01
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 to as a geomag...
Optimization and mathematical modeling in computer architecture
Sankaralingam, Karu; Nowatzki, Tony
2013-01-01
In this book we give an overview of modeling techniques used to describe computer systems to mathematical optimization tools. We give a brief introduction to various classes of mathematical optimization frameworks with special focus on mixed integer linear programming which provides a good balance between solver time and expressiveness. We present four detailed case studies -- instruction set customization, data center resource management, spatial architecture scheduling, and resource allocation in tiled architectures -- showing how MILP can be used and quantifying by how much it outperforms t
Mathematical modeling models, analysis and applications
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 Simple Mathematical Model of Cyclic Circadian Learning
Directory of Open Access Journals (Sweden)
J. Šimon
2014-01-01
Full Text Available This paper deals with the derivation of a simple mathematical model of cyclic learning with a period of 24 hours. Various requirements are met with an emphasis and approach which relies on simple mathematical operations, the prediction of measurable quantities, and the creation of uncomplicated processes of calibration. The presented model can be used to answer questions such as the following. Will I be able to memorize a given set of information? How long will it take to memorize information? How long will I remember the information that was memorized? The model is based on known memory retention functions that are in good agreement with experimental results. By the use of these functions and by formalism of differential equations, the concurrent processes of learning and forgetting are described mathematically. The usability of this model is limited to scenarios where logical bonds (connections to prior learning are not created and mnemonic devices cannot be utilized during the learning process.
Effectiveness of discovery learning model on mathematical problem solving
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 of the flash converting process
Energy Technology Data Exchange (ETDEWEB)
Sohn, H.Y.; Perez-Tello, M.; Riihilahti, K.M. [Utah Univ., Salt Lake City, UT (United States)
1996-12-31
An axisymmetric mathematical model for the Kennecott-Outokumpu flash converting process for converting solid copper matte to copper is presented. The model is an adaptation of the comprehensive mathematical model formerly developed at the University of Utah for the flash smelting of copper concentrates. The model incorporates the transport of momentum, heat, mass, and reaction kinetics between gas and particles in a particle-laden turbulent gas jet. The standard k-{epsilon} model is used to describe gas-phase turbulence in an Eulerian framework. The particle-phase is treated from a Lagrangian viewpoint which is coupled to the gas-phase via the source terms in the Eulerian gas-phase governing equations. Matte particles were represented as Cu{sub 2}S yFeS, and assumed to undergo homogeneous oxidation to Cu{sub 2}O, Fe{sub 3}O{sub 4}, and SO{sub 2}. A reaction kinetics mechanism involving both external mass transfer of oxygen gas to the particle surface and diffusion of oxygen through the porous oxide layer is proposed to estimate the particle oxidation rate Predictions of the mathematical model were compared with the experimental data collected in a bench-scale flash converting facility. Good agreement between the model predictions and the measurements was obtained. The model was used to study the effect of different gas-injection configurations on the overall fluid dynamics in a commercial size flash converting shaft. (author)
Modeling life the mathematics of biological systems
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 ...
Dealing with dissatisfaction in mathematical modelling to integrate QFD and Kano’s model
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.
Mathematical Models of Breast and Ovarian Cancers
Botesteanu, Dana-Adriana; Lipkowitz, Stanley; Lee, Jung-Min; Levy, Doron
2016-01-01
Women constitute the majority of the aging United States (US) population, and this has substantial implications on cancer population patterns and management practices. Breast cancer is the most common women's malignancy, while ovarian cancer is the most fatal gynecological malignancy in the US. In this review we focus on these subsets of women's cancers, seen more commonly in postmenopausal and elderly women. In order to systematically investigate the complexity of cancer progression and response to treatment in breast and ovarian malignancies, we assert that integrated mathematical modeling frameworks viewed from a systems biology perspective are needed. Such integrated frameworks could offer innovative contributions to the clinical women's cancers community, since answers to clinical questions cannot always be reached with contemporary clinical and experimental tools. Here, we recapitulate clinically known data regarding the progression and treatment of the breast and ovarian cancers. We compare and contrast the two malignancies whenever possible, in order to emphasize areas where substantial contributions could be made by clinically inspired and validated mathematical modeling. We show how current paradigms in the mathematical oncology community focusing on the two malignancies do not make comprehensive use of, nor substantially reflect existing clinical data, and we highlight the modeling areas in most critical need of clinical data integration. We emphasize that the primary goal of any mathematical study of women's cancers should be to address clinically relevant questions. PMID:27259061
Causal Bayes Model of Mathematical Competence in Kindergarten
Directory of Open Access Journals (Sweden)
Božidar Tepeš
2016-06-01
Full Text Available In this paper authors define mathematical competences in the kindergarten. The basic objective was to measure the mathematical competences or mathematical knowledge, skills and abilities in mathematical education. Mathematical competences were grouped in the following areas: Arithmetic and Geometry. Statistical set consisted of 59 children, 65 to 85 months of age, from the Kindergarten Milan Sachs from Zagreb. The authors describe 13 variables for measuring mathematical competences. Five measuring variables were described for the geometry, and eight measuring variables for the arithmetic. Measuring variables are tasks which children solved with the evaluated results. By measuring mathematical competences the authors make causal Bayes model using free software Tetrad 5.2.1-3. Software makes many causal Bayes models and authors as experts chose the model of the mathematical competences in the kindergarten. Causal Bayes model describes five levels for mathematical competences. At the end of the modeling authors use Bayes estimator. In the results, authors describe by causal Bayes model of mathematical competences, causal effect mathematical competences or how intervention on some competences cause other competences. Authors measure mathematical competences with their expectation as random variables. When expectation of competences was greater, competences improved. Mathematical competences can be improved with intervention on causal competences. Levels of mathematical competences and the result of intervention on mathematical competences can help mathematical teachers.
Constraint theory multidimensional mathematical model management
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 modelling of flooding at Magela Creek
International Nuclear Information System (INIS)
Vardavas, I.
1989-01-01
The extent and frequency of the flooding at Magela Creek can be predicted from a mathematical/computer model describing the hydrological phases of surface runoff. Surface runoff involves complex water transfer processes over very inhomogeneous terrain. A simple mathematical model of these has been developed which includes the interception of rainfall by the plant canopy, evapotranspiration, infiltration of surface water into the soil, the storage of water in surface depressions, and overland and subsurface water flow. The rainfall-runoff model has then been incorporated into a more complex computer model to predict the amount of water that enters and leaves the Magela Creek flood plain, downstream of the mine. 2 figs., ills
A mathematical model of embodied consciousness.
Rudrauf, David; Bennequin, Daniel; Granic, Isabela; Landini, Gregory; Friston, Karl; Williford, Kenneth
2017-09-07
We introduce a mathematical model of embodied consciousness, the Projective Consciousness Model (PCM), which is based on the hypothesis that the spatial field of consciousness (FoC) is structured by a projective geometry and under the control of a process of active inference. The FoC in the PCM combines multisensory evidence with prior beliefs in memory and frames them by selecting points of view and perspectives according to preferences. The choice of projective frames governs how expectations are transformed by consciousness. Violations of expectation are encoded as free energy. Free energy minimization drives perspective taking, and controls the switch between perception, imagination and action. In the PCM, consciousness functions as an algorithm for the maximization of resilience, using projective perspective taking and imagination in order to escape local minima of free energy. The PCM can account for a variety of psychological phenomena: the characteristic spatial phenomenology of subjective experience, the distinctions and integral relationships between perception, imagination and action, the role of affective processes in intentionality, but also perceptual phenomena such as the dynamics of bistable figures and body swap illusions in virtual reality. It relates phenomenology to function, showing the computational advantages of consciousness. It suggests that changes of brain states from unconscious to conscious reflect the action of projective transformations and suggests specific neurophenomenological hypotheses about the brain, guidelines for designing artificial systems, and formal principles for psychology. Copyright © 2017 Elsevier Ltd. All rights reserved.
A mathematical model of forgetting and amnesia
Directory of Open Access Journals (Sweden)
Jaap M. J. Murre
2013-02-01
Full Text Available We describe a mathematical model of learning and memory and apply it to the dynamics of forgetting and amnesia. The model is based on the hypothesis that the neural systems involved in memory at different time-scales share two fundamental properties: (1 representations in a store decline in strength (2 while trying to induce new representations in higher-level more permanent stores. This paper addresses several types of experimental and clinical phenomena: (i the temporal gradient of retrograde amnesia (Ribot's Law, (ii forgetting curves with and without anterograde amnesia, and (iii learning and forgetting curves with impaired cortical plasticity. Results are in the form of closed-form expressions that are applied to studies with mice, rats, and monkeys. In order to analyze human data in a quantitative manner, we also derive a relative measure of retrograde amnesia that removes the effects of non-equal item difficulty for different time periods commonly found with clinical retrograde amnesia tests. Using these analytical tools, we review studies of temporal gradients in the memory of patients with Korsakoff's Disease, Alzheimer's Dementia, Huntington's Disease, and other disorders.
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
Models and structures: mathematical physics
International Nuclear Information System (INIS)
2003-01-01
This document gathers research activities along 5 main directions. 1) Quantum chaos and dynamical systems. Recent results concern the extension of the exact WKB method that has led to a host of new results on the spectrum and wave functions. Progress have also been made in the description of the wave functions of chaotic quantum systems. Renormalization has been applied to the analysis of dynamical systems. 2) Combinatorial statistical physics. We see the emergence of new techniques applied to various such combinatorial problems, from random walks to random lattices. 3) Integrability: from structures to applications. Techniques of conformal field theory and integrable model systems have been developed. Progress is still made in particular for open systems with boundary conditions, in connection to strings and branes physics. Noticeable links between integrability and exact WKB quantization to 2-dimensional disordered systems have been highlighted. New correlations of eigenvalues and better connections to integrability have been formulated for random matrices. 4) Gravities and string theories. We have developed aspects of 2-dimensional string theory with a particular emphasis on its connection to matrix models as well as non-perturbative properties of M-theory. We have also followed an alternative path known as loop quantum gravity. 5) Quantum field theory. The results obtained lately concern its foundations, in flat or curved spaces, but also applications to second-order phase transitions in statistical systems
Models and structures: mathematical physics
Energy Technology Data Exchange (ETDEWEB)
NONE
2003-07-01
This document gathers research activities along 5 main directions. 1) Quantum chaos and dynamical systems. Recent results concern the extension of the exact WKB method that has led to a host of new results on the spectrum and wave functions. Progress have also been made in the description of the wave functions of chaotic quantum systems. Renormalization has been applied to the analysis of dynamical systems. 2) Combinatorial statistical physics. We see the emergence of new techniques applied to various such combinatorial problems, from random walks to random lattices. 3) Integrability: from structures to applications. Techniques of conformal field theory and integrable model systems have been developed. Progress is still made in particular for open systems with boundary conditions, in connection to strings and branes physics. Noticeable links between integrability and exact WKB quantization to 2-dimensional disordered systems have been highlighted. New correlations of eigenvalues and better connections to integrability have been formulated for random matrices. 4) Gravities and string theories. We have developed aspects of 2-dimensional string theory with a particular emphasis on its connection to matrix models as well as non-perturbative properties of M-theory. We have also followed an alternative path known as loop quantum gravity. 5) Quantum field theory. The results obtained lately concern its foundations, in flat or curved spaces, but also applications to second-order phase transitions in statistical systems.
mathematical modelling of atmospheric dispersion of pollutants
International Nuclear Information System (INIS)
Mohamed, M.E.
2002-01-01
the main objectives of this thesis are dealing with environmental problems adopting mathematical techniques. in this respect, atmospheric dispersion processes have been investigated by improving the analytical models to realize the realistic physical phenomena. to achieve these aims, the skeleton of this work contained both mathematical and environmental topics,performed in six chapters. in chapter one we presented a comprehensive review study of most important informations related to our work such as thermal stability , plume rise, inversion, advection , dispersion of pollutants, gaussian plume models dealing with both radioactive and industrial contaminants. chapter two deals with estimating the decay distance as well as the decay time of either industrial or radioactive airborne pollutant. further, highly turbulent atmosphere has been investigated as a special case in the three main thermal stability classes namely, neutral, stable, and unstable atmosphere. chapter three is concerned with obtaining maximum ground level concentration of air pollutant. the variable effective height of pollutants has been considered throughout the mathematical treatment. as a special case the constancy of effective height has been derived mathematically and the maximum ground level concentration as well as its location have been established
Mathematical 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.
The stability of colorectal cancer mathematical models
Khairudin, Nur Izzati; Abdullah, Farah Aini
2013-04-01
Colorectal cancer is one of the most common types of cancer. To better understand about the kinetics of cancer growth, mathematical models are used to provide insight into the progression of this natural process which enables physicians and oncologists to determine optimal radiation and chemotherapy schedules and develop a prognosis, both of which are indispensable for treating cancer. This thesis investigates the stability of colorectal cancer mathematical models. We found that continuous saturating feedback is the best available model of colorectal cancer growth. We also performed stability analysis. The result shows that cancer progress in sequence of genetic mutations or epigenetic which lead to a very large number of cells population until become unbounded. The cell population growth initiate and its saturating feedback is overcome when mutation changes causing the net per-capita growth rate of stem or transit cells exceed critical threshold.
Mathematical Models of College Myopia.
Greene, Peter R; Grill, Zachary W; Medina, Antonio
2016-01-01
Experimental design phase of a pilot study at Annapolis is described, using reading glasses, +1.5 D. to +3.0 D. to alleviate college myopia. College students often become 1.0 to 2.0 diopters more myopic, so reading glasses were explored to partially cancel the effects of the study environment. N = 25 different sets of (+)Add lenses are evaluated, for required adjustment period and reading comfort. Three computer models are developed to predict refraction versus time. Basic control system equations predict exponential myopia shift of refractive state R(t) with time constant t0 = 100 days. Linear, exponential and Gompertz computer results are compared calculating refraction R(t) during the college years, showing correlation coefficients |r| = 0.96 to 0.97, accurate +/-0.31 D. over a 14 year interval. Typical college myopia rate is -0.3 to -0.4 D/yr. Reading glasses may be a simple, practical solution to stabilize college myopia.
Mathematical Modelling of Turbidity Currents
Fay, G. L.; Fowler, A.; Howell, P.
2011-12-01
A turbidity current is a submarine sediment flow which propagates downslope through the ocean into the deep sea. Turbidity currents can occur randomly and without much warning and consequently are hard to observe and measure. The driving force in a turbidity current is the presence of sediment in the current - gravity acts on the sediment in suspension, causing it to move downstream through the ocean water. A phenomenon known as ignition or autosuspension has been observed in turbidity currents in submarine canyons, and it occurs when a current travelling downslope gathers speed as it erodes sediment from the sea floor in a self-reinforcing cycle. Using the turbidity current model of Parker et al. (Journal of Fluid Mechanics, 1986) we investigate the evolution of a 1-D turbidity current as it moves downstream. To seek a better understanding of the dynamics of flow as the current evolves in space and time, we present analytical results alongside computed numerical solutions, incorporating entrainment of water and erosion and deposition of sediment. We consider varying slope functions and inlet conditions and attempt to predict when the current will become extinct. We examine currents which are in both supercritical and subcritical flow regimes and consider the dynamics of the flow as the current switches regime.
Implementing the Standards: Incorporating Mathematical Modeling into the Curriculum.
Swetz, Frank
1991-01-01
Following a brief historical review of the mechanism of mathematical modeling, examples are included that associate a mathematical model with given data (changes in sea level) and that model a real-life situation (process of parallel parking). Also provided is the rationale for the curricular implementation of mathematical modeling. (JJK)
Directory of Open Access Journals (Sweden)
Zili Zhang
Full Text Available Bi-objective Traveling Salesman Problem (bTSP is an important field in the operations research, its solutions can be widely applied in the real world. Many researches of Multi-objective Ant Colony Optimization (MOACOs have been proposed to solve bTSPs. However, most of MOACOs suffer premature convergence. This paper proposes an optimization strategy for MOACOs by optimizing the initialization of pheromone matrix with the prior knowledge of Physarum-inspired Mathematical Model (PMM. PMM can find the shortest route between two nodes based on the positive feedback mechanism. The optimized algorithms, named as iPM-MOACOs, can enhance the pheromone in the short paths and promote the search ability of ants. A series of experiments are conducted and experimental results show that the proposed strategy can achieve a better compromise solution than the original MOACOs for solving bTSPs.
Metabolic flux distribution and mathematical models for dynamic ...
African Journals Online (AJOL)
A simple model was build for the metabolic flux determination based on published articles. A method for metabolic flux determination by carbon labeling experiments was described and developed here in the first part of this study that allows mathematical description relating the measured quantities and the intracellular ...
Mathematical modelling : a tool for hospital infection control
Grundmann, H; Hellriegel, B
Health-care-associated infections caused by antibiotic-resistant pathogens have become a menace in hospitals worldwide and infection control measures have lead to vastly different outcomes in different countries. During the past 6 years, a theoretical framework based on mathematical models has
Mathematical modelling: a tool for hospital infection control
Grundmann, Hajo; Hellriegel, B.
2006-01-01
Health-care-associated infections caused by antibiotic-resistant pathogens have become a menace in hospitals worldwide and infection control measures have lead to vastly different outcomes in different countries. During the past 6 years, a theoretical framework based on mathematical models has
Mathematical modelling: a tool for hospital infection control.
Grundmann, Hajo; Hellriegel, B
2006-01-01
Health-care-associated infections caused by antibiotic-resistant pathogens have become a menace in hospitals worldwide and infection control measures have lead to vastly different outcomes in different countries. During the past 6 years, a theoretical framework based on mathematical models has
A mathematical model for stock price forecasting | Ogwuche | West ...
African Journals Online (AJOL)
Many mathematical models of stochastic dynamical systems were based on the assumption that the drift and volatility coefficients were linear function of the solution. In this work, we arrive at the drift and the volatility by observing the dynamics of change in the selected stocks in a sufficiently small interval △t . We assumed ...
Antioxidant Capacity: Experimental Determination by EPR Spectroscopy and Mathematical Modeling.
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 Model of Serodiagnostic Immunochromatographic Assay.
Sotnikov, Dmitriy V; Zherdev, Anatoly V; Dzantiev, Boris B
2017-04-18
This article describes the mathematical model for an immunochromatographic assay for the detection of specific immunoglobulins against a target antigen (antibodies) in blood/serum (serodiagnosis). The model utilizes an analytical (non-numerical) approach and allows the calculation of the kinetics of immune complexes' formation in a continuous-flow system using commonly available software, such as Microsoft Excel. The developed model could identify the nature of the influence of immunochemical interaction constants and reagent concentrations on the kinetics of the formation of the detected target complex. On the basis of the model, recommendations are developed to decrease the detection limit for an immunochromatographic assay of specific immunoglobulins.
Mathematical models of ABE fermentation: review and analysis.
Mayank, Rahul; Ranjan, Amrita; Moholkar, Vijayanand S
2013-12-01
Among different liquid biofuels that have emerged in the recent past, biobutanol produced via fermentation processes is of special interest due to very similar properties to that of gasoline. For an effective design, scale-up, and optimization of the acetone-butanol-ethanol (ABE) fermentation process, it is necessary to have insight into the micro- and macro-mechanisms of the process. The mathematical models for ABE fermentation are efficient tools for this purpose, which have evolved from simple stoichiometric fermentation equations in the 1980s to the recent sophisticated and elaborate kinetic models based on metabolic pathways. In this article, we have reviewed the literature published in the area of mathematical modeling of the ABE fermentation. We have tried to present an analysis of these models in terms of their potency in describing the overall physiology of the process, design features, mode of operation along with comparison and validation with experimental results. In addition, we have also highlighted important facets of these models such as metabolic pathways, basic kinetics of different metabolites, biomass growth, inhibition modeling and other additional features such as cell retention and immobilized cultures. Our review also covers the mathematical modeling of the downstream processing of ABE fermentation, i.e. recovery and purification of solvents through flash distillation, liquid-liquid extraction, and pervaporation. We believe that this review will be a useful source of information and analysis on mathematical models for ABE fermentation for both the appropriate scientific and engineering communities.
Tay, S K; Hsu, T-Y; Pavelyev, A; Walia, A; Kulkarni, A S
2018-03-01
To examine the epidemiological and economic impact of a nine-valent (nonavalent) human papillomavirus (HPV) 6/11/16/18/31/33/45/52/58 vaccine programme for young teenagers in Singapore. Mathematical modelling. Pharmaco-economic simulation projection. Singapore demography. Clinical, epidemiological and financial data from Singapore were used in a validated HPV transmission dynamic mathematical model to analyse the impact of nonavalent HPV vaccination over quadrivalent and bivalent vaccines in a school-based 2-dose vaccination for 11- to 12-year-old girls in the country. The model assumed routine cytology screening in the current rate (50%) and vaccine coverage rate of 80%. Changes over a 100-year time period in the incidence and mortality rates of cervical cancer, case load of genital warts, and incremental cost-effectiveness ratio (ICER). Compared with bivalent and quadrivalent HPV vaccination programmes, nonavalent HPV universal vaccination resulted in an additional reduction of HPV31/33/45/52/58 related CIN1 of 40.5%, CIN 2/3 of 35.4%, cervical cancer of 23.5%, and cervical cancer mortality of 20.2%. Compared with bivalent HPV vaccination, there was an additional reduction in HPV-6/11 related CIN1 of 75.7%, and genital warts of 78.9% in women and 73.4% in men. Over the 100 years, after applying a discount of 3%, disease management cost will be reduced by 32.5% (versus bivalent) and 7.5% (versus quadrivalent). The incremental cost-effectiveness ratio (ICER) per quality-adjusted life-year gained was SGD 929 compared with bivalent vaccination and SGD 9864 compared with quadrivalent vaccination. Universal two-dose nonavalent HPV vaccination for 11- to 12-year-old adolescent women is very cost-effective in Singapore. Nonavalent HPV vaccination of 11- to 12-year-old girls is cost-effective in Singapore. © 2017 Royal College of Obstetricians and Gynaecologists.
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...
Building Mathematical Models of Simple Harmonic and Damped Motion.
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)
Mathematical modeling of vertebrate limb development.
Zhang, Yong-Tao; Alber, Mark S; Newman, Stuart A
2013-05-01
In this paper, we review the major mathematical and computational models of vertebrate limb development and their roles in accounting for different aspects of this process. The main aspects of limb development that have been modeled include outgrowth and shaping of the limb bud, establishment of molecular gradients within the bud, and formation of the skeleton. These processes occur interdependently during development, although (as described in this review), there are various interpretations of the biological relationships among them. A wide range of mathematical and computational methods have been used to study these processes, including ordinary and partial differential equation systems, cellular automata and discrete, stochastic models, finite difference methods, finite element methods, the immersed boundary method, and various combinations of the above. Multiscale mathematical modeling and associated computational simulation have become integrated into the study of limb morphogenesis and pattern formation to an extent with few parallels in the field of developmental biology. These methods have contributed to the design and analysis of experiments employing microsurgical and genetic manipulations, evaluation of hypotheses for limb bud outgrowth, interpretation of the effects of natural mutations, and the formulation of scenarios for the origination and evolution of the limb skeleton. Copyright © 2012 Elsevier Inc. All rights reserved.
Mathematical model for spreading dynamics of social network worms
International Nuclear Information System (INIS)
Sun, Xin; Liu, Yan-Heng; Han, Jia-Wei; Liu, Xue-Jie; Li, Bin; Li, Jin
2012-01-01
In this paper, a mathematical model for social network worm spreading is presented from the viewpoint of social engineering. This model consists of two submodels. Firstly, a human behavior model based on game theory is suggested for modeling and predicting the expected behaviors of a network user encountering malicious messages. The game situation models the actions of a user under the condition that the system may be infected at the time of opening a malicious message. Secondly, a social network accessing model is proposed to characterize the dynamics of network users, by which the number of online susceptible users can be determined at each time step. Several simulation experiments are carried out on artificial social networks. The results show that (1) the proposed mathematical model can well describe the spreading dynamics of social network worms; (2) weighted network topology greatly affects the spread of worms; (3) worms spread even faster on hybrid social networks
Mathematical models of HIV replication and pathogenesis.
Wodarz, Dominik
2014-01-01
This review outlines how mathematical models have been helpful, and continue to be so, for obtaining insights into the in vivo dynamics of HIV infection. The review starts with a discussion of a basic mathematical model that has been frequently used to study HIV dynamics. Some crucial results are described, including the estimation of key parameters that characterize the infection, and the generation of influential theories which argued that in vivo virus evolution is a key player in HIV pathogenesis. Subsequently, more recent concepts are reviewed that have relevance for disease progression, including the multiple infection of cells and the direct cell-to-cell transmission of the virus through the formation of virological synapses. These are important mechanisms that can influence the rate at which HIV spreads through its target cell population, which is tightly linked to the rate at which the disease progresses towards AIDS.
Martins, Ana Margarida; Vera-Licona, Paola; Laubenbacher, Reinhard
2008-01-01
This article describes a mathematical biology workshop given to secondary school teachers of the Danville area in Virginia, USA. The goal of the workshop was to enable teams of teachers with biology and mathematics expertise to incorporate lesson plans in mathematical modelling into the curriculum. The biological focus of the activities is the…
Mathematical modelling of wood and briquettes torrefaction
Energy Technology Data Exchange (ETDEWEB)
Felfli, Felix Fonseca; Luengo, Carlos Alberto [Universidade Estadual de Campinas (UNICAMP), SP (Brazil). Inst. de Fisica Gleb Wataghin. Grupo Combustiveis Alternativos; Soler, Pedro Beaton [Universidad de Oriente, Santiago de Cuba (Cuba). Fac. de Ingenieria Mecanica. Centro de Estudios de Eficiencia Energetica; Rocha, Jose Dilcio [Universidade Estadual de Campinas (UNICAMP), SP (Brazil). Nucleo Interdisciplinar de Planejamento Energetico (NIPE)
2004-07-01
A mathematical model valid for the torrefaction of wood logs and biomass briquettes is presented. The model described both chemical and physical processes, which take place in a moist piece of wood heated at temperatures between 503 and 573 K. Calibration measurements of the temperature profile and mass loss, were performed on dry cylinders of wood samples during torrefaction in an inert atmosphere at 503, 533, and 553 K. The calculated data shows a good agreement with experiments. The model can be a useful tool to estimate projecting and operating parameters for torrefaction furnaces such as minimum time of torrefaction, energy consumption and the mass yield. (author)
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.
IMPROVEMENT OF MATHEMATICAL MODELS FOR ESTIMATION OF TRAIN DYNAMICS
Directory of Open Access Journals (Sweden)
L. V. Ursulyak
2017-12-01
Full Text Available Purpose. Using scientific publications the paper analyzes the mathematical models developed in Ukraine, CIS countries and abroad for theoretical studies of train dynamics and also shows the urgency of their further improvement. Methodology. Information base of the research was official full-text and abstract databases, scientific works of domestic and foreign scientists, professional periodicals, materials of scientific and practical conferences, methodological materials of ministries and departments. Analysis of publications on existing mathematical models used to solve a wide range of problems associated with the train dynamics study shows the expediency of their application. Findings. The results of these studies were used in: 1 design of new types of draft gears and air distributors; 2 development of methods for controlling the movement of conventional and connected trains; 3 creation of appropriate process flow diagrams; 4 development of energy-saving methods of train driving; 5 revision of the Construction Codes and Regulations (SNiP ΙΙ-39.76; 6 when selecting the parameters of the autonomous automatic control system, created in DNURT, for an auxiliary locomotive that is part of a connected train; 7 when creating computer simulators for the training of locomotive drivers; 8 assessment of the vehicle dynamic indices characterizing traffic safety. Scientists around the world conduct numerical experiments related to estimation of train dynamics using mathematical models that need to be constantly improved. Originality. The authors presented the main theoretical postulates that allowed them to develop the existing mathematical models for solving problems related to the train dynamics. The analysis of scientific articles published in Ukraine, CIS countries and abroad allows us to determine the most relevant areas of application of mathematical models. Practicalvalue. The practical value of the results obtained lies in the scientific validity
Learning to teach mathematical modelling in secondary and tertiary education
Ferri, Rita Borromeo
2017-07-01
Since 2003 mathematical modelling in Germany is not only a topic for scientific disciplines in university mathematics courses, but also in school starting with primary school. This paper shows what mathematical modelling means in school and how it can be taught as a basis for complex modeling problems in tertiary education.
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 Models and the Experimental Analysis of Behavior
Mazur, James E.
2006-01-01
The use of mathematical models in the experimental analysis of behavior has increased over the years, and they offer several advantages. Mathematical models require theorists to be precise and unambiguous, often allowing comparisons of competing theories that sound similar when stated in words. Sometimes different mathematical models may make…
A Computational and Mathematical Model for Device Induced Thrombosis
Wu, Wei-Tao; Aubry, Nadine; Massoudi, Mehrdad; Antaki, James
2015-11-01
Based on the Sorenson's model of thrombus formation, a new mathematical model describing the process of thrombus growth is developed. In this model the blood is treated as a Newtonian fluid, and the transport and reactions of the chemical and biological species are modeled using CRD (convection-reaction-diffusion) equations. A computational fluid dynamic (CFD) solver for the mathematical model is developed using the libraries of OpenFOAM. Applying the CFD solver, several representative benchmark problems are studied: rapid thrombus growth in vivo by injecting Adenosine diphosphate (ADP) using iontophoretic method and thrombus growth in rectangular microchannel with a crevice which usually appears as a joint between components of devices and often becomes nidus of thrombosis. Very good agreements between the numerical and the experimental results validate the model and indicate its potential to study a host of complex and practical problems in the future, such as thrombosis in blood pumps and artificial lungs.
Unlocking the black box: teaching mathematical modeling with popular culture.
Lofgren, Eric T
2016-10-01
Mathematical modeling is an important tool in biological research, allowing for the synthesis of results from many studies into an understanding of a system. Despite this, the need for extensive subject matter knowledge and complex mathematics often leaves modeling as an esoteric subspecialty. A 2-fold approach can be used to make modeling more approachable for students and those interested in obtaining a functional knowledge of modeling. The first is the use of a popular culture disease system-a zombie epidemic-to allow for exploration of the concepts of modeling using a flexible framework. The second is the use of available interactive and non-calculus-based tools to allow students to work with and implement models to cement their understanding. © FEMS 2016. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.
Preservice Mathematics Teachers' Perceptions of Drama Based Instruction
Bulut, Neslihan
2016-01-01
The purpose of this study was to determine the perceptions of pre-service mathematics teachers related to drama-based instruction. For this purpose, effects of a drama-based mathematics course on senior class pre-service mathematics teachers' knowledge about drama-based instruction and teacher candidates' competencies for developing and…
Directory of Open Access Journals (Sweden)
Maria eArepeva
2015-04-01
Full Text Available Acquired bacterial resistance is one of the causes of mortality and morbidity from infectious diseases. Mathematical modeling allows us to predict the spread of resistance and to some extent to control its dynamics. The purpose of this review was to examine existing mathematical models in order to understand pros and cons of currently used approaches and to build our own model. During the analysis, seven articles about the mathematical approaches to studying resistance that satisfied the inclusion / exclusion criteria were selected. All models were classified according to the approach used to study resistance in the presence of antibiotic and were analyzed in terms of our research. Some models require modifications associated with the specific of the research. Further work plan of model building is as follows: modify some models, according to our research, check all obtained models on our data, and select the optimal model or several models with the best quality of prediction. After that we would be able to build a model for the development of resistance using the obtained results.
Mathematical Model of Nicholson’s Experiment
Directory of Open Access Journals (Sweden)
Sergey D. Glyzin
2017-01-01
Full Text Available Considered is a mathematical model of insects population dynamics, and an attempt is made to explain classical experimental results of Nicholson with its help. In the first section of the paper Nicholson’s experiment is described and dynamic equations for its modeling are chosen. A priori estimates for model parameters can be made more precise by means of local analysis of the dynamical system, that is carried out in the second section. For parameter values found there the stability loss of the problem equilibrium of the leads to the bifurcation of a stable two-dimensional torus. Numerical simulations based on the estimates from the second section allows to explain the classical Nicholson’s experiment, whose detailed theoretical substantiation is given in the last section. There for an atrractor of the system the largest Lyapunov exponent is computed. The nature of this exponent change allows to additionally narrow the area of model parameters search. Justification of this experiment was made possible only due to the combination of analytical and numerical methods in studying equations of insects population dynamics. At the same time, the analytical approach made it possible to perform numerical analysis in a rather narrow region of the parameter space. It is not possible to get into this area, based only on general considerations.
Laser filamentation mathematical methods and models
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...
Thermoregulation in premature infants: A mathematical model.
Pereira, Carina Barbosa; Heimann, Konrad; Czaplik, Michael; Blazek, Vladimir; Venema, Boudewijn; Leonhardt, Steffen
2016-12-01
In 2010, approximately 14.9 million babies (11.1%) were born preterm. Because preterm infants suffer from an immature thermoregulatory system they have difficulty maintaining their core body temperature at a constant level. Therefore, it is essential to maintain their temperature at, ideally, around 37°C. For this, mathematical models can provide detailed insight into heat transfer processes and body-environment interactions for clinical applications. A new multi-node mathematical model of the thermoregulatory system of newborn infants is presented. It comprises seven compartments, one spherical and six cylindrical, which represent the head, thorax, abdomen, arms and legs, respectively. The model is customizable, i.e. it meets individual characteristics of the neonate (e.g. gestational age, postnatal age, weight and length) which play an important role in heat transfer mechanisms. The model was validated during thermal neutrality and in a transient thermal environment. During thermal neutrality the model accurately predicted skin and core temperatures. The difference in mean core temperature between measurements and simulations averaged 0.25±0.21°C and that of skin temperature averaged 0.36±0.36°C. During transient thermal conditions, our approach simulated the thermoregulatory dynamics/responses. Here, for all infants, the mean absolute error between core temperatures averaged 0.12±0.11°C and that of skin temperatures hovered around 0.30°C. The mathematical model appears able to predict core and skin temperatures during thermal neutrality and in case of a transient thermal conditions. Copyright Â© 2016 Elsevier Ltd. All rights reserved.
Mathematical models for atmospheric pollutants. Final report
International Nuclear Information System (INIS)
Drake, R.L.; Barrager, S.M.
1979-08-01
The present and likely future roles of mathematical modeling in air quality decisions are described. The discussion emphasizes models and air pathway processes rather than the chemical and physical behavior of specific anthropogenic emissions. Summarized are the characteristics of various types of models used in the decision-making processes. Specific model subclasses are recommended for use in making air quality decisions that have site-specific, regional, national, or global impacts. The types of exposure and damage models that are currently used to predict the effects of air pollutants on humans, other animals, plants, ecosystems, property, and materials are described. The aesthetic effects of odor and visibility and the impact of pollutants on weather and climate are also addressed. Technical details of air pollution meteorology, chemical and physical properties of air pollutants, solution techniques, and air quality models are discussed in four appendices bound in separate volumes
Mathematical models of human african trypanosomiasis epidemiology.
Rock, Kat S; Stone, Chris M; Hastings, Ian M; Keeling, Matt J; Torr, Steve J; Chitnis, Nakul
2015-03-01
Human African trypanosomiasis (HAT), commonly called sleeping sickness, is caused by Trypanosoma spp. and transmitted by tsetse flies (Glossina spp.). HAT is usually fatal if untreated and transmission occurs in foci across sub-Saharan Africa. Mathematical modelling of HAT began in the 1980s with extensions of the Ross-Macdonald malaria model and has since consisted, with a few exceptions, of similar deterministic compartmental models. These models have captured the main features of HAT epidemiology and provided insight on the effectiveness of the two main control interventions (treatment of humans and tsetse fly control) in eliminating transmission. However, most existing models have overestimated prevalence of infection and ignored transient dynamics. There is a need for properly validated models, evolving with improved data collection, that can provide quantitative predictions to help guide control and elimination strategies for HAT. Copyright © 2015 Elsevier Ltd. All rights reserved.
A mathematical model of 'Pride and Prejudice'.
Rinaldi, Sergio; Rossa, Fabio Della; Landi, Pietro
2014-04-01
A mathematical model is proposed for interpreting the love story between Elizabeth and Darcy portrayed by Jane Austen in the popular novel Pride and Prejudice. The analysis shows that the story is characterized by a sudden explosion of sentimental involvements, revealed by the existence of a saddle-node bifurcation in the model. The paper is interesting not only because it deals for the first time with catastrophic bifurcations in romantic relation-ships, but also because it enriches the list of examples in which love stories are described through ordinary differential equations.
Mathematical methods and models in composites
Mantic, Vladislav
2014-01-01
This book provides a representative selection of the most relevant, innovative, and useful mathematical methods and models applied to the analysis and characterization of composites and their behaviour on micro-, meso-, and macroscale. It establishes the fundamentals for meaningful and accurate theoretical and computer modelling of these materials in the future. Although the book is primarily concerned with fibre-reinforced composites, which have ever-increasing applications in fields such as aerospace, many of the results presented can be applied to other kinds of composites. The topics cover
Andriani, Ade; Dewi, Izwita; Halomoan, Budi
2018-03-01
In general, this research is conducted to improve the quality of lectures on mathematics learning strategy in Mathematics Department. The specific objective of this research is to develop learning instrument of mathematics learning strategy based on Higher Order Thinking Skill (HOTS) that can be used to improve mathematical communication and self efficacy of mathematics education students. The type of research is development research (Research & Development), where this research aims to develop a new product or improve the product that has been made. This development research refers to the four-D Model, which consists of four stages: defining, designing, developing, and disseminating. The instrument of this research is the validation sheet and the student response sheet of the instrument.
An introduction to mathematical modeling of infectious diseases
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.
Declarative representation of uncertainty in mathematical models.
Miller, Andrew K; Britten, Randall D; Nielsen, Poul M F
2012-01-01
An important aspect of multi-scale modelling is the ability to represent mathematical models in forms that can be exchanged between modellers and tools. While the development of languages like CellML and SBML have provided standardised declarative exchange formats for mathematical models, independent of the algorithm to be applied to the model, to date these standards have not provided a clear mechanism for describing parameter uncertainty. Parameter uncertainty is an inherent feature of many real systems. This uncertainty can result from a number of situations, such as: when measurements include inherent error; when parameters have unknown values and so are replaced by a probability distribution by the modeller; when a model is of an individual from a population, and parameters have unknown values for the individual, but the distribution for the population is known. We present and demonstrate an approach by which uncertainty can be described declaratively in CellML models, by utilising the extension mechanisms provided in CellML. Parameter uncertainty can be described declaratively in terms of either a univariate continuous probability density function or multiple realisations of one variable or several (typically non-independent) variables. We additionally present an extension to SED-ML (the Simulation Experiment Description Markup Language) to describe sampling sensitivity analysis simulation experiments. We demonstrate the usability of the approach by encoding a sample model in the uncertainty markup language, and by developing a software implementation of the uncertainty specification (including the SED-ML extension for sampling sensitivty analyses) in an existing CellML software library, the CellML API implementation. We used the software implementation to run sampling sensitivity analyses over the model to demonstrate that it is possible to run useful simulations on models with uncertainty encoded in this form.
Declarative representation of uncertainty in mathematical models.
Directory of Open Access Journals (Sweden)
Andrew K Miller
Full Text Available An important aspect of multi-scale modelling is the ability to represent mathematical models in forms that can be exchanged between modellers and tools. While the development of languages like CellML and SBML have provided standardised declarative exchange formats for mathematical models, independent of the algorithm to be applied to the model, to date these standards have not provided a clear mechanism for describing parameter uncertainty. Parameter uncertainty is an inherent feature of many real systems. This uncertainty can result from a number of situations, such as: when measurements include inherent error; when parameters have unknown values and so are replaced by a probability distribution by the modeller; when a model is of an individual from a population, and parameters have unknown values for the individual, but the distribution for the population is known. We present and demonstrate an approach by which uncertainty can be described declaratively in CellML models, by utilising the extension mechanisms provided in CellML. Parameter uncertainty can be described declaratively in terms of either a univariate continuous probability density function or multiple realisations of one variable or several (typically non-independent variables. We additionally present an extension to SED-ML (the Simulation Experiment Description Markup Language to describe sampling sensitivity analysis simulation experiments. We demonstrate the usability of the approach by encoding a sample model in the uncertainty markup language, and by developing a software implementation of the uncertainty specification (including the SED-ML extension for sampling sensitivty analyses in an existing CellML software library, the CellML API implementation. We used the software implementation to run sampling sensitivity analyses over the model to demonstrate that it is possible to run useful simulations on models with uncertainty encoded in this form.
Mathematical Modeling of an Oscillating Droplet
Berry, S.; Hyers, R. W.; Racz, L. M.; Abedian, B.; Rose, M. Franklin (Technical Monitor)
2000-01-01
Oscillating droplets are of interest in a number of disciplines. A practical application is the oscillating drop method, which is a technique for measuring surface tension and viscosity of liquid metals. It is especially suited to undercooled and highly reactive metals, because it is performed by electromagnetic levitation. The natural oscillation frequency of the droplets is related to the surface tension of the material, and the decay of oscillations is related to its viscosity. The fluid flow inside the droplet must be laminar in order for this technique to yield good results. Because no experimental method has yet been developed to visualize flow in electromagnetically-levitated oscillating metal droplets, mathematical modeling is required to determine whether or not turbulence occurs. Three mathematical models of the flow: (1) assuming laminar conditions, (2) using the k-epsilon turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity.
Development of a Multidisciplinary Middle School Mathematics Infusion Model
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…
Assessment of Primary 5 Students' Mathematical Modelling Competencies
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…
Assessing Children's Mathematical Thinking in Practical Modelling Situations.
Tanner, Howard; Jones, Sonia
2002-01-01
Investigates the use of mathematical modeling tasks in 11- and 12-year-old students and the development of mathematical thinking skills using practical modeling activities. Analyzes the development of students' mathematical thinking with interviews of a form of dynamic assessment. Reports that some students proved to be naturally mindful and…
Exploring the Relationship between Mathematical Modelling and Classroom Discourse
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…
Directory of Open Access Journals (Sweden)
Orekhov Vyacheslav Valentinovich
Full Text Available The interaction process of a power plant building with the soil base is studied basing on mathematical modeling of the construction process of Kambarata-2 HPP, taking into account the excavation of foundation pit, the concreting schedule of the building construction, the HPP units putting into operation and territory planning. Mathematical modeling of stress-strain state of the system “power plant - soil base” in the process of construction was performed by using the computer program “Zemlya” (the Earth, which implements the method of finite elements. Such a behavior of soil was described using elastoplastic soil model, the parameters of which were determined from the results of the triaxial tests. As shown by the results of the research, the continuous change of settlement, slope, deflection and torsion of the bottom plate and accordingly change of stressed-strained state of power plant are noted during the construction process. The installed HPP construction schedule, starting from the construction of the first block and the adjacent mounting platform, is leading to the formation of initial roll of bottom plate to the path of the mounting pad. In the process of further construction of powerhouse, up to the 29th phase of construction (out of 40, a steady increase in its subsidence (maximum values of about 4.5 cm is noted. Filling of foundation pit hollows and territorial planning of the construction area lead to drastic situation. In this case, as a territory planning points exceeded the relief, the plastic deformation in the soil evolves, resulting in significant subsidence of the bottom plate under the first block (up to 7.4 cm. As a result, the additional subsidence of the soil of bottom plate edges lead to the large vertical movement in relation to its central part and it is bent around the X axis, resulting in a large horizontal tensile stress values of Sz (up to 2.17 MPa in the constructive elements of the upper part of the
Modelling of and Conjecturing on a Soccer Ball in a Korean Eighth Grade Mathematics Classroom
Lee, Kyeong-Hwa
2011-01-01
The purpose of this article was to describe the task design and implementation of cultural artefacts in a mathematics lesson based on the integration of modelling and conjecturing perspectives. The conceived process of integrating a soccer ball into mathematics lessons via modelling- and conjecturing-based instruction was first detailed. Next, the…
Determining of the Optimal Device Lifetime using Mathematical Renewal Models
Directory of Open Access Journals (Sweden)
Knežo Dušan
2016-05-01
Full Text Available Paper deals with the operations and equipment of the machine in the process of organizing production. During operation machines require maintenance and repairs, while in case of failure or machine wears it is necessary to replace them with new ones. For the process of replacement of old machines with new ones the term renewal is used. Qualitative aspects of the renewal process observe renewal theory, which is mainly based on the theory of probability and mathematical statistics. Devices lifetimes are closely related to the renewal of the devices. Presented article is focused on mathematical deduction of mathematical renewal models and determining optimal lifetime of the devices from the aspect of expenditures on renewal process.
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.
A Mathematical Model of Cardiovascular Response to Dynamic Exercise
National Research Council Canada - National Science Library
Magosso, E
2001-01-01
A mathematical model of cardiovascular response to dynamic exercise is presented, The model includes the pulsating heart, the systemic and pulmonary, circulation, a functional description of muscle...
Mathematical model of the Amazon Stirling engine
Energy Technology Data Exchange (ETDEWEB)
Vidal Medina, Juan Ricardo [Universidad Autonoma de Occidente (Colombia)], e-mail: jrvidal@uao.edu.co; Cobasa, Vladimir Melian; Silva, Electo [Universidade Federal de Itajuba, MG (Brazil)], e-mail: vlad@unifei.edu.br
2010-07-01
The Excellency Group in Thermoelectric and Distributed Generation (NEST, for its acronym in Portuguese) at the Federal University of Itajuba, has designed a Stirling engine prototype to provide electricity to isolated regions of Brazil. The engine was designed to operate with residual biomass from timber process. This paper presents mathematical models of heat exchangers (hot, cold and regenerator) integrated into second order adiabatic models. The general model takes into account the pressure drop losses, hysteresis and internal losses. The results of power output, engine efficiency, optimal velocity of the exhaust gases and the influence of dead volume in engine efficiency are presented in this paper. The objective of this modeling is to propose improvements to the manufactured engine design. (author)
Yan, Lincan; Zhou, Chenming; Reyes, Miguel; Whisner, Bruce; Damiano, Nicholas
2017-01-01
There are two types of through-the-earth (TTE) wireless communication in the mining industry: magnetic loop TTE and electrode-based (or linear) TTE. While the magnetic loop systems send signal through magnetic fields, the transmitter of an electrode-based TTE system sends signal directly through the mine overburden by driving an extremely low frequency (ELF) or ultralow frequency (ULF) AC current into the earth. The receiver at the other end (underground or surface) detects the resultant curr...
Mathematical modeling to predict residential solid waste generation.
Benítez, Sara Ojeda; Lozano-Olvera, Gabriela; Morelos, Raúl Adalberto; Vega, Carolina Armijo de
2008-01-01
One of the challenges faced by waste management authorities is determining the amount of waste generated by households in order to establish waste management systems, as well as trying to charge rates compatible with the principle applied worldwide, and design a fair payment system for households according to the amount of residential solid waste (RSW) they generate. The goal of this research work was to establish mathematical models that correlate the generation of RSW per capita to the following variables: education, income per household, and number of residents. This work was based on data from a study on generation, quantification and composition of residential waste in a Mexican city in three stages. In order to define prediction models, five variables were identified and included in the model. For each waste sampling stage a different mathematical model was developed, in order to find the model that showed the best linear relation to predict residential solid waste generation. Later on, models to explore the combination of included variables and select those which showed a higher R(2) were established. The tests applied were normality, multicolinearity and heteroskedasticity. Another model, formulated with four variables, was generated and the Durban-Watson test was applied to it. Finally, a general mathematical model is proposed to predict residential waste generation, which accounts for 51% of the total.
Mathematical Modeling of Diaphragm Pneumatic Motors
Directory of Open Access Journals (Sweden)
Fojtášek Kamil
2014-03-01
Full Text Available Pneumatic diaphragm motors belong to the group of motors with elastic working parts. This part is usually made of rubber with a textile insert and it is deformed under the pressure of a compressed air or from the external mass load. This is resulting in a final working effect. In this type of motors are in contact two different elastic environments – the compressed air and the esaltic part. These motors are mainly the low-stroke and working with relatively large forces. This paper presents mathematical modeling static properties of diaphragm motors.
Mathematics of tsunami: modelling and identification
Krivorotko, Olga; Kabanikhin, Sergey
2015-04-01
Tsunami (long waves in the deep water) motion caused by underwater earthquakes is described by shallow water equations ( { ηtt = div (gH (x,y)-gradη), (x,y) ∈ Ω, t ∈ (0,T ); η|t=0 = q(x,y), ηt|t=0 = 0, (x,y) ∈ Ω. ( (1) Bottom relief H(x,y) characteristics and the initial perturbation data (a tsunami source q(x,y)) are required for the direct simulation of tsunamis. The main difficulty problem of tsunami modelling is a very big size of the computational domain (Ω = 500 × 1000 kilometres in space and about one hour computational time T for one meter of initial perturbation amplitude max|q|). The calculation of the function η(x,y,t) of three variables in Ω × (0,T) requires large computing resources. We construct a new algorithm to solve numerically the problem of determining the moving tsunami wave height S(x,y) which is based on kinematic-type approach and analytical representation of fundamental solution. Proposed algorithm of determining the function of two variables S(x,y) reduces the number of operations in 1.5 times than solving problem (1). If all functions does not depend on the variable y (one dimensional case), then the moving tsunami wave height satisfies of the well-known Airy-Green formula: S(x) = S(0)° --- 4H (0)/H (x). The problem of identification parameters of a tsunami source using additional measurements of a passing wave is called inverse tsunami problem. We investigate two different inverse problems of determining a tsunami source q(x,y) using two different additional data: Deep-ocean Assessment and Reporting of Tsunamis (DART) measurements and satellite altimeters wave-form images. These problems are severely ill-posed. The main idea consists of combination of two measured data to reconstruct the source parameters. We apply regularization techniques to control the degree of ill-posedness such as Fourier expansion, truncated singular value decomposition, numerical regularization. The algorithm of selecting the truncated number of
Directory of Open Access Journals (Sweden)
Jones Anne E
2011-02-01
Full Text Available Abstract Background A warm and humid climate triggers several water-associated diseases such as malaria. Climate- or weather-driven malaria models, therefore, allow for a better understanding of malaria transmission dynamics. The Liverpool Malaria Model (LMM is a mathematical-biological model of malaria parasite dynamics using daily temperature and precipitation data. In this study, the parameter settings of the LMM are refined and a new mathematical formulation of key processes related to the growth and size of the vector population are developed. Methods One of the most comprehensive studies to date in terms of gathering entomological and parasitological information from the literature was undertaken for the development of a new version of an existing malaria model. The knowledge was needed to allow the justification of new settings of various model parameters and motivated changes of the mathematical formulation of the LMM. Results The first part of the present study developed an improved set of parameter settings and mathematical formulation of the LMM. Important modules of the original LMM version were enhanced in order to achieve a higher biological and physical accuracy. The oviposition as well as the survival of immature mosquitoes were adjusted to field conditions via the application of a fuzzy distribution model. Key model parameters, including the mature age of mosquitoes, the survival probability of adult mosquitoes, the human blood index, the mosquito-to-human (human-to-mosquito transmission efficiency, the human infectious age, the recovery rate, as well as the gametocyte prevalence, were reassessed by means of entomological and parasitological observations. This paper also revealed that various malaria variables lack information from field studies to be set properly in a malaria modelling approach. Conclusions Due to the multitude of model parameters and the uncertainty involved in the setting of parameters, an extensive
Mathematical modeling of infectious disease dynamics.
Siettos, Constantinos I; Russo, Lucia
2013-05-15
Over the last years, an intensive worldwide effort is speeding up the developments in the establishment of a global surveillance network for combating pandemics of emergent and re-emergent infectious diseases. Scientists from different fields extending from medicine and molecular biology to computer science and applied mathematics have teamed up for rapid assessment of potentially urgent situations. Toward this aim mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. To better understand and model the contagious dynamics the impact of numerous variables ranging from the micro host-pathogen level to host-to-host interactions, as well as prevailing ecological, social, economic, and demographic factors across the globe have to be analyzed and thoroughly studied. Here, we present and discuss the main approaches that are used for the surveillance and modeling of infectious disease dynamics. We present the basic concepts underpinning their implementation and practice and for each category we give an annotated list of representative works.
Mathematical modeling of tornadoes and squall storms
Directory of Open Access Journals (Sweden)
Sergey A. Arsen’yev
2011-04-01
Full Text Available Recent advances in modeling of tornadoes and twisters consist of significant achievements in mathematical calculation of occurrence and evolution of a violent F5-class tornado on the Fujita scale, and four-dimensional mathematical modeling of a tornado with the fourth coordinate time multiplied by its characteristic velocity. Such a tornado can arise in a thunderstorm supercell filled with turbulent whirlwinds. A theory of the squall storms is proposed. The squall storm is modeled by running perturbation of the temperature inversion on the lower boundary of cloudiness. This perturbation is induced by the action of strong, hurricane winds in the upper and middle troposphere, and looks like a running solitary wave (soliton; which is developed also in a field of pressure and velocity of a wind. If a soliton of a squall storm gets into the thunderstorm supercell then this soliton is captured by supercell. It leads to additional pressure fall of air inside a storm supercell and stimulate amplification of wind velocity here. As a result, a cyclostrophic balance inside a storm supercell generates a tornado. Comparison of the radial distribution of wind velocity inside a tornado calculated by using the new formulas and equations with radar observations of the wind velocity inside Texas Tornado Dummit in 1995 and inside the 3 May 1999 Oklahoma City Tornado shows good correspondence.
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.
[Three dimensional mathematical model of tooth for finite element analysis].
Puskar, Tatjana; Vasiljević, Darko; Marković, Dubravka; Jevremović, Danimir; Pantelić, Dejan; Savić-Sević, Svetlana; Murić, Branka
2010-01-01
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. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analysing 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. 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. 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.
Velocity of detonation-a mathematical model.
Türker, Lemi
2010-06-01
Based on the principles of conservation of energy and momentum, a mathematical formula has been derived for the squares of detonation velocities of a large set of explosives. The equation is a function of the total energy and molecular weight of an explosive compound considered. A regressed equation has been obtained for a pool of explosives of various types including nitramines, aliphatic and aromatic nitro compounds. Also another regressed equation for nitramines only is given. For the regression, the total energies are obtained using DFT (UB3LYP/6-31G(d)). The regression statistics are given and discussed.
Ma, Jianlong; Pan, Hui; Zeng, Yan; Lv, Yehui; Zhang, Heng; Xue, Aimin; Jiang, Jieqing; Ma, Kaijun; Chen, Long
2015-12-01
Precise estimation of postmortem interval (PMI) is crucial in some criminal cases. This study aims to find some optimal markers for PMI estimation and build a mathematical model that could be used in various temperature conditions. Different mRNA and microRNA markers in rat brain samples were detected using real-time fluorescent quantitative PCR at 12 time points within 144 h postmortem and at temperatures of 4, 15, 25, and 35 °C. Samples from 36 other rats were used to verify the animal mathematical model. Brain-specific mir-9 and mir-125b are effective endogenous control markers that are not affected by PMI up to 144 h postmortem under these temperatures, whereas the commonly used U6 is not a suitable endogenous control in this study. Among all the candidate markers, ΔCt (β-actin) has the best correlation coefficient with PMI and was used to build a new model using R software which can simultaneously manage both PMI and temperature parameters. This animal mathematical model is verified using samples from 36 other rats and shows increased accuracy for higher temperatures and longer PMI. In this study, β-actin was found to be an optimal marker to estimate PMI and some other markers were found to be suitable to act as endogenous controls. Additionally, we have used R code software to build a model of PMI estimation that could be used in various temperature conditions.
Energy Technology Data Exchange (ETDEWEB)
Thiele, Ines; Hyduke, Daniel R.; Steeb, Benjamin; Fankam, Guy; Allen, Douglas K.; Bazzani, Susanna; Charusanti, Pep; Chen, Feng-Chi; Fleming, Ronan MT; Hsiung, Chao A.; De Keersmaecker, Sigrid CJ; Liao, Yu-Chieh; Marchal, Kathleen; Mo, Monica L.; Özdemir, Emre; Raghunathan, Anu; Reed, Jennifer L.; Shin, Sook-Il; Sigurbjörnsdóttir, Sara; Steinmann, Jonas; Sudarsan, Suresh; Swainston, Neil; Thijs, Inge M.; Zengler, Karsten; Palsson, Bernhard O.; Adkins, Joshua N.; Bumann, Dirk
2011-01-01
Metabolic reconstructions (MRs) are common denominators in systems biology and represent biochemical, genetic, and genomic (BiGG) knowledge-bases for target organisms by capturing currently available information in a consistent, structured manner. Salmonella enterica subspecies I serovar Typhimurium is a human pathogen, causes various diseases and its increasing antibiotic resistance poses a public health problem. Here, we describe a community-driven effort, in which more than 20 experts in S. Typhimurium biology and systems biology collaborated to reconcile and expand the S. Typhimurium BiGG knowledge-base. The consensus MR was obtained starting from two independently developed MRs for S. Typhimurium. Key results of this reconstruction jamboree include i) development and implementation of a community-based workflow for MR annotation and reconciliation; ii) incorporation of thermodynamic information; and iii) use of the consensus MR to identify potential multi-target drug therapy approaches. Finally, taken together, with the growing number of parallel MRs a structured, community-driven approach will be necessary to maximize quality while increasing adoption of MRs in experimental design and interpretation.
Comparison of Different Mathematical Models of Cavitation
Directory of Open Access Journals (Sweden)
Dorota HOMA
2014-12-01
Full Text Available Cavitation occurs during the flow when local pressure drops to the saturation pressure according to the temperature of the flow. It includes both evaporation and condensation of the vapor bubbles, which occur alternately with high frequency. Cavitation can be very dangerous, especially for pumps, because it leads to break of flow continuity, noise, vibration, erosion of blades and change in pump’s characteristics. Therefore it is very important for pump designers and users to avoid working in cavitation conditions. Simulation of flow can be very useful in that and can indicate if there is risk of cavitating flow occurrence. As this is a multiphase flow and quite complicated phenomena, there are a few mathematical models describing it. The aim of this paper is to make a short review of them and describe their approach to model cavitation. It is desirable to know differences between them to model this phenomenon properly.
Mathematical modeling of the Phoenix Rising pathway.
Directory of Open Access Journals (Sweden)
Chad Liu
2014-02-01
Full Text Available Apoptosis is a tightly controlled process in mammalian cells. It is important for embryogenesis, tissue homoeostasis, and cancer treatment. Apoptosis not only induces cell death, but also leads to the release of signals that promote rapid proliferation of surrounding cells through the Phoenix Rising (PR pathway. To quantitatively understand the kinetics of interactions of different molecules in this pathway, we developed a mathematical model to simulate the effects of various changes in the PR pathway on the secretion of prostaglandin E2 (PGE2, a key factor for promoting cell proliferation. These changes include activation of caspase 3 (C3, caspase 7 (C7, and nuclear factor κB (NFκB. In addition, we simulated the effects of cyclooxygenase-2 (COX2 inhibition and C3 knockout on the level of secreted PGE2. The model predictions on PGE2 in MEF and 4T1 cells at 48 hours after 10-Gray radiation were quantitatively consistent with the experimental data in the literature. Compared to C7, the model predicted that C3 activation was more critical for PGE2 production. The model also predicted that PGE2 production could be significantly reduced when COX2 expression was blocked via either NFκB inactivation or treatment of cells with exogenous COX2 inhibitors, which led to a decrease in the rate of conversion from arachidonic acid to prostaglandin H2 in the PR pathway. In conclusion, the mathematical model developed in this study yielded new insights into the process of tissue regrowth stimulated by signals from apoptotic cells. In future studies, the model can be used for experimental data analysis and assisting development of novel strategies/drugs for improving cancer treatment or normal tissue regeneration.
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…
Lin, Z; Gehring, R; Mochel, J P; Lavé, T; Riviere, J E
2016-10-01
This review provides a tutorial for individuals interested in quantitative veterinary pharmacology and toxicology and offers a basis for establishing guidelines for physiologically based pharmacokinetic (PBPK) model development and application in veterinary medicine. This is important as the application of PBPK modeling in veterinary medicine has evolved over the past two decades. PBPK models can be used to predict drug tissue residues and withdrawal times in food-producing animals, to estimate chemical concentrations at the site of action and target organ toxicity to aid risk assessment of environmental contaminants and/or drugs in both domestic animals and wildlife, as well as to help design therapeutic regimens for veterinary drugs. This review provides a comprehensive summary of PBPK modeling principles, model development methodology, and the current applications in veterinary medicine, with a focus on predictions of drug tissue residues and withdrawal times in food-producing animals. The advantages and disadvantages of PBPK modeling compared to other pharmacokinetic modeling approaches (i.e., classical compartmental/noncompartmental modeling, nonlinear mixed-effects modeling, and interspecies allometric scaling) are further presented. The review finally discusses contemporary challenges and our perspectives on model documentation, evaluation criteria, quality improvement, and offers solutions to increase model acceptance and applications in veterinary pharmacology and toxicology. © 2016 John Wiley & Sons Ltd.
Mathematical model of highways network optimization
Sakhapov, R. L.; Nikolaeva, R. V.; Gatiyatullin, M. H.; Makhmutov, M. M.
2017-12-01
The article deals with the issue of highways network design. Studies show that the main requirement from road transport for the road network is to ensure the realization of all the transport links served by it, with the least possible cost. The goal of optimizing the network of highways is to increase the efficiency of transport. It is necessary to take into account a large number of factors that make it difficult to quantify and qualify their impact on the road network. In this paper, we propose building an optimal variant for locating the road network on the basis of a mathematical model. The article defines the criteria for optimality and objective functions that reflect the requirements for the road network. The most fully satisfying condition for optimality is the minimization of road and transport costs. We adopted this indicator as a criterion of optimality in the economic-mathematical model of a network of highways. Studies have shown that each offset point in the optimal binding road network is associated with all other corresponding points in the directions providing the least financial costs necessary to move passengers and cargo from this point to the other corresponding points. The article presents general principles for constructing an optimal network of roads.
Preparing Secondary Mathematics Teachers: A Focus on Modeling in Algebra
Jung, Hyunyi; Mintos, Alexia; Newton, Jill
2015-01-01
This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities.…
Mathematical Model of the Jet Engine Fuel System
Directory of Open Access Journals (Sweden)
Klimko Marek
2015-01-01
Full Text Available The paper discusses the design of a simplified mathematical model of the jet (turbo-compressor engine fuel system. The solution will be based on the regulation law, where the control parameter is a fuel mass flow rate and the regulated parameter is the rotational speed. A differential equation of the jet engine and also differential equations of other fuel system components (fuel pump, throttle valve, pressure regulator will be described, with respect to advanced predetermined simplifications.
Mathematical Model of the Jet Engine Fuel System
Klimko Marek
2015-01-01
The paper discusses the design of a simplified mathematical model of the jet (turbo-compressor) engine fuel system. The solution will be based on the regulation law, where the control parameter is a fuel mass flow rate and the regulated parameter is the rotational speed. A differential equation of the jet engine and also differential equations of other fuel system components (fuel pump, throttle valve, pressure regulator) will be described, with respect to advanced predetermined simplifications.
Mathematical Model of the Jet Engine Fuel System
Klimko, Marek
2015-05-01
The paper discusses the design of a simplified mathematical model of the jet (turbo-compressor) engine fuel system. The solution will be based on the regulation law, where the control parameter is a fuel mass flow rate and the regulated parameter is the rotational speed. A differential equation of the jet engine and also differential equations of other fuel system components (fuel pump, throttle valve, pressure regulator) will be described, with respect to advanced predetermined simplifications.
International Nuclear Information System (INIS)
Murav’ev, V. P.; Kochetkov, A. V.; Glazova, E. G.
2016-01-01
A mathematical model and algorithms are proposed for automatic calculation of the optimum flow rate of cooling water in nuclear and thermal power plants with cooling systems of arbitrary complexity. An unlimited number of configuration and design variants are assumed with the possibility of obtaining a result for any computational time interval, from monthly to hourly. The structural solutions corresponding to an optimum cooling water flow rate can be used for subsequent engineering-economic evaluation of the best cooling system variant. The computerized mathematical model and algorithms make it possible to determine the availability and degree of structural changes for the cooling system in all stages of the life cycle of a plant.
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
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 analysis of intermittent gas injection model in oil production
Tasmi, Silvya, D. R.; Pudjo, S.; Leksono, M.; Edy, S.
2016-02-01
Intermittent gas injection is a method to help oil production process. Gas is injected through choke in surface and then gas into tubing. Gas forms three areas in tubing: gas column area, film area and slug area. Gas column is used to propel slug area until surface. A mathematical model of intermittent gas injection is developed in gas column area, film area and slug area. Model is expanding based on mass and momentum conservation. Using assume film thickness constant in tubing, model has been developed by Tasmi et. al. [14]. Model consists of 10 ordinary differential equations. In this paper, assumption of pressure in gas column is uniform. Model consist of 9 ordinary differential equations. Connection of several variables can be obtained from this model. Therefore, dynamics of all variables that affect to intermittent gas lift process can be seen from four equations. To study the behavior of variables can be analyzed numerically and mathematically. In this paper, simple mathematically analysis approach is used to study behavior of the variables. Variables that affect to intermittent gas injection are pressure in upstream valve and in gas column. Pressure in upstream valve will decrease when gas mass in valve greater than gas mass in choke. Dynamic of the pressure in the gas column will decrease and increase depending on pressure in upstream valve.
Multiscale mathematical modeling of the hypothalamo-pituitary-gonadal axis.
Clément, Frédérique
2016-07-01
Although the fields of systems and integrative biology are in full expansion, few teams are involved worldwide into the study of reproductive function from the mathematical modeling viewpoint. This may be due to the fact that the reproductive function is not compulsory for individual organism survival, even if it is for species survival. Alternatively, the complexity of reproductive physiology may be discouraging. Indeed, the hypothalamo-pituitary-gonadal (HPG) axis involves not only several organs and tissues but also intricate time (from the neuronal millisecond timescale to circannual rhythmicity) and space (from molecules to organs) scales. Yet, mathematical modeling, and especially multiscale modeling, can renew our approaches of the molecular, cellular, and physiological processes underlying the control of reproductive functions. In turn, the remarkable dynamic features exhibited by the HPG axis raise intriguing and challenging questions to modelers and applied mathematicians. In this article, we draw a panoramic review of some mathematical models designed in the framework of the female HPG, with a special focus on the gonadal and central control of follicular development. On the gonadal side, the modeling of follicular development calls to the generic formalism of structured cell populations, that allows one to make mechanistic links between the control of cell fate (proliferation, differentiation, or apoptosis) and that of the follicle fate (ovulation or degeneration) or to investigate how the functional interactions between the oocyte and its surrounding cells shape the follicle morphogenesis. On the central, mainly hypothalamic side, models based on dynamical systems with multiple timescales allow one to represent within a single framework both the pulsatile and surge patterns of the neurohormone GnRH. Beyond their interest in basic research investigations, mathematical models can also be at the source of useful tools to study the encoding and decoding of
Mathematical programming solver based on local search
Gardi, Frédéric; Darlay, Julien; Estellon, Bertrand; Megel, Romain
2014-01-01
This book covers local search for combinatorial optimization and its extension to mixed-variable optimization. Although not yet understood from the theoretical point of view, local search is the paradigm of choice for tackling large-scale real-life optimization problems. Today's end-users demand interactivity with decision support systems. For optimization software, this means obtaining good-quality solutions quickly. Fast iterative improvement methods, like local search, are suited to satisfying such needs. Here the authors show local search in a new light, in particular presenting a new kind of mathematical programming solver, namely LocalSolver, based on neighborhood search. First, an iconoclast methodology is presented to design and engineer local search algorithms. The authors' concern about industrializing local search approaches is of particular interest for practitioners. This methodology is applied to solve two industrial problems with high economic stakes. Software based on local search induces ex...
Description of mathematical models and computer programs
International Nuclear Information System (INIS)
1977-01-01
The paper gives a description of mathematical models and computer programs for analysing possible strategies for spent fuel management, with emphasis on economic analysis. The computer programs developed, describe the material flows, facility construction schedules, capital investment schedules and operating costs for the facilities used in managing the spent fuel. The computer programs use a combination of simulation and optimization procedures for the economic analyses. Many of the fuel cycle steps (such as spent fuel discharges, storage at the reactor, and transport to the RFCC) are described in physical and economic terms through simulation modeling, while others (such as reprocessing plant size and commissioning schedules, interim storage facility commissioning schedules etc.) are subjected to economic optimization procedures to determine the approximate lowest-cost plans from among the available feasible alternatives
A mathematical model of aerosol holding chambers
DEFF Research Database (Denmark)
Zak, M; Madsen, J; Berg, E
1999-01-01
A mathematical model of aerosol delivery from holding chambers (spacers) was developed incorporating tidal volume (VT), chamber volume (Vch), apparatus dead space (VD), effect of valve insufficiency and other leaks, loss of aerosol by immediate impact on the chamber wall, and fallout of aerosol...... in the chamber with time. Four different spacers were connected via filters to a mechanical lung model, and aerosol delivery during "breathing" was determined from drug recovery from the filters. The formula correctly predicted the delivery of budesonide aerosol from the AeroChamber (Trudell Medical, London......-mentioned factors, initial loss of aerosol by impact on the chamber wall is most important for the efficiency of a spacer. With a VT of 195 mL, the AeroChamber and Babyhaler were emptied in two breaths, the NebuChamber in four breaths, and the Nebuhaler in six breaths. Insufficiencies of the expiratory valves were...
A mathematical model of aerosol holding chambers
DEFF Research Database (Denmark)
Zak, M; Madsen, J; Berg, E
1999-01-01
A mathematical model of aerosol delivery from holding chambers (spacers) was developed incorporating tidal volume (VT), chamber volume (Vch), apparatus dead space (VD), effect of valve insufficiency and other leaks, loss of aerosol by immediate impact on the chamber wall, and fallout of aerosol...... in the chamber with time. Four different spacers were connected via filters to a mechanical lung model, and aerosol delivery during "breathing" was determined from drug recovery from the filters. The formula correctly predicted the delivery of budesonide aerosol from the AeroChamber (Trudell Medical, London......, Ontario, Canada), NebuChamber (Astra, Södirtälje, Sweden) and Nebuhaler (Astra) adapted for babies. The dose of fluticasone proportionate delivered by the Babyhaler (Glaxco Wellcome, Oxbridge, Middlesex, UK) was 80% of that predicted, probably because of incomplete priming of this spacer. Of the above...
Mathematical Models and Methods for Living Systems
Chaplain, Mark; Pugliese, Andrea
2016-01-01
The aim of these lecture notes is to give an introduction to several mathematical models and methods that can be used to describe the behaviour of living systems. This emerging field of application intrinsically requires the handling of phenomena occurring at different spatial scales and hence the use of multiscale methods. Modelling and simulating the mechanisms that cells use to move, self-organise and develop in tissues is not only fundamental to an understanding of embryonic development, but is also relevant in tissue engineering and in other environmental and industrial processes involving the growth and homeostasis of biological systems. Growth and organization processes are also important in many tissue degeneration and regeneration processes, such as tumour growth, tissue vascularization, heart and muscle functionality, and cardio-vascular diseases.
Mathematical modeling of a thermovoltaic cell
White, Ralph E.; Kawanami, Makoto
1992-01-01
A new type of battery named 'Vaporvolt' cell is in the early stage of its development. A mathematical model of a CuO/Cu 'Vaporvolt' cell is presented that can be used to predict the potential and the transport behavior of the cell during discharge. A sensitivity analysis of the various transport and electrokinetic parameters indicates which parameters have the most influence on the predicted energy and power density of the 'Vaporvolt' cell. This information can be used to decide which parameters should be optimized or determined more accurately through further modeling or experimental studies. The optimal thicknesses of electrodes and separator, the concentration of the electrolyte, and the current density are determined by maximizing the power density. These parameter sensitivities and optimal design parameter values will help in the development of a better CuO/Cu 'Vaporvolt' cell.
Mathematics Teacher Education: A Model from Crimea.
Ferrucci, Beverly J.; Evans, Richard C.
1993-01-01
Reports on the mathematics teacher preparation program at Simferopol State University, the largest institution of higher education in the Crimea. The article notes the value of investigating what other countries consider essential in mathematics teacher education to improve the mathematical competence of students in the United States. (SM)
Missing the Promise of Mathematical Modeling
Meyer, Dan
2015-01-01
The Common Core State Standards for Mathematics (CCSSM) have exerted enormous pressure on every participant in a child's education. Students are struggling to meet new standards for mathematics learning, and parents are struggling to understand how to help them. Teachers are growing in their capacity to develop new mathematical competencies, and…
Villa-Ochoa, Jhony; Córdoba, Francisco
2013-01-01
In Colombia, the mathematical training of students in primary and secondary school has, among other purposes, to recognize the cultural diversity, the need for greater equity levels and individuals able to be have a critic position facing the different social and democratic requirements; hence the mathematical modeling has gained ground as a way to meet these education purposes and, therefore, it is suggested as one of the processes the mathematics curriculum must articulate. Such realities r...
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 Model of the Laser Gyro Errors
Directory of Open Access Journals (Sweden)
V. N. Enin
2017-01-01
Full Text Available The paper presents the analysed and systemised results of the experimental study of laser gyro (LG errors. Determines a structure of the resulting LG error, as a linear combination of the random processes, characterizing natural and technical fluctuations of difference frequency of the counter-propagating waves, with a random constant zero shift available in the sensor readings. Formulates the requirements for the structure and form of the analytic description of the error model. Shows a generalized model of the LG fluctuation processes, on the basis of which a mathematical model of LG errors was developed as an inertial sensor.The model is represented by a system of the stochastic differential equations and functional relationships to characterize a resulting error of the sensor. The paper provides a correlation analysis of the model equations and final equations obtained for the mean-square values of the particular components, which allow us to identify the resulting error parameters. The model parameters are presented through the values of the power spectral density of the particular components. The discrete form of the model is considered, the convergence of continuous and difference equations is shown in fulfilling conditions of the limiting transition. Further research activities are defined.
Mathematical Modelling in Engineering: A Proposal to Introduce Linear Algebra Concepts
Cárcamo Bahamonde, Andrea; Gómez Urgelles, Joan; Fortuny Aymemí, Josep
2016-01-01
The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasise the development of mathematical abilities primarily associated with modelling and interpreting, which are not exclusively calculus abilities. Considering this, an instructional design was created based on mathematical modelling and…
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.
AN ECONOMIC-AND-MATHEMATICAL MODEL OF OPENING PARAMETERS OF PREPARATION WORKS
Directory of Open Access Journals (Sweden)
A. H. Vahonova
2010-03-01
Full Text Available We propose an economic-and-mathematical model of opening and preparation of mine field based on the graph theory. The model is optimized by the factor of minimum amounts of conducting the preparation underground works.
Linear models in the mathematics of uncertainty
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...
Mathematical and computational modelling of skin biophysics: a review.
Limbert, Georges
2017-07-01
The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, through anelasticity, including growth, to thermoelasticity. Microstructural and phenomenological approaches combining imaging techniques are also discussed. Finally, recent research applications on skin wrinkles will be presented to highlight the potential of physics-based modelling of skin in tackling global challenges such as ageing of the population and the associated skin degradation, diseases and traumas.
Mechanical-mathematical modeling for landslide process
Svalova, V.
2009-04-01
500 m and displacement of a landslide in the plan over 1 m. Last serious activization of a landslide has taken place in 2002 with a motion on 53 cm. Catastrophic activization of the deep blockglide landslide in the area of Khoroshevo in Moscow took place in 2006-2007. A crack of 330 m long appeared in the old sliding circus, along which a new 220 m long creeping block was separated from the plateau and began sinking with a displaced surface of the plateau reaching to 12 m. Such activization of the landslide process was not observed in Moscow since mid XIX century. The sliding area of Khoroshevo was stable during long time without manifestations of activity. Revealing of the reasons of deformation and development of ways of protection from deep landslide motions is extremely actual and difficult problem which decision is necessary for preservation of valuable historical monuments and modern city constructions. The reasons of activization and protective measures are discussed. Structure of monitoring system for urban territories is elaborated. Mechanical-mathematical model of high viscous fluid was used for modeling of matter behavior on landslide slopes. Equation of continuity and an approximated equation of the Navier-Stockes for slow motions in a thin layer were used. The results of modelling give possibility to define the place of highest velocity on landslide surface, which could be the best place for monitoring post position. Model can be used for calibration of monitoring equipment and gives possibility to investigate some fundamental aspects of matter movement on landslide slope.
Problem based learning to improve proportional reasoning of students in mathematics learning
Misnasanti, Utami, Ratna Widianti; Suwanto, Fevi Rahmawati
2017-08-01
This paper reviews about the using of Problem Based Learning (PBL) to improve proportional reasoning of students in mathematics learning. Mathematics is one of the subjects at school which generally has a goal to help students preparing themselves in this growth century. To achieve the goal of mathematics learning, student's good reasoning is needed as the base of mathematics itself. This reasoning is an ability to think through logic ideas about mathematics concept. One of reasoning mathematics ability is the proportional reasoning. Proportional reasoning is knowing the multiplicative relationship between the base ratio and the proportional situation to which it's applied. Proportional reasoning is important to have by students in learning mathematics. Many topics within the school mathematics require knowledge and understanding of ratio and proportion, for examples problem solving and calculation activities in domains involving scale, probability, percent, rate, trigonometry, equivalence, measurement, the geometry of plane shapes, algebra are assisted through ratio and proportion knowledge. But, the mastership of proportional reasoning ability, of course, can't be apart from teacher's role. In learning, a teacher has to choose and apply the right model so that it can improve the proportional reasoning ability of students. One of the alternative ways which could be applied to improve proportional reasoning ability of students is by applying PBL Model. Applying PBL which based on problem indirectly has trained students to solve every problem in front of them. Thus, applying PBL can improve mathematics proportional reasoning of students in mathematics learning.
Dynamics of pathologic clot formation: a mathematical model.
Shavlyugin, Evgeny A; Hanin, Leonid G; Khanin, Mikhail A
2014-01-07
Recent studies have provided evidence of a significant role of the Hageman factor in pathologic clot formation. Since auto-activation of the Hageman factor triggers the intrinsic coagulation pathway, we study the dynamics of pathologic clot formation considering the intrinsic pathway as the predominant mechanism of this process. Our methodological approach to studying the dynamics of clot formation is based on mathematical modelling. Activation of the blood coagulation cascade, particularly its intrinsic pathway, is known to involve platelets. Therefore, equations accounting for the effects of activated platelets on the intrinsic pathway activation are included in our model. This brings about a considerable increase in the values of kinetic constants involved in the model of the principal biochemical processes resulting in clot formation. The purpose of this study is to elucidate the mechanism of pathologic clot formation. Since the time window of thrombolysis is 3-6h, we hypothesize that in many cases the rate of pathologic clot formation is much lower than that of haemostatic clot. This assumption is used to simplify the mathematical model and to estimate kinetic constants of biochemical reactions that initiate pathologic clot formation. The insights we gained from our mathematical model may lead to new approaches to the prophylaxis of pathologic clot formation. We believe that one of the most efficient ways to prevent pathologic clot formation is simultaneous inhibition of activated factors ХII and ХI. © 2013 Elsevier Ltd. All rights reserved.
Modified Mathematical Model For Neutralization System In Stirred Tank Reactor
Directory of Open Access Journals (Sweden)
Ahmmed Saadi Ibrehem
2011-05-01
Full Text Available A modified model for the neutralization process of Stirred Tank Reactors (CSTR reactor is presented in this study. The model accounts for the effect of strong acid [HCL] flowrate and strong base [NaOH] flowrate with the ionic concentrations of [Cl-] and [Na+] on the Ph of the system. In this work, the effect of important reactor parameters such as ionic concentrations and acid and base flowrates on the dynamic behavior of the CSTR is investigated and the behavior of mathematical model is compared with the reported models for the McAvoy model and Jutila model. Moreover, the results of the model are compared with the experimental data in terms of pH dynamic study. A good agreement is observed between our model prediction and the actual plant data. © 2011 BCREC UNDIP. All rights reserved(Received: 1st March 2011, Revised: 28th March 2011; Accepted: 7th April 2011[How to Cite: A.S. Ibrehem. (2011. Modified Mathematical Model For Neutralization System In Stirred Tank Reactor. Bulletin of Chemical Reaction Engineering & Catalysis, 6(1: 47-52. doi:10.9767/bcrec.6.1.825.47-52][How to Link / DOI: http://dx.doi.org/10.9767/bcrec.6.1.825.47-52 || or local: http://ejournal.undip.ac.id/index.php/bcrec/article/view/825 ] | View in
Mathematical problems in modeling artificial heart
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Ahmed N. U.
1995-01-01
Full Text Available In this paper we discuss some problems arising in mathematical modeling of artificial hearts. The hydrodynamics of blood flow in an artificial heart chamber is governed by the Navier-Stokes equation, coupled with an equation of hyperbolic type subject to moving boundary conditions. The flow is induced by the motion of a diaphragm (membrane inside the heart chamber attached to a part of the boundary and driven by a compressor (pusher plate. On one side of the diaphragm is the blood and on the other side is the compressor fluid. For a complete mathematical model it is necessary to write the equation of motion of the diaphragm and all the dynamic couplings that exist between its position, velocity and the blood flow in the heart chamber. This gives rise to a system of coupled nonlinear partial differential equations; the Navier-Stokes equation being of parabolic type and the equation for the membrane being of hyperbolic type. The system is completed by introducing all the necessary static and dynamic boundary conditions. The ultimate objective is to control the flow pattern so as to minimize hemolysis (damage to red blood cells by optimal choice of geometry, and by optimal control of the membrane for a given geometry. The other clinical problems, such as compatibility of the material used in the construction of the heart chamber, and the membrane, are not considered in this paper. Also the dynamics of the valve is not considered here, though it is also an important element in the overall design of an artificial heart. We hope to model the valve dynamics in later paper.
Mathematical Modeling of Contact Resistance in Silicon Photovoltaic Cells
Black, J. P.
2013-10-22
In screen-printed silicon-crystalline solar cells, the contact resistance of a thin interfacial glass layer between the silicon and the silver electrode plays a limiting role for electron transport. We analyze a simple model for electron transport across this layer, based on the driftdiffusion equations. We utilize the size of the current/Debye length to conduct asymptotic techniques to simplify the model; we solve the model numerically to find that the effective contact resistance may be a monotonic increasing, monotonic decreasing, or nonmonotonic function of the electron flux, depending on the values of the physical parameters. © 2013 Society for Industrial and Applied Mathematics.
Mathematical modelling of ultrasound propagation in multi-phase flow
DEFF Research Database (Denmark)
Simurda, Matej
violates the repeatability of the measurements and thus impairs the device accuracy. Development of new flow meter designs for these conditions based on a purely experimental approach is expensive both in terms of time and economy. An attractive alternative is the employment of a mathematical model...... is further extended by mesh adaptation techniques to accurately resolve acoustic scattering in complex geometries. The presented numerical model is, to the best of the author's knowledge, the only pseudospectral model available in the open literature that solves propagation of acoustic waves in moving...
Mathematical modelling of steam generator and design of temperature regulator
Energy Technology Data Exchange (ETDEWEB)
Bogdanovic, S.S. [EE Institute Nikola Tesla, Belgrade (Yugoslavia)
1999-07-01
The paper considers mathematical modelling of once-through power station boiler and numerical algorithm for simulation of the model. Fast and numerically stable algorithm based on the linearisation of model equations and on the simultaneous solving of differential and algebraic equations is proposed. The paper also presents the design of steam temperature regulator by using the method of projective controls. Dynamic behaviour of the system closed with optimal linear quadratic regulator is taken as the reference system. The desired proprieties of the reference system are retained and solutions for superheated steam temperature regulator are determined. (author)
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....
Evaluation of Mathematical Models for Tankers’ Maneuvering Motions
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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.
How should mathematical models of geomorphic processes be judged?
Iverson, Richard M.
Mathematical models of geomorphic processes can have value as both predictive tools and precise conceptual frameworks. Well-posed mechanistic models have great conceptual value because they link geomorphic processes to universal scientific principles, such as conservation of energy, momentum, and mass. Models without this linkage (e.g., models based exclusively on cellular rules or empirical correlations) have less conceptual value but offer logical methodology for making practical predictions in some circumstances. Clear tests of the predictive power of mechanistic models can be achieved in controlled experiments, whereas natural landscapes typically have uncontrolled initial and boundary conditions and unresolved geological heterogeneities that preclude decisive tests. The best mechanistic models have a simplicity that results from minimizing assumptions and postulates, rather than minimizing mathematics, and this simplicity promotes conclusive tests. Optimal models also employ only parameters that are defined and measured outside the model context. Common weaknesses in geomorphic models result from use of freely coined equations without clear links to conservation laws or compelling data, use of fitted rather than measured values of parameters, lack of clear distinction between assumptions and approximations, and neglect of the four-dimensional (space + time) nature of most geomorphic processes. Models for predicting landslide runout illustrate principles and pitfalls that are common to all geomorphic modeling.
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)
Optlang: An algebraic modeling language for mathematical optimization
DEFF Research Database (Denmark)
Jensen, Kristian; Cardoso, Joao; Sonnenschein, Nikolaus
2016-01-01
Optlang is a Python package implementing a modeling language for solving mathematical optimization problems, i.e., maximizing or minimizing an objective function over a set of variables subject to a number of constraints. It provides a common native Python interface to a series of optimization...... tools, so different solver backends can be used and changed in a transparent way. Optlang’s object-oriented API takes advantage of the symbolic math library SymPy (Team 2016) to allow objective functions and constraints to be easily formulated algebraically from symbolic expressions of variables....... Optlang targets scientists who can thus focus on formulating optimization problems based on mathematical equations derived from domain knowledge. Solver interfaces can be added by subclassing the four main classes of the optlang API (Variable, Constraint, Objective, and Model) and implementing...
Algebraic Reasoning in Solving Mathematical Problem Based on Learning Style
Indraswari, N. F.; Budayasa, I. K.; Ekawati, R.
2018-01-01
This study aimed to describe algebraic reasoning of secondary school’s pupils with different learning styles in solving mathematical problem. This study begins by giving the questionnaire to find out the learning styles and followed by mathematical ability test to get three subjects of 8th-grade whereas the learning styles of each pupil is visual, auditory, kinesthetic and had similar mathematical abilities. Then it continued with given algebraic problems and interviews. The data is validated using triangulation of time. The result showed that in the pattern of seeking indicator, subjects identified the things that were known and asked based on them observations. The visual and kinesthetic learners represented the known information in a chart, whereas the auditory learner in a table. In addition, they found the elements which makes the pattern and made a relationship between two quantities. In the pattern recognition indicator, they created conjectures on the relationship between two quantities and proved it. In the generalization indicator, they were determining the general rule of pattern found on each element of pattern using algebraic symbols and created a mathematical model. Visual and kinesthetic learners determined the general rule of equations which was used to solve problems using algebraic symbols, but auditory learner in a sentence.
Mathematical modeling of wiped-film evaporators
International Nuclear Information System (INIS)
Sommerfeld, J.T.
1976-05-01
A mathematical model and associated computer program were developed to simulate the steady-state operation of wiped-film evaporators for the concentration of typical waste solutions produced at the Savannah River Plant. In this model, which treats either a horizontal or a vertical wiped-film evaporator as a plug-flow device with no backmixing, three fundamental phenomena are described: sensible heating of the waste solution, vaporization of water, and crystallization of solids from solution. Physical property data were coded into the computer program, which performs the calculations of this model. Physical properties of typical waste solutions and of the heating steam, generally as analytical functions of temperature, were obtained from published data or derived by regression analysis of tabulated or graphical data. Preliminary results from tests of the Savannah River Laboratory semiworks wiped-film evaporators were used to select a correlation for the inside film heat transfer coefficient. This model should be a useful aid in the specification, operation, and control of the full-scale wiped-film evaporators proposed for application under plant conditions. In particular, it should be of value in the development and analysis of feed-forward control schemes for the plant units. Also, this model can be readily adapted, with only minor changes, to simulate the operation of wiped-film evaporators for other conceivable applications, such as the concentration of acid wastes
Mathematical models for indoor radon prediction
International Nuclear Information System (INIS)
Malanca, A.; Pessina, V.; Dallara, G.
1995-01-01
It is known that the indoor radon (Rn) concentration can be predicted by means of mathematical models. The simplest model relies on two variables only: the Rn source strength and the air exchange rate. In the Lawrence Berkeley Laboratory (LBL) model several environmental parameters are combined into a complex equation; besides, a correlation between the ventilation rate and the Rn entry rate from the soil is admitted. The measurements were carried out using activated carbon canisters. Seventy-five measurements of Rn concentrations were made inside two rooms placed on the second floor of a building block. One of the rooms had a single-glazed window whereas the other room had a double pane window. During three different experimental protocols, the mean Rn concentration was always higher into the room with a double-glazed window. That behavior can be accounted for by the simplest model. A further set of 450 Rn measurements was collected inside a ground-floor room with a grounding well in it. This trend maybe accounted for by the LBL model
A Mathematical Model of Cigarette Smoldering Process
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Chen P
2014-12-01
Full Text Available A mathematical model for a smoldering cigarette has been proposed. In the analysis of the cigarette combustion and pyrolysis processes, a receding burning front is defined, which has a constant temperature (~450 °C and divides the cigarette into two zones, the burning zone and the pyrolysis zone. The char combustion processes in the burning zone and the pyrolysis of virgin tobacco and evaporation of water in the pyrolysis zone are included in the model. The hot gases flow from the burning zone, are assumed to go out as sidestream smoke during smoldering. The internal heat transport is characterized by effective thermal conductivities in each zone. Thermal conduction of cigarette paper and convective and radiative heat transfer at the outer surface were also considered. The governing partial differential equations were solved using an integral method. Model predictions of smoldering speed as well as temperature and density profiles in the pyrolysis zone for different kinds of cigarettes were found to agree with the experimental data. The model also predicts the coal length and the maximum coal temperatures during smoldering conditions. The model provides a relatively fast and efficient way to simulate the cigarette burning processes. It offers a practical tool for exploring important parameters for cigarette smoldering processes, such as tobacco components, properties of cigarette paper, and heat generation in the burning zone and its dependence on the mass burn rate.
Mathematical foundations of the dendritic growth models.
Villacorta, José A; Castro, Jorge; Negredo, Pilar; Avendaño, Carlos
2007-11-01
At present two growth models describe successfully the distribution of size and topological complexity in populations of dendritic trees with considerable accuracy and simplicity, the BE model (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) and the S model (Van Pelt and Verwer in Bull. Math. Biol. 48:197-211, 1986). This paper discusses the mathematical basis of these models and analyzes quantitatively the relationship between the BE model and the S model assumed in the literature by developing a new explicit equation describing the BES model (a dendritic growth model integrating the features of both preceding models; Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997). In numerous studies it is implicitly presupposed that the S model is conditionally linked to the BE model (Granato and Van Pelt in Brain Res. Dev. Brain Res. 142:223-227, 2003; Uylings and Van Pelt in Network 13:397-414, 2002; Van Pelt, Dityatev and Uylings in J. Comp. Neurol. 387:325-340, 1997; Van Pelt and Schierwagen in Math. Biosci. 188:147-155, 2004; Van Pelt and Uylings in Network. 13:261-281, 2002; Van Pelt, Van Ooyen and Uylings in Modeling Dendritic Geometry and the Development of Nerve Connections, pp 179, 2000). In this paper we prove the non-exactness of this assumption, quantify involved errors and determine the conditions under which the BE and S models can be separately used instead of the BES model, which is more exact but considerably more difficult to apply. This study leads to a novel expression describing the BE model in an analytical closed form, much more efficient than the traditional iterative equation (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) in many neuronal classes. Finally we propose a new algorithm in order to obtain the values of the parameters of the BE model when this growth model is matched to experimental data, and discuss its advantages and improvements over the more commonly used procedures.
Akgün, Levent
2015-01-01
The aim of this study is to identify prospective secondary mathematics teachers' opinions about the mathematical modeling method and the applicability of this method in high schools. The case study design, which is among the qualitative research methods, was used in the study. The study was conducted with six prospective secondary mathematics…
Lamb, Janeen; Kawakami, Takashi; Saeki, Akihiko; Matsuzaki, Akio
2014-01-01
The aim of this study was to investigate the use of the "dual mathematical modelling cycle framework" as one way to meet the espoused goals of the Australian Curriculum Mathematics. This study involved 23 Year 6 students from one Australian primary school who engaged in an "Oil Tank Task" that required them to develop two…
Mathematical analysis of epidemiological models with heterogeneity
Energy Technology Data Exchange (ETDEWEB)
Van Ark, J.W.
1992-01-01
For many diseases in human populations the disease shows dissimilar characteristics in separate subgroups of the population; for example, the probability of disease transmission for gonorrhea or AIDS is much higher from male to female than from female to male. There is reason to construct and analyze epidemiological models which allow this heterogeneity of population, and to use these models to run computer simulations of the disease to predict the incidence and prevalence of the disease. In the models considered here the heterogeneous population is separated into subpopulations whose internal and external interactions are homogeneous in the sense that each person in the population can be assumed to have all average actions for the people of that subpopulation. The first model considered is an SIRS models; i.e., the Susceptible can become Infected, and if so he eventually Recovers with temporary immunity, and after a period of time becomes Susceptible again. Special cases allow for permanent immunity or other variations. This model is analyzed and threshold conditions are given which determine whether the disease dies out or persists. A deterministic model is presented; this model is constructed using difference equations, and it has been used in computer simulations for the AIDS epidemic in the homosexual population in San Francisco. The homogeneous version and the heterogeneous version of the differential-equations and difference-equations versions of the deterministic model are analyzed mathematically. In the analysis, equilibria are identified and threshold conditions are set forth for the disease to die out if the disease is below the threshold so that the disease-free equilibrium is globally asymptotically stable. Above the threshold the disease persists so that the disease-free equilibrium is unstable and there is a unique endemic equilibrium.
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.
Mathematical Modeling of the Origins of Life
Pohorille, Andrew
2006-01-01
The emergence of early metabolism - a network of catalyzed chemical reactions that supported self-maintenance, growth, reproduction and evolution of the ancestors of contemporary cells (protocells) was a critical, but still very poorly understood step on the path from inanimate to animate matter. Here, it is proposed and tested through mathematical modeling of biochemically plausible systems that the emergence of metabolism and its initial evolution towards higher complexity preceded the emergence of a genome. Even though the formation of protocellular metabolism was driven by non-genomic, highly stochastic processes the outcome was largely deterministic, strongly constrained by laws of chemistry. It is shown that such concepts as speciation and fitness to the environment, developed in the context of genomic evolution, also held in the absence of a genome.
Noise in restaurants: levels and mathematical model.
To, Wai Ming; Chung, Andy
2014-01-01
Noise affects the dining atmosphere and is an occupational hazard to restaurant service employees worldwide. This paper examines the levels of noise in dining areas during peak hours in different types of restaurants in Hong Kong SAR, China. A mathematical model that describes the noise level in a restaurant is presented. The 1-h equivalent continuous noise level (L(eq,1-h)) was measured using a Type-1 precision integral sound level meter while the occupancy density, the floor area of the dining area, and the ceiling height of each of the surveyed restaurants were recorded. It was found that the measured noise levels using Leq,1-h ranged from 67.6 to 79.3 dBA in Chinese restaurants, from 69.1 to 79.1 dBA in fast food restaurants, and from 66.7 to 82.6 dBA in Western restaurants. Results of the analysis of variance show that there were no significant differences between means of the measured noise levels among different types of restaurants. A stepwise multiple regression analysis was employed to determine the relationships between geometrical and operational parameters and the measured noise levels. Results of the regression analysis show that the measured noise levels depended on the levels of occupancy density only. By reconciling the measured noise levels and the mathematical model, it was found that people in restaurants increased their voice levels when the occupancy density increased. Nevertheless, the maximum measured hourly noise level indicated that the noise exposure experienced by restaurant service employees was below the regulated daily noise exposure value level of 85 dBA.
Noise in restaurants: Levels and mathematical model
Directory of Open Access Journals (Sweden)
Wai Ming To
2014-01-01
Full Text Available Noise affects the dining atmosphere and is an occupational hazard to restaurant service employees worldwide. This paper examines the levels of noise in dining areas during peak hours in different types of restaurants in Hong Kong SAR, China. A mathematical model that describes the noise level in a restaurant is presented. The 1-h equivalent continuous noise level (Leq,1-h was measured using a Type-1 precision integral sound level meter while the occupancy density, the floor area of the dining area, and the ceiling height of each of the surveyed restaurants were recorded. It was found that the measured noise levels using Leq,1-h ranged from 67.6 to 79.3 dBA in Chinese restaurants, from 69.1 to 79.1 dBA in fast food restaurants, and from 66.7 to 82.6 dBA in Western restaurants. Results of the analysis of variance show that there were no significant differences between means of the measured noise levels among different types of restaurants. A stepwise multiple regression analysis was employed to determine the relationships between geometrical and operational parameters and the measured noise levels. Results of the regression analysis show that the measured noise levels depended on the levels of occupancy density only. By reconciling the measured noise levels and the mathematical model, it was found that people in restaurants increased their voice levels when the occupancy density increased. Nevertheless, the maximum measured hourly noise level indicated that the noise exposure experienced by restaurant service employees was below the regulated daily noise exposure value level of 85 dBA.
Mathematical and computer modeling of component surface shaping
Lyashkov, A.
2016-04-01
The process of shaping technical surfaces is an interaction of a tool (a shape element) and a component (a formable element or a workpiece) in their relative movements. It was established that the main objects of formation are: 1) a discriminant of a surfaces family, formed by the movement of the shape element relatively the workpiece; 2) an enveloping model of the real component surface obtained after machining, including transition curves and undercut lines; 3) The model of cut-off layers obtained in the process of shaping. When modeling shaping objects there are a lot of insufficiently solved or unsolved issues that make up a single scientific problem - a problem of qualitative shaping of the surface of the tool and then the component surface produced by this tool. The improvement of known metal-cutting tools, intensive development of systems of their computer-aided design requires further improvement of the methods of shaping the mating surfaces. In this regard, an important role is played by the study of the processes of shaping of technical surfaces with the use of the positive aspects of analytical and numerical mathematical methods and techniques associated with the use of mathematical and computer modeling. The author of the paper has posed and has solved the problem of development of mathematical, geometric and algorithmic support of computer-aided design of cutting tools based on computer simulation of the shaping process of surfaces.
Developing Understanding of Mathematical Modeling in Secondary Teacher Preparation
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…
Mathematics in Nature Modeling Patterns in the Natural World
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
An introduction to mathematical modeling a course in mechanics
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...
Zero-dimensional mathematical model of the torch ignited engine
International Nuclear Information System (INIS)
Cruz, Igor William Santos Leal; Alvarez, Carlos Eduardo Castilla; Teixeira, Alysson Fernandes; Valle, Ramon Molina
2016-01-01
Highlights: • Publications about the torch ignition system are mostly CFD or experimental research. • A zero-dimensional mathematical model is presented. • The model is based on classical thermodynamic equations. • Approximations are based on empirical functions. • The model is applied to a prototype by means of a computer code. - Abstract: Often employed in the analysis of conventional SI and CI engines, mathematical models can also be applied to engines with torch ignition, which have been researched almost exclusively by CFD or experimentally. The objective of this work is to describe the development and application of a zero-dimensional model of the compression and power strokes of a torch ignited engine. It is an initial analysis that can be used as a basis for future models. The processes of compression, combustion and expansion were described mathematically and applied to an existing prototype by means of a computer code written in MATLAB language. Conservation of energy and mass and the ideal gas law were used in determining gas temperature, pressure, and mass flow rate within the cylinder. Gas motion through the orifice was modelled as an isentropic compressible flow. The thermodynamic properties of the mixture were found by a weighted arithmetic mean of the data for each component, computed by polynomial functions of temperature. Combustion was modelled by the Wiebe function. Heat transfer to the cylinder walls was estimated by Annand’s correlations. Results revealed the behaviour of pressure, temperature, jet velocity, energy transfer, thermodynamic properties, among other variables, and how some of these are influenced by others.
Ocular hemodynamics and glaucoma: the role of mathematical modeling.
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.
Игорь Николаевич Макарьев
2013-01-01
In this article the author dwells on the content and structure of the model of integration of system of distance learning to mathematics of senior pupils and traditional paradigm of education. This kind of integration is based on such principles as independence, individualization, flexibility, nonlinearity, openness. Specifics of the methodological support of distance mathematics learning are also analyzed. Particularly the author asserts that the system of distance mathematics learning can t...
Garcia-Santillán, Arturo; Moreno-Garcia, Elena; Escalera-Chávez, Milka E.; Rojas-Kramer, Carlos A.; Pozos-Texon, Felipe
2016-01-01
Most mathematics students show a definite tendency toward an attitudinal deficiency, which can be primarily understood as intolerance to the matter, affecting their scholar performance adversely. In addition, information and communication technologies have been gradually included within the process of teaching mathematics. Such adoption of…
Filler segmentation of SEM paper images based on mathematical morphology.
Ait Kbir, M; Benslimane, Rachid; Princi, Elisabetta; Vicini, Silvia; Pedemonte, Enrico
2007-07-01
Recent developments in microscopy and image processing have made digital measurements on high-resolution images of fibrous materials possible. This helps to gain a better understanding of the structure and other properties of the material at micro level. In this paper SEM image segmentation based on mathematical morphology is proposed. In fact, paper models images (Whatman, Murillo, Watercolor, Newsprint paper) selected in the context of the Euro Mediterranean PaperTech Project have different distributions of fibers and fillers, caused by the presence of SiAl and CaCO3 particles. It is a microscopy challenge to make filler particles in the sheet distinguishable from the other components of the paper surface. This objectif is reached here by using switable strutural elements and mathematical morphology operators.
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.
Proposal of a pedagogical model for mathematics teacher education
Directory of Open Access Journals (Sweden)
Alfonso Jiménez Espinosa
2011-01-01
Full Text Available This research-based article reflects on mathematics teacher education, and proposes a pedagogical model for this purpose, called Gradual Research Pedagogical Model (MPGI. This model considers the central curricular elements of any academic education process: student, teacher and contents, with evaluation as transversal element for analysis and feedback. The training of future teachers is constituted by three moments, each with its specific emphasis: the first is “contextualization”, which aims at having the student understand his or her new academic role, and identify and overcome his or her academic weak points, the second is “knowledge foundation”, which offers basic education in the fields of mathematics and pedagogy, as well as sensibilization towards social issues, opening up the student’s possibilities as leader and agent of change, and lastly, “knowledge immersion”, which is centered on research and the identification and study of topics and problems of the mathematical discipline as well as the pedagogical field.
Mathematical model of one-man air revitalization system
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.
Energy Technology Data Exchange (ETDEWEB)
Willenbring, James M.; Bartlett, Roscoe Ainsworth (Oak Ridge National Laboratory, Oak Ridge, TN); Heroux, Michael Allen
2012-01-01
Software lifecycles are becoming an increasingly important issue for computational science and engineering (CSE) software. The process by which a piece of CSE software begins life as a set of research requirements and then matures into a trusted high-quality capability is both commonplace and extremely challenging. Although an implicit lifecycle is obviously being used in any effort, the challenges of this process - respecting the competing needs of research vs. production - cannot be overstated. Here we describe a proposal for a well-defined software lifecycle process based on modern Lean/Agile software engineering principles. What we propose is appropriate for many CSE software projects that are initially heavily focused on research but also are expected to eventually produce usable high-quality capabilities. The model is related to TriBITS, a build, integration and testing system, which serves as a strong foundation for this lifecycle model, and aspects of this lifecycle model are ingrained in the TriBITS system. Here, we advocate three to four phases or maturity levels that address the appropriate handling of many issues associated with the transition from research to production software. The goals of this lifecycle model are to better communicate maturity levels with customers and to help to identify and promote Software Engineering (SE) practices that will help to improve productivity and produce better software. An important collection of software in this domain is Trilinos, which is used as the motivation and the initial target for this lifecycle model. However, many other related and similar CSE (and non-CSE) software projects can also make good use of this lifecycle model, especially those that use the TriBITS system. Indeed this lifecycle process, if followed, will enable large-scale sustainable integration of many complex CSE software efforts across several institutions.
Application of Mathematical Modeling Activities in Costarican High School Education
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Karen Porras-Lizano
2015-01-01
Full Text Available This paper describes the experience gained in implementing mathematical modeling activities as a methodological strategy in teaching issues such as proportions, with a group of eighth year of an academic-day-school, located in the province of San Jose, Costa Rica in 2012. Different techniques for gathering information were applied, such as participant observation and questionnaires. Among the relevant results are the cyclical development of mathematical thinking of students in the stages of mathematical modeling (description, manipulation, prediction and validation for solving the problem; developing of teamwork skills; and appreciation of mathematics as a useful and effective discipline. To resolve the activities proposed in this study, social interactions such as sharing information, thoughts and ideas, were generated, stimulating the zone of proximal development of the participating students. Likewise, the mathematical modeling activities allowed students to have a positive role in mathematics classes, stimulating, in turn, a different attitude compared to regular classes.
Mathematical Modeling of Linear and Non-Linear Aircraft Structures.
1980-07-01
7 A-A OBO 439 LISORY GROUP FOR AEROSPACE RESEARCH AND DEVELOPMENT--ETC F IG 1/2 MATHENATICAL MODELING OF LINEAR AND NON-LINEAR AIRCRAFT STRUCTu...theoretical model. (see Fig.1): Continuum Physical Model Mathematical Model Numerical computation ] Analytical treatment (Discretization)Ft Fig.: 1...this model neglecting unessential details. This "Mathematical Model" is usually solved by numerical computation , which means that a discretization of
A Mathematical Model of a Simple Amplifier Using a Ferroelectric Transistor
Sayyah, Rana; Hunt, Mitchell; MacLeod, Todd C.; Ho, Fat D.
2009-01-01
This paper presents a mathematical model characterizing the behavior of a simple amplifier using a FeFET. The model is based on empirical data and incorporates several variables that affect the output, including frequency, load resistance, and gate-to-source voltage. Since the amplifier is the basis of many circuit configurations, a mathematical model that describes the behavior of a FeFET-based amplifier will help in the integration of FeFETs into many other circuits.
Logistics of Mathematical Modeling-Focused Projects
Harwood, R. Corban
2018-01-01
This article addresses the logistics of implementing projects in an undergraduate mathematics class and is intended both for new instructors and for instructors who have had negative experiences implementing projects in the past. Project implementation is given for both lower- and upper-division mathematics courses with an emphasis on mathematical…
Modelling Mathematical Reasoning in Physics Education
Uhden, Olaf; Karam, Ricardo; Pietrocola, Mauricio; Pospiech, Gesche
2012-01-01
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…
MODELS FOR MATHEMATICS IN THE SCHOOL.
KENNEDY, LEONARD M.
THE PURPOSE OF THIS BOOK IS TO DESCRIBE LEARNING AIDS THAT MAY BE MADE BY A TEACHER OR CHILDREN FOR USE IN MATHEMATICS PROGRAMS IN THE ELEMENTARY SCHOOL. THESE AIDS ARE OF TWO TYPES--MANIPULATIVE AND VISUAL. DESCRIPTIONS IN THIS BOOK INCLUDE (1) THE PURPOSE OF THE TEACHING AID IN A MODERN MATHEMATICS PROGRAM, (2) EXAMPLES OF ITS USE, AND (3) ITS…
Marshall, Neil; Buteau, Chantal
2014-01-01
As part of their undergraduate mathematics curriculum, students at Brock University learn to create and use computer-based tools with dynamic, visual interfaces, called Exploratory Objects, developed for the purpose of conducting pure or applied mathematical investigations. A student's Development Process Model of creating and using an Exploratory…
Mathematical modeling and signal processing in speech and hearing sciences
Xin, Jack
2014-01-01
The aim of the book is to give an accessible introduction of mathematical models and signal processing methods in speech and hearing sciences for senior undergraduate and beginning graduate students with basic knowledge of linear algebra, differential equations, numerical analysis, and probability. Speech and hearing sciences are fundamental to numerous technological advances of the digital world in the past decade, from music compression in MP3 to digital hearing aids, from network based voice enabled services to speech interaction with mobile phones. Mathematics and computation are intimately related to these leaps and bounds. On the other hand, speech and hearing are strongly interdisciplinary areas where dissimilar scientific and engineering publications and approaches often coexist and make it difficult for newcomers to enter.
Research Methods in Healthcare Epidemiology and Antimicrobial Stewardship-Mathematical Modeling.
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 programming model for the optimization of nutritional ...
African Journals Online (AJOL)
The use of a mathematical programming model for determining optimal nutritional strategy for a dairy cow is described. Mixed Integer Programming (MIP) may be used to fit curvilinear functions, such as the changes in the nutrient requirements of the cow, into a standard mathematical programme. The model determines the.
iSTEM: Promoting Fifth Graders' Mathematical Modeling
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…
An Integrated Approach to Mathematical Modeling: A Classroom Study.
Doerr, Helen M.
Modeling, simulation, and discrete mathematics have all been identified by professional mathematics education organizations as important areas for secondary school study. This classroom study focused on the components and tools for modeling and how students use these tools to construct their understanding of contextual problems in the content area…
Mathematical 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 ...
Plotnitsky, Arkady
2017-06-01
The history of mathematical modeling outside physics has been dominated by the use of classical mathematical models, C-models, primarily those of a probabilistic or statistical nature. More recently, however, quantum mathematical models, Q-models, based in the mathematical formalism of quantum theory have become more prominent in psychology, economics, and decision science. The use of Q-models in these fields remains controversial, in part because it is not entirely clear whether Q-models are necessary for dealing with the phenomena in question or whether C-models would still suffice. My aim, however, is not to assess the necessity of Q-models in these fields, but instead to reflect on what the possible applicability of Q-models may tell us about the corresponding phenomena there, vis-à-vis quantum phenomena in physics. In order to do so, I shall first discuss the key reasons for the use of Q-models in physics. In particular, I shall examine the fundamental principles that led to the development of quantum mechanics. Then I shall consider a possible role of similar principles in using Q-models outside physics. Psychology, economics, and decision science borrow already available Q-models from quantum theory, rather than derive them from their own internal principles, while quantum mechanics was derived from such principles, because there was no readily available mathematical model to handle quantum phenomena, although the mathematics ultimately used in quantum did in fact exist then. I shall argue, however, that the principle perspective on mathematical modeling outside physics might help us to understand better the role of Q-models in these fields and possibly to envision new models, conceptually analogous to but mathematically different from those of quantum theory, helpful or even necessary there or in physics itself. I shall suggest one possible type of such models, singularized probabilistic, SP, models, some of which are time-dependent, TDSP-models. The
Mathematical Modeling of Tuberculosis Granuloma Activation
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Steve M. Ruggiero
2017-12-01
Full Text Available Tuberculosis (TB is one of the most common infectious diseases worldwide. It is estimated that one-third of the world’s population is infected with TB. Most have the latent stage of the disease that can later transition to active TB disease. TB is spread by aerosol droplets containing Mycobacterium tuberculosis (Mtb. Mtb bacteria enter through the respiratory system and are attacked by the immune system in the lungs. The bacteria are clustered and contained by macrophages into cellular aggregates called granulomas. These granulomas can hold the bacteria dormant for long periods of time in latent TB. The bacteria can be perturbed from latency to active TB disease in a process called granuloma activation when the granulomas are compromised by other immune response events in a host, such as HIV, cancer, or aging. Dysregulation of matrix metalloproteinase 1 (MMP-1 has been recently implicated in granuloma activation through experimental studies, but the mechanism is not well understood. Animal and human studies currently cannot probe the dynamics of activation, so a computational model is developed to fill this gap. This dynamic mathematical model focuses specifically on the latent to active transition after the initial immune response has successfully formed a granuloma. Bacterial leakage from latent granulomas is successfully simulated in response to the MMP-1 dynamics under several scenarios for granuloma activation.
Simple mathematical models of gene regulatory dynamics
Mackey, Michael C; Tyran-Kamińska, Marta; Zeron, Eduardo S
2016-01-01
This is a short and self-contained introduction to the field of mathematical modeling of gene-networks in bacteria. As an entry point to the field, we focus on the analysis of simple gene-network dynamics. The notes commence with an introduction to the deterministic modeling of gene-networks, with extensive reference to applicable results coming from dynamical systems theory. The second part of the notes treats extensively several approaches to the study of gene-network dynamics in the presence of noise—either arising from low numbers of molecules involved, or due to noise external to the regulatory process. The third and final part of the notes gives a detailed treatment of three well studied and concrete examples of gene-network dynamics by considering the lactose operon, the tryptophan operon, and the lysis-lysogeny switch. The notes contain an index for easy location of particular topics as well as an extensive bibliography of the current literature. The target audience of these notes are mainly graduat...
Mathematical model I. Electron and quantum mechanics
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Nitin Ramchandra Gadre
2011-03-01
Full Text Available The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is ‘difficult’ to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.
Mathematical modeling of Chikungunya fever control
Hincapié-Palacio, Doracelly; Ospina, Juan
2015-05-01
Chikungunya fever is a global concern due to the occurrence of large outbreaks, the presence of persistent arthropathy and its rapid expansion throughout various continents. Globalization and climate change have contributed to the expansion of the geographical areas where mosquitoes Aedes aegypti and Aedes albopictus (Stegomyia) remain. It is necessary to improve the techniques of vector control in the presence of large outbreaks in The American Region. We derive measures of disease control, using a mathematical model of mosquito-human interaction, by means of three scenarios: a) a single vector b) two vectors, c) two vectors and human and non-human reservoirs. The basic reproductive number and critical control measures were deduced by using computer algebra with Maple (Maplesoft Inc, Ontario Canada). Control measures were simulated with parameter values obtained from published data. According to the number of households in high risk areas, the goals of effective vector control to reduce the likelihood of mosquito-human transmission would be established. Besides the two vectors, if presence of other non-human reservoirs were reported, the monthly target of effective elimination of the vector would be approximately double compared to the presence of a single vector. The model shows the need to periodically evaluate the effectiveness of vector control measures.
Mathematical model I. Electron and quantum mechanics
Gadre, Nitin Ramchandra
2011-03-01
The basic particle electron obeys various theories like electrodynamics, quantum mechanics and special relativity. Particle under different experimental conditions behaves differently, allowing us to observe different characteristics which become basis for these theories. In this paper, we have made an attempt to suggest a classical picture by studying the requirements of these three modern theories. The basic presumption is: There must be certain structural characteristics in a particle like electron which make it obey postulates of modern theories. As it is `difficult' to find structure of electron experimentally, we make a mathematical attempt. For a classical approach, we require well defined systems and we have studied a system with two charged particles, proton and electron in a hydrogen atom. An attempt has been made to give a model to describe electron as seen by the proton. We then discuss how the model can satisfy the requirements of the three modern theories in a classical manner. The paper discusses basic aspects of relativity and electrodynamics. However the focus of the paper is on quantum mechanics.
The limitations of mathematical modeling in high school physics education
Forjan, Matej
The theme of the doctoral dissertation falls within the scope of didactics of physics. Theoretical analysis of the key constraints that occur in the transmission of mathematical modeling of dynamical systems into field of physics education in secondary schools is presented. In an effort to explore the extent to which current physics education promotes understanding of models and modeling, we analyze the curriculum and the three most commonly used textbooks for high school physics. We focus primarily on the representation of the various stages of modeling in the solved tasks in textbooks and on the presentation of certain simplifications and idealizations, which are in high school physics frequently used. We show that one of the textbooks in most cases fairly and reasonably presents the simplifications, while the other two half of the analyzed simplifications do not explain. It also turns out that the vast majority of solved tasks in all the textbooks do not explicitly represent model assumptions based on what we can conclude that in high school physics the students do not develop sufficiently a sense of simplification and idealizations, which is a key part of the conceptual phase of modeling. For the introduction of modeling of dynamical systems the knowledge of students is also important, therefore we performed an empirical study on the extent to which high school students are able to understand the time evolution of some dynamical systems in the field of physics. The research results show the students have a very weak understanding of the dynamics of systems in which the feedbacks are present. This is independent of the year or final grade in physics and mathematics. When modeling dynamical systems in high school physics we also encounter the limitations which result from the lack of mathematical knowledge of students, because they don't know how analytically solve the differential equations. We show that when dealing with one-dimensional dynamical systems
Is there Life after Modelling? Student conceptions of mathematics
Houston, Ken; Mather, Glyn; Wood, Leigh N.; Petocz, Peter; Reid, Anna; Harding, Ansie; Engelbrecht, Johann; Smith, Geoff H.
2010-09-01
We have been investigating university student conceptions of mathematics over a number of years, with the goal of enhancing student learning and professional development. We developed an open-ended survey of three questions, on "What is mathematics" and two questions about the role of mathematics in the students' future. This questionnaire was completed by 1,200 undergraduate students of mathematics in Australia, the UK, Canada, South Africa, and Brunei. The sample included students ranging from those majoring in mathematics to those taking only one or two modules in mathematics. Responses were analysed starting from a previously-developed phenomenographic framework that required only minor modification, leading to an outcome space of four levels of conceptions about mathematics. We found that for many students modelling is fundamental to their conception of "What is mathematics?". In a small number of students, we identified a broader conception of mathematics, that we have labelled Life. This describes a view of mathematics as a way of thinking about reality and as an integral part of life, and represents an ideal aim for university mathematics education.
International Nuclear Information System (INIS)
Begum, N.N.; Ahmed, J.
2006-01-01
A classification of the existing mathematical models of flow-injection (FI) manifolds based on the main principles on which they are built, have been proposed. Numerous mathematical models of FI systems employing ideas from different scientific areas (e.g. mathematical statistics, chemical engineering, chromatography) have been developed so far. The models have been compared with respect to their predictive power, the complexity of their mathematical treatment, and the requirements for computation time when applied to single-line, multi-channel and conjugated two-line FI systems. It is concluded that the axially dispersed plug flow model deserves special attention because it offers an acceptable compromise between the conflicting requirements for maximal possible mathematical simplicity and maximal possible precision. Applicability of these existing flow-injection models to single-line, multi-channel and conjugated two-line systems for environmental monitoring have been discussed. (author)
Developing Student-Centered Learning Model to Improve High Order Mathematical Thinking Ability
Saragih, Sahat; Napitupulu, Elvis
2015-01-01
The purpose of this research was to develop student-centered learning model aiming to improve high order mathematical thinking ability of junior high school students of based on curriculum 2013 in North Sumatera, Indonesia. The special purpose of this research was to analyze and to formulate the purpose of mathematics lesson in high order…
Mathematical modeling of the neuron morphology using two dimensional images.
Rajković, Katarina; Marić, Dušica L; Milošević, Nebojša T; Jeremic, Sanja; Arsenijević, Valentina Arsić; Rajković, Nemanja
2016-02-07
In this study mathematical analyses such as the analysis of area and length, fractal analysis and modified Sholl analysis were applied on two dimensional (2D) images of neurons from adult human dentate nucleus (DN). Using mathematical analyses main morphological properties were obtained including the size of neuron and soma, the length of all dendrites, the density of dendritic arborization, the position of the maximum density and the irregularity of dendrites. Response surface methodology (RSM) was used for modeling the size of neurons and the length of all dendrites. However, the RSM model based on the second-order polynomial equation was only possible to apply to correlate changes in the size of the neuron with other properties of its morphology. Modeling data provided evidence that the size of DN neurons statistically depended on the size of the soma, the density of dendritic arborization and the irregularity of dendrites. The low value of mean relative percent deviation (MRPD) between the experimental data and the predicted neuron size obtained by RSM model showed that model was suitable for modeling the size of DN neurons. Therefore, RSM can be generally used for modeling neuron size from 2D images. Copyright © 2015 Elsevier Ltd. All rights reserved.
Mathematical modeling and computational prediction of cancer drug resistance.
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
MATHEMATICAL MODELING OF AC ELECTRIC POINT MOTOR
Directory of Open Access Journals (Sweden)
S. YU. Buryak
2014-03-01
Full Text Available Purpose. In order to ensure reliability, security, and the most important the continuity of the transportation process, it is necessary to develop, implement, and then improve the automated methods of diagnostic mechanisms, devices and rail transport systems. Only systems that operate in real time mode and transmit data on the instantaneous state of the control objects can timely detect any faults and thus provide additional time for their correction by railway employees. Turnouts are one of the most important and responsible components, and therefore require the development and implementation of such diagnostics system.Methodology. Achieving the goal of monitoring and control of railway automation objects in real time is possible only with the use of an automated process of the objects state diagnosing. For this we need to know the diagnostic features of a control object, which determine its state at any given time. The most rational way of remote diagnostics is the shape and current spectrum analysis that flows in the power circuits of railway automatics. Turnouts include electric motors, which are powered by electric circuits, and the shape of the current curve depends on both the condition of the electric motor, and the conditions of the turnout maintenance. Findings. For the research and analysis of AC electric point motor it was developed its mathematical model. The calculation of parameters and interdependencies between the main factors affecting the operation of the asynchronous machine was conducted. The results of the model operation in the form of time dependences of the waveform curves of current on the load on engine shaft were obtained. Originality. During simulation the model of AC electric point motor, which satisfies the conditions of adequacy was built. Practical value. On the basis of the constructed model we can study the AC motor in various mode of operation, record and analyze current curve, as a response to various changes
Mathematical model of kinetostatithic calculation of flat lever mechanisms
Directory of Open Access Journals (Sweden)
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.
A mathematical model of microalgae growth in cylindrical photobioreactor
Bakeri, Noorhadila Mohd; Jamaian, Siti Suhana
2017-08-01
Microalgae are unicellular organisms, which exist individually or in chains or groups but can be utilized in many applications. Researchers have done various efforts in order to increase the growth rate of microalgae. Microalgae have a potential as an effective tool for wastewater treatment, besides as a replacement for natural fuel such as coal and biodiesel. The growth of microalgae can be estimated by using Geider model, which this model is based on photosynthesis irradiance curve (PI-curve) and focused on flat panel photobioreactor. Therefore, in this study a mathematical model for microalgae growth in cylindrical photobioreactor is proposed based on the Geider model. The light irradiance is the crucial part that affects the growth rate of microalgae. The absorbed photon flux will be determined by calculating the average light irradiance in a cylindrical system illuminated by unidirectional parallel flux and considering the cylinder as a collection of differential parallelepipeds. Results from this study showed that the specific growth rate of microalgae increases until the constant level is achieved. Therefore, the proposed mathematical model can be used to estimate the rate of microalgae growth in cylindrical photobioreactor.
Mathematical models in marketing a collection of abstracts
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...
Mathematics of epidemics on networks from exact to approximate models
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...
Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century.
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.