UH-60A Black Hawk engineering simulation program. Volume 1: Mathematical model

NASA Technical Reports Server (NTRS)

Howlett, J. J.

1981-01-01

A nonlinear mathematical model of the UR-60A Black Hawk helicopter was developed. This mathematical model, which was based on the Sikorsky General Helicopter (Gen Hel) Flight Dynamics Simulation, provides NASA with an engineering simulation for performance and handling qualities evaluations. This mathematical model is total systems definition of the Black Hawk helicopter represented at a uniform level of sophistication considered necessary for handling qualities evaluations. The model is a total force, large angle representation in six rigid body degrees of freedom. Rotor blade flapping, lagging, and hub rotational degrees of freedom are also represented. In addition to the basic helicopter modules, supportive modules were defined for the landing interface, power unit, ground effects, and gust penetration. Information defining the cockpit environment relevant to pilot in the loop simulation is presented.

Mathematization Competencies of Pre-Service Elementary Mathematics Teachers in the Mathematical Modelling Process

ERIC Educational Resources Information Center

Yilmaz, Suha; Tekin-Dede, Ayse

2016-01-01

Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified…

Friction-Stir Welding and Mathematical Modeling

NASA Technical Reports Server (NTRS)

Rostant, Victor D.

1999-01-01

The friction-stir welding process is a remarkable way for making butt and lap joints in aluminum alloys. This process operates by passing a rotating tool between two closely butted plates. Through this process it generates a lot of heat and heated material is stirred from both sides of the plates in which the outcome will one high quality weld. My research has been done to study the FSW through mathematical modeling, and using modeling to better understand what take place during the friction-stir weld.

Mathematical Modeling: A Structured Process

ERIC Educational Resources Information Center

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…

Specific Quality Criteria for Research Papers on Adults Learning Mathematics?

ERIC Educational Resources Information Center

Wedege, Tine

2009-01-01

Since 1997, the identity of the research field of adults learning mathematics has been debated; the research field has grown in quantity and quality; and the research forum Adults Learning Mathematics (ALM) has established an international journal. In practice, the researchers answer the question about identity and quality of research papers in…

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

ERIC Educational Resources Information Center

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…

Mathematical Modeling in Science: Using Spreadsheets to Create Mathematical Models and Address Scientific Inquiry

ERIC Educational Resources Information Center

Horton, Robert M.; Leonard, William H.

2005-01-01

In science, inquiry is used as students explore important and interesting questions concerning the world around them. In mathematics, one contemporary inquiry approach is to create models that describe real phenomena. Creating mathematical models using spreadsheets can help students learn at deep levels in both science and mathematics, and give…

The 24-Hour Mathematical Modeling Challenge

ERIC Educational Resources Information Center

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 model of design loading vessel

NASA Astrophysics Data System (ADS)

Budnik, V. Yu

2017-10-01

Transport by ferry is very important in our time. The paper shows the factors that affect the operation of the ferry. The constraints of the designed system were identified. The indicators of quality were articulated. It can be done by means of improving the decision-making process and the choice of the optimum loading options to ensure efficient functioning of Kerch strait ferry line. The algorithm and a mathematical model were developed.

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

ERIC Educational Resources Information Center

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…

Mathematical modelling in developmental biology.

PubMed

Vasieva, Olga; Rasolonjanahary, Manan'Iarivo; Vasiev, Bakhtier

2013-06-01

In recent decades, molecular and cellular biology has benefited from numerous fascinating developments in experimental technique, generating an overwhelming amount of data on various biological objects and processes. This, in turn, has led biologists to look for appropriate tools to facilitate systematic analysis of data. Thus, the need for mathematical techniques, which can be used to aid the classification and understanding of this ever-growing body of experimental data, is more profound now than ever before. Mathematical modelling is becoming increasingly integrated into biological studies in general and into developmental biology particularly. This review outlines some achievements of mathematics as applied to developmental biology and demonstrates the mathematical formulation of basic principles driving morphogenesis. We begin by describing a mathematical formalism used to analyse the formation and scaling of morphogen gradients. Then we address a problem of interplay between the dynamics of morphogen gradients and movement of cells, referring to mathematical models of gastrulation in the chick embryo. In the last section, we give an overview of various mathematical models used in the study of the developmental cycle of Dictyostelium discoideum, which is probably the best example of successful mathematical modelling in developmental biology.

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

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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

2017-01-01

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

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

ERIC Educational Resources Information Center

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…

Instructional Qualities of a Successful Mathematical Problem-Solving Class.

ERIC Educational Resources Information Center

Santos-Trigo, Manuel

1998-01-01

Describes activities that have been successfully implemented by an expert during a mathematical problem-solving course. Focuses on the identification of the qualities of these problems used to promote the development of student strategies and values that reflect mathematical practice in the classroom. Contains 17 references. (ASK)

Mathematical Modeling: Convoying Merchant Ships

ERIC Educational Resources Information Center

Mathews, Susann M.

2004-01-01

This article describes a mathematical model that connects mathematics with social studies. Students use mathematics to model independent versus convoyed ship deployments and sinkings to determine if the British should have convoyed their merchant ships during World War I. During the war, the British admiralty opposed sending merchant ships grouped…

A Primer for Mathematical Modeling

ERIC Educational Resources Information Center

Sole, Marla

2013-01-01

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

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

ERIC Educational Resources Information Center

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…

A Mathematical Diet Model

ERIC Educational Resources Information Center

Toumasis, Charalampos

2004-01-01

Emphasis on problem solving and mathematical modeling has gained considerable attention in the last few years. Connecting mathematics to other subjects and to the real world outside the classroom has received increased attention in mathematics programs. This article describes an application of simple differential equations in the field of…

Quality of Teaching Mathematics and Learning Achievement Gains: Evidence from Primary Schools in Kenya

ERIC Educational Resources Information Center

Ngware, Moses W.; Ciera, James; Musyoka, Peter K.; Oketch, Moses

2015-01-01

This paper examines the contribution of quality mathematics teaching to student achievement gains. Quality of mathematics teaching is assessed through teacher demonstration of the five strands of mathematical proficiency, the level of cognitive task demands, and teacher mathematical knowledge. Data is based on 1907 grade 6 students who sat for the…

Developing a Mathematics Education Quality Scale

ERIC Educational Resources Information Center

Ciftci, S. Koza; Karadag, Engin

2016-01-01

The aim of this study was to evaluate students' perceptions of the quality of mathematics education and to develop a reliable and valid measurement tool. The research was conducted with 638 (first study) and 407 (second study) secondary school students in Eskisehir, Turkey. Item discrimination, structural validity (exploratory factor analysis and…

Mathematical Modeling: Challenging the Figured Worlds of Elementary Mathematics

ERIC Educational Resources Information Center

Wickstrom, Megan H.

2017-01-01

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

Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape

ERIC Educational Resources Information Center

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

2014-01-01

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

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

NASA Astrophysics Data System (ADS)

Juandi, D.; Priatna, N.

2018-05-01

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

Mathematical Modeling in the Undergraduate Curriculum

ERIC Educational Resources Information Center

Toews, Carl

2012-01-01

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

Teachers' Conceptions of Mathematical Modeling

ERIC Educational Resources Information Center

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…

Mathematics Teaching Today

ERIC Educational Resources Information Center

Martin, Tami S.; Speer, William R.

2009-01-01

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

Mathematical Modeling: A Bridge to STEM Education

ERIC Educational Resources Information Center

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…

Mathematical models for plant-herbivore interactions

USGS Publications Warehouse

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.

Mathematics teachers' conceptions about modelling activities and its reflection on their beliefs about mathematics

NASA Astrophysics Data System (ADS)

Shahbari, Juhaina Awawdeh

2018-07-01

The current study examines whether the engagement of mathematics teachers in modelling activities and subsequent changes in their conceptions about these activities affect their beliefs about mathematics. The sample comprised 52 mathematics teachers working in small groups in four modelling activities. The data were collected from teachers' Reports about features of each activity, interviews and questionnaires on teachers' beliefs about mathematics. The findings indicated changes in teachers' conceptions about the modelling activities. Most teachers referred to the first activity as a mathematical problem but emphasized only the mathematical notions or the mathematical operations in the modelling process; changes in their conceptions were gradual. Most of the teachers referred to the fourth activity as a mathematical problem and emphasized features of the whole modelling process. The results of the interviews indicated that changes in the teachers' conceptions can be attributed to structure of the activities, group discussions, solution paths and elicited models. These changes about modelling activities were reflected in teachers' beliefs about mathematics. The quantitative findings indicated that the teachers developed more constructive beliefs about mathematics after engagement in the modelling activities and that the difference was significant, however there was no significant difference regarding changes in their traditional beliefs.

Complexity analysis and mathematical tools towards the modelling of living systems.

PubMed

Bellomo, N; Bianca, C; Delitala, M

2009-09-01

This paper is a review and critical analysis of the mathematical kinetic theory of active particles applied to the modelling of large living systems made up of interacting entities. The first part of the paper is focused on a general presentation of the mathematical tools of the kinetic theory of active particles. The second part provides a review of a variety of mathematical models in life sciences, namely complex social systems, opinion formation, evolution of epidemics with virus mutations, and vehicular traffic, crowds and swarms. All the applications are technically related to the mathematical structures reviewed in the first part of the paper. The overall contents are based on the concept that living systems, unlike the inert matter, have the ability to develop behaviour geared towards their survival, or simply to improve the quality of their life. In some cases, the behaviour evolves in time and generates destructive and/or proliferative events.

Turbine Engine Mathematical Model Validation

DTIC Science & Technology

1976-12-01

AEDC-TR-76-90 ~Ec i ? Z985 TURBINE ENGINE MATHEMATICAL MODEL VALIDATION ENGINE TEST FACILITY ARNOLD ENGINEERING DEVELOPMENT CENTER AIR FORCE...i f n e c e s e a ~ ~ d i den t i f y by b l ock number) YJI01-GE-100 engine turbine engines mathematical models computations mathematical...report presents and discusses the results of an investigation to develop a rationale and technique for the validation of turbine engine steady-state

Total Quality Management in the Classroom: Applications to University-Level Mathematics.

ERIC Educational Resources Information Center

Williams, Frank

1995-01-01

Describes a Total Quality Management-based system of instruction that is used in a variety of undergraduate mathematics courses. The courses that incorporate this approach include mathematics appreciation, introductory calculus, and advanced applied linear algebra. (DDR)

Systems oncology: towards patient-specific treatment regimes informed by multiscale mathematical modelling.

PubMed

Powathil, Gibin G; Swat, Maciej; Chaplain, Mark A J

2015-02-01

The multiscale complexity of cancer as a disease necessitates a corresponding multiscale modelling approach to produce truly predictive mathematical models capable of improving existing treatment protocols. To capture all the dynamics of solid tumour growth and its progression, mathematical modellers need to couple biological processes occurring at various spatial and temporal scales (from genes to tissues). Because effectiveness of cancer therapy is considerably affected by intracellular and extracellular heterogeneities as well as by the dynamical changes in the tissue microenvironment, any model attempt to optimise existing protocols must consider these factors ultimately leading to improved multimodal treatment regimes. By improving existing and building new mathematical models of cancer, modellers can play important role in preventing the use of potentially sub-optimal treatment combinations. In this paper, we analyse a multiscale computational mathematical model for cancer growth and spread, incorporating the multiple effects of radiation therapy and chemotherapy in the patient survival probability and implement the model using two different cell based modelling techniques. We show that the insights provided by such multiscale modelling approaches can ultimately help in designing optimal patient-specific multi-modality treatment protocols that may increase patients quality of life. Copyright © 2014 Elsevier Ltd. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Mathematical Modeling and Computational Thinking

ERIC Educational Resources Information Center

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…

Faculty Sufficiency and AACSB Accreditation Compliance within a Global University: A Mathematical Modeling Approach

ERIC Educational Resources Information Center

Boronico, Jess; Murdy, Jim; Kong, Xinlu

2014-01-01

This manuscript proposes a mathematical model to address faculty sufficiency requirements towards assuring overall high quality management education at a global university. Constraining elements include full-time faculty coverage by discipline, location, and program, across multiple campus locations subject to stated service quality standards of…

Summer Camp of Mathematical Modeling in China

ERIC Educational Resources Information Center

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…

Strategies to Support Students' Mathematical Modeling

ERIC Educational Resources Information Center

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…

Explorations in Elementary Mathematical Modeling

ERIC Educational Resources Information Center

Shahin, Mazen

2010-01-01

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

Mathematical models of cell motility.

PubMed

Flaherty, Brendan; McGarry, J P; McHugh, P E

2007-01-01

Cell motility is an essential biological action in the creation, operation and maintenance of our bodies. Developing mathematical models elucidating cell motility will greatly advance our understanding of this fundamental biological process. With accurate models it is possible to explore many permutations of the same event and concisely investigate their outcome. While great advancements have been made in experimental studies of cell motility, it now has somewhat fallen on mathematical models to taking a leading role in future developments. The obvious reason for this is the complexity of cell motility. Employing the processing power of today's computers will give researches the ability to run complex biophysical and biochemical scenarios, without the inherent difficulty and time associated with in vitro investigations. Before any great advancement can be made, the basics of cell motility will have to be well-defined. Without this, complicated mathematical models will be hindered by their inherent conjecture. This review will look at current mathematical investigations of cell motility, explore the reasoning behind such work and conclude with how best to advance this interesting and challenging research area.

Mathematical Modeling of Diverse Phenomena

NASA Technical Reports Server (NTRS)

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.

The Effect of Instruction through Mathematical Modelling on Modelling Skills of Prospective Elementary Mathematics Teachers

ERIC Educational Resources Information Center

Ciltas, Alper; Isik, Ahmet

2013-01-01

The aim of this study was to examine the modelling skills of prospective elementary mathematics teachers who were studying the mathematical modelling method. The research study group was composed of 35 prospective teachers. The exploratory case analysis method was used in the study. The data were obtained via semi-structured interviews and a…

A mathematical model of reservoir sediment quality prediction based on land-use and erosion processes in watershed

NASA Astrophysics Data System (ADS)

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.

Correlation of spacecraft thermal mathematical models to reference data

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-02-01

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

Mathematical modeling of fluxgate magnetic gradiometers

NASA Astrophysics Data System (ADS)

Milovzorov, D. G.; Yasoveev, V. Kh.

2017-07-01

Issues of designing fluxgate magnetic gradiometers are considered. The areas of application of fluxgate magnetic gradiometers are determined. The structure and layout of a two-component fluxgate magnetic gradiometer are presented. It is assumed that the fluxgates are strictly coaxial in the gradiometer body. Elements of the classical approach to the mathematical modeling of the spatial arrangement of solids are considered. The bases of the gradiometer body and their transformations during spatial displacement of the gradiometer are given. The problems of mathematical modeling of gradiometers are formulated, basic mathematical models of a two-component fluxgate gradiometer are developed, and the mathematical models are analyzed. A computer experiment was performed. Difference signals from the gradiometer fluxgates for the vertical and horizontal position of the gradiometer body are shown graphically as functions of the magnitude and direction of the geomagnetic field strength vector.

Mathematical models of behavior of individual animals.

PubMed

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.

Opinions of Secondary School Mathematics Teachers on Mathematical Modelling

ERIC Educational Resources Information Center

Tutak, Tayfun; Güder, Yunus

2013-01-01

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

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

ERIC Educational Resources Information Center

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…

Current problems in applied mathematics and mathematical modeling

NASA Astrophysics Data System (ADS)

Alekseev, A. S.

Papers are presented on mathematical modeling noting applications to such fields as geophysics, chemistry, atmospheric optics, and immunology. Attention is also given to models of ocean current fluxes, atmospheric and marine interactions, and atmospheric pollution. The articles include studies of catalytic reactors, models of global climate phenomena, and computer-assisted atmospheric models.

Mathematical Models for Doppler Measurements

NASA Technical Reports Server (NTRS)

Lear, William M.

1987-01-01

Error analysis increases precision of navigation. Report presents improved mathematical models of analysis of Doppler measurements and measurement errors of spacecraft navigation. To take advantage of potential navigational accuracy of Doppler measurements, precise equations relate measured cycle count to position and velocity. Drifts and random variations in transmitter and receiver oscillator frequencies taken into account. Mathematical models also adapted to aircraft navigation, radar, sonar, lidar, and interferometry.

An Experimental Approach to Mathematical Modeling in Biology

ERIC Educational Resources Information Center

Ledder, Glenn

2008-01-01

The simplest age-structured population models update a population vector via multiplication by a matrix. These linear models offer an opportunity to introduce mathematical modeling to students of limited mathematical sophistication and background. We begin with a detailed discussion of mathematical modeling, particularly in a biological context.…

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

ERIC Educational Resources Information Center

Zbiek, Rose Mary; Conner, Annamarie

2006-01-01

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

Mathematical form models of tree trunks

Treesearch

Rudolfs Ozolins

2000-01-01

Assortment structure analysis of tree trunks is a characteristic and proper problem that can be solved by using mathematical modeling and standard computer programs. Mathematical form model of tree trunks consists of tapering curve equations and their parameters. Parameters for nine species were obtained by processing measurements of 2,794 model trees and studying the...

ASTP ranging system mathematical model

NASA Technical Reports Server (NTRS)

Ellis, M. R.; Robinson, L. H.

1973-01-01

A mathematical model is presented of the VHF ranging system to analyze the performance of the Apollo-Soyuz test project (ASTP). The system was adapted for use in the ASTP. The ranging system mathematical model is presented in block diagram form, and a brief description of the overall model is also included. A procedure for implementing the math model is presented along with a discussion of the validation of the math model and the overall summary and conclusions of the study effort. Detailed appendices of the five study tasks are presented: early late gate model development, unlock probability development, system error model development, probability of acquisition and model development, and math model validation testing.

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

NASA Astrophysics Data System (ADS)

Khusna, H.; Heryaningsih, N. Y.

2018-01-01

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

Mathematical Modelling as a Professional Task

ERIC Educational Resources Information Center

Frejd, Peter; Bergsten, Christer

2016-01-01

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

Using Covariation Reasoning to Support Mathematical Modeling

ERIC Educational Resources Information Center

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…

Rescheduling nursing shifts: scoping the challenge and examining the potential of mathematical model based tools.

PubMed

Clark, Alistair; Moule, Pam; Topping, Annie; Serpell, Martin

2015-05-01

To review research in the literature on nursing shift scheduling / rescheduling, and to report key issues identified in a consultation exercise with managers in four English National Health Service trusts to inform the development of mathematical tools for rescheduling decision-making. Shift rescheduling is unrecognised as an everyday time-consuming management task with different imperatives from scheduling. Poor rescheduling decisions can have quality, cost and morale implications. A systematic critical literature review identified rescheduling issues and existing mathematic modelling tools. A consultation exercise with nursing managers examined the complex challenges associated with rescheduling. Minimal research exists on rescheduling compared with scheduling. Poor rescheduling can result in greater disruption to planned nursing shifts and may impact negatively on the quality and cost of patient care, and nurse morale and retention. Very little research examines management challenges or mathematical modelling for rescheduling. Shift rescheduling is a complex and frequent management activity that is more challenging than scheduling. Mathematical modelling may have potential as a tool to support managers to minimise rescheduling disruption. The lack of specific methodological support for rescheduling that takes into account its complexity, increases the likelihood of harm for patients and stress for nursing staff and managers. © 2013 John Wiley & Sons Ltd.

Detecting Strengths and Weaknesses in Learning Mathematics through a Model Classifying Mathematical Skills

ERIC Educational Resources Information Center

Karagiannakis, Giannis N.; Baccaglini-Frank, Anna E.; Roussos, Petros

2016-01-01

Through a review of the literature on mathematical learning disabilities (MLD) and low achievement in mathematics (LA) we have proposed a model classifying mathematical skills involved in learning mathematics into four domains (Core number, Memory, Reasoning, and Visual-spatial). In this paper we present a new experimental computer-based battery…

Automatic mathematical modeling for space application

NASA Technical Reports Server (NTRS)

Wang, Caroline K.

1987-01-01

A methodology for automatic mathematical modeling is described. The major objective is to create a very friendly environment for engineers to design, maintain and verify their model and also automatically convert the mathematical model into FORTRAN code for conventional computation. A demonstration program was designed for modeling the Space Shuttle Main Engine simulation mathematical model called Propulsion System Automatic Modeling (PSAM). PSAM provides a very friendly and well organized environment for engineers to build a knowledge base for base equations and general information. PSAM contains an initial set of component process elements for the Space Shuttle Main Engine simulation and a questionnaire that allows the engineer to answer a set of questions to specify a particular model. PSAM is then able to automatically generate the model and the FORTRAN code. A future goal is to download the FORTRAN code to the VAX/VMS system for conventional computation.

Mathematical models frame environmental dispute [Review of the article Useless arithmetic: Ten points to ponder when using mathematical models in environmental decision making

USGS Publications Warehouse

Lamb, Berton Lee; Burkardt, Nina

2008-01-01

When Linda Pilkey- Jarvis and Orrin Pilkey state in their article, "Useless Arithmetic," that "mathematical models are simplified, generalized representations of a process or system," they probably do not mean to imply that these models are simple. Rather, the models are simpler than nature and that is the heart of the problem with predictive models. We have had a long professional association with the developers and users of one of these simplifications of nature in the form of a mathematical model known as Physical Habitat Simulation (PHABSIM), which is part of the Instream Flow Incremental Methodology (IFIM). The IFIM is a suite of techniques, including PHABSIM, that allows the analyst to incorporate hydrology , hydraulics, habitat, water quality, stream temperature, and other variables into a tradeoff analysis that decision makers can use to design a flow regime to meet management objectives (Stalnaker et al. 1995). Although we are not the developers of the IFIM, we have worked with those who did design it, and we have tried to understand how the IFIM and PHABSIM are actually used in decision making (King, Burkardt, and Clark 2006; Lamb 1989).

On Fences, Forms and Mathematical Modeling

ERIC Educational Resources Information Center

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 Modeling in the High School Curriculum

ERIC Educational Resources Information Center

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…

Students' Mathematical Modeling of Motion

ERIC Educational Resources Information Center

Marshall, Jill A.; Carrejo, David J.

2008-01-01

We present results of an investigation of university students' development of mathematical models of motion in a physical science course for preservice teachers and graduate students in science and mathematics education. Although some students were familiar with the standard concepts of position, velocity, and acceleration from physics classes,…

Mathematical Modeling Approaches in Plant Metabolomics.

PubMed

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

2018-01-01

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

V/STOL tilt rotor aircraft study mathematical model for a real time simulation of a tilt rotor aircraft (Boeing Vertol Model 222), volume 8

NASA Technical Reports Server (NTRS)

Rosenstein, H.; Mcveigh, M. A.; Mollenkof, P. A.

1973-01-01

A mathematical model for a real time simulation of a tilt rotor aircraft was developed. The mathematical model is used for evaluating aircraft performance and handling qualities. The model is based on an eleven degree of freedom total force representation. The rotor is treated as a point source of forces and moments with appropriate response time lags and actuator dynamics. The aerodynamics of the wing, tail, rotors, landing gear, and fuselage are included.

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

ERIC Educational Resources Information Center

Stohlmann, Micah S.

2017-01-01

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

Problem Posing and Solving with Mathematical Modeling

ERIC Educational Resources Information Center

English, Lyn D.; Fox, Jillian L.; Watters, James J.

2005-01-01

Mathematical modeling is explored as both problem posing and problem solving from two perspectives, that of the child and the teacher. Mathematical modeling provides rich learning experiences for elementary school children and their teachers.

Examples of Mathematical Modeling

PubMed Central

Johnston, Matthew D.; Edwards, Carina M.; Bodmer, Walter F.; Maini, Philip K.; Chapman, S. Jonathan

2008-01-01

Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological systems. The heavily regulated cell renewal cycle in the colonic crypt provides a good example of how modeling can be used to find out key features of the system kinetics, and help to explain both the breakdown of homeostasis and the initiation of tumorigenesis. We use the cell population model by Johnston et al.5 to illustrate the power of mathematical modeling by considering two key questions about the cell population dynamics in the colonic crypt. We ask: how can a model describe both homeostasis and unregulated growth in tumorigenesis; and to which parameters in the system is the model most sensitive? In order to address these questions, we discuss what type of modeling approach is most appropriate in the crypt. We use the model to argue why tumorigenesis is observed to occur in stages with long lag phases between periods of rapid growth, and we identify the key parameters. PMID:17873520

Perception on mathematics teachers' quality of teaching between all boys secondary schools and all girls secondary schools

NASA Astrophysics Data System (ADS)

Arbin, Norazman; Kamarudin, Norsyazana; Abu, Mohd Syafarudy; Hamzah, Firdaus Mohamad; Ghani, Sazelli Abdul

2015-05-01

This survey research was designed to identify the secondary mathematics teachers' quality of teaching. Specifically, this study focused on students' perception, based on genders on the quality of teaching of their secondary mathematics teachers and, its relationship with the former's mathematics achievement. This research was carried in four different schools: two all boys' secondary schools and two all girls' secondary schools. Thus, a comparison between these two types of schools was made. The sample of the study involved 100 form four students from those schools. The result showed that the students from those schools had positive perception on their teachers' quality of teaching. Statistically, there was no difference between the boys' and girls' perceptions. There was a significant relationship between the boys' perception on the quality of their teachers' teaching and the boys' achievement. However, there was no significant relationship between the girls' perceptions on the quality of their teachers' teaching and the girls' achievement. The findings of this research could be used as a useful guideline for mathematics teachers and future mathematics teachers in enhancing the quality of their teaching and learning.

Mathematical models and qualities of shredded Thai-style instant rice under a combined gas-fired infrared and air convection drying

NASA Astrophysics Data System (ADS)

Nachaisin, Mali; Teeta, Suminya; Deejing, Konlayut; Pharanat, Wanida

2017-09-01

Instant food is a product produced for convenience for consumer. Qualities are an important attribute of food materials reflecting consumer acceptance. The most problem of instant rice is casehardening during drying process resulted in the longer rehydration time. The objective of this research was to study the qualities of shredded Thai-style instant rice under a combined gas-fired infrared and air convection drying. Additionally, the mathematical models for gas-fired infrared assisted thin-layer drying of shredded Thai-style rice for traditional was investigated. The thin-layer drying of shredded Thai-style rice was carried out under gas-fired infrared intensities of 1000W/m2, air temperatures of 70°C and air velocities of 1 m/s. The drying occurred in the falling rate of drying period. The Page model was found to satisfactorily describe the drying behavior of shredded Thai-style rice, providing the highest R2 (0.997) and the lowest MBE and RMSE (0.01 and 0.18) respectively. A 9 point hedonic test showed in softness and color, but odor and overall acceptance were very similar.

Subject-Specific Characteristics of Instructional Quality in Mathematics Education

ERIC Educational Resources Information Center

Schlesinger, Lena; Jentsch, Armin; Kaiser, Gabriele; König, Johannes; Blömeke, Sigrid

2018-01-01

Instructional research in German-speaking countries has conceptualized teaching quality recently according to three generic dimensions, namely, classroom management, student support and cognitive activation. However, as these dimensions are mainly regarded as generic, subject-specific aspects of mathematics instruction, e.g., the mathematical…

Analyzing the quality robustness of chemotherapy plans with respect to model uncertainties.

PubMed

Hoffmann, Anna; Scherrer, Alexander; Küfer, Karl-Heinz

2015-01-01

Mathematical models of chemotherapy planning problems contain various biomedical parameters, whose values are difficult to quantify and thus subject to some uncertainty. This uncertainty propagates into the therapy plans computed on these models, which poses the question of robustness to the expected therapy quality. This work introduces a combined approach for analyzing the quality robustness of plans in terms of dosing levels with respect to model uncertainties in chemotherapy planning. It uses concepts from multi-criteria decision making for studying parameters related to the balancing between the different therapy goals, and concepts from sensitivity analysis for the examination of parameters describing the underlying biomedical processes and their interplay. This approach allows for a profound assessment of a therapy plan, how stable its quality is with respect to parametric changes in the used mathematical model. Copyright © 2014 Elsevier Inc. All rights reserved.

The mathematics of cancer: integrating quantitative models.

PubMed

Altrock, Philipp M; Liu, Lin L; Michor, Franziska

2015-12-01

Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.

Mathematical modeling of laser lipolysis

PubMed Central

Mordon, Serge R; Wassmer, Benjamin; Reynaud, Jean Pascal; Zemmouri, Jaouad

2008-01-01

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 depends on the applied

An Analysis of Instruments that Measure the Quality of Mathematics Teaching in Early Childhood

ERIC Educational Resources Information Center

Kilday, Carolyn R.; Kinzie, Mable B.

2009-01-01

The evaluation of teaching quality in mathematics has become increasingly important following research reports indicating that preschoolers are developmentally able to engage in mathematic thought and that child performance in mathematics at this level is a strong predictor of later school achievement. As attention turns to early mathematics…

From Biology to Mathematical Models and Back: Teaching Modeling to Biology Students, and Biology to Math and Engineering Students

PubMed Central

McManus, Jeffrey M.; Shaw, Kendrick M.

2010-01-01

We describe the development of a course to teach modeling and mathematical analysis skills to students of biology and to teach biology to students with strong backgrounds in mathematics, physics, or engineering. The two groups of students have different ways of learning material and often have strong negative feelings toward the area of knowledge that they find difficult. To give students a sense of mastery in each area, several complementary approaches are used in the course: 1) a “live” textbook that allows students to explore models and mathematical processes interactively; 2) benchmark problems providing key skills on which students make continuous progress; 3) assignment of students to teams of two throughout the semester; 4) regular one-on-one interactions with instructors throughout the semester; and 5) a term project in which students reconstruct, analyze, extend, and then write in detail about a recently published biological model. Based on student evaluations and comments, an attitude survey, and the quality of the students' term papers, the course has significantly increased the ability and willingness of biology students to use mathematical concepts and modeling tools to understand biological systems, and it has significantly enhanced engineering students' appreciation of biology. PMID:20810957

From biology to mathematical models and back: teaching modeling to biology students, and biology to math and engineering students.

PubMed

Chiel, Hillel J; McManus, Jeffrey M; Shaw, Kendrick M

2010-01-01

We describe the development of a course to teach modeling and mathematical analysis skills to students of biology and to teach biology to students with strong backgrounds in mathematics, physics, or engineering. The two groups of students have different ways of learning material and often have strong negative feelings toward the area of knowledge that they find difficult. To give students a sense of mastery in each area, several complementary approaches are used in the course: 1) a "live" textbook that allows students to explore models and mathematical processes interactively; 2) benchmark problems providing key skills on which students make continuous progress; 3) assignment of students to teams of two throughout the semester; 4) regular one-on-one interactions with instructors throughout the semester; and 5) a term project in which students reconstruct, analyze, extend, and then write in detail about a recently published biological model. Based on student evaluations and comments, an attitude survey, and the quality of the students' term papers, the course has significantly increased the ability and willingness of biology students to use mathematical concepts and modeling tools to understand biological systems, and it has significantly enhanced engineering students' appreciation of biology.

Exploring Yellowstone National Park with Mathematical Modeling

ERIC Educational Resources Information Center

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…

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

ERIC Educational Resources Information Center

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…

A simplified rotor system mathematical model for piloted flight dynamics simulation

NASA Technical Reports Server (NTRS)

Chen, R. T. N.

1979-01-01

The model was developed for real-time pilot-in-the-loop investigation of helicopter flying qualities. The mathematical model included the tip-path plane dynamics and several primary rotor design parameters, such as flapping hinge restraint, flapping hinge offset, blade Lock number, and pitch-flap coupling. The model was used in several exploratory studies of the flying qualities of helicopters with a variety of rotor systems. The basic assumptions used and the major steps involved in the development of the set of equations listed are described. The equations consisted of the tip-path plane dynamic equation, the equations for the main rotor forces and moments, and the equation for control phasing required to achieve decoupling in pitch and roll due to cyclic inputs.

Teaching Mathematical Modelling for Earth Sciences via Case Studies

NASA Astrophysics Data System (ADS)

Yang, Xin-She

2010-05-01

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

Rival approaches to mathematical modelling in immunology

NASA Astrophysics Data System (ADS)

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

2007-08-01

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

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

PubMed

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

2010-01-01

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

An Examination of Pre-Service Mathematics Teachers' Approaches to Construct and Solve Mathematical Modelling Problems

ERIC Educational Resources Information Center

Bukova-Guzel, Esra

2011-01-01

This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling…

UNCERTAINTY ANALYSIS IN WATER QUALITY MODELING USING QUAL2E

EPA Science Inventory

A strategy for incorporating uncertainty analysis techniques (sensitivity analysis, first order error analysis, and Monte Carlo simulation) into the mathematical water quality model QUAL2E is described. The model, named QUAL2E-UNCAS, automatically selects the input variables or p...

Mathematical modeling of urea transport in the kidney.

PubMed

Layton, Anita T

2014-01-01

Mathematical modeling techniques have been useful in providing insights into biological systems, including the kidney. This article considers some of the mathematical models that concern urea transport in the kidney. Modeling simulations have been conducted to investigate, in the context of urea cycling and urine concentration, the effects of hypothetical active urea secretion into pars recta. Simulation results suggest that active urea secretion induces a "urea-selective" improvement in urine concentrating ability. Mathematical models have also been built to study the implications of the highly structured organization of tubules and vessels in the renal medulla on urea sequestration and cycling. The goal of this article is to show how physiological problems can be formulated and studied mathematically, and how such models may provide insights into renal functions.

The (Mathematical) Modeling Process in Biosciences

PubMed Central

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. PMID:26734063

The (Mathematical) Modeling Process in Biosciences.

PubMed

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.

Establishing an Explanatory Model for Mathematics Identity.

PubMed

Cribbs, Jennifer D; Hazari, Zahra; Sonnert, Gerhard; Sadler, Philip M

2015-04-01

This article empirically tests a previously developed theoretical framework for mathematics identity based on students' beliefs. The study employs data from more than 9,000 college calculus students across the United States to build a robust structural equation model. While it is generally thought that students' beliefs about their own competence in mathematics directly impact their identity as a "math person," findings indicate that students' self-perceptions related to competence and performance have an indirect effect on their mathematics identity, primarily by association with students' interest and external recognition in mathematics. Thus, the model indicates that students' competence and performance beliefs are not sufficient for their mathematics identity development, and it highlights the roles of interest and recognition. © 2015 The Authors. Child Development © 2015 Society for Research in Child Development, Inc.

Mathematical modeling for resource and energy saving control of extruders in multi-assortment productions of polymeric films

NASA Astrophysics Data System (ADS)

Polosin, A. N.; Chistyakova, T. B.

2018-05-01

In this article, the authors describe mathematical modeling of polymer processing in extruders of various types used in extrusion and calender productions of film materials. The method consists of the synthesis of a static model for calculating throughput, energy consumption of the extruder, extrudate quality indices, as well as a dynamic model for evaluating polymer residence time in the extruder, on which the quality indices depend. Models are adjusted according to the extruder type (single-screw, reciprocating, twin-screw), its screw and head configuration, extruder’s work temperature conditions, and the processed polymer type. Models enable creating extruder screw configurations and determining extruder controlling action values that provide the extrudate of required quality while satisfying extruder throughput and energy consumption requirements. Model adequacy has been verified using polyolefins’ and polyvinylchloride processing data in different extruders. The program complex, based on mathematical models, has been developed in order to control extruders of various types in order to ensure resource and energy saving in multi-assortment productions of polymeric films. Using the program complex in the control system for the extrusion stage of the polymeric film productions enables improving film quality, reducing spoilage, lessening the time required for production line change-over to other throughput and film type assignment.

Mathematical modelling of intra-aortic balloon pump.

PubMed

Abdolrazaghi, Mona; Navidbakhsh, Mahdi; Hassani, Kamran

2010-10-01

Ischemic heart diseases now afflict thousands of Iranians and are the major cause of death in many industrialised countries. Mathematical modelling of an intra-aortic balloon pump (IABP) could provide a better understanding of its performance and help to represent blood flow and pressure in systemic arteries before and after inserting the pump. A mathematical modelling of the whole cardiovascular system was formulated using MATLAB software. The block diagram of the model consists of 43 compartments. All the anatomical data was extracted from the physiological references. In the next stage, myocardial infarction (MI) was induced in the model by decreasing the contractility of the left ventricle. The IABP was mathematically modelled and inserted in the model in the thoracic aorta I artery just before the descending aorta. The effects of IABP on MI were studied using the mathematical model. The normal operation of the cardiovascular system was studied firstly. The pressure-time graphs of the ventricles, atriums, aorta, pulmonary system, capillaries and arterioles were obtained. The volume-time curve of the left ventricle was also presented. The pressure-time curves of the left ventricle and thoracic aorta I were obtained for normal, MI, and inserted IABP conditions. Model verification was performed by comparing the simulation results with the clinical observations reported in the literature. IABP can be described by a theoretical model. Our model representing the cardiovascular system is capable of showing the effects of different pathologies such as MI and we have shown that MI effects can be reduced using IABP in accordance with the modelling results. The mathematical model should serve as a useful tool to simulate and better understand cardiovascular operation in normal and pathological conditions.

Mathematical modeling of aeroelastic systems

NASA Astrophysics Data System (ADS)

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.

Modelling and Optimizing Mathematics Learning in Children

ERIC Educational Resources Information Center

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

2013-01-01

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

A Review of Mathematical Models for Leukemia and Lymphoma

PubMed Central

Clapp, Geoffrey; Levy, Doron

2014-01-01

Recently, there has been significant activity in the mathematical community, aimed at developing quantitative tools for studying leukemia and lymphoma. Mathematical models have been applied to evaluate existing therapies and to suggest novel therapies. This article reviews the recent contributions of mathematical modeling to leukemia and lymphoma research. These developments suggest that mathematical modeling has great potential in this field. Collaboration between mathematicians, clinicians, and experimentalists can significantly improve leukemia and lymphoma therapy. PMID:26744598

Gulf of Mexico dissolved oxygen model (GoMDOM) research and quality assurance project plan

EPA Science Inventory

An integrated high resolution mathematical modeling framework is being developed that will link hydrodynamic, atmospheric, and water quality models for the northern Gulf of Mexico. This Research and Quality Assurance Project Plan primarily focuses on the deterministic Gulf of Me...

Mathematical modeling of a process the rolling delivery

NASA Astrophysics Data System (ADS)

Stepanov, Mikhail A.; Korolev, Andrey A.

2018-03-01

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

Mathematical Modeling in the Secondary School Curriculum.

ERIC Educational Resources Information Center

Swetz, Frank, Ed.; Hartzler, J. S., Ed.

Over the past 10 years, national conferences and committees investigating the state of American mathematics education have advocated an increased emphasis on problem solving and mathematical modeling situations in the secondary school curriculum. However, little effort has been made to prepare secondary school teachers to use mathematical modeling…

A Survey of Mathematics Education Technology Dissertation Scope and Quality: 1968-2009

ERIC Educational Resources Information Center

Ronau, Robert N.; Rakes, Christopher R.; Bush, Sarah B.; Driskell, Shannon O.; Niess, Margaret L.; Pugalee, David K.

2014-01-01

We examined 480 dissertations on the use of technology in mathematics education and developed a Quality Framework (QF) that provided structure to consistently define and measure quality. Dissertation studies earned an average of 64.4% of the possible quality points across all methodology types, compared to studies in journals that averaged 47.2%.…

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

NASA Astrophysics Data System (ADS)

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

2017-09-01

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

Modelling Mathematical Reasoning in Physics Education

NASA Astrophysics Data System (ADS)

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

2012-04-01

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

Scaffolding Mathematical Modelling with a Solution Plan

ERIC Educational Resources Information Center

Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner

2015-01-01

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

Leading Undergraduate Research Projects in Mathematical Modeling

ERIC Educational Resources Information Center

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…

Predicting human chronically paralyzed muscle force: a comparison of three mathematical models.

PubMed

Frey Law, Laura A; Shields, Richard K

2006-03-01

Chronic spinal cord injury (SCI) induces detrimental musculoskeletal adaptations that adversely affect health status, ranging from muscle paralysis and skin ulcerations to osteoporosis. SCI rehabilitative efforts may increasingly focus on preserving the integrity of paralyzed extremities to maximize health quality using electrical stimulation for isometric training and/or functional activities. Subject-specific mathematical muscle models could prove valuable for predicting the forces necessary to achieve therapeutic loading conditions in individuals with paralyzed limbs. Although numerous muscle models are available, three modeling approaches were chosen that can accommodate a variety of stimulation input patterns. To our knowledge, no direct comparisons between models using paralyzed muscle have been reported. The three models include 1) a simple second-order linear model with three parameters and 2) two six-parameter nonlinear models (a second-order nonlinear model and a Hill-derived nonlinear model). Soleus muscle forces from four individuals with complete, chronic SCI were used to optimize each model's parameters (using an increasing and decreasing frequency ramp) and to assess the models' predictive accuracies for constant and variable (doublet) stimulation trains at 5, 10, and 20 Hz in each individual. Despite the large differences in modeling approaches, the mean predicted force errors differed only moderately (8-15% error; P=0.0042), suggesting physiological force can be adequately represented by multiple mathematical constructs. The two nonlinear models predicted specific force characteristics better than the linear model in nearly all stimulation conditions, with minimal differences between the two nonlinear models. Either nonlinear mathematical model can provide reasonable force estimates; individual application needs may dictate the preferred modeling strategy.

The Spectrum of Mathematical Models.

ERIC Educational Resources Information Center

Karplus, Walter J.

1983-01-01

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

Development of a Multidisciplinary Middle School Mathematics Infusion Model

ERIC Educational Resources Information Center

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…

Teaching Mathematical Word Problem Solving: The Quality of Evidence for Strategy Instruction Priming the Problem Structure

ERIC Educational Resources Information Center

Jitendra, Asha K.; Petersen-Brown, Shawna; Lein, Amy E.; Zaslofsky, Anne F.; Kunkel, Amy K.; Jung, Pyung-Gang; Egan, Andrea M.

2015-01-01

This study examined the quality of the research base related to strategy instruction priming the underlying mathematical problem structure for students with learning disabilities and those at risk for mathematics difficulties. We evaluated the quality of methodological rigor of 18 group research studies using the criteria proposed by Gersten et…

Ocular hemodynamics and glaucoma: the role of mathematical modeling.

PubMed

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.

Understanding the Impact of Interventions to Prevent Antimicrobial Resistant Infections in the Long-Term Care Facility: A Review and Practical Guide to Mathematical Modeling.

PubMed

Rosello, Alicia; Horner, Carolyne; Hopkins, Susan; Hayward, Andrew C; Deeny, Sarah R

2017-02-01

OBJECTIVES (1) To systematically search for all dynamic mathematical models of infectious disease transmission in long-term care facilities (LTCFs); (2) to critically evaluate models of interventions against antimicrobial resistance (AMR) in this setting; and (3) to develop a checklist for hospital epidemiologists and policy makers by which to distinguish good quality models of AMR in LTCFs. METHODS The CINAHL, EMBASE, Global Health, MEDLINE, and Scopus databases were systematically searched for studies of dynamic mathematical models set in LTCFs. Models of interventions targeting methicillin-resistant Staphylococcus aureus in LTCFs were critically assessed. Using this analysis, we developed a checklist for good quality mathematical models of AMR in LTCFs. RESULTS AND DISCUSSION Overall, 18 papers described mathematical models that characterized the spread of infectious diseases in LTCFs, but no models of AMR in gram-negative bacteria in this setting were described. Future models of AMR in LTCFs require a more robust methodology (ie, formal model fitting to data and validation), greater transparency regarding model assumptions, setting-specific data, realistic and current setting-specific parameters, and inclusion of movement dynamics between LTCFs and hospitals. CONCLUSIONS Mathematical models of AMR in gram-negative bacteria in the LTCF setting, where these bacteria are increasingly becoming prevalent, are needed to help guide infection prevention and control. Improvements are required to develop outputs of sufficient quality to help guide interventions and policy in the future. We suggest a checklist of criteria to be used as a practical guide to determine whether a model is robust enough to test policy. Infect Control Hosp Epidemiol 2017;38:216-225.

Mathematics, Modelling and Students in Transition

ERIC Educational Resources Information Center

Wake, Geoff

2016-01-01

This article is based on data from two major research projects that investigated students involved in mathematically demanding courses during their transition through college and into university. It explores the nature of modelling as a mathematical practice in this important transition phase for students. Theoretical considerations are informed…

a Discrete Mathematical Model to Simulate Malware Spreading

NASA Astrophysics Data System (ADS)

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 of metabolism and hemodynamics.

PubMed

Costalat, R; Francoise, J-P; Menuel, C; Lahutte, M; Vallée, J-N; de Marco, G; Chiras, J; Guillevin, R

2012-06-01

We provide a mathematical study of a model of energy metabolism and hemodynamics of glioma allowing a better understanding of metabolic modifications leading to anaplastic transformation from low grade glioma. This mathematical analysis allows ultimately to unveil the solution to a viability problem which seems quite pertinent for applications to medecine.

The Nature of Spontaneity in High Quality Mathematics Learning Experiences

ERIC Educational Resources Information Center

Williams, Gaye

2004-01-01

Spontaneity has been linked to high quality learning experiences in mathematics (Csikszentmihalyi & Csikszentmihalyi, 1992; Williams, 2002).This paper shows how spontaneity can be identified by attending to the nature of social elements in the process of abstracting (Dreyfus, Hershkowitz, & Schwarz, 2001). This process is elaborated…

"Model Your Genes the Mathematical Way"--A Mathematical Biology Workshop for Secondary School Teachers

ERIC Educational Resources Information Center

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…

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

NASA Astrophysics Data System (ADS)

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

Some Reflections on the Teaching of Mathematical Modeling

ERIC Educational Resources Information Center

Warwick, Jon

2007-01-01

This paper offers some reflections on the difficulties of teaching mathematical modeling to students taking higher education courses in which modeling plays a significant role. In the author's experience, other aspects of the model development process often cause problems rather than the use of mathematics. Since these other aspects involve…

Investigating the impact of mindfulness meditation training on working memory: a mathematical modeling approach.

PubMed

van Vugt, Marieke K; Jha, Amishi P

2011-09-01

We investigated whether mindfulness training (MT) influences information processing in a working memory task with complex visual stimuli. Participants were tested before (T1) and after (T2) participation in an intensive one-month MT retreat, and their performance was compared with that of an age- and education-matched control group. Accuracy did not differ across groups at either time point. Response times were faster and significantly less variable in the MT versus the control group at T2. Since these results could be due to changes in mnemonic processes, speed-accuracy trade-off, or nondecisional factors (e.g., motor execution), we used a mathematical modeling approach to disentangle these factors. The EZ-diffusion model (Wagenmakers, van der Maas, & Grasman, Psychonomic Bulletin & Review 14:(1), 3-22, 2007) suggested that MT leads to improved information quality and reduced response conservativeness, with no changes in nondecisional factors. The noisy exemplar model further suggested that the increase in information quality reflected a decrease in encoding noise and not an increase in forgetting. Thus, mathematical modeling may help clarify the mechanisms by which MT produces salutary effects on performance.

Mathematical Manipulative Models: In Defense of “Beanbag Biology”

PubMed Central

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

To Assess Students' Attitudes, Skills and Competencies in Mathematical Modeling

ERIC Educational Resources Information Center

Lingefjard, Thomas; Holmquist, Mikael

2005-01-01

Peer-to-peer assessment, take-home exams and a mathematical modeling survey were used to monitor and assess students' attitudes, skills and competencies in mathematical modeling. The students were all in a secondary mathematics, teacher education program with a comprehensive amount of mathematics studies behind them. Findings indicate that…

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

PubMed

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

2017-02-01

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

Mathematical model for prediction of efficiency indicators of educational activity in high school

NASA Astrophysics Data System (ADS)

Tikhonova, O. M.; Kushnikov, V. A.; Fominykh, D. S.; Rezchikov, A. F.; Ivashchenko, V. A.; Bogomolov, A. S.; Filimonyuk, L. Yu; Dolinina, O. N.; Kushnikov, O. V.; Shulga, T. E.; Tverdokhlebov, V. A.

2018-05-01

The quality of high school is a current problem all over the world. The paper presents the system dedicated to predicting the accreditation indicators of technical universities based on J. Forrester mechanism of system dynamics. The mathematical model is developed for prediction of efficiency indicators of the educational activity and is based on the apparatus of nonlinear differential equations.

Quality Teaching in Mathematics

ERIC Educational Resources Information Center

Ediger, Marlow

2012-01-01

The best teaching possible needs to accrue in the mathematics curriculum. Pupils also need to become proficient in using mathematics in every day situations in life. Individuals buy goods and services. They pay for these in different ways, including cash. Here, persons need to be able to compute the total cost of items purchased and then pay for…

Mathematical modelling of methanogenic reactor start-up: Importance of volatile fatty acids degrading population.

PubMed

Jabłoński, Sławomir J; Łukaszewicz, Marcin

2014-12-01

Development of balanced community of microorganisms is one of the obligatory for stable anaerobic digestion. Application of mathematical models might be helpful in development of reliable procedures during the process start-up period. Yet, the accuracy of forecast depends on the quality of input and parameters. In this study, the specific anaerobic activity (SAA) tests were applied in order to estimate microbial community structure. Obtained data was applied as input conditions for mathematical model of anaerobic digestion. The initial values of variables describing the amount of acetate and propionate utilizing microorganisms could be calculated on the basis of SAA results. The modelling based on those optimized variables could successfully reproduce the behavior of a real system during the continuous fermentation. Copyright © 2014 The Authors. Published by Elsevier Ltd.. All rights reserved.

Mathematical model of compact type evaporator

NASA Astrophysics Data System (ADS)

Borovička, Martin; Hyhlík, Tomáš

2018-06-01

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

Modellus: Learning Physics with Mathematical Modelling

NASA Astrophysics Data System (ADS)

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

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

NASA Astrophysics Data System (ADS)

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.

Learning to teach mathematical modelling in secondary and tertiary education

NASA Astrophysics Data System (ADS)

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.

The Perception of Preservice Mathematics Teachers on the Role of Scaffolding in Achieving Quality Mathematics Classroom Instruction

ERIC Educational Resources Information Center

Bature, Iliya Joseph; Jibrin, Adamu Gagdi

2015-01-01

This paper was designed to investigate the perceptions of four preservice mathematics teachers on the role of scaffolding in supporting and assisting them achieves quality classroom teaching. A collaborative approach to teaching through a community of practice was used to obtain data for the three research objectives that were postulated. Two…

Mathematical Manipulative Models: In Defense of "Beanbag Biology"

ERIC Educational Resources Information Center

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

2010-01-01

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process--1) use of physical manipulatives, 2) interactive exploration of computer…

Mathematical Modeling of Loop Heat Pipes

NASA Technical Reports Server (NTRS)

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.

Building Mathematical Models of Simple Harmonic and Damped Motion.

ERIC Educational Resources Information Center

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 modelling and quantitative methods.

PubMed

Edler, L; Poirier, K; Dourson, M; Kleiner, J; Mileson, B; Nordmann, H; Renwick, A; Slob, W; Walton, K; Würtzen, G

2002-01-01

The present review reports on the mathematical methods and statistical techniques presently available for hazard characterisation. The state of the art of mathematical modelling and quantitative methods used currently for regulatory decision-making in Europe and additional potential methods for risk assessment of chemicals in food and diet are described. Existing practices of JECFA, FDA, EPA, etc., are examined for their similarities and differences. A framework is established for the development of new and improved quantitative methodologies. Areas for refinement, improvement and increase of efficiency of each method are identified in a gap analysis. Based on this critical evaluation, needs for future research are defined. It is concluded from our work that mathematical modelling of the dose-response relationship would improve the risk assessment process. An adequate characterisation of the dose-response relationship by mathematical modelling clearly requires the use of a sufficient number of dose groups to achieve a range of different response levels. This need not necessarily lead to an increase in the total number of animals in the study if an appropriate design is used. Chemical-specific data relating to the mode or mechanism of action and/or the toxicokinetics of the chemical should be used for dose-response characterisation whenever possible. It is concluded that a single method of hazard characterisation would not be suitable for all kinds of risk assessments, and that a range of different approaches is necessary so that the method used is the most appropriate for the data available and for the risk characterisation issue. Future refinements to dose-response characterisation should incorporate more clearly the extent of uncertainty and variability in the resulting output.

Mathematical modelling of liquid transport in swelling pharmaceutical immediate release tablets.

PubMed

Markl, Daniel; Yassin, Samy; Wilson, D Ian; Goodwin, Daniel J; Anderson, Andrew; Zeitler, J Axel

2017-06-30

Oral dosage forms are an integral part of modern health care and account for the majority of drug delivery systems. Traditionally the analysis of the dissolution behaviour of a dosage form is used as the key parameter to assess the performance of a drug product. However, understanding the mechanisms of disintegration is of critical importance to improve the quality of drug delivery systems. The disintegration performance is primarily impacted by the hydration and subsequent swelling of the powder compact. Here we compare liquid ingress and swelling data obtained using terahertz pulsed imaging (TPI) to a set of mathematical models. The interlink between hydration kinetics and swelling is described by a model based on Darcy's law and a modified swelling model based on that of Schott. Our new model includes the evolution of porosity, pore size and permeability as a function of hydration time. Results obtained from two sets of samples prepared from pure micro-crystalline cellulose (MCC) indicate a clear difference in hydration and swelling for samples of different porosities and particle sizes, which are captured by the model. Coupling a novel imaging technique, such as TPI, and mathematical models allows better understanding of hydration and swelling and eventually tablet disintegration. Copyright © 2017 The Author(s). Published by Elsevier B.V. All rights reserved.

A Seminar in Mathematical Model-Building.

ERIC Educational Resources Information Center

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)

iSTEM: Promoting Fifth Graders' Mathematical Modeling

ERIC Educational Resources Information Center

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…

Physical and mathematical cochlear models

NASA Astrophysics Data System (ADS)

Lim, Kian-Meng

2000-10-01

The cochlea is an intricate organ in the inner ear responsible for our hearing. Besides acting as a transducer to convert mechanical sound vibrations to electrical neural signals, the cochlea also amplifies and separates the sound signal into its spectral components for further processing in the brain. It operates over a broad-band of frequency and a huge dynamic range of input while maintaining a low power consumption. The present research takes the approach of building cochlear models to study and understand the underlying mechanics involved in the functioning of the cochlea. Both physical and mathematical models of the cochlea are constructed. The physical model is a first attempt to build a life- sized replica of the human cochlea using advanced micro- machining techniques. The model takes a modular design, with a removable silicon-wafer based partition membrane encapsulated in a plastic fluid chamber. Preliminary measurements in the model are obtained and they compare roughly with simulation results. Parametric studies on the design parameters of the model leads to an improved design of the model. The studies also revealed that the width and orthotropy of the basilar membrane in the cochlea have significant effects on the sharply tuned responses observed in the biological cochlea. The mathematical model is a physiologically based model that includes three-dimensional viscous fluid flow and a tapered partition with variable properties along its length. A hybrid asymptotic and numerical method provides a uniformly valid and efficient solution to the short and long wave regions in the model. Both linear and non- linear activity are included in the model to simulate the active cochlea. The mathematical model has successfully reproduced many features of the response in the biological cochlea, as observed in experiment measurements performed on animals. These features include sharply tuned frequency responses, significant amplification with inclusion of activity

Mathematical models for principles of gyroscope theory

NASA Astrophysics Data System (ADS)

Usubamatov, Ryspek

2017-01-01

Gyroscope devices are primary units for navigation and control systems that have wide application in engineering. The main property of the gyroscope device is maintaining the axis of a spinning rotor. This gyroscope peculiarity is represented in terms of gyroscope effects in which known mathematical models have been formulated on the law of kinetic energy conservation and the change in the angular momentum. The gyroscope theory is represented by numerous publications, which mathematical models do not match the actual torques and motions in these devices.. The nature of gyroscope effects is more complex than represented in known publications. Recent investigations in this area have demonstrated that on a gyroscope can act until eleven internal torques simultaneously and interdependently around two axes. These gyroscope torques are generated by spinning rotor's mass-elements and by the gyroscope center-mass based on action of several inertial forces. The change in the angular momentum does not play first role for gyroscope motions. The external load generates several internal torques which directions may be distinguished. This situation leads changing of the angular velocities of gyroscope motions around two axes. Formulated mathematical models of gyroscope internal torques are representing the fundamental principle of gyroscope theory. In detail, the gyroscope is experienced the resistance torque generated by the centrifugal and Coriolis forces of the spinning rotor and the precession torque generated by the common inertial forces and the change in the angular momentum. The new mathematical models for the torques and motions of the gyroscope confirmed for most unsolvable problems. The mathematical models practically tested and the results are validated the theoretical approach.

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

ERIC Educational Resources Information Center

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…

Supporting High Quality Teacher-Child Interactions in Pre-K Mathematics

ERIC Educational Resources Information Center

McGuire, Patrick

2010-01-01

The purpose of this three-paper manuscript dissertation is to add value to the limited knowledge base of research surrounding the quality of teacher-child interactions in pre-k mathematics contexts. The first paper, based on an extensive review of literature, presents a theoretical basis for using five-frames to support children's development of…

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

NASA Astrophysics Data System (ADS)

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.

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

ERIC Educational Resources Information Center

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…

Developing Understanding of Mathematical Modeling in Secondary Teacher Preparation

ERIC Educational Resources Information Center

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…

Using a Functional Model to Develop a Mathematical Formula

ERIC Educational Resources Information Center

Otto, Charlotte A.; Everett, Susan A.; Luera, Gail R.

2008-01-01

The unifying theme of models was incorporated into a required Science Capstone course for pre-service elementary teachers based on national standards in science and mathematics. A model of a teeter-totter was selected for use as an example of a functional model for gathering data as well as a visual model of a mathematical equation for developing…

Molecular modeling: An open invitation for applied mathematics

NASA Astrophysics Data System (ADS)

Mezey, Paul G.

2013-10-01

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

Application of mathematical modeling in sustained release delivery systems.

PubMed

Grassi, Mario; Grassi, Gabriele

2014-08-01

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

Mathematical modeling for novel cancer drug discovery and development.

PubMed

Zhang, Ping; Brusic, Vladimir

2014-10-01

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

The use of mathematical models in teaching wastewater treatment engineering.

PubMed

Morgenroth, E; Arvin, E; Vanrolleghem, P

2002-01-01

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

Mathematical modeling of swirled flows in industrial applications

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

THE LAKE MICHIGAN MASS BALANCE PROJECT: QUALITY ASSURANCE PLAN FOR MATHEMATICAL MODELLING

EPA Science Inventory

This report documents the quality assurance process for the development and application of the Lake Michigan Mass Balance Models. The scope includes the overall modeling framework as well as the specific submodels that are linked to form a comprehensive synthesis of physical, che...

A Mathematical Evaluation of the Core Conductor Model

PubMed Central

Clark, John; Plonsey, Robert

1966-01-01

This paper is a mathematical evaluation of the core conductor model where its three dimensionality is taken into account. The problem considered is that of a single, active, unmyelinated nerve fiber situated in an extensive, homogeneous, conducting medium. Expressions for the various core conductor parameters have been derived in a mathematically rigorous manner according to the principles of electromagnetic theory. The purpose of employing mathematical rigor in this study is to bring to light the inherent assumptions of the one dimensional core conductor model, providing a method of evaluating the accuracy of this linear model. Based on the use of synthetic squid axon data, the conclusion of this study is that the linear core conductor model is a good approximation for internal but not external parameters. PMID:5903155

Mathematical modeling relevant to closed artificial ecosystems

USGS Publications Warehouse

DeAngelis, D.L.

2003-01-01

The mathematical modeling of ecosystems has contributed much to the understanding of the dynamics of such systems. Ecosystems can include not only the natural variety, but also artificial systems designed and controlled by humans. These can range from agricultural systems and activated sludge plants, down to mesocosms, microcosms, and aquaria, which may have practical or research applications. Some purposes may require the design of systems that are completely closed, as far as material cycling is concerned. In all cases, mathematical modeling can help not only to understand the dynamics of the system, but also to design methods of control to keep the system operating in desired ranges. This paper reviews mathematical modeling relevant to the simulation and control of closed or semi-closed artificial ecosystems designed for biological production and recycling in applications in space. Published by Elsevier Science Ltd on behalf of COSPAR.

Mathematical modelling of clostridial acetone-butanol-ethanol fermentation.

PubMed

Millat, Thomas; Winzer, Klaus

2017-03-01

Clostridial acetone-butanol-ethanol (ABE) fermentation features a remarkable shift in the cellular metabolic activity from acid formation, acidogenesis, to the production of industrial-relevant solvents, solventogensis. In recent decades, mathematical models have been employed to elucidate the complex interlinked regulation and conditions that determine these two distinct metabolic states and govern the transition between them. In this review, we discuss these models with a focus on the mechanisms controlling intra- and extracellular changes between acidogenesis and solventogenesis. In particular, we critically evaluate underlying model assumptions and predictions in the light of current experimental knowledge. Towards this end, we briefly introduce key ideas and assumptions applied in the discussed modelling approaches, but waive a comprehensive mathematical presentation. We distinguish between structural and dynamical models, which will be discussed in their chronological order to illustrate how new biological information facilitates the 'evolution' of mathematical models. Mathematical models and their analysis have significantly contributed to our knowledge of ABE fermentation and the underlying regulatory network which spans all levels of biological organization. However, the ties between the different levels of cellular regulation are not well understood. Furthermore, contradictory experimental and theoretical results challenge our current notion of ABE metabolic network structure. Thus, clostridial ABE fermentation still poses theoretical as well as experimental challenges which are best approached in close collaboration between modellers and experimentalists.

Teaching mathematical word problem solving: the quality of evidence for strategy instruction priming the problem structure.

PubMed

Jitendra, Asha K; Petersen-Brown, Shawna; Lein, Amy E; Zaslofsky, Anne F; Kunkel, Amy K; Jung, Pyung-Gang; Egan, Andrea M

2015-01-01

This study examined the quality of the research base related to strategy instruction priming the underlying mathematical problem structure for students with learning disabilities and those at risk for mathematics difficulties. We evaluated the quality of methodological rigor of 18 group research studies using the criteria proposed by Gersten et al. and 10 single case design (SCD) research studies using criteria suggested by Horner et al. and the What Works Clearinghouse. Results indicated that 14 group design studies met the criteria for high-quality or acceptable research, whereas SCD studies did not meet the standards for an evidence-based practice. Based on these findings, strategy instruction priming the mathematics problem structure is considered an evidence-based practice using only group design methodological criteria. Implications for future research and for practice are discussed. © Hammill Institute on Disabilities 2013.

The impact of mathematical models of teaching materials on square and rectangle concepts to improve students' mathematical connection ability and mathematical disposition in middle school

NASA Astrophysics Data System (ADS)

Afrizal, Irfan Mufti; Dachlan, Jarnawi Afghani

2017-05-01

The aim of this study was to determine design of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition in middle school through experimental studies. The design in this study was quasi-experimental with non-equivalent control group type. This study consisted of two phases, the first phase was identify students' learning obstacle on square and rectangle concepts to obtain the appropriate design of teaching materials, beside that there were internalization of the values or characters expected to appear on students through the teaching materials. Second phase was experiments on the effectiveness and efficiency of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition. The result of this study are 1) Students' learning obstacle that have identified was categorized as an epistemological obstacle. 2) The improvement of students' mathematical connection ability and mathematical disposition who used mathematical teaching materials is better than the students who used conventional learning.

Mathematical Modelling in the Early School Years

ERIC Educational Resources Information Center

English, Lyn D.; Watters, James J.

2005-01-01

In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the "Butter Beans Problem" and the "Airplane Problem"). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data,…

Strengthening Mathematics And Science Education (SMASE) For Improving The Quality Of Teachers in Nigeria

NASA Astrophysics Data System (ADS)

Shuaibu, Zainab Muhammad

2016-04-01

Strengthening Mathematics And Science Education (SMASE) in training and re-training of teachers at enhancing quality classroom activities in Mathematics and Science subjects through Activity, Student-centre, Experiments, Improvisation (ASEI)-Plan, Do, See, Improve (PDSI) instructional strategy. This instructional strategy has cultivates learner's mathematical and scientific thinking ability and have provided one of the best regular INSET for primary and secondary Mathematics and Science teachers as observed during the SMASE impact survey in the three piloted states in Nigeria. To build a common ground for teaching method irrespective of teacher and teaching style School-Based Training (SBT) is now advocated in SMASE, SBT is aimed at improving teaching and learning activities in the classroom through Lesson Study model. Lesson Study is a teaching improvement and knowledge building process that has its origin in the Japanese elementary education it involves a comprehensive process of planning, observation, analysis and identifying the best approaches in a classroom. This an inquiry approach to professional development that requires teachers to identify an area of instructional interest, collect data to analyses and make instructional changes based on the data. This kind of professional development make teachers acquires current and up to date knowledge in the field of mathematics and science.

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

ERIC Educational Resources Information Center

Rash, Agnes M.; Zurbach, E. Peter

2004-01-01

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

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

PubMed

Gilbert, Scott F

2018-01-31

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

Head Start Program Quality: Examination of Classroom Quality and Parent Involvement in Predicting Children's Vocabulary, Literacy, and Mathematics Achievement Trajectories

ERIC Educational Resources Information Center

Wen, Xiaoli; Bulotsky-Shearer, Rebecca J.; Hahs-Vaughn, Debbie L.; Korfmacher, Jon

2012-01-01

Guided by a developmental-ecological framework and Head Start's two-generational approach, this study examined two dimensions of Head Start program quality, classroom quality and parent involvement and their unique and interactive contribution to children's vocabulary, literacy, and mathematics skills growth from the beginning of Head Start…

Mathematical Modeling Is Also Physics--Interdisciplinary Teaching between Mathematics and Physics in Danish Upper Secondary Education

ERIC Educational Resources Information Center

Michelsen, Claus

2015-01-01

Mathematics plays a crucial role in physics. This role is brought about predominantly through the building, employment, and assessment of mathematical models, and teachers and educators should capture this relationship in the classroom in an effort to improve students' achievement and attitude in both physics and mathematics. But although there…

A Framework for Authenticity in the Mathematics and Statistics Classroom

ERIC Educational Resources Information Center

Garrett, Lauretta; Huang, Li; Charleton, Maria Calhoun

2016-01-01

Authenticity is a term commonly used in reference to pedagogical and curricular qualities of mathematics teaching and learning, but its use lacks a coherent framework. The work of researchers in engineering education provides such a framework. Authentic qualities of mathematics teaching and learning are fit within a model described by Strobel,…

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Automatic mathematical modeling for real time simulation program (AI application)

NASA Technical Reports Server (NTRS)

Wang, Caroline; Purinton, Steve

1989-01-01

A methodology is described for automatic mathematical modeling and generating simulation models. The major objective was to create a user friendly environment for engineers to design, maintain, and verify their models; to automatically convert the mathematical models into conventional code for computation; and finally, to document the model automatically.

A Mathematical Model for the Middle Ear Ventilation

NASA Astrophysics Data System (ADS)

Molnárka, G.; Miletics, E. M.; Fücsek, M.

2008-09-01

The otitis media is one of the mostly existing illness for the children, therefore investigation of the human middle ear ventilation is an actual problem. In earlier investigations both experimental and theoretical approach one can find in ([l]-[3]). Here we give a new mathematical and computer model to simulate this ventilation process. This model able to describe the diffusion and flow processes simultaneously, therefore it gives more precise results than earlier models did. The article contains the mathematical model and some results of the simulation.

Developing Teachers' Models for Assessing Students' Competence in Mathematical Modelling through Lesson Study

ERIC Educational Resources Information Center

Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat; Cakiroglu, Erdinc; Alacaci, Cengiz; Cetinkaya, Bulent

2017-01-01

Applications and modelling have gained a prominent role in mathematics education reform documents and curricula. Thus, there is a growing need for studies focusing on the effective use of mathematical modelling in classrooms. Assessment is an integral part of using modelling activities in classrooms, since it allows teachers to identify and manage…

Mathematical modeling of inhalation exposure

NASA Technical Reports Server (NTRS)

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.

A Case Study of Teachers' Development of Well-Structured Mathematical Modelling Activities

ERIC Educational Resources Information Center

Stohlmann, Micah; Maiorca, Cathrine; Allen, Charlie

2017-01-01

This case study investigated how three teachers developed mathematical modelling activities integrated with content standards through participation in a course on mathematical modelling. The class activities involved experiencing a mathematical modelling activity, reading and rating example mathematical modelling activities, reading articles about…

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

ERIC Educational Resources Information Center

Karatas, Ilhan

2014-01-01

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

Authenticity of Mathematical Modeling

ERIC Educational Resources Information Center

Tran, Dung; Dougherty, Barbara J.

2014-01-01

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

Mathematical modeling of a Ti:sapphire solid-state laser

NASA Technical Reports Server (NTRS)

Swetits, John J.

1987-01-01

The project initiated a study of a mathematical model of a tunable Ti:sapphire solid-state laser. A general mathematical model was developed for the purpose of identifying design parameters which will optimize the system, and serve as a useful predictor of the system's behavior.

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

ERIC Educational Resources Information Center

Schwerdtfeger, Sara

2017-01-01

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

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

ERIC Educational Resources Information Center

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

2015-01-01

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

Mathematical models of ABE fermentation: review and analysis.

PubMed

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.

The mathematical and computer modeling of the worm tool shaping

NASA Astrophysics Data System (ADS)

Panchuk, K. L.; Lyashkov, A. A.; Ayusheev, T. V.

2017-06-01

Traditionally mathematical profiling of the worm tool is carried out on the first T. Olivier method, known in the theory of gear gearings, with receiving an intermediate surface of the making lath. It complicates process of profiling and its realization by means of computer 3D-modeling. The purpose of the work is the improvement of mathematical model of profiling and its realization based on the methods of 3D-modeling. Research problems are: receiving of the mathematical model of profiling which excludes the presence of the making lath in it; realization of the received model by means of frame and superficial modeling; development and approbation of technology of solid-state modeling for the solution of the problem of profiling. As the basic, the kinematic method of research of the mutually envelope surfaces is accepted. Computer research is executed by means of CAD based on the methods of 3D-modeling. We have developed mathematical model of profiling of the worm tool; frame, superficial and solid-state models of shaping of the mutually enveloping surfaces of the detail and the tool are received. The offered mathematical models and the technologies of 3D-modeling of shaping represent tools for theoretical and experimental profiling of the worm tool. The results of researches can be used at design of metal-cutting tools.

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

ERIC Educational Resources Information Center

Crisan, Cosette; Rodd, Melissa

2017-01-01

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

A Mathematical Model Development for the Lateral Collapse of Octagonal Tubes

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Validation and upgrading of physically based mathematical models

NASA Technical Reports Server (NTRS)

Duval, Ronald

1992-01-01

The validation of the results of physically-based mathematical models against experimental results was discussed. Systematic techniques are used for: (1) isolating subsets of the simulator mathematical model and comparing the response of each subset to its experimental response for the same input conditions; (2) evaluating the response error to determine whether it is the result of incorrect parameter values, incorrect structure of the model subset, or unmodeled external effects of cross coupling; and (3) modifying and upgrading the model and its parameter values to determine the most physically appropriate combination of changes.

Modeling in the quality by design environment: Regulatory requirements and recommendations for design space and control strategy appointment.

PubMed

Djuris, Jelena; Djuric, Zorica

2017-11-30

Mathematical models can be used as an integral part of the quality by design (QbD) concept throughout the product lifecycle for variety of purposes, including appointment of the design space and control strategy, continual improvement and risk assessment. Examples of different mathematical modeling techniques (mechanistic, empirical and hybrid) in the pharmaceutical development and process monitoring or control are provided in the presented review. In the QbD context, mathematical models are predominantly used to support design space and/or control strategies. Considering their impact to the final product quality, models can be divided into the following categories: high, medium and low impact models. Although there are regulatory guidelines on the topic of modeling applications, review of QbD-based submission containing modeling elements revealed concerns regarding the scale-dependency of design spaces and verification of models predictions at commercial scale of manufacturing, especially regarding real-time release (RTR) models. Authors provide critical overview on the good modeling practices and introduce concepts of multiple-unit, adaptive and dynamic design space, multivariate specifications and methods for process uncertainty analysis. RTR specification with mathematical model and different approaches to multivariate statistical process control supporting process analytical technologies are also presented. Copyright © 2017 Elsevier B.V. All rights reserved.

Effective Teacher Qualities from International Mathematics, Science, and Computer Teachers' Perspectives

ERIC Educational Resources Information Center

Sahin, Alpaslan; Adiguzel, Tufan

2014-01-01

The purpose of this study is to investigate how international teachers, who were from overseas but taught in the United States, rate effective teacher qualities in three domains; personal, professional, and classroom management skills. The study includes 130 international mathematics, science, and computer teachers who taught in a multi-school…

Components of Mathematics Anxiety: Factor Modeling of the MARS30-Brief.

PubMed

Pletzer, Belinda; Wood, Guilherme; Scherndl, Thomas; Kerschbaum, Hubert H; Nuerk, Hans-Christoph

2016-01-01

Mathematics anxiety involves feelings of tension, discomfort, high arousal, and physiological reactivity interfering with number manipulation and mathematical problem solving. Several factor analytic models indicate that mathematics anxiety is rather a multidimensional than unique construct. However, the factor structure of mathematics anxiety has not been fully clarified by now. This issue shall be addressed in the current study. The Mathematics Anxiety Rating Scale (MARS) is a reliable measure of mathematics anxiety (Richardson and Suinn, 1972), for which several reduced forms have been developed. Most recently, a shortened version of the MARS (MARS30-brief) with comparable reliability was published. Different studies suggest that mathematics anxiety involves up to seven different factors. Here we examined the factor structure of the MARS30-brief by means of confirmatory factor analysis. The best model fit was obtained by a six-factor model, dismembering the known two general factors "Mathematical Test Anxiety" (MTA) and "Numerical Anxiety" (NA) in three factors each. However, a more parsimonious 5-factor model with two sub-factors for MTA and three for NA fitted the data comparably well. Factors were differentially susceptible to sex differences and differences between majors. Measurement invariance for sex was established.

To What Extent Do Teacher-Student Interaction Quality and Student Gender Contribute to Fifth Graders' Engagement in Mathematics Learning?

ERIC Educational Resources Information Center

Rimm-Kaufman, Sara E.; Baroody, Alison E.; Larsen, Ross A. A.; Curby, Timothy W.; Abry, Tashia

2015-01-01

This study examines concurrent teacher-student interaction quality and 5th graders' (n = 387) engagement in mathematics classrooms (n = 63) and considers how teacher-student interaction quality relates to engagement differently for boys and girls. Three approaches were used to measure student engagement in mathematics: Research assistants observed…

An Integrated Approach to Mathematical Modeling: A Classroom Study.

ERIC Educational Resources Information Center

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…

EUTROPHICATION MODELING CAPABILITIES FOR WATER QUALITY AND INTEGRATION TOWARDS ECOLOGICAL ENDPOINTS

EPA Science Inventory

A primary environmental focus for the use of mathematical models is for characterization of sources of nutrients and sediments and their relative loadings from large river basins, and the impact of land uses from smaller sub-basins on water quality in rivers, lakes, and estuaries...

Evaluation of Limb Load Asymmetry Using Two New Mathematical Models

PubMed Central

Kumar, Senthil NS; Omar, Baharudin; Joseph, Leonard H.; Htwe, Ohnmar; Jagannathan, K.; Hamdan, Nor M Y; Rajalakshmi, D.

2015-01-01

Quantitative measurement of limb loading is important in orthopedic and neurological rehabilitation. In current practice, mathematical models such as Symmetry index (SI), Symmetry ratio (SR), and Symmetry angle (SA) are used to quantify limb loading asymmetry. Literatures have identified certain limitations with the above mathematical models. Hence this study presents two new mathematical models Modified symmetry index (MSI) and Limb loading error (LLE) that would address these limitations. Furthermore, the current mathematical models were compared against the new model with the goal of achieving a better model. This study uses hypothetical data to simulate an algorithmic preliminary computational measure to perform with all numerical possibilities of even and uneven limb loading that can occur in human legs. Descriptive statistics are used to interpret the limb loading patterns: symmetry, asymmetry and maximum asymmetry. The five mathematical models were similar in analyzing symmetry between limbs. However, for asymmetry and maximum asymmetry data, the SA and SR values do not give any meaningful interpretation, and SI gives an inflated value. The MSI and LLE are direct, easy to interpret and identify the loading patterns with the side of asymmetry. The new models are notable as they quantify the amount and side of asymmetry under different loading patterns. PMID:25716372

Reflection on Cuboid Net with Mathematical Learning Quality

NASA Astrophysics Data System (ADS)

Sari, Atikah; Suryadi, Didi; Syaodih, Ernawulan

2017-09-01

This research aims to formulate an alternative to the reflection in mathematics learning activities related to the activities of the professionalism of teachers motivated by a desire to improve the quality of learning. This study is a qualitative study using the Didactical Design research. This study was conducted in one of the elementary schools. The data collection techniques are triangulation with the research subject is teacher 5th grade. The results of this study indicate that through deep reflection, teachers can design learning design in accordance with the conditions of the class. Also revealed that teachers have difficulty in choosing methods of learning and contextual learning media. Based on the implementation of activities of reflection and make the learning design based on the results of reflection can be concluded that the quality of learning in the class will develop.

Quality Mathematics Instructional Practices Contributing to Student Achievements in Five High-Achieving Asian Education Systems: An Analysis Using TIMSS 2011 Data

ERIC Educational Resources Information Center

Cheng, Qiang

2014-01-01

Although teaching quality is seen as crucial in affecting students' performance, what types of instructional practices constitute quality teaching remains a question. With the theoretical assumptions of conceptual and procedural mathematics teaching as a guide, this study examined the types of quality mathematics instructional practices that…

Mathematical modeling of molecular diffusion through mucus

PubMed Central

Cu, Yen; Saltzman, W. Mark

2008-01-01

The rate of molecular transport through the mucus gel can be an important determinant of efficacy for therapeutic agents delivered by oral, intranasal, intravaginal/rectal, and intraocular routes. Transport through mucus can be described by mathematical models based on principles of physical chemistry and known characteristics of the mucus gel, its constituents, and of the drug itself. In this paper, we review mathematical models of molecular diffusion in mucus, as well as the techniques commonly used to measure diffusion of solutes in the mucus gel, mucus gel mimics, and mucosal epithelia. PMID:19135488

Physical disintegration of toilet papers in wastewater systems: experimental analysis and mathematical modeling.

PubMed

Eren, Beytullah; Karadagli, Fatih

2012-03-06

Physical disintegration of representative toilet papers was investigated in this study to assess their disintegration potential in sewer systems. Characterization of toilet papers from different parts of the world indicated two main categories as premium and average quality. Physical disintegration experiments were conducted with representative products from each category according to standard protocols with improvements. The experimental results were simulated by mathematical model to estimate best-fit values of disintegration rate coefficients and fractional distribution ratios. Our results from mathematical modeling and experimental work show that premium products release more amounts of small fibers and disintegrate more slowly than average ones. Comparison of the toilet papers with the tampon applicators studied previously indicates that premium quality toilet papers present significant potential to persist in sewer pipes. Comparison of turbulence level in our experimental setup with those of partial flow conditions in sewer pipes indicates that drains and small sewer pipes are critical sections where disintegration of toilet papers will be limited. For improvement, requirements for minimum pipe slopes may be increased to sustain transport and disintegration of flushable products in small pipes. In parallel, toilet papers can be improved to disintegrate rapidly in sewer systems, while they meet consumer expectations.

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

PubMed

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

2014-08-28

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

Mathematical Models of Breast and Ovarian Cancers

PubMed Central

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

Mathematical model for gyroscope effects

NASA Astrophysics Data System (ADS)

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).

Mathematical Modelling Research in Turkey: A Content Analysis Study

ERIC Educational Resources Information Center

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.…

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

PubMed

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.

Components of Mathematics Anxiety: Factor Modeling of the MARS30-Brief

PubMed Central

Pletzer, Belinda; Wood, Guilherme; Scherndl, Thomas; Kerschbaum, Hubert H.; Nuerk, Hans-Christoph

2016-01-01

Mathematics anxiety involves feelings of tension, discomfort, high arousal, and physiological reactivity interfering with number manipulation and mathematical problem solving. Several factor analytic models indicate that mathematics anxiety is rather a multidimensional than unique construct. However, the factor structure of mathematics anxiety has not been fully clarified by now. This issue shall be addressed in the current study. The Mathematics Anxiety Rating Scale (MARS) is a reliable measure of mathematics anxiety (Richardson and Suinn, 1972), for which several reduced forms have been developed. Most recently, a shortened version of the MARS (MARS30-brief) with comparable reliability was published. Different studies suggest that mathematics anxiety involves up to seven different factors. Here we examined the factor structure of the MARS30-brief by means of confirmatory factor analysis. The best model fit was obtained by a six-factor model, dismembering the known two general factors “Mathematical Test Anxiety” (MTA) and “Numerical Anxiety” (NA) in three factors each. However, a more parsimonious 5-factor model with two sub-factors for MTA and three for NA fitted the data comparably well. Factors were differentially susceptible to sex differences and differences between majors. Measurement invariance for sex was established. PMID:26924996

A mathematical model of chemoreception for odours and taste.

PubMed

Maurin, Francis

2002-04-07

We propose a mathematical model based on the occupation theory and on the hypothesis that, for a given stimulus, there exist two kinds of receptors. The receptors of the first kind react by a two-step process, first forming an intermediate inactive compound which is then changed into an active depolarizing form (this scheme was already used by Del Castillo & Katz, 1957). In the same way, the receptors of the second kind react by a two-step process, first forming an intermediate inactive compound which is then changed into an active hyperpolarizing form. The response is assumed to be proportional to the difference between the fraction of the active depolarizing compound and that of the active hyperpolarizing compound. The present paper deals only with the time course of the intensity of the response: in the first part, when a continuous flow of stimulus is applied and in the second part, when this continuous flow is removed. It does not deal with the quality and the discrimination of odours. The proposed mathematical model accounts for the depolarizing responses (which are the most frequent ones), the hyperpolarizing responses, the mixed responses reported by Patte et al. (1989), the off-responses reported by Takagi & Shibuya (1959) and for their variability, and the latent period in the olfactory response (Ottoson, 1974). Copyright 2002 Elsevier Science Ltd. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Vlachos, Dimitrios; Vagenas, Elias C.

2015-09-01

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

Mathematical modeling of cancer metabolism.

PubMed

Medina, Miguel Ángel

2018-04-01

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

The mathematical model of dynamic stabilization system for autonomous car

NASA Astrophysics Data System (ADS)

Saikin, A. M.; Buznikov, S. E.; Shabanov, N. S.; Elkin, D. S.

2018-02-01

Leading foreign companies and domestic enterprises carry out extensive researches and developments in the field of control systems for autonomous cars and in the field of improving driver assistance systems. The search for technical solutions, as a rule, is based on heuristic methods and does not always lead to satisfactory results. The purpose of this research is to formalize the road safety problem in the terms of modern control theory, to construct the adequate mathematical model for solving it, including the choice of software and hardware environment. For automatic control of the object, it is necessary to solve the problem of dynamic stabilization in the most complete formulation. The solution quality of the problem on a finite time interval is estimated by the value of the quadratic functional. Car speed, turn angle and additional yaw rate (during car drift or skidding) measurements are performed programmatically by the original virtual sensors. The limit speeds at which drift, skidding or rollover begins are calculated programmatically taking into account the friction coefficient identified in motion. The analysis of the results confirms both the adequacy of the mathematical models and the algorithms and the possibility of implementing the system in the minimal technical configuration.

Quality assessment and artificial neural networks modeling for characterization of chemical and physical parameters of potable water.

PubMed

Salari, Marjan; Salami Shahid, Esmaeel; Afzali, Seied Hosein; Ehteshami, Majid; Conti, Gea Oliveri; Derakhshan, Zahra; Sheibani, Solmaz Nikbakht

2018-04-22

Today, due to the increase in the population, the growth of industry and the variety of chemical compounds, the quality of drinking water has decreased. Five important river water quality properties such as: dissolved oxygen (DO), total dissolved solids (TDS), total hardness (TH), alkalinity (ALK) and turbidity (TU) were estimated by parameters such as: electric conductivity (EC), temperature (T), and pH that could be measured easily with almost no costs. Simulate water quality parameters were examined with two methods of modeling include mathematical and Artificial Neural Networks (ANN). Mathematical methods are based on polynomial fitting with least square method and ANN modeling algorithms are feed-forward networks. All conditions/circumstances covered by neural network modeling were tested for all parameters in this study, except for Alkalinity. All optimum ANN models developed to simulate water quality parameters had precision value as R-value close to 0.99. The ANN model extended to simulate alkalinity with R-value equals to 0.82. Moreover, Surface fitting techniques were used to refine data sets. Presented models and equations are reliable/useable tools for studying water quality parameters at similar rivers, as a proper replacement for traditional water quality measuring equipment's. Copyright © 2018 Elsevier Ltd. All rights reserved.

PREFACE: IC-MSQUARE 2012: International Conference on Mathematical Modelling in Physical Sciences

NASA Astrophysics Data System (ADS)

Kosmas, Theocharis; Vagenas, Elias; Vlachos, Dimitrios

2013-02-01

The first International Conference on Mathematical Modelling in Physical Sciences (IC-MSQUARE) took place in Budapest, Hungary, from Monday 3 to Friday 7 September 2012. The conference was attended by more than 130 participants, and hosted about 290 oral, poster and virtual papers by more than 460 pre-registered authors. The first IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields in which mathematical modelling is used, such as theoretical/mathematical physics, neutrino physics, non-integrable systems, dynamical systems, computational nanoscience, biological physics, computational biomechanics, complex networks, stochastic modelling, fractional statistics, DNA dynamics, and macroeconomics. The scientific program was rather heavy since after the Keynote and Invited Talks in the morning, two parallel sessions ran every day. However, according to all attendees, the program was excellent with a high level of talks and the scientific environment was fruitful; thus all attendees had a creative time. The mounting question is whether this occurred accidentally, or whether IC-MSQUARE is a necessity in the field of physical and mathematical modelling. For all of us working in the field, the existing and established conferences in this particular field suffer from two distinguished and recognized drawbacks: the first is the increasing orientation, while the second refers to the extreme specialization of the meetings. Therefore, a conference which aims to promote the knowledge and development of high-quality research in mathematical fields concerned with applications of other scientific fields as well as modern technological trends in physics, chemistry, biology, medicine, economics, sociology, environmental sciences etc., appears to be a necessity. This is the key role that IC-MSQUARE will play. We would like to thank the Keynote Speaker and the Invited Speakers for their significant contributions to IC-MSQUARE. We would also

Mathematical model of polyethylene pipe bending stress state

NASA Astrophysics Data System (ADS)

Serebrennikov, Anatoly; Serebrennikov, Daniil

2018-03-01

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

Mathematical models to characterize early epidemic growth: A Review

PubMed Central

Chowell, Gerardo; Sattenspiel, Lisa; Bansal, Shweta; Viboud, Cécile

2016-01-01

There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-15 Ebola epidemic in West Africa. PMID:27451336

Mathematical models to characterize early epidemic growth: A review

NASA Astrophysics Data System (ADS)

Chowell, Gerardo; Sattenspiel, Lisa; Bansal, Shweta; Viboud, Cécile

2016-09-01

There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-2015 Ebola epidemic in West Africa.

Mathematical model comparing of the multi-level economics systems

NASA Astrophysics Data System (ADS)

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.

Evolution of Mathematics Teachers' Pedagogical Knowledge When They Are Teaching through Modeling

ERIC Educational Resources Information Center

Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat; Alacaci, Cengiz; Cakiroglu, Erdinc; Cetinkaya, Bulent

2017-01-01

Use of mathematical modeling in mathematics education has been receiving significant attention as a way to develop students' mathematical knowledge and skills. As effective use of modeling in classes depends on the competencies of teachers we need to know more about the nature of teachers' knowledge to use modeling in mathematics education and how…

Mathematical Model Development and Simulation Support

NASA Technical Reports Server (NTRS)

Francis, Ronald C.; Tobbe, Patrick A.

2000-01-01

This report summarizes the work performed in support of the Contact Dynamics 6DOF Facility and the Flight Robotics Lab at NASA/ MSFC in the areas of Mathematical Model Development and Simulation Support.

Trade Books in the Mathematics Classroom: The Impact of Many, Varied Perspectives on Determinations of Quality

ERIC Educational Resources Information Center

Nesmith, Suzanne; Cooper, Sandi

2010-01-01

The integration of children's trade books in the mathematics classroom has experienced a dramatic surge in its popularity; yet, though the positive benefits of this strategy have been well documented, these benefits may only be realized if the literature is of high quality. Utilizing a mathematics trade book evaluation instrument, this inquiry…

Predicting the Quality of Elementary Mathematics Teachers Utilizing Pre-Graduation Data Collected from Teacher Preparation Programs

ERIC Educational Resources Information Center

Robertson, Mary Amos

2016-01-01

In order to change the direction of mathematics education, the training of elementary teachers in the United States needs to be of equal or higher quality than top preforming countries. However, pre-service elementary teachers in the United States fall behind their peers in other countries in mathematical content knowledge and mathematical…

On a Mathematical Model with Noncompact Boundary Conditions Describing Bacterial Population

NASA Astrophysics Data System (ADS)

Boulanouar, Mohamed

2013-04-01

In this work, we are concerned with the well-posedness of a mathematical model describing a maturation-velocity structured bacterial population. Each bacterium is distinguished by its degree of maturity and its maturation velocity. The bacterial mitosis is mathematically described by noncompact boundary conditions. We show that the mathematical model is governed by a positive strongly continuous semigroup.

Mathematical Modeling: Are Prior Experiences Important?

ERIC Educational Resources Information Center

Czocher, Jennifer A.; Moss, Diana L.

2017-01-01

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

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

ERIC Educational Resources Information Center

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

2013-01-01

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

A parsimonious dynamic model for river water quality assessment.

PubMed

Mannina, Giorgio; Viviani, Gaspare

2010-01-01

Water quality modelling is of crucial importance for the assessment of physical, chemical, and biological changes in water bodies. Mathematical approaches to water modelling have become more prevalent over recent years. Different model types ranging from detailed physical models to simplified conceptual models are available. Actually, a possible middle ground between detailed and simplified models may be parsimonious models that represent the simplest approach that fits the application. The appropriate modelling approach depends on the research goal as well as on data available for correct model application. When there is inadequate data, it is mandatory to focus on a simple river water quality model rather than detailed ones. The study presents a parsimonious river water quality model to evaluate the propagation of pollutants in natural rivers. The model is made up of two sub-models: a quantity one and a quality one. The model employs a river schematisation that considers different stretches according to the geometric characteristics and to the gradient of the river bed. Each stretch is represented with a conceptual model of a series of linear channels and reservoirs. The channels determine the delay in the pollution wave and the reservoirs cause its dispersion. To assess the river water quality, the model employs four state variables: DO, BOD, NH(4), and NO. The model was applied to the Savena River (Italy), which is the focus of a European-financed project in which quantity and quality data were gathered. A sensitivity analysis of the model output to the model input or parameters was done based on the Generalised Likelihood Uncertainty Estimation methodology. The results demonstrate the suitability of such a model as a tool for river water quality management.

Mathematical modelling of skeletal repair.

PubMed

MacArthur, B D; Please, C P; Taylor, M; Oreffo, R O C

2004-01-23

Tissue engineering offers significant promise as a viable alternative to current clinical strategies for replacement of damaged tissue as a consequence of disease or trauma. Since mathematical modelling is a valuable tool in the analysis of complex systems, appropriate use of mathematical models has tremendous potential for advancing the understanding of the physical processes involved in such tissue reconstruction. In this review, the potential benefits, and limitations, of theoretical modelling in tissue engineering applications are examined with specific emphasis on tissue engineering of bone. A central tissue engineering approach is the in vivo implantation of a biomimetic scaffold seeded with an appropriate population of stem or progenitor cells. This review will therefore consider the theory behind a number of key factors affecting the success of such a strategy including: stem cell or progenitor population expansion and differentiation ex vivo; cell adhesion and migration, and the effective design of scaffolds; and delivery of nutrient to avascular structures. The focus will be on current work in this area, as well as on highlighting limitations and suggesting possible directions for future work to advance health-care for all.

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

NASA Astrophysics Data System (ADS)

Widayanto, Arif; Pratiwi, Hasih; Mardiyana

2018-04-01

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

Automatic mathematical modeling for real time simulation system

NASA Technical Reports Server (NTRS)

Wang, Caroline; Purinton, Steve

1988-01-01

A methodology for automatic mathematical modeling and generating simulation models is described. The models will be verified by running in a test environment using standard profiles with the results compared against known results. The major objective is to create a user friendly environment for engineers to design, maintain, and verify their model and also automatically convert the mathematical model into conventional code for conventional computation. A demonstration program was designed for modeling the Space Shuttle Main Engine Simulation. It is written in LISP and MACSYMA and runs on a Symbolic 3670 Lisp Machine. The program provides a very friendly and well organized environment for engineers to build a knowledge base for base equations and general information. It contains an initial set of component process elements for the Space Shuttle Main Engine Simulation and a questionnaire that allows the engineer to answer a set of questions to specify a particular model. The system is then able to automatically generate the model and FORTRAN code. The future goal which is under construction is to download the FORTRAN code to VAX/VMS system for conventional computation. The SSME mathematical model will be verified in a test environment and the solution compared with the real data profile. The use of artificial intelligence techniques has shown that the process of the simulation modeling can be simplified.

Review and verification of CARE 3 mathematical model and code

NASA Technical Reports Server (NTRS)

Rose, D. M.; Altschul, R. E.; Manke, J. W.; Nelson, D. L.

1983-01-01

The CARE-III mathematical model and code verification performed by Boeing Computer Services were documented. The mathematical model was verified for permanent and intermittent faults. The transient fault model was not addressed. The code verification was performed on CARE-III, Version 3. A CARE III Version 4, which corrects deficiencies identified in Version 3, is being developed.

Mathematical models of continuous flow electrophoresis: Electrophoresis technology

NASA Technical Reports Server (NTRS)

Saville, Dudley A.

1986-01-01

Two aspects of continuous flow electrophoresis were studied: (1) the structure of the flow field in continuous flow devices; and (2) the electrokinetic properties of suspended particles relevant to electrophoretic separations. Mathematical models were developed to describe flow structure and stability, with particular emphasis on effects due to buoyancy. To describe the fractionation of an arbitrary particulate sample by continuous flow electrophoresis, a general mathematical model was constructed. In this model, chamber dimensions, field strength, buffer composition, and other design variables can be altered at will to study their effects on resolution and throughput. All these mathematical models were implemented on a digital computer and the codes are available for general use. Experimental and theoretical work with particulate samples probed how particle mobility is related to buffer composition. It was found that ions on the surface of small particles are mobile, contrary to the widely accepted view. This influences particle mobility and suspension conductivity. A novel technique was used to measure the mobility of particles in concentrated suspensions.

A model for rotorcraft flying qualities studies

NASA Technical Reports Server (NTRS)

Mittal, Manoj; Costello, Mark F.

1993-01-01

This paper outlines the development of a mathematical model that is expected to be useful for rotorcraft flying qualities research. A computer model is presented that can be applied to a range of different rotorcraft configurations. The algorithm computes vehicle trim and a linear state-space model of the aircraft. The trim algorithm uses non linear optimization theory to solve the nonlinear algebraic trim equations. The linear aircraft equations consist of an airframe model and a flight control system dynamic model. The airframe model includes coupled rotor and fuselage rigid body dynamics and aerodynamics. The aerodynamic model for the rotors utilizes blade element theory and a three state dynamic inflow model. Aerodynamics of the fuselage and fuselage empennages are included. The linear state-space description for the flight control system is developed using standard block diagram data.

Mathematical modeling of infectious disease dynamics

PubMed Central

Siettos, Constantinos I.; Russo, Lucia

2013-01-01

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

Mathematical model of glucose-insulin homeostasis in healthy rats.

PubMed

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

2013-10-01

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

Modeling eBook acceptance: A study on mathematics teachers

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

Choice of mathematical models for technological process of glass rod drawing

NASA Astrophysics Data System (ADS)

Alekseeva, L. B.

2017-10-01

The technological process of drawing glass rods (light guides) is considered. Automated control of the drawing process is reduced to the process of making decisions to ensure a given quality. The drawing process is considered as a control object, including the drawing device (control device) and the optical fiber forming zone (control object). To study the processes occurring in the formation zone, mathematical models are proposed, based on the continuum mechanics basics. To assess the influence of disturbances, a transfer function is obtained from the basis of the wave equation. Obtaining the regression equation also adequately describes the drawing process.

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

NASA Astrophysics Data System (ADS)

Easters, D. J.

2014-03-01

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

Illustrations of mathematical modeling in biology: epigenetics, meiosis, and an outlook.

PubMed

Richards, D; Berry, S; Howard, M

2012-01-01

In the past few years, mathematical modeling approaches in biology have begun to fulfill their promise by assisting in the dissection of complex biological systems. Here, we review two recent examples of predictive mathematical modeling in plant biology. The first involves the quantitative epigenetic silencing of the floral repressor gene FLC in Arabidopsis, mediated by a Polycomb-based system. The second involves the spatiotemporal dynamics of telomere bouquet formation in wheat-rye meiosis. Although both the biology and the modeling framework of the two systems are different, both exemplify how mathematical modeling can help to accelerate discovery of the underlying mechanisms in complex biological systems. In both cases, the models that developed were relatively minimal, including only essential features, but both nevertheless yielded fundamental insights. We also briefly review the current state of mathematical modeling in biology, difficulties inherent in its application, and its potential future development.

Mathematical Modeling of Food Supply for Long Term Space Missions Using Advanced Life Support

NASA Technical Reports Server (NTRS)

Cruthirds, John E.

2003-01-01

A habitat for long duration missions which utilizes Advanced Life Support (ALS), the Bioregenerative Planetary Life Support Systems Test Complex (BIO-Plex), is currently being built at JSC. In this system all consumables will be recycled and reused. In support of this effort, a menu is being planned utilizing ALS crops that will meet nutritional and psychological requirements. The need exists in the food system to identify specific physical quantities that define life support systems from an analysis and modeling perspective. Once these quantities are defined, they need to be fed into a mathematical model that takes into consideration other systems in the BIO-Plex. This model, if successful, will be used to understand the impacts of changes in the food system on the other systems and vice versa. The Equivalent System Mass (ESM) metric has been used to describe systems and subsystems, including the food system options, in terms of the single parameter, mass. There is concern that this approach might not adequately address the important issues of food quality and psychological impact on crew morale of a supply of fiesh food items. In fact, the mass of food can also depend on the quality of the food. This summer faculty fellow project will involve creating an appropriate mathematical model for the food plan developed by the Food Processing System for BIO-Plex. The desired outcome of this work will be a quantitative model that can be applied to the various options of supplying food on long-term space missions.

Mathematical modeling of processes of heat and mass transfer in channels of water evaporating coolers

NASA Astrophysics Data System (ADS)

Gulevsky, V. A.; Ryazantsev, A. A.; Nikulichev, A. A.; Menzhulova, A. S.

2018-05-01

The variety of cooling systems is dictated by a wide range of demands placed on them. This is the price, operating costs, quality of work, ecological safety, etc. These requirements in a positive sense are put into correspondence by water evaporating plate coolers. Currently, their widespread use is limited by a lack of theoretical base. To solve this problem, the best method is mathematical modeling.

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

PubMed

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.

Development of the Mathematical Model for Ingot Quality Forecasting with Consideration of Thermal and Physical Characteristics of Mould Powder

NASA Astrophysics Data System (ADS)

Anisimov, K. N.; Loginov, A. M.; Gusev, M. P.; Zarubin, S. V.; Nikonov, S. V.; Krasnov, A. V.

2017-12-01

This paper presents the results of physical modelling of the mould powder skull in the gap between an ingot and the mould. Based on the results obtained from this and previous works, the mathematical model of mould powder behaviour in the gap and its influence on formation of surface defects was developed. The results of modelling satisfactorily conform to the industrial data on ingot surface defects.

The prediction of epidemics through mathematical modeling.

PubMed

Schaus, Catherine

2014-01-01

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

Mathematical modeling to predict residential solid waste generation.

PubMed

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.

Two Mathematical Models of Nonlinear Vibrations

NASA Technical Reports Server (NTRS)

Brugarolas, Paul; Bayard, David; Spanos, John; Breckenridge, William

2007-01-01

Two innovative mathematical models of nonlinear vibrations, and methods of applying them, have been conceived as byproducts of an effort to develop a Kalman filter for highly precise estimation of bending motions of a large truss structure deployed in outer space from a space-shuttle payload bay. These models are also applicable to modeling and analysis of vibrations in other engineering disciplines, on Earth as well as in outer space.

Effectiveness of discovery learning model on mathematical problem solving

NASA Astrophysics Data System (ADS)

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.

DMPy: a Python package for automated mathematical model construction of large-scale metabolic systems.

PubMed

Smith, Robert W; van Rosmalen, Rik P; Martins Dos Santos, Vitor A P; Fleck, Christian

2018-06-19

Models of metabolism are often used in biotechnology and pharmaceutical research to identify drug targets or increase the direct production of valuable compounds. Due to the complexity of large metabolic systems, a number of conclusions have been drawn using mathematical methods with simplifying assumptions. For example, constraint-based models describe changes of internal concentrations that occur much quicker than alterations in cell physiology. Thus, metabolite concentrations and reaction fluxes are fixed to constant values. This greatly reduces the mathematical complexity, while providing a reasonably good description of the system in steady state. However, without a large number of constraints, many different flux sets can describe the optimal model and we obtain no information on how metabolite levels dynamically change. Thus, to accurately determine what is taking place within the cell, finer quality data and more detailed models need to be constructed. In this paper we present a computational framework, DMPy, that uses a network scheme as input to automatically search for kinetic rates and produce a mathematical model that describes temporal changes of metabolite fluxes. The parameter search utilises several online databases to find measured reaction parameters. From this, we take advantage of previous modelling efforts, such as Parameter Balancing, to produce an initial mathematical model of a metabolic pathway. We analyse the effect of parameter uncertainty on model dynamics and test how recent flux-based model reduction techniques alter system properties. To our knowledge this is the first time such analysis has been performed on large models of metabolism. Our results highlight that good estimates of at least 80% of the reaction rates are required to accurately model metabolic systems. Furthermore, reducing the size of the model by grouping reactions together based on fluxes alters the resulting system dynamics. The presented pipeline automates the

Implementation of Formative Assessment--Effects of Quality of Programme Delivery on Students' Mathematics Achievement and Interest

ERIC Educational Resources Information Center

Pinger, Petra; Rakoczy, Katrin; Besser, Michael; Klieme, Eckhard

2018-01-01

The aim of this study was to contribute to the understanding of the effectiveness of formative assessment interventions by analysing how the "quality of programme delivery" affects students' mathematics achievement and interest. Teachers (n = 17) implemented formative assessment in their ninth-grade mathematics classes and provided their…

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

NASA Astrophysics Data System (ADS)

Bartley, Sarah R.; Ingram, Naomi

2017-12-01

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

Analysis of mathematical literacy ability based on self-efficacy in model eliciting activities using metaphorical thinking approach

NASA Astrophysics Data System (ADS)

Setiani, C.; Waluya, S. B.; Wardono

2018-03-01

The purposes of this research are: (1) to identify learning quality in Model Eliciting Activities (MEAs) using a Metaphorical Thinking (MT) approach regarding qualitative and quantitative; (2) to analyze mathematical literacy of students based on Self-Efficacy (SE). This research is mixed method concurrent embedded design with qualitative research as the primary method. The quantitative research used quasi-experimental with non-equivalent control group design. The population is VIII grade students of SMP Negeri 3 Semarang Indonesia. Quantitative data is examined by conducting completeness mean test, standard completeness test, mean differentiation test and proportional differentiation test. Qualitative data is analyzed descriptively. The result of this research shows that MEAs learning using MT approach accomplishes good criteria both quantitatively and qualitatively. Students with low self-efficacy can identify problems, but they are lack ability to arrange problem-solving strategy on mathematical literacy questions. Students with medium self-efficacy can identify information provided in issues, but they find difficulties to use math symbols in making a representation. Students with high self-efficacy are excellent to represent problems into mathematical models as well as figures by using appropriate symbols and tools, so they can arrange strategy easily to solve mathematical literacy questions.

Mathematical modeling of hydromechanical extrusion

NASA Astrophysics Data System (ADS)

Agapitova, O. Yu.; Byvaltsev, S. V.; Zalazinsky, A. G.

2017-12-01

The mathematical modeling of the hydromechanical extrusion of metals through two sequentially installed cone dies is carried out. The optimum parameters of extrusion tools are determined to minimize the extrusion force. A software system has been developed to solve problems of plastic deformation of metals and to provide an optimum design of extrusion tools.

Developing teachers' models for assessing students' competence in mathematical modelling through lesson study

NASA Astrophysics Data System (ADS)

Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat; Cakiroglu, Erdinc; Alacaci, Cengiz; Cetinkaya, Bulent

2017-08-01

Applications and modelling have gained a prominent role in mathematics education reform documents and curricula. Thus, there is a growing need for studies focusing on the effective use of mathematical modelling in classrooms. Assessment is an integral part of using modelling activities in classrooms, since it allows teachers to identify and manage problems that arise in various stages of the modelling process. However, teachers' difficulties in assessing student modelling work are a challenge to be considered when implementing modelling in the classroom. Thus, the purpose of this study was to investigate how teachers' knowledge on generating assessment criteria for assessing student competence in mathematical modelling evolved through a professional development programme, which is based on a lesson study approach and modelling perspective. The data was collected with four teachers from two public high schools over a five-month period. The professional development programme included a cyclical process, with each cycle consisting of an introductory meeting, the implementation of a model-eliciting activity with students, and a follow-up meeting. The results showed that the professional development programme contributed to teachers' knowledge for generating assessment criteria on the products, and the observable actions that affect the modelling cycle.

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

ERIC Educational Resources Information Center

Gould, Heather; Wasserman, Nicholas H.

2014-01-01

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

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

ERIC Educational Resources Information Center

Jacobs, Gerrie J.; Durandt, Rina

2017-01-01

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

Cooking Potatoes: Experimentation and Mathematical Modeling.

ERIC Educational Resources Information Center

Chen, Xiao Dong

2002-01-01

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

Mathematical modeling of forest fire initiation in three dimensional setting

Treesearch

Valeriy Perminov

2007-01-01

In this study, the assignment and theoretical investigations of the problems of forest fire initiation were carried out, including development of a mathematical model for description of heat and mass transfer processes in overterrestrial layer of atmosphere at crown forest fire initiation, taking into account their mutual influence. Mathematical model of forest fire...

About a mathematical model of market

NASA Astrophysics Data System (ADS)

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

ERIC Educational Resources Information Center

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 models and epidemiological analysis].

PubMed

Gerasimov, A N

2010-01-01

The limited use of mathematical simulation in epidemiology is due not only to the difficulty of monitoring the epidemic process and identifying its parameters but also to the application of oversimplified models. It is shown that realistic reproduction of actual morbidity dynamics requires taking into account heterogeneity and finiteness of the population and seasonal character of pathogen transmission mechanism.

Methods of Analysis and Overall Mathematics Teaching Quality in At-Risk Prekindergarten Classrooms

ERIC Educational Resources Information Center

McGuire, Patrick R.; Kinzie, Mable; Thunder, Kateri; Berry, Robert

2016-01-01

Research Findings: This study analyzed the quality of teacher-child interactions across 10 videotaped observations drawn from 5 different prekindergarten classrooms delivering the same mathematics curriculum: "MyTeachingPartner-Math." Interactions were coded using 2 observational measures: (a) a general measure, the Classroom Assessment…

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

NASA Astrophysics Data System (ADS)

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-04-01

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

Rigorous mathematical modelling for a Fast Corrector Power Supply in TPS

NASA Astrophysics Data System (ADS)

Liu, K.-B.; Liu, C.-Y.; Chien, Y.-C.; Wang, B.-S.; Wong, Y. S.

2017-04-01

To enhance the stability of beam orbit, a Fast Orbit Feedback System (FOFB) eliminating undesired disturbances was installed and tested in the 3rd generation synchrotron light source of Taiwan Photon Source (TPS) of National Synchrotron Radiation Research Center (NSRRC). The effectiveness of the FOFB greatly depends on the output performance of Fast Corrector Power Supply (FCPS); therefore, the design and implementation of an accurate FCPS is essential. A rigorous mathematical modelling is very useful to shorten design time and improve design performance of a FCPS. A rigorous mathematical modelling derived by the state-space averaging method for a FCPS in the FOFB of TPS composed of a full-bridge topology is therefore proposed in this paper. The MATLAB/SIMULINK software is used to construct the proposed mathematical modelling and to conduct the simulations of the FCPS. Simulations for the effects of the different resolutions of ADC on the output accuracy of the FCPS are investigated. A FCPS prototype is realized to demonstrate the effectiveness of the proposed rigorous mathematical modelling for the FCPS. Simulation and experimental results show that the proposed mathematical modelling is helpful for selecting the appropriate components to meet the accuracy requirements of a FCPS.

Mathematics Student Teachers' Modelling Approaches While Solving the Designed Esme Rug Problem

ERIC Educational Resources Information Center

Hidiroglu, Çaglar Naci; Dede, Ayse Tekin; Ünver, Semiha Kula; Güzel, Esra Bukova

2017-01-01

The purpose of the study is to analyze the mathematics student teachers' solutions on the Esme Rug Problem through 7-stage mathematical modelling process. This problem was designed by the researchers by considering the modelling problems' main properties. The study was conducted with twenty one secondary mathematics student teachers. The data were…

Examining of Model Eliciting Activities Developed by Mathematics Student Teachers

ERIC Educational Resources Information Center

Dede, Ayse Tekin; Hidiroglu, Çaglar Naci; Güzel, Esra Bukova

2017-01-01

The purpose of this study is to examine the model eliciting activities developed by the mathematics student teachers in the context of the principles of the model eliciting activities. The participants of the study conducted as a case study design were twenty one mathematics student teachers working on seven groups. The data collection tools were…

Visual Modeling as a Motivation for Studying Mathematics and Art

ERIC Educational Resources Information Center

Sendova, Evgenia; Grkovska, Slavica

2005-01-01

The paper deals with the possibility of enriching the curriculum in mathematics, informatics and art by means of visual modeling of abstract paintings. The authors share their belief that in building a computer model of a construct, one gains deeper insight into the construct, and is motivated to elaborate one's knowledge in mathematics and…

Development of innovative problem based learning model with PMRI-scientific approach using ICT to increase mathematics literacy and independence-character of junior high school students

NASA Astrophysics Data System (ADS)

Wardono; Waluya, B.; Kartono; Mulyono; Mariani, S.

2018-03-01

This research is very urgent in relation to the national issue of human development and the nation's competitiveness because of the ability of Indonesian Junior High School students' mathematics literacy results of the Programme for International Student Assessment (PISA) by OECD field of Mathematics is still very low compared to other countries. Curriculum 2013 launched one of them reflect the results of PISA which is still far from the expectations of the Indonesian nation and to produce a better quality of education, PISA ratings that reflect the nation's better competitiveness need to be developed innovative, interactive learning models such as innovative interactive learning Problem Based Learning (PBL) based on the approach of Indonesian Realistic Mathematics Education (PMRI) and the Scientific approach using Information and Communication Technology (ICT).The research was designed using Research and Development (R&D), research that followed up the development and dissemination of a product/model. The result of the research shows the innovative interactive learning PBL model based on PMRI-Scientific using ICT that developed valid, practical and effective and can improve the ability of mathematics literacy and independence-character of junior high school students. While the quality of innovative interactive learning PBL model based on PMRI-Scientific using ICT meet the good category.

The stability of colorectal cancer mathematical models

NASA Astrophysics Data System (ADS)

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 modeling of moving boundary problems in thermal energy storage

NASA Technical Reports Server (NTRS)

Solomon, A. D.

1980-01-01

The capability for predicting the performance of thermal energy storage (RES) subsystems and components using PCM's based on mathematical and physical models is developed. Mathematical models of the dynamic thermal behavior of (TES) subsystems using PCM's based on solutions of the moving boundary thermal conduction problem and on heat and mass transfer engineering correlations are also discussed.

Program Helps Generate Boundary-Element Mathematical Models

NASA Technical Reports Server (NTRS)

Goldberg, R. K.

1995-01-01

Composite Model Generation-Boundary Element Method (COM-GEN-BEM) computer program significantly reduces time and effort needed to construct boundary-element mathematical models of continuous-fiber composite materials at micro-mechanical (constituent) scale. Generates boundary-element models compatible with BEST-CMS boundary-element code for anlaysis of micromechanics of composite material. Written in PATRAN Command Language (PCL).

Mathematical modelling and numerical simulation of forces in milling process

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Mathematical properties and parameter estimation for transit compartment pharmacodynamic models.

PubMed

Yates, James W T

2008-07-03

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

Mathematical Modeling of an Oscillating Droplet

NASA Technical Reports Server (NTRS)

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.

Leading a New Pedagogical Approach to Australian Curriculum Mathematics: Using the Dual Mathematical Modelling Cycle Framework

ERIC Educational Resources Information Center

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 Methods of Subjective Modeling in Scientific Research: I. The Mathematical and Empirical Basis

NASA Astrophysics Data System (ADS)

Pyt'ev, Yu. P.

2018-01-01

mathematical formalism for subjective modeling, based on modelling of uncertainty, reflecting unreliability of subjective information and fuzziness that is common for its content. The model of subjective judgments on values of an unknown parameter x ∈ X of the model M( x) of a research object is defined by the researcher-modeler as a space1 ( X, p( X), P{I^{\\bar x}}, Be{l^{\\bar x}}) with plausibility P{I^{\\bar x}} and believability Be{l^{\\bar x}} measures, where x is an uncertain element taking values in X that models researcher—modeler's uncertain propositions about an unknown x ∈ X, measures P{I^{\\bar x}}, Be{l^{\\bar x}} model modalities of a researcher-modeler's subjective judgments on the validity of each x ∈ X: the value of P{I^{\\bar x}}(\\tilde x = x) determines how relatively plausible, in his opinion, the equality (\\tilde x = x) is, while the value of Be{l^{\\bar x}}(\\tilde x = x) determines how the inequality (\\tilde x = x) should be relatively believed in. Versions of plausibility Pl and believability Bel measures and pl- and bel-integrals that inherit some traits of probabilities, psychophysics and take into account interests of researcher-modeler groups are considered. It is shown that the mathematical formalism of subjective modeling, unlike "standard" mathematical modeling, •enables a researcher-modeler to model both precise formalized knowledge and non-formalized unreliable knowledge, from complete ignorance to precise knowledge of the model of a research object, to calculate relative plausibilities and believabilities of any features of a research object that are specified by its subjective model M(\\tilde x), and if the data on observations of a research object is available, then it: •enables him to estimate the adequacy of subjective model to the research objective, to correct it by combining subjective ideas and the observation data after testing their consistency, and, finally, to empirically recover the model of a research

Assessing Journal Quality in Mathematics Education

ERIC Educational Resources Information Center

Nivens, Ryan Andrew; Otten, Samuel

2017-01-01

In this Research Commentary, we describe 3 journal metrics--the Web of Science's Impact Factor, Scopus's SCImago Journal Rank, and Google Scholar Metrics' h5-index--and compile the rankings (if they exist) for 69 mathematics education journals. We then discuss 2 paths that the mathematics education community should consider with regard to these…

Development of mathematical models of environmental physiology

NASA Technical Reports Server (NTRS)

Stolwijk, J. A. J.; Mitchell, J. W.; Nadel, E. R.

1971-01-01

Selected articles concerned with mathematical or simulation models of human thermoregulation are presented. The articles presented include: (1) development and use of simulation models in medicine, (2) model of cardio-vascular adjustments during exercise, (3) effective temperature scale based on simple model of human physiological regulatory response, (4) behavioral approach to thermoregulatory set point during exercise, and (5) importance of skin temperature in sweat regulation.

Mathematical model for predicting human vertebral fracture

NASA Technical Reports Server (NTRS)

Benedict, J. V.

1973-01-01

Mathematical model has been constructed to predict dynamic response of tapered, curved beam columns in as much as human spine closely resembles this form. Model takes into consideration effects of impact force, mass distribution, and material properties. Solutions were verified by dynamic tests on curved, tapered, elastic polyethylene beam.

Mathematical model of an air-filled alpha stirling refrigerator

NASA Astrophysics Data System (ADS)

McFarlane, Patrick; Semperlotti, Fabio; Sen, Mihir

2013-10-01

This work develops a mathematical model for an alpha Stirling refrigerator with air as the working fluid and will be useful in optimizing the mechanical design of these machines. Two pistons cyclically compress and expand air while moving sinusoidally in separate chambers connected by a regenerator, thus creating a temperature difference across the system. A complete non-linear mathematical model of the machine, including air thermodynamics, and heat transfer from the walls, as well as heat transfer and fluid resistance in the regenerator, is developed. Non-dimensional groups are derived, and the mathematical model is numerically solved. The heat transfer and work are found for both chambers, and the coefficient of performance of each chamber is calculated. Important design parameters are varied and their effect on refrigerator performance determined. This sensitivity analysis, which shows what the significant parameters are, is a useful tool for the design of practical Stirling refrigeration systems.

Frequencies as Proportions: Using a Teaching Model Based on Pirie and Kieren's Model of Mathematical Understanding

ERIC Educational Resources Information Center

Wright, Vince

2014-01-01

Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Modelling Mathematics Problem Solving Item Responses Using a Multidimensional IRT Model

ERIC Educational Resources Information Center

Wu, Margaret; Adams, Raymond

2006-01-01

This research examined students' responses to mathematics problem-solving tasks and applied a general multidimensional IRT model at the response category level. In doing so, cognitive processes were identified and modelled through item response modelling to extract more information than would be provided using conventional practices in scoring…

A Conceptual Model of Mathematical Reasoning for School Mathematics

ERIC Educational Resources Information Center

Jeannotte, Doris; Kieran, Carolyn

2017-01-01

The development of students' mathematical reasoning (MR) is a goal of several curricula and an essential element of the culture of the mathematics education research community. But what mathematical reasoning consists of is not always clear; it is generally assumed that everyone has a sense of what it is. Wanting to clarify the elements of MR,…

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

ERIC Educational Resources Information Center

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

2016-01-01

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

Mathematical modelling of tissue formation in chondrocyte filter cultures.

PubMed

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

2011-12-17

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

Quality Assurance in Educational Administration in the Teaching of Farm Mathematics for National Integration in Nigeria

ERIC Educational Resources Information Center

Enemali, I. A.; Adah, Obe Christopher

2015-01-01

Farm mathematics, an aspect of agricultural science education is being taught in our educational institutions in the country. This effort is to enhance agricultural productivity and quality of agricultural science education for national integration. For the realization of this, a quality assured educational administration is vital. The paper…

Teaching Writing and Communication in a Mathematical Modeling Course

ERIC Educational Resources Information Center

Linhart, Jean Marie

2014-01-01

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

Neutral model analysis of landscape patterns from mathematical morphology

Treesearch

Kurt H. Riitters; Peter Vogt; Pierre Soille; Jacek Kozak; Christine Estreguil

2007-01-01

Mathematical morphology encompasses methods for characterizing land-cover patterns in ecological research and biodiversity assessments. This paper reports a neutral model analysis of patterns in the absence of a structuring ecological process, to help set standards for comparing and interpreting patterns identified by mathematical morphology on real land-cover maps. We...

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

ERIC Educational Resources Information Center

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…

Mathematical knowledge for teaching: Making the tacit more explicit in mathematics teacher education

NASA Astrophysics Data System (ADS)

Abdullah, Mohd Faizal Nizam Lee; Vimalanandan, Lena

2017-05-01

Teaching practice during school based experiences, afford an opportunity for pre service teachers to put into practice their knowledge for teaching mathematics. Like all knowledge, Mathematical Knowledge for Teaching (MKT) is held in both tacit and explicit form, making it especially difficult to study and map during instruction. This study investigates the tacit and explicit nature of MKT held by pre service teachers in a Malaysian Teacher Education Program and how it impacts the Mathematical Quality of their instruction (MQI). This study of three mathematics pre-service teachers (PSTs), utilised videos of mathematics lessons, reflective debriefs and interviews. The findings suggest that factors such as reflecting, peer-sharing, conferencing with mentors and observing support in making tacit knowledge more explicit during planning and instruction. Implications for preparation of mathematics teachers capable of high Mathematical Quality of Instruction are also discussed.

Mathematical, Constitutive and Numerical Modelling of Catastrophic Landslides and Related Phenomena

NASA Astrophysics Data System (ADS)

Pastor, M.; Fernández Merodo, J. A.; Herreros, M. I.; Mira, P.; González, E.; Haddad, B.; Quecedo, M.; Tonni, L.; Drempetic, V.

2008-02-01

Mathematical and numerical models are a fundamental tool for predicting the behaviour of geostructures and their interaction with the environment. The term “mathematical model” refers to a mathematical description of the more relevant physical phenomena which take place in the problem being analyzed. It is indeed a wide area including models ranging from the very simple ones for which analytical solutions can be obtained to those more complicated requiring the use of numerical approximations such as the finite element method. During the last decades, mathematical, constitutive and numerical models have been very much improved and today their use is widespread both in industry and in research. One special case is that of fast catastrophic landslides, for which simplified methods are not able to provide accurate solutions in many occasions. Moreover, many finite element codes cannot be applied for propagation of the mobilized mass. The purpose of this work is to present an overview of the different alternative mathematical and numerical models which can be applied to both the initiation and propagation mechanisms of fast catastrophic landslides and other related problems such as waves caused by landslides.

Mathematical modelling of an electromagnetics automobile suspension

NASA Astrophysics Data System (ADS)

Amin, Ahmad Zaki Mohamad; Ahmad, Shamsuddin; Hoe, Yeak Su

2017-04-01

The mathematical modelling of the electromagnetic automobile suspension (EAS) is presented. The solution of the model is found using Runge-Kutta Method via MAPLE. The graphs of the vertical displacement, different vertical displacement and road profiles and acceleration of car body against time are investigated and validated using certain criteria.

Optimal healthcare decision making under multiple mathematical models: application in prostate cancer screening.

PubMed

Bertsimas, Dimitris; Silberholz, John; Trikalinos, Thomas

2018-03-01

Important decisions related to human health, such as screening strategies for cancer, need to be made without a satisfactory understanding of the underlying biological and other processes. Rather, they are often informed by mathematical models that approximate reality. Often multiple models have been made to study the same phenomenon, which may lead to conflicting decisions. It is natural to seek a decision making process that identifies decisions that all models find to be effective, and we propose such a framework in this work. We apply the framework in prostate cancer screening to identify prostate-specific antigen (PSA)-based strategies that perform well under all considered models. We use heuristic search to identify strategies that trade off between optimizing the average across all models' assessments and being "conservative" by optimizing the most pessimistic model assessment. We identified three recently published mathematical models that can estimate quality-adjusted life expectancy (QALE) of PSA-based screening strategies and identified 64 strategies that trade off between maximizing the average and the most pessimistic model assessments. All prescribe PSA thresholds that increase with age, and 57 involve biennial screening. Strategies with higher assessments with the pessimistic model start screening later, stop screening earlier, and use higher PSA thresholds at earlier ages. The 64 strategies outperform 22 previously published expert-generated strategies. The 41 most "conservative" ones remained better than no screening with all models in extensive sensitivity analyses. We augment current comparative modeling approaches by identifying strategies that perform well under all models, for various degrees of decision makers' conservativeness.

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

ERIC Educational Resources Information Center

Unlu, Melihan; Ertekin, Erhan; Dilmac, Bulent

2017-01-01

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

Mathematical Model Of Nerve/Muscle Interaction

NASA Technical Reports Server (NTRS)

Hannaford, Blake

1990-01-01

Phasic Excitation/Activation (PEA) mathematical model simulates short-term nonlinear dynamics of activation and control of muscle by nerve. Includes electronic and mechanical elements. Is homeomorphic at level of its three major building blocks, which represent motoneuron, dynamics of activation of muscle, and mechanics of muscle.

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

ERIC Educational Resources Information Center

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

2018-01-01

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

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

ERIC Educational Resources Information Center

Ludwig, Patrice; Tongen, Anthony; Walton, Brian

2018-01-01

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

[Flavouring estimation of quality of grape wines with use of methods of mathematical statistics].

PubMed

Yakuba, Yu F; Khalaphyan, A A; Temerdashev, Z A; Bessonov, V V; Malinkin, A D

2016-01-01

The questions of forming of wine's flavour integral estimation during the tasting are discussed, the advantages and disadvantages of the procedures are declared. As investigating materials we used the natural white and red wines of Russian manufactures, which were made with the traditional technologies from Vitis Vinifera, straight hybrids, blending and experimental wines (more than 300 different samples). The aim of the research was to set the correlation between the content of wine's nonvolatile matter and wine's tasting quality rating by mathematical statistics methods. The content of organic acids, amino acids and cations in wines were considered as the main factors influencing on the flavor. Basically, they define the beverage's quality. The determination of those components in wine's samples was done by the electrophoretic method «CAPEL». Together with the analytical checking of wine's samples quality the representative group of specialists simultaneously carried out wine's tasting estimation using 100 scores system. The possibility of statistical modelling of correlation of wine's tasting estimation based on analytical data of amino acids and cations determination reasonably describing the wine's flavour was examined. The statistical modelling of correlation between the wine's tasting estimation and the content of major cations (ammonium, potassium, sodium, magnesium, calcium), free amino acids (proline, threonine, arginine) and the taking into account the level of influence on flavour and analytical valuation within fixed limits of quality accordance were done with Statistica. Adequate statistical models which are able to predict tasting estimation that is to determine the wine's quality using the content of components forming the flavour properties have been constructed. It is emphasized that along with aromatic (volatile) substances the nonvolatile matter - mineral substances and organic substances - amino acids such as proline, threonine, arginine

Mathematical Modeling of Renal Hemodynamics in Physiology and Pathophysiology

PubMed Central

Sgouralis, Ioannis; Layton, Anita T.

2015-01-01

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. PMID:25765886

Mathematical modeling of the aerodynamics of high-angle-of-attack maneuvers

NASA Technical Reports Server (NTRS)

Schiff, L. B.; Tobak, M.; Malcolm, G. N.

1980-01-01

This paper is a review of the current state of aerodynamic mathematical modeling for aircraft motions at high angles of attack. The mathematical model serves to define a set of characteristic motions from whose known aerodynamic responses the aerodynamic response to an arbitrary high angle-of-attack flight maneuver can be predicted. Means are explored of obtaining stability parameter information in terms of the characteristic motions, whether by wind-tunnel experiments, computational methods, or by parameter-identification methods applied to flight-test data. A rationale is presented for selecting and verifying the aerodynamic mathematical model at the lowest necessary level of complexity. Experimental results describing the wing-rock phenomenon are shown to be accommodated within the most recent mathematical model by admitting the existence of aerodynamic hysteresis in the steady-state variation of the rolling moment with roll angle. Interpretation of the experimental results in terms of bifurcation theory reveals the general conditions under which aerodynamic hysteresis must exist.

Explorations in the Modeling of the Learning of Mathematics.

ERIC Educational Resources Information Center

Fuson, Karen C., Ed.; And Others

Eleven research reports in the area of models of learning mathematics are presented in this publication of the Mathematics Education Reports series. The papers represent a mixture of theories, viewpoints, and references to other areas. Content areas addressed range from preschool to college levels. All the papers are concerned with the learning of…

Understanding the Difficulties Faced by Engineering Undergraduates in Learning Mathematical Modelling

ERIC Educational Resources Information Center

Soon, Wanmei; Lioe, Luis Tirtasanjaya; McInnes, Brett

2011-01-01

The teaching of mathematics in Singapore continues, in most cases, to follow a traditional model. While this traditional approach has many advantages, it does not always adequately prepare students for University-level mathematics, especially applied mathematics. In particular, it does not cultivate the ability to deal with "non-routine…

Aspects of Mathematical Modelling of Pressure Retarded Osmosis

PubMed Central

Anissimov, Yuri G.

2016-01-01

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

Integrity Model Application: A Quality Support System for Decision-makers on Water Quality Assessment and Improvement

NASA Astrophysics Data System (ADS)

Mirauda, D.; Ostoich, M.; Di Maria, F.; Benacchio, S.; Saccardo, I.

2018-03-01

In this paper, a mathematical model has been applied to a river in North-East Italy to describe vulnerability scenarios due to environmental pollution phenomena. Such model, based on the influence diagrams theory, allowed identifying the extremely critical factors, such as wastewater discharges, drainage of diffuse pollution from agriculture and climate changes, which might affect the water quality of the river. The obtained results underlined how the water quality conditions have improved thanks to the continuous controls on the territory, following the application of Water Framework Directive 2000/60/EC. Nevertheless, some fluvial stretches did not reach the “good ecological status” by 2015, because of the increasing population in urban areas recorded in the last years and the high presence of tourists during the summer months, not balanced by a treatment plants upgrade.

Mathematical Modelling as a Tool to Understand Cell Self-renewal and Differentiation.

PubMed

Getto, Philipp; Marciniak-Czochra, Anna

2015-01-01

Mathematical modeling is a powerful technique to address key questions and paradigms in a variety of complex biological systems and can provide quantitative insights into cell kinetics, fate determination and development of cell populations. The chapter is devoted to a review of modeling of the dynamics of stem cell-initiated systems using mathematical methods of ordinary differential equations. Some basic concepts and tools for cell population dynamics are summarized and presented as a gentle introduction to non-mathematicians. The models take into account different plausible mechanisms regulating homeostasis. Two mathematical frameworks are proposed reflecting, respectively, a discrete (punctuated by division events) and a continuous character of transitions between differentiation stages. Advantages and constraints of the mathematical approaches are presented on examples of models of blood systems and compared to patients data on healthy hematopoiesis.

A Structural Equation Model Explaining 8th Grade Students' Mathematics Achievements

ERIC Educational Resources Information Center

Yurt, Eyüp; Sünbül, Ali Murat

2014-01-01

The purpose of this study is to investigate, via a model, the explanatory and predictive relationships among the following variables: Mathematical Problem Solving and Reasoning Skills, Sources of Mathematics Self-Efficacy, Spatial Ability, and Mathematics Achievements of Secondary School 8th Grade Students. The sample group of the study, itself…

Mathematical models of thermoregulation and heat transfer in mammals. A compendium of research

NASA Technical Reports Server (NTRS)

Shitzer, A.

1972-01-01

An annotated compendium on mathematical modeling of mammal thermoregulation systems is presented. Author abstracts, tables containing the more used mathematical models, solutions to these models, and each thermoregulation mechanism considered are included.

Editorial: Mathematical Methods and Modeling in Machine Fault Diagnosis

DOE PAGES

Yan, Ruqiang; Chen, Xuefeng; Li, Weihua; ...

2014-12-18

Modern mathematics has commonly been utilized as an effective tool to model mechanical equipment so that their dynamic characteristics can be studied analytically. This will help identify potential failures of mechanical equipment by observing change in the equipment’s dynamic parameters. On the other hand, dynamic signals are also important and provide reliable information about the equipment’s working status. Modern mathematics has also provided us with a systematic way to design and implement various signal processing methods, which are used to analyze these dynamic signals, and to enhance intrinsic signal components that are directly related to machine failures. This special issuemore » is aimed at stimulating not only new insights on mathematical methods for modeling but also recently developed signal processing methods, such as sparse decomposition with potential applications in machine fault diagnosis. Finally, the papers included in this special issue provide a glimpse into some of the research and applications in the field of machine fault diagnosis through applications of the modern mathematical methods.« less

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

USGS Publications Warehouse

Kuniansky, Eve L.

2014-01-01

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

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

PubMed

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.

Mathematical Model of Armed Helicopter vs Tank Duel

DTIC Science & Technology

The purpose of this thesis is to mathematically model a duel between the armed helicopter and the tank. In addition to providing a parametric...analysis of B. O. Koopman’s classical Detection-Destruction Duel , two additional models were constructed and analyzed. All three models stem from stochastic

Some Aspects of Mathematical Model of Collaborative Learning

ERIC Educational Resources Information Center

Nakamura, Yasuyuki; Yasutake, Koichi; Yamakawa, Osamu

2012-01-01

There are some mathematical learning models of collaborative learning, with which we can learn how students obtain knowledge and we expect to design effective education. We put together those models and classify into three categories; model by differential equations, so-called Ising spin and a stochastic process equation. Some of the models do not…

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

PubMed Central

Ganusov, Vitaly V.

2016-01-01

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

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

ERIC Educational Resources Information Center

Nasser-Abu Alhija, Fadia; Amasha, Marcel

2012-01-01

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

"When Mathematical Activity Moves You": An Exploration of the Design and Use of Purposefully Embodied Mathematical Activities, Models, Contexts, and Environments

ERIC Educational Resources Information Center

Campbell, William James

2017-01-01

This dissertation describes a mathematics curriculum and instruction design experiment involving a series of embodied mathematical activities conducted in two Colorado elementary schools Activities designed for this experiment include multi-scalar number line models focused on supporting students' understanding of elementary mathematics. Realistic…

Mathematical models of bipolar disorder

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

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

2015-09-01

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

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

ERIC Educational Resources Information Center

Hidiroglu, Çaglar Naci; Güzel, Esra Bukova

2017-01-01

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

The use of mathematical models to inform influenza pandemic preparedness and response

PubMed Central

Wu, Joseph T; Cowling, Benjamin J

2011-01-01

Summary Influenza pandemics have occurred throughout history and were associated with substantial excess mortality and morbidity. Mathematical models of infectious diseases permit quantitative description of epidemic processes based on the underlying biological mechanisms. Mathematical models have been widely used in the past decade to aid pandemic planning by allowing detailed predictions of the speed of spread of an influenza pandemic and the likely effectiveness of alternative control strategies. During the initial waves of the 2009 influenza pandemic, mathematical models were used to track the spread of the virus, predict the time course of the pandemic and assess the likely impact of large-scale vaccination. While mathematical modeling has made substantial contributions to influenza pandemic preparedness, its use as a real-time tool for pandemic control is currently limited by the lack of essential surveillance information such as serologic data. Mathematical modeling provided a useful framework for analyzing and interpreting surveillance data during the 2009 influenza pandemic, for highlighting limitations in existing pandemic surveillance systems, and for guiding how these systems should be strengthened in order to cope with future epidemics of influenza or other emerging infectious diseases. PMID:21727183

Redundancy management of electrohydraulic servoactuators by mathematical model referencing

NASA Technical Reports Server (NTRS)

Campbell, R. A.

1971-01-01

A description of a mathematical model reference system is presented which provides redundancy management for an electrohydraulic servoactuator. The mathematical model includes a compensation network that calculates reference parameter perturbations induced by external disturbance forces. This is accomplished by using the measured pressure differential data taken from the physical system. This technique was experimentally verified by tests performed using the H-1 engine thrust vector control system for Saturn IB. The results of these tests are included in this report. It was concluded that this technique improves the tracking accuracy of the model reference system to the extent that redundancy management of electrohydraulic servosystems may be performed using this method.

Mathematical modeling of renal hemodynamics in physiology and pathophysiology.

PubMed

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.

Making Sense of Mathematics

ERIC Educational Resources Information Center

Umphrey, Jan

2011-01-01

The National Council of Teachers of Mathematics (NCTM) is a voice and advocate for mathematics educators, working to ensure that all students receive equitable mathematics learning of the highest quality. To help teachers and school leaders understand the Common Core State Standards for Mathematics (CCSSM) and to point out how the CCSSM can be…

Study of ecological compensation in complex river networks based on a mathematical model.

PubMed

Wang, Xiao; Shen, Chunqi; Wei, Jun; Niu, Yong

2018-05-31

Transboundary water pollution has resulted in increasing conflicts between upstream and downstream administrative districts. Ecological compensation is an efficient means of restricting pollutant discharge and achieving sustainable utilization of water resources. The tri-provincial region of Taihu Basin is a typical river networks area. Pollutant flux across provincial boundaries in the Taihu Basin is hard to determine due to complex hydrologic and hydrodynamic conditions. In this study, ecological compensation estimation for the tri-provincial area based on a mathematical model is investigated for better environmental management. River discharge and water quality are predicted with the one-dimensional mathematical model and validated with field measurements. Different ecological compensation criteria are identified considering the notable regional discrepancy in sewage treatment costs. Finally, the total compensation payment is estimated. Our study indicates that Shanghai should be the receiver of payment from both Jiangsu and Zhenjiang in 2013, with 305 million and 300 million CNY, respectively. Zhejiang also contributes more pollutants to Jiangsu, and the compensation to Jiangsu is estimated as 9.3 million CNY. The proposed ecological compensation method provides an efficient way for solving the transboundary conflicts in a complex river networks area and is instructive for future policy-making.

Mathematical Modeling Of A Nuclear/Thermionic Power Source

NASA Technical Reports Server (NTRS)

Vandersande, Jan W.; Ewell, Richard C.

1992-01-01

Report discusses mathematical modeling to predict performance and lifetime of spacecraft power source that is integrated combination of nuclear-fission reactor and thermionic converters. Details of nuclear reaction, thermal conditions in core, and thermionic performance combined with model of swelling of fuel.

Mathematical model of a smoldering log.

Treesearch

Fernando de Souza Costa; David Sandberg

2004-01-01

A mathematical model is developed describing the natural smoldering of logs. It is considered the steady one dimensional propagation of infinitesimally thin fronts of drying, pyrolysis, and char oxidation in a horizontal semi-infinite log. Expressions for the burn rates, distribution profiles of temperature, and positions of the drying, pyrolysis, and smoldering fronts...

Mathematical and Computational Modeling in Complex Biological Systems

PubMed Central

Li, Wenyang; Zhu, Xiaoliang

2017-01-01

The biological process and molecular functions involved in the cancer progression remain difficult to understand for biologists and clinical doctors. Recent developments in high-throughput technologies urge the systems biology to achieve more precise models for complex diseases. Computational and mathematical models are gradually being used to help us understand the omics data produced by high-throughput experimental techniques. The use of computational models in systems biology allows us to explore the pathogenesis of complex diseases, improve our understanding of the latent molecular mechanisms, and promote treatment strategy optimization and new drug discovery. Currently, it is urgent to bridge the gap between the developments of high-throughput technologies and systemic modeling of the biological process in cancer research. In this review, we firstly studied several typical mathematical modeling approaches of biological systems in different scales and deeply analyzed their characteristics, advantages, applications, and limitations. Next, three potential research directions in systems modeling were summarized. To conclude, this review provides an update of important solutions using computational modeling approaches in systems biology. PMID:28386558

Mathematical and Computational Modeling in Complex Biological Systems.

PubMed

Ji, Zhiwei; Yan, Ke; Li, Wenyang; Hu, Haigen; Zhu, Xiaoliang

2017-01-01

The biological process and molecular functions involved in the cancer progression remain difficult to understand for biologists and clinical doctors. Recent developments in high-throughput technologies urge the systems biology to achieve more precise models for complex diseases. Computational and mathematical models are gradually being used to help us understand the omics data produced by high-throughput experimental techniques. The use of computational models in systems biology allows us to explore the pathogenesis of complex diseases, improve our understanding of the latent molecular mechanisms, and promote treatment strategy optimization and new drug discovery. Currently, it is urgent to bridge the gap between the developments of high-throughput technologies and systemic modeling of the biological process in cancer research. In this review, we firstly studied several typical mathematical modeling approaches of biological systems in different scales and deeply analyzed their characteristics, advantages, applications, and limitations. Next, three potential research directions in systems modeling were summarized. To conclude, this review provides an update of important solutions using computational modeling approaches in systems biology.

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

ERIC Educational Resources Information Center

Tian, Xiaoxi

2014-01-01

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

A Mathematical Model of Marine Diesel Engine Speed Control System

NASA Astrophysics Data System (ADS)

Sinha, Rajendra Prasad; Balaji, Rajoo

2018-02-01

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

Achieving Quality Mathematics Classroom Instruction through Productive Pedagogies

ERIC Educational Resources Information Center

Bature, Iliya Joseph; Atweh, Bill

2016-01-01

This paper seeks to investigate the implementation of the Productive Pedagogies Framework in Nigerian mathematics classroom setting. The researcher adopted a qualitative case study approach to seeking data for the three research questions postulated for the study. Three mathematics teachers taught mathematics in two secondary schools in two…

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

PubMed

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

2016-10-01

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

A simple parametric model observer for quality assurance in computer tomography

NASA Astrophysics Data System (ADS)

Anton, M.; Khanin, A.; Kretz, T.; Reginatto, M.; Elster, C.

2018-04-01

Model observers are mathematical classifiers that are used for the quality assessment of imaging systems such as computer tomography. The quality of the imaging system is quantified by means of the performance of a selected model observer. For binary classification tasks, the performance of the model observer is defined by the area under its ROC curve (AUC). Typically, the AUC is estimated by applying the model observer to a large set of training and test data. However, the recording of these large data sets is not always practical for routine quality assurance. In this paper we propose as an alternative a parametric model observer that is based on a simple phantom, and we provide a Bayesian estimation of its AUC. It is shown that a limited number of repeatedly recorded images (10–15) is already sufficient to obtain results suitable for the quality assessment of an imaging system. A MATLAB® function is provided for the calculation of the results. The performance of the proposed model observer is compared to that of the established channelized Hotelling observer and the nonprewhitening matched filter for simulated images as well as for images obtained from a low-contrast phantom on an x-ray tomography scanner. The results suggest that the proposed parametric model observer, along with its Bayesian treatment, can provide an efficient, practical alternative for the quality assessment of CT imaging systems.

Research Area 3: Mathematics (3.1 Modeling of Complex Systems)

DTIC Science & Technology

2017-10-31

RESEARCH AREA 3: MATHEMATICS (3.1 Modeling of Complex Systems). Proposal should be directed to Dr. John Lavery The views, opinions and/or findings...so designated by other documentation. 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS (ES) U.S. Army Research Office P.O. Box 12211 Research ...Title: RESEARCH AREA 3: MATHEMATICS (3.1 Modeling of Complex Systems). Proposal should be directed to Dr. John Lavery Report Term: 0-Other Email

Some aspects of mathematical and chemical modeling of complex chemical processes

NASA Technical Reports Server (NTRS)

Nemes, I.; Botar, L.; Danoczy, E.; Vidoczy, T.; Gal, D.

1983-01-01

Some theoretical questions involved in the mathematical modeling of the kinetics of complex chemical process are discussed. The analysis is carried out for the homogeneous oxidation of ethylbenzene in the liquid phase. Particular attention is given to the determination of the general characteristics of chemical systems from an analysis of mathematical models developed on the basis of linear algebra.

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

PubMed

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

2014-12-11

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

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

NASA Astrophysics Data System (ADS)

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-Artificial Neural Network Hybrid Model to Predict Roll Force during Hot Rolling of Steel

NASA Astrophysics Data System (ADS)

Rath, S.; Sengupta, P. P.; Singh, A. P.; Marik, A. K.; Talukdar, P.

2013-07-01

Accurate prediction of roll force during hot strip rolling is essential for model based operation of hot strip mills. Traditionally, mathematical models based on theory of plastic deformation have been used for prediction of roll force. In the last decade, data driven models like artificial neural network have been tried for prediction of roll force. Pure mathematical models have accuracy limitations whereas data driven models have difficulty in convergence when applied to industrial conditions. Hybrid models by integrating the traditional mathematical formulations and data driven methods are being developed in different parts of world. This paper discusses the methodology of development of an innovative hybrid mathematical-artificial neural network model. In mathematical model, the most important factor influencing accuracy is flow stress of steel. Coefficients of standard flow stress equation, calculated by parameter estimation technique, have been used in the model. The hybrid model has been trained and validated with input and output data collected from finishing stands of Hot Strip Mill, Bokaro Steel Plant, India. It has been found that the model accuracy has been improved with use of hybrid model, over the traditional mathematical model.

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

PubMed

Peper, Abraham

2004-08-21

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

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

ERIC Educational Resources Information Center

Carrejo, David J.; Marshall, Jill

2007-01-01

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

Learning and Teaching Mathematics through Real Life Models

ERIC Educational Resources Information Center

Takaci, Djurdjica; Budinski, Natalija

2011-01-01

This paper proposes modelling based learning as a tool for learning and teaching mathematics in high school. We report on an example of modelling real world problems in two high schools in Serbia where students were introduced for the first time to the basic concepts of modelling. Student use of computers and educational software, GeoGebra, was…

Physical and mathematical modeling of antimicrobial photodynamic therapy

NASA Astrophysics Data System (ADS)

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

2014-07-01

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

Reaching All Students with Mathematics.

ERIC Educational Resources Information Center

Cuevas, Gilbert, Ed.; Driscoll, Mark, Ed.

The National Council of Teachers of Mathematics'"Curriculum and Evaluation Standards for School Mathematics" and "Professional Standards for Teaching Mathematics" reflect the belief that all students can learn a significant core of high-quality mathematics. Recognizing the magnitude of the task of reaching all students, this…

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

PubMed

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

Computing Linear Mathematical Models Of Aircraft

NASA Technical Reports Server (NTRS)

Duke, Eugene L.; Antoniewicz, Robert F.; Krambeer, Keith D.

1991-01-01

Derivation and Definition of Linear Aircraft Model (LINEAR) computer program provides user with powerful, and flexible, standard, documented, and verified software tool for linearization of mathematical models of aerodynamics of aircraft. Intended for use in software tool to drive linear analysis of stability and design of control laws for aircraft. Capable of both extracting such linearized engine effects as net thrust, torque, and gyroscopic effects, and including these effects in linear model of system. Designed to provide easy selection of state, control, and observation variables used in particular model. Also provides flexibility of allowing alternate formulations of both state and observation equations. Written in FORTRAN.

Mathematical modeling of human brain physiological data

NASA Astrophysics Data System (ADS)

Böhm, Matthias; Faltermeier, Rupert; Brawanski, Alexander; Lang, Elmar W.

2013-12-01

Recently, a mathematical model of the basic physiological processes regulating the cerebral perfusion and oxygen supply was introduced [Jung , J. Math. Biol.JMBLAJ0303-681210.1007/s00285-005-0343-5 51, 491 (2005)]. Although this model correctly describes the interdependence of arterial blood pressure (ABP) and intracranial pressure (ICP), it fails badly when it comes to explaining certain abnormal correlations seen in about 80% of the recordings of ABP together with ICP and the partial oxygen pressure (TiPO2) of the neuronal tissue, taken at an intensive care unit during neuromonitoring of patients with a severe brain trauma. Such recordings occasionally show segments, where the mean arterial blood pressure is correlated with the partial oxygen pressure in tissue but anticorrelated with the intracranial pressure. The origin of such abnormal correlations has not been fully understood yet. Here, two extensions to the previous approach are proposed which can reproduce such abnormal correlations in simulations quantitatively. Furthermore, as the simulations are based on a mathematical model, additional insight into the physiological mechanisms from which such abnormal correlations originate can be gained.

Validation of a digital mammographic unit model for an objective and highly automated clinical image quality assessment.

PubMed

Perez-Ponce, Hector; Daul, Christian; Wolf, Didier; Noel, Alain

2013-08-01

In mammography, image quality assessment has to be directly related to breast cancer indicator (e.g. microcalcifications) detectability. Recently, we proposed an X-ray source/digital detector (XRS/DD) model leading to such an assessment. This model simulates very realistic contrast-detail phantom (CDMAM) images leading to gold disc (representing microcalcifications) detectability thresholds that are very close to those of real images taken under the simulated acquisition conditions. The detection step was performed with a mathematical observer. The aim of this contribution is to include human observers into the disc detection process in real and virtual images to validate the simulation framework based on the XRS/DD model. Mathematical criteria (contrast-detail curves, image quality factor, etc.) are used to assess and to compare, from the statistical point of view, the cancer indicator detectability in real and virtual images. The quantitative results given in this paper show that the images simulated by the XRS/DD model are useful for image quality assessment in the case of all studied exposure conditions using either human or automated scoring. Also, this paper confirms that with the XRS/DD model the image quality assessment can be automated and the whole time of the procedure can be drastically reduced. Compared to standard quality assessment methods, the number of images to be acquired is divided by a factor of eight. Copyright © 2012 IPEM. Published by Elsevier Ltd. All rights reserved.

Using Spreadsheets to Teach Aspects of Biology Involving Mathematical Models

ERIC Educational Resources Information Center

Carlton, Kevin; Nicholls, Mike; Ponsonby, David

2004-01-01

Some aspects of biology, for example the Hardy-Weinberg simulation of population genetics or modelling heat flow in lizards, have an undeniable mathematical basis. Students can find the level of mathematical skill required to deal with such concepts to be an insurmountable hurdle to understanding. If not used effectively, spreadsheet models…

Mathematical modeling of kidney transport.

PubMed

Layton, Anita T

2013-01-01

In addition to metabolic waste and toxin excretion, the kidney also plays an indispensable role in regulating the balance of water, electrolytes, nitrogen, and acid-base. In this review, we describe representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, epithelial transport, and regulation of renal oxygen transport. We discuss the extent to which these modeling efforts have expanded our understanding of renal function in both health and disease. Copyright © 2013 Wiley Periodicals, Inc.

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

ERIC Educational Resources Information Center

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-01-01

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

A Mathematical Model of a Simple Amplifier Using a Ferroelectric Transistor

NASA Technical Reports Server (NTRS)

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.

Perturbing the Hypothalamic Pituitary Adrenal Axis:A Mathematical Model for Interpreting PTSDAssessment Tests

DTIC Science & Technology

2017-08-15

RESEARCH Perturbing the Hypothalamic–Pituitary–Adrenal Axis: A Mathematical Model for Interpreting PTSD Assessment Tests Lae Un Kim1, Maria R...D’Orsogna2, and Tom Chou1 1Department of Biomathematics, University of California, Los Angeles, USA 2Department of Mathematics , California State University...observed features and experimental responses can arise from a bistable mathematical model containing two steady-states, rather than relying on specific

Mathematical learning models that depend on prior knowledge and instructional strategies

NASA Astrophysics Data System (ADS)

Pritchard, David E.; Lee, Young-Jin; Bao, Lei

2008-06-01

We present mathematical learning models—predictions of student’s knowledge vs amount of instruction—that are based on assumptions motivated by various theories of learning: tabula rasa, constructivist, and tutoring. These models predict the improvement (on the post-test) as a function of the pretest score due to intervening instruction and also depend on the type of instruction. We introduce a connectedness model whose connectedness parameter measures the degree to which the rate of learning is proportional to prior knowledge. Over a wide range of pretest scores on standard tests of introductory physics concepts, it fits high-quality data nearly within error. We suggest that data from MIT have low connectedness (indicating memory-based learning) because the test used the same context and representation as the instruction and that more connected data from the University of Minnesota resulted from instruction in a different representation from the test.

Development of Mathematic Model of Cold Welding at Drawing-up the Flange Joint of Pneumohydraulic Systems

NASA Astrophysics Data System (ADS)

Boyko, Y. S.

2002-01-01

Provision of high airtightness of joints of pipe- lines of pneumohydraulic systems (PHS) operating under high pressure, is an important task for designing and operation of launch vehicles. In the process of assembly and tests of PHS of launch vehicles, it was found that detachable flange joints do not lose their airtightness after removal of fastening elements, even in conditions of standard loads. The task of this work is in studying a phenomenon connected with initiation of the observed effect of adhesion and also stresses in the zone of contact at drawing- up the flange detachable joints with a plastic gasket. Investigations have shown that density of the joint is kept due to cold welding, as the created conditions are helpful for that process. As a result of the investigations performed, we have developed a mathematic model which is based on application of the theory of metal bonds; that theory explains the essence of the effect observed. Basic factors which provide optimum mode of cold welding, are effort which can cause microplastic deformation and form maximum contact, and also quality of processing the material of the surfaces joined. Strength of all- metal joint depends on factual area of contact. So, surface processing quality defines a configuration of microbulges which come into contact not simultaneously, and their stressed state is different, and it influences the character of dependence of the contact area on loading. Results of calculations by the mathematic model are expressed by dependencies of factual area of contact and a single diameter of the contact spot on the load applied which compresses the materials with various physical properties, and on the surface processing quality. The mathematic model allows to explain the common character of the cold welding process in detachable flange joints with the plastic gasket, to determine the nature and the character of acting forces, to define kinetics and the mechanism of formation of cold welding of

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

ERIC Educational Resources Information Center

Bal, Aytgen Pinar; Doganay, Ahmet

2014-01-01

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

Envisioning migration: Mathematics in both experimental analysis and modeling of cell behavior

PubMed Central

Zhang, Elizabeth R.; Wu, Lani F.; Altschuler, Steven J.

2013-01-01

The complex nature of cell migration highlights the power and challenges of applying mathematics to biological studies. Mathematics may be used to create model equations that recapitulate migration, which can predict phenomena not easily uncovered by experiments or intuition alone. Alternatively, mathematics may be applied to interpreting complex data sets with better resolution—potentially empowering scientists to discern subtle patterns amid the noise and heterogeneity typical of migrating cells. Iteration between these two methods is necessary in order to reveal connections within the cell migration signaling network, as well as to understand the behavior that arises from those connections. Here, we review recent quantitative analysis and mathematical modeling approaches to the cell migration problem. PMID:23660413

The Role of Real-Life Mathematics Instruction on Mathematics Outcomes in Kindergarten

ERIC Educational Resources Information Center

Gottfried, Michael

2016-01-01

In an era of a declining quality and quantity of students entering and persisting in mathematics in the USA, researchers and policy makers are looking for new strategies to engage students in these fields and improve mathematics outcomes. One push has been to make mathematics instruction more relevant with real-world applications throughout the…

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

PubMed

Campitelli, Guillermo; Gerrans, Paul

2014-04-01

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

Authentic Integration: A Model for Integrating Mathematics and Science in the Classroom

ERIC Educational Resources Information Center

Treacy, Páraic; O'Donoghue, John

2014-01-01

Attempts at integrating mathematics and science have been made previously but no definitive, widely adopted teaching model has been developed to date. Research suggests that hands-on, practical, student-centred tasks should form a central element when designing an effective model for the integration of mathematics and science. Aided by this…

PREFACE: Physics-Based Mathematical Models for Nanotechnology

NASA Astrophysics Data System (ADS)

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

Reality-Theoretical Models-Mathematics: A Ternary Perspective on Physics Lessons in Upper-Secondary School

ERIC Educational Resources Information Center

Hansson, Lena; Hansson, Örjan; Juter, Kristina; Redfors, Andreas

2015-01-01

This article discusses the role of mathematics during physics lessons in upper-secondary school. Mathematics is an inherent part of theoretical models in physics and makes powerful predictions of natural phenomena possible. Ability to use both theoretical models and mathematics is central in physics. This paper takes as a starting point that the…

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Optimization of grapevine yield by applying mathematical models to obtain quality wine products

NASA Astrophysics Data System (ADS)

Alina, Dobrei; Alin, Dobrei; Eleonora, Nistor; Teodor, Cristea; Marius, Boldea; Florin, Sala

2016-06-01

Relationship between the crop load and the grape yield and quality is a dynamic process, specific for wine cultivars and for fresh consumption varieties. Modeling these relations is important for the improvement of technological works. This study evaluated the interrelationship of crop load (B - buds number) and several production parameters (Y - yield; S - sugar; A - acidity; GaI - Glucoacidimetric index; AP - alcoholic potential; F - flavorings, WA - wine alcohol; SR - sugar residue, in Muscat Ottonel wine cultivar and Y - yield; S - sugar; A - acidity; GaI - Glucoacidimetric Index; CP - commercial production; BS - berries size in the Victoria table grape cultivar). In both varieties have been identified correlations between the independent variable (B - buds number as a result of pruning and training practices) and quality parameters analyzed (r = -0.699 for B vsY relationship; r = 0.961 for the relationship B vs S; r = -0.959 for B vs AP relationship; r = 0.743 for the relationship Y vs S, p <0.01, in the Muscat Ottonel cultivar, respectively r = -0.907 for relationship B vs Y; r = -0.975 for B vs CP relationship; r = -0.971 for relationship B vs BS; r = 0.990 for CP vs BS relationship in the Victoria cultivar. Through regression analysis were obtained models that describe the variation concerning production and quality parameters in relation to the independent variable (B - buds number) with statistical significance results.

Application of a Functional Mathematical Index to the Evaluation of the Nutritional Quality of Potatoes

USDA-ARS?s Scientific Manuscript database

This paper describes the derivation and application of a new functional mathematical index that was used to evaluate the nutritional, safety, and processing quality aspects of potatoes. The index introduces the concept of an “optimal potato”, using appropriate distance and N-dimensional parameter sp...

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

ERIC Educational Resources Information Center

Schoenfeld, Alan H.

2013-01-01

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

Mathematical model of the SH-3G helicopter

NASA Technical Reports Server (NTRS)

Phillips, J. D.

1982-01-01

A mathematical model of the Sikorsky SH-3G helicopter based on classical nonlinear, quasi-steady rotor theory was developed. The model was validated statically and dynamically by comparison with Navy flight-test data. The model incorporates ad hoc revisions which address the ideal assumptions of classical rotor theory and improve the static trim characteristics to provide a more realistic simulation, while retaining the simplicity of the classical model.

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

PubMed

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

2011-01-01

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

Revitalising Mathematics Classroom Teaching through Lesson Study (LS): A Malaysian Case Study

ERIC Educational Resources Information Center

Lim, Chap Sam; Kor, Liew Kee; Chia, Hui Min

2016-01-01

This paper discusses how implementation of Lesson Study (LS) has brought about evolving changes in the quality of mathematics classroom teaching in one Chinese primary school. The Japanese model of LS was adapted as a teacher professional development to improve mathematics teachers' teaching practices. The LS group consisted of five mathematics…

UAH mathematical model of the variable polarity plasma ARC welding system calculation

NASA Technical Reports Server (NTRS)

Hung, R. J.

1994-01-01

Significant advantages of Variable Polarity Plasma Arc (VPPA) welding process include faster welding, fewer repairs, less joint preparation, reduced weldment distortion, and absence of porosity. A mathematical model is presented to analyze the VPPA welding process. Results of the mathematical model were compared with the experimental observation accomplished by the GDI team.

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

ERIC Educational Resources Information Center

Macinko Kovac, Maja; Eret, Lidija

2012-01-01

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

The Singing Wineglass: An Exercise in Mathematical Modelling

ERIC Educational Resources Information Center

Voges, E. L.; Joubert, S. V.

2008-01-01

Lecturers in mathematical modelling courses are always on the lookout for new examples to illustrate the modelling process. A physical phenomenon, documented as early as the nineteenth century, was recalled: when a wineglass "sings", waves are visible on the surface of the wine. These surface waves are used as an exercise in mathematical…

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

PubMed

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.

Mathematical modelling of the growth of human fetus anatomical structures.

PubMed

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

2017-09-01

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

Envisioning migration: mathematics in both experimental analysis and modeling of cell behavior.

PubMed

Zhang, Elizabeth R; Wu, Lani F; Altschuler, Steven J

2013-10-01

The complex nature of cell migration highlights the power and challenges of applying mathematics to biological studies. Mathematics may be used to create model equations that recapitulate migration, which can predict phenomena not easily uncovered by experiments or intuition alone. Alternatively, mathematics may be applied to interpreting complex data sets with better resolution--potentially empowering scientists to discern subtle patterns amid the noise and heterogeneity typical of migrating cells. Iteration between these two methods is necessary in order to reveal connections within the cell migration signaling network, as well as to understand the behavior that arises from those connections. Here, we review recent quantitative analysis and mathematical modeling approaches to the cell migration problem. Copyright © 2013 Elsevier Ltd. All rights reserved.

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

PubMed

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

2018-01-01

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

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

ERIC Educational Resources Information Center

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

2016-01-01

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

How Long is my Toilet Roll?--A Simple Exercise in Mathematical Modelling

ERIC Educational Resources Information Center

Johnston, Peter R.

2013-01-01

The simple question of how much paper is left on my toilet roll is studied from a mathematical modelling perspective. As is typical with applied mathematics, models of increasing complexity are introduced and solved. Solutions produced at each step are compared with the solution from the previous step. This process exposes students to the typical…

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

PubMed

Braatz, Elise M; Coleman, Randolph A

2015-06-01

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

Pedagogical Content Knowledge in Mathematical Modelling Instruction

ERIC Educational Resources Information Center

Tan, Liang Soon; Ang, Keng Cheng

2012-01-01

This paper posits that teachers' pedagogical content knowledge in mathematical modelling instruction can be demonstrated in the crafting of action plans and expected teaching and learning moves via their lesson images (Schoenfeld, 1998). It can also be developed when teachers shape appropriate teaching moves in response to students' learning…

Mathematics Underground

ERIC Educational Resources Information Center

Luther, Kenneth H.

2012-01-01

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

Mathematical model to predict drivers' reaction speeds.

PubMed

Long, Benjamin L; Gillespie, A Isabella; Tanaka, Martin L

2012-02-01

Mental distractions and physical impairments can increase the risk of accidents by affecting a driver's ability to control the vehicle. In this article, we developed a linear mathematical model that can be used to quantitatively predict drivers' performance over a variety of possible driving conditions. Predictions were not limited only to conditions tested, but also included linear combinations of these tests conditions. Two groups of 12 participants were evaluated using a custom drivers' reaction speed testing device to evaluate the effect of cell phone talking, texting, and a fixed knee brace on the components of drivers' reaction speed. Cognitive reaction time was found to increase by 24% for cell phone talking and 74% for texting. The fixed knee brace increased musculoskeletal reaction time by 24%. These experimental data were used to develop a mathematical model to predict reaction speed for an untested condition, talking on a cell phone with a fixed knee brace. The model was verified by comparing the predicted reaction speed to measured experimental values from an independent test. The model predicted full braking time within 3% of the measured value. Although only a few influential conditions were evaluated, we present a general approach that can be expanded to include other types of distractions, impairments, and environmental conditions.

Mathematical models for optimization of the centrifugal stage of a refrigerating compressor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nuzhdin, A.S.

1987-09-01

The authors describe a general approach to the creating of mathematical models of energy and head losses in the flow part of the centrifugal compressor. The mathematical model of the pressure head and efficiency of a two-section stage proposed in this paper is meant for determining its characteristics for the assigned geometric dimensions and for optimizing by variance calculations. Characteristic points on the plot of velocity distribution over the margin of the vanes of the impeller and the diffuser of the centrifugal stage with a combined diffuser are presented. To assess the reliability of the mathematical model the authors comparedmore » some calculated data with the experimental ones.« less

Nonconvex Model of Material Growth: Mathematical Theory

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

A mathematical model of aortic aneurysm formation

PubMed Central

Hao, Wenrui; Gong, Shihua; Wu, Shuonan; Xu, Jinchao; Go, Michael R.; Friedman, Avner; Zhu, Dai

2017-01-01

Abdominal aortic aneurysm (AAA) is a localized enlargement of the abdominal aorta, such that the diameter exceeds 3 cm. The natural history of AAA is progressive growth leading to rupture, an event that carries up to 90% risk of mortality. Hence there is a need to predict the growth of the diameter of the aorta based on the diameter of a patient’s aneurysm at initial screening and aided by non-invasive biomarkers. IL-6 is overexpressed in AAA and was suggested as a prognostic marker for the risk in AAA. The present paper develops a mathematical model which relates the growth of the abdominal aorta to the serum concentration of IL-6. Given the initial diameter of the aorta and the serum concentration of IL-6, the model predicts the growth of the diameter at subsequent times. Such a prediction can provide guidance to how closely the patient’s abdominal aorta should be monitored. The mathematical model is represented by a system of partial differential equations taking place in the aortic wall, where the media is assumed to have the constituency of an hyperelastic material. PMID:28212412

Genetic demographic networks: Mathematical model and applications.

PubMed

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

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

PubMed

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

2018-06-01

Antibiotic resistance is a major global threat to the provision of safe and effective health care. To control antibiotic resistance, vaccines have been proposed as an essential intervention, complementing improvements in diagnostic testing, antibiotic stewardship, and drug pipelines. The decision to introduce or amend vaccination programmes is routinely based on mathematical modelling. However, few mathematical models address the impact of vaccination on antibiotic resistance. We reviewed the literature using PubMed to identify all studies that used an original mathematical model to quantify the impact of a vaccine on antibiotic resistance transmission within a human population. We reviewed the models from the resulting studies in the context of a new framework to elucidate the pathways through which vaccination might impact antibiotic resistance. We identified eight mathematical modelling studies; the state of the literature highlighted important gaps in our understanding. Notably, studies are limited in the range of pathways represented, their geographical scope, and the vaccine-pathogen combinations assessed. Furthermore, to translate model predictions into public health decision making, more work is needed to understand how model structure and parameterisation affects model predictions and how to embed these predictions within economic frameworks. Copyright © 2018 Elsevier Ltd. All rights reserved.

A 3D mathematical model for the horizontal anode baking furnace

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kocaefe, Y.S.; Dernedde, E.; Kocaefe, D.

In the aluminum industry, carbon anodes are baked in large horizontal or vertical ring-type furnaces. The anode quality depends strongly on the baking conditions (heating rate, soaking time and final anode temperature). A three-dimensional mathematical model has been developed for a horizontal anode baking furnace to assess the effects of different parameters on the baking process and to improve the furnace operation and design at Noranda Aluminum Smelter in New Madrid, Missouri. The commercial CFD code CFDS-FLOW3D is used to solve the governing differential equations. The model gives the temperature, velocity and concentration distributions in the flue, and the variationmore » of the temperature distribution with time in the pit. In this paper, a description of the 3D model for the horizontal anode baking furnace will be given. Some of the results from a case study will also be presented. The results show clearly the importance of flue geometry on the gas flow distribution in the flue and the heat transfer to the anodes.« less

Mathematical modeling in chronobiology.

PubMed

Bordyugov, G; Westermark, P O; Korenčič, A; Bernard, S; Herzel, H

2013-01-01

Circadian clocks are autonomous oscillators entrained by external Zeitgebers such as light-dark and temperature cycles. On the cellular level, rhythms are generated by negative transcriptional feedback loops. In mammals, the suprachiasmatic nucleus (SCN) in the anterior part of the hypothalamus plays the role of the central circadian pacemaker. Coupling between individual neurons in the SCN leads to precise self-sustained oscillations even in the absence of external signals. These neuronal rhythms orchestrate the phasing of circadian oscillations in peripheral organs. Altogether, the mammalian circadian system can be regarded as a network of coupled oscillators. In order to understand the dynamic complexity of these rhythms, mathematical models successfully complement experimental investigations. Here we discuss basic ideas of modeling on three different levels (1) rhythm generation in single cells by delayed negative feedbacks, (2) synchronization of cells via external stimuli or cell-cell coupling, and (3) optimization of chronotherapy.

Exploring Differential Effects of Mathematics Courses on Mathematics Achievement

ERIC Educational Resources Information Center

Ma, Xin; McIntyre, Laureen J.

2005-01-01

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

Establishing an Explanatory Model for Mathematics Identity

ERIC Educational Resources Information Center

Cribbs, Jennifer D.; Hazari, Zahra; Sonnert, Gerhard; Sadler, Philip M.

2015-01-01

This article empirically tests a previously developed theoretical framework for mathematics identity based on students' beliefs. The study employs data from more than 9,000 college calculus students across the United States to build a robust structural equation model. While it is generally thought that students' beliefs about their own competence…

Mathematical Modeling Projects: Success for All Students

ERIC Educational Resources Information Center

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…

Mathematical models used in segmentation and fractal methods of 2-D ultrasound images

NASA Astrophysics Data System (ADS)

Moldovanu, Simona; Moraru, Luminita; Bibicu, Dorin

2012-11-01

Mathematical models are widely used in biomedical computing. The extracted data from images using the mathematical techniques are the "pillar" achieving scientific progress in experimental, clinical, biomedical, and behavioural researches. This article deals with the representation of 2-D images and highlights the mathematical support for the segmentation operation and fractal analysis in ultrasound images. A large number of mathematical techniques are suitable to be applied during the image processing stage. The addressed topics cover the edge-based segmentation, more precisely the gradient-based edge detection and active contour model, and the region-based segmentation namely Otsu method. Another interesting mathematical approach consists of analyzing the images using the Box Counting Method (BCM) to compute the fractal dimension. The results of the paper provide explicit samples performed by various combination of methods.

Mathematical modeling of gene expression: a guide for the perplexed biologist

PubMed Central

Ay, Ahmet; Arnosti, David N.

2011-01-01

The detailed analysis of transcriptional networks holds a key for understanding central biological processes, and interest in this field has exploded due to new large-scale data acquisition techniques. Mathematical modeling can provide essential insights, but the diversity of modeling approaches can be a daunting prospect to investigators new to this area. For those interested in beginning a transcriptional mathematical modeling project we provide here an overview of major types of models and their applications to transcriptional networks. In this discussion of recent literature on thermodynamic, Boolean and differential equation models we focus on considerations critical for choosing and validating a modeling approach that will be useful for quantitative understanding of biological systems. PMID:21417596

Mathematical modeling of systemic factors determining the risk of deterioration of drinking water supply and development of allergic diseases of population

NASA Astrophysics Data System (ADS)

Bespalov, Yurii G.; Nosov, Konstantin V.; Vysotska, Olena V.; Porvan, Andrii P.; Omiotek, Zbigniew; Burlibay, Aron; Assembay, Azat; Szatkowska, Małgorzata

2017-08-01

This study aims at mathematical modeling of systemic factors threatening the sanitary and hygienic state of sources of water supply. It is well-known, that this state affects health of population consuming water from different water sources (lakes, reservoirs, rivers). In particular, water quality problem may cause allergic reactions that are the important problem of health care. In the paper, the authors present the mathematical model, that enables on the basis of observations of a natural system to predict the system's behavior and determine the risks related to deterioration of drinking water resources. As a case study, we uses supply of drinking water from Lake Sevan, but the approach developed in the study can be applied to wide area of adjacent problems.