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

PubMed

Bürger, Raimund; Diehl, Stefan; Nopens, Ingmar

2011-03-01

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

Does Writing Have Any Effect on Mathematics Success?

ERIC Educational Resources Information Center

Dündar, Sefa

2016-01-01

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

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

ERIC Educational Resources Information Center

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

2009-01-01

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

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…

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.

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.

Automation of reliability evaluation procedures through CARE - The computer-aided reliability estimation program.

NASA Technical Reports Server (NTRS)

Mathur, F. P.

1972-01-01

Description of an on-line interactive computer program called CARE (Computer-Aided Reliability Estimation) which can model self-repair and fault-tolerant organizations and perform certain other functions. Essentially CARE consists of a repository of mathematical equations defining the various basic redundancy schemes. These equations, under program control, are then interrelated to generate the desired mathematical model to fit the architecture of the system under evaluation. The mathematical model is then supplied with ground instances of its variables and is then evaluated to generate values for the reliability-theoretic functions applied to the model.

Modeling of Geometric Error in Linear Guide Way to Improved the vertical three-axis CNC Milling machine’s accuracy

NASA Astrophysics Data System (ADS)

Kwintarini, Widiyanti; Wibowo, Agung; Arthaya, Bagus M.; Yuwana Martawirya, Yatna

2018-03-01

The purpose of this study was to improve the accuracy of three-axis CNC Milling Vertical engines with a general approach by using mathematical modeling methods of machine tool geometric errors. The inaccuracy of CNC machines can be caused by geometric errors that are an important factor during the manufacturing process and during the assembly phase, and are factors for being able to build machines with high-accuracy. To improve the accuracy of the three-axis vertical milling machine, by knowing geometric errors and identifying the error position parameters in the machine tool by arranging the mathematical modeling. The geometric error in the machine tool consists of twenty-one error parameters consisting of nine linear error parameters, nine angle error parameters and three perpendicular error parameters. The mathematical modeling approach of geometric error with the calculated alignment error and angle error in the supporting components of the machine motion is linear guide way and linear motion. The purpose of using this mathematical modeling approach is the identification of geometric errors that can be helpful as reference during the design, assembly and maintenance stages to improve the accuracy of CNC machines. Mathematically modeling geometric errors in CNC machine tools can illustrate the relationship between alignment error, position and angle on a linear guide way of three-axis vertical milling machines.

Evaluation of Instructional Practice in the Secondary School Mathematics Classroom: A Cognitive Perspective.

ERIC Educational Resources Information Center

Artzt, Alice F.; Armour-Thomas, Eleanor

The purpose of this exploratory study was to develop a model for evaluating teachers' instructional practices in mathematics and the cognitions associated with these practices. The sample consisted of seven beginning and seven experienced teachers of secondary school mathematics, who each taught one lesson of his or her own design. To evaluate…

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.

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

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.

[Influence of sample surface roughness on mathematical model of NIR quantitative analysis of wood density].

PubMed

Huang, An-Min; Fei, Ben-Hua; Jiang, Ze-Hui; Hse, Chung-Yun

2007-09-01

Near infrared spectroscopy is widely used as a quantitative method, and the main multivariate techniques consist of regression methods used to build prediction models, however, the accuracy of analysis results will be affected by many factors. In the present paper, the influence of different sample roughness on the mathematical model of NIR quantitative analysis of wood density was studied. The result of experiments showed that if the roughness of predicted samples was consistent with that of calibrated samples, the result was good, otherwise the error would be much higher. The roughness-mixed model was more flexible and adaptable to different sample roughness. The prediction ability of the roughness-mixed model was much better than that of the single-roughness model.

Mathematical estimation of the level of microbial contamination on spacecraft surfaces by volumetric air sampling

NASA Technical Reports Server (NTRS)

Oxborrow, G. S.; Roark, A. L.; Fields, N. D.; Puleo, J. R.

1974-01-01

Microbiological sampling methods presently used for enumeration of microorganisms on spacecraft surfaces require contact with easily damaged components. Estimation of viable particles on surfaces using air sampling methods in conjunction with a mathematical model would be desirable. Parameters necessary for the mathematical model are the effect of angled surfaces on viable particle collection and the number of viable cells per viable particle. Deposition of viable particles on angled surfaces closely followed a cosine function, and the number of viable cells per viable particle was consistent with a Poisson distribution. Other parameters considered by the mathematical model included deposition rate and fractional removal per unit time. A close nonlinear correlation between volumetric air sampling and airborne fallout on surfaces was established with all fallout data points falling within the 95% confidence limits as determined by the mathematical model.

The fractional volatility model: An agent-based interpretation

NASA Astrophysics Data System (ADS)

Vilela Mendes, R.

2008-06-01

Based on the criteria of mathematical simplicity and consistency with empirical market data, a model with volatility driven by fractional noise has been constructed which provides a fairly accurate mathematical parametrization of the data. Here, some features of the model are reviewed and extended to account for leverage effects. Using agent-based models, one tries to find which agent strategies and (or) properties of the financial institutions might be responsible for the features of the fractional volatility model.

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.

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

ERIC Educational Resources Information Center

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

2017-01-01

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

Mathematical modeling of human cardiovascular system for simulation of orthostatic response

NASA Technical Reports Server (NTRS)

Melchior, F. M.; Srinivasan, R. S.; Charles, J. B.

1992-01-01

This paper deals with the short-term response of the human cardiovascular system to orthostatic stresses in the context of developing a mathematical model of the overall system. It discusses the physiological issues involved and how these issues have been handled in published cardiovascular models for simulation of orthostatic response. Most of the models are stimulus specific with no demonstrated capability for simulating the responses to orthostatic stimuli of different types. A comprehensive model incorporating all known phenomena related to cardiovascular regulation would greatly help to interpret the various orthostatic responses of the system in a consistent manner and to understand the interactions among its elements. This paper provides a framework for future efforts in mathematical modeling of the entire cardiovascular system.

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.

Crocodile Mathematics 1.1. [CD-ROM].

ERIC Educational Resources Information Center

2002

This CD-ROM consists of software that allows both teachers and students to create and experiment with mathematical models by linking shapes, graphs, numbers, and equations. It is usable for demonstrations, home learning, reinforcing concepts, illustrating concepts that are difficult to visualize, further pupil investigations, and project work.…

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Gamma Ray Observatory (GRO) dynamics simulator requirements and mathematical specifications, revision 1

NASA Technical Reports Server (NTRS)

Harman, R.; Blejer, D.

1990-01-01

The requirements and mathematical specifications for the Gamma Ray Observatory (GRO) Dynamics Simulator are presented. The complete simulator system, which consists of the profie subsystem, simulation control and input/output subsystem, truth model subsystem, onboard computer model subsystem, and postprocessor, is described. The simulator will be used to evaluate and test the attitude determination and control models to be used on board GRO under conditions that simulate the expected in-flight environment.

Mathematics understanding and anxiety in collaborative teaching

NASA Astrophysics Data System (ADS)

Ansari, B. I.; Wahyu, N.

2017-12-01

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

Mathematical modeling of a nickel-cadmium battery

NASA Technical Reports Server (NTRS)

Fan, Deyuan; White, Ralph E.

1991-01-01

Extensions are presented for a mathematical model of an Ni-CD cell (Fan and White, 1991). These extensions consist of intercalation thermodynamics for the nickel electrode and oxygen generation and reduction reactions during charge and overcharge. The simulated results indicate that intercalation may be important in the nickel electrode and that including the oxygen reactions provides a means of predicting the efficiency of the cell on charge and discharge.

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.

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

Jablonská, Jana, E-mail: jana.jablonska@vsb.cz; Kozubková, Milada, E-mail: milada.kozubkova@vsb.cz

Cavitation today is a very important problem that is solved by means of experimental and mathematical methods. The article deals with the generation of cavitation in convergent divergent nozzle of rectangular cross section. Measurement of pressure, flow rate, temperature, amount of dissolved air in the liquid and visualization of cavitation area using high-speed camera was performed for different flow rates. The measurement results were generalized by dimensionless analysis, which allows easy detection of cavitation in the nozzle. For numerical simulation the multiphase mathematical model of cavitation consisting of water and vapor was created. During verification the disagreement with the measurementsmore » for higher flow rates was proved, therefore the model was extended to multiphase mathematical model (water, vapor and air), due to release of dissolved air. For the mathematical modeling the multiphase turbulence RNG k-ε model for low Reynolds number flow with vapor and air cavitation was used. Subsequently the sizes of the cavitation area were verified. In article the inlet pressure and loss coefficient depending on the amount of air added to the mathematical model are evaluated. On the basis of the approach it may be create a methodology to estimate the amount of released air added at the inlet to the modeled area.« less

The effect of mathematical model development on the instruction of acceleration to introductory physics students

NASA Astrophysics Data System (ADS)

Sauer, Tim Allen

The purpose of this study was to evaluate the effectiveness of utilizing student constructed theoretical math models when teaching acceleration to high school introductory physics students. The goal of the study was for the students to be able to utilize mathematical modeling strategies to improve their problem solving skills, as well as their standardized scientific and conceptual understanding. This study was based on mathematical modeling research, conceptual change research and constructivist theory of learning, all of which suggest that mathematical modeling is an effective way to influence students' conceptual connectiveness and sense making of formulaic equations and problem solving. A total of 48 students in two sections of high school introductory physics classes received constructivist, inquiry-based, cooperative learning, and conceptual change-oriented instruction. The difference in the instruction for the 24 students in the mathematical modeling treatment group was that they constructed every formula they needed to solve problems from data they collected. In contrast, the instructional design for the control group of 24 students allowed the same instruction with assigned problems solved with formulas given to them without explanation. The results indicated that the mathematical modeling students were able to solve less familiar and more complicated problems with greater confidence and mental flexibility than the control group students. The mathematical modeling group maintained fewer alternative conceptions consistently in the interviews than did the control group. The implications for acceleration instruction from these results were discussed.

Students’ Representation in Mathematical Word Problem-Solving: Exploring Students’ Self-efficacy

NASA Astrophysics Data System (ADS)

Sahendra, A.; Budiarto, M. T.; Fuad, Y.

2018-01-01

This descriptive qualitative research aims at investigating student represented in mathematical word problem solving based on self-efficacy. The research subjects are two eighth graders at a school in Surabaya with equal mathematical ability consisting of two female students with high and low self-efficacy. The subjects were chosen based on the results of test of mathematical ability, documentation of the result of middle test in even semester of 2016/2017 academic year, and results of questionnaire of mathematics word problem in terms of self-efficacy scale. The selected students were asked to do mathematical word problem solving and be interviewed. The result of this study shows that students with high self-efficacy tend to use multiple representations of sketches and mathematical models, whereas students with low self-efficacy tend to use single representation of sketches or mathematical models only in mathematical word problem-solving. This study emphasizes that teachers should pay attention of student’s representation as a consideration of designing innovative learning in order to increase the self-efficacy of each student to achieve maximum mathematical achievement although it still requires adjustment to the school situation and condition.

Generalized mathematical model of red muds’ thickener of alumina production

NASA Astrophysics Data System (ADS)

Fedorova, E. R.; Vinogradova, A. A.

2018-03-01

The article describes the principle of a generalized mathematical model of the red mud’s thickener construction. The model of the red muds’ thickener of alumina production consists of sub-models of flocculation zones containing solid fraction feed slurry, free-fall and cramped sedimentation zones or effective sedimentation zones, bleaching zones. The generalized mathematical model of thickener allows predicting the content of solid fraction in the condensed product and in the upper discharge. The sub-model of solid phase aggregation allows one to count up average size of floccules, which is created during the flocculation process in feedwell. The sub-model of the free-fall and cramped sedimentation zone allows one to count up the concentration profile taking into account the variable cross-sectional area of the thickener. The sub-model of the bleaching zone is constructed on the basis of the theory of the precipitation of Kinc, supplemented by correction factors.

Mathematical modeling and computer simulation of isoelectric focusing with electrochemically defined ampholytes

NASA Technical Reports Server (NTRS)

Palusinski, O. A.; Allgyer, T. T.; Mosher, R. A.; Bier, M.; Saville, D. A.

1981-01-01

A mathematical model of isoelectric focusing at the steady state has been developed for an M-component system of electrochemically defined ampholytes. The model is formulated from fundamental principles describing the components' chemical equilibria, mass transfer resulting from diffusion and electromigration, and electroneutrality. The model consists of ordinary differential equations coupled with a system of algebraic equations. The model is implemented on a digital computer using FORTRAN-based simulation software. Computer simulation data are presented for several two-component systems showing the effects of varying the isoelectric points and dissociation constants of the constituents.

Environmental Pathway Models-Ground-Water Modeling in Support of Remedial Decision Making at Sites Contaminated with Radioactive Material

EPA Pesticide Factsheets

The Joint Interagency Environmental Pathway Modeling Working Group wrote this report to promote appropriate and consistent use of mathematical environmental models in the remediation and restoration of sites contaminated by radioactive substances.

The effect of creative problem solving on students’ mathematical adaptive reasoning

NASA Astrophysics Data System (ADS)

Muin, A.; Hanifah, S. H.; Diwidian, F.

2018-01-01

This research was conducted to analyse the effect of creative problem solving (CPS) learning model on the students’ mathematical adaptive reasoning. The method used in this study was a quasi-experimental with randomized post-test only control group design. Samples were taken as many as two classes by cluster random sampling technique consisting of experimental class (CPS) as many as 40 students and control class (conventional) as many as 40 students. Based on the result of hypothesis testing with the t-test at the significance level of 5%, it was obtained that significance level of 0.0000 is less than α = 0.05. This shows that the students’ mathematical adaptive reasoning skills who were taught by CPS model were higher than the students’ mathematical adaptive reasoning skills of those who were taught by conventional model. The result of this research showed that the most prominent aspect of adaptive reasoning that could be developed through a CPS was inductive intuitive. Two aspects of adaptive reasoning, which were inductive intuitive and deductive intuitive, were mostly balanced. The different between inductive intuitive and deductive intuitive aspect was not too big. CPS model can develop student mathematical adaptive reasoning skills. CPS model can facilitate development of mathematical adaptive reasoning skills thoroughly.

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.

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.

Improving Mathematics Achievement of Indonesian 5th Grade Students through Guided Discovery Learning

ERIC Educational Resources Information Center

Yurniwati; Hanum, Latipa

2017-01-01

This research aims to find information about the improvement of mathematics achievement of grade five student through guided discovery learning. This research method is classroom action research using Kemmis and Taggart model consists of three cycles. Data used in this study is learning process and learning results. Learning process data is…

Using PISA 2003, Examining the Factors Affecting Students' Mathematics Achievement

ERIC Educational Resources Information Center

Demir, Ibrahim; Kilic, Serpil

2010-01-01

The purpose of this study is to examine the effects of learning strategies on mathematics achievement. The sample was compiled from students who participated in Programme for International Student Assessment (PISA) in Turkey. The data consisted of 4493 15 years old Turkish students in 158 schools, and analyzed by two levels Bernoulli model as a…

A Teachable Agent Game Engaging Primary School Children to Learn Arithmetic Concepts and Reasoning

ERIC Educational Resources Information Center

Pareto, Lena

2014-01-01

In this paper we will describe a learning environment designed to foster conceptual understanding and reasoning in mathematics among younger school children. The learning environment consists of 48 2-player game variants based on a graphical model of arithmetic where the mathematical content is intrinsically interwoven with the game idea. The…

Model-Based Design of Biochemical Microreactors

PubMed Central

Elbinger, Tobias; Gahn, Markus; Neuss-Radu, Maria; Hante, Falk M.; Voll, Lars M.; Leugering, Günter; Knabner, Peter

2016-01-01

Mathematical modeling of biochemical pathways is an important resource in Synthetic Biology, as the predictive power of simulating synthetic pathways represents an important step in the design of synthetic metabolons. In this paper, we are concerned with the mathematical modeling, simulation, and optimization of metabolic processes in biochemical microreactors able to carry out enzymatic reactions and to exchange metabolites with their surrounding medium. The results of the reported modeling approach are incorporated in the design of the first microreactor prototypes that are under construction. These microreactors consist of compartments separated by membranes carrying specific transporters for the input of substrates and export of products. Inside the compartments of the reactor multienzyme complexes assembled on nano-beads by peptide adapters are used to carry out metabolic reactions. The spatially resolved mathematical model describing the ongoing processes consists of a system of diffusion equations together with boundary and initial conditions. The boundary conditions model the exchange of metabolites with the neighboring compartments and the reactions at the surface of the nano-beads carrying the multienzyme complexes. Efficient and accurate approaches for numerical simulation of the mathematical model and for optimal design of the microreactor are developed. As a proof-of-concept scenario, a synthetic pathway for the conversion of sucrose to glucose-6-phosphate (G6P) was chosen. In this context, the mathematical model is employed to compute the spatio-temporal distributions of the metabolite concentrations, as well as application relevant quantities like the outflow rate of G6P. These computations are performed for different scenarios, where the number of beads as well as their loading capacity are varied. The computed metabolite distributions show spatial patterns, which differ for different experimental arrangements. Furthermore, the total output of G6P increases for scenarios where microcompartimentation of enzymes occurs. These results show that spatially resolved models are needed in the description of the conversion processes. Finally, the enzyme stoichiometry on the nano-beads is determined, which maximizes the production of glucose-6-phosphate. PMID:26913283

Behavioral variability of choices versus structural inconsistency of preferences.

PubMed

Regenwetter, Michel; Davis-Stober, Clintin P

2012-04-01

Theories of rational choice often make the structural consistency assumption that every decision maker's binary strict preference among choice alternatives forms a strict weak order. Likewise, the very concept of a utility function over lotteries in normative, prescriptive, and descriptive theory is mathematically equivalent to strict weak order preferences over those lotteries, while intransitive heuristic models violate such weak orders. Using new quantitative interdisciplinary methodologies, we dissociate the variability of choices from the structural inconsistency of preferences. We show that laboratory choice behavior among stimuli of a classical "intransitivity" paradigm is, in fact, consistent with variable strict weak order preferences. We find that decision makers act in accordance with a restrictive mathematical model that, for the behavioral sciences, is extraordinarily parsimonious. Our findings suggest that the best place to invest future behavioral decision research is not in the development of new intransitive decision models but rather in the specification of parsimonious models consistent with strict weak order(s), as well as heuristics and other process models that explain why preferences appear to be weakly ordered.

State of charge modeling of lithium-ion batteries using dual exponential functions

NASA Astrophysics Data System (ADS)

Kuo, Ting-Jung; Lee, Kung-Yen; Huang, Chien-Kang; Chen, Jau-Horng; Chiu, Wei-Li; Huang, Chih-Fang; Wu, Shuen-De

2016-05-01

A mathematical model is developed by fitting the discharging curve of LiFePO4 batteries and used to investigate the relationship between the state of charge and the closed-circuit voltage. The proposed mathematical model consists of dual exponential terms and a constant term which can fit the characteristics of dual equivalent RC circuits closely, representing a LiFePO4 battery. One exponential term presents the stable discharging behavior and the other one presents the unstable discharging behavior and the constant term presents the cut-off voltage.

Stability analysis for a delay differential equations model of a hydraulic turbine speed governor

NASA Astrophysics Data System (ADS)

Halanay, Andrei; Safta, Carmen A.; Dragoi, Constantin; Piraianu, Vlad F.

2017-01-01

The paper aims to study the dynamic behavior of a speed governor for a hydraulic turbine using a mathematical model. The nonlinear mathematical model proposed consists in a system of delay differential equations (DDE) to be compared with already established mathematical models of ordinary differential equations (ODE). A new kind of nonlinearity is introduced as a time delay. The delays can characterize different running conditions of the speed governor. For example, it is considered that spool displacement of hydraulic amplifier might be blocked due to oil impurities in the oil supply system and so the hydraulic amplifier has a time delay in comparison to the time control. Numerical simulations are presented in a comparative manner. A stability analysis of the hydraulic control system is performed, too. Conclusions of the dynamic behavior using the DDE model of a hydraulic turbine speed governor are useful in modeling and controlling hydropower plants.

Numerical modelling in biosciences using delay differential equations

NASA Astrophysics Data System (ADS)

Bocharov, Gennadii A.; Rihan, Fathalla A.

2000-12-01

Our principal purposes here are (i) to consider, from the perspective of applied mathematics, models of phenomena in the biosciences that are based on delay differential equations and for which numerical approaches are a major tool in understanding their dynamics, (ii) to review the application of numerical techniques to investigate these models. We show that there are prima facie reasons for using such models: (i) they have a richer mathematical framework (compared with ordinary differential equations) for the analysis of biosystem dynamics, (ii) they display better consistency with the nature of certain biological processes and predictive results. We analyze both the qualitative and quantitative role that delays play in basic time-lag models proposed in population dynamics, epidemiology, physiology, immunology, neural networks and cell kinetics. We then indicate suitable computational techniques for the numerical treatment of mathematical problems emerging in the biosciences, comparing them with those implemented by the bio-modellers.

Mathematical modeling of a class of multibody flexible spacecraft structures

NASA Technical Reports Server (NTRS)

Kelkar, Atul, G.

1994-01-01

A mathematical model for a general multibody flexible spacecraft is obtained. The generic spacecraft considered consists of a flexible central body to which a number of flexible multibody structures are attached. The coordinate systems used in the derivation allow effective decoupling of the translational motion of the entire spacecraft from its rotational motion about its center of mass. The derivation assumes that the deformations in the bodies are only due to elastic motions. The dynamic model derived is a closed-form vector-matrix differential equation. The model developed can be used for analysis and simulation of many realistic spacecraft configurations.

The Development of Learning Model Based on Problem Solving to Construct High-Order Thinking Skill on the Learning Mathematics of 11th Grade in SMA/MA

ERIC Educational Resources Information Center

Syahputra, Edi; Surya, Edy

2017-01-01

This paper is a summary study of team Postgraduate on 11th grade. The objective of this study is to develop a learning model based on problem solving which can construct high-order thinking on the learning mathematics in SMA/MA. The subject of dissemination consists of Students of 11th grade in SMA/MA in 3 kabupaten/kota in North Sumatera, namely:…

The Latent Structure of Spatial Skills and Mathematics: A Replication of the Two-Factor Model

ERIC Educational Resources Information Center

Mix, Kelly S.; Levine, Susan C.; Cheng, Yi-Lang; Young, Christopher J.; Hambrick, David Z.; Konstantopoulos, Spyros

2017-01-01

In a previous study, Mix et al. (2016) reported that spatial skill and mathematics were composed of 2 highly correlated, domain-specific factors, with a few cross-domain loadings. The overall structure was consistent across grade (kindergarten, 3rd grade, 6th grade), but the cross-domain loadings varied with age. The present study sought to…

Using the Concrete Representational Abstract (CRA) Instructional Framework for Mathematics with Students with Emotional and Behavioral Disorders

ERIC Educational Resources Information Center

Peltier, Corey; Vannest, Kimberly J.

2018-01-01

Mr. Buxton is a perplexed elementary mathematics teacher. He co-teaches a second-grade classroom, with Ms. Snyder. In their classroom they have 25 students; five are identified as academically at risk, and three receive special education services. In the past Mr. Buxton successfully used an instructional approach consisting of (a) modeling, (b)…

Implications of Interactions among Society, Education and Technology: A Comparison of Multiple Linear Regression and Multilevel Modeling in Mathematics Achievement Analyses

ERIC Educational Resources Information Center

Deering, Pamela Rose

2014-01-01

This research compares and contrasts two approaches to predictive analysis of three years' of school district data to investigate relationships between student and teacher characteristics and math achievement as measured by the state-mandated Maryland School Assessment mathematics exam. The sample for the study consisted of 3,514 students taught…

Do Mathematics and Reading Competencies Integrated into Career and Technical Education Courses Improve High School Student State Assessment Scores?

ERIC Educational Resources Information Center

Pierce, Kristin B.; Hernandez, Victor M.

2015-01-01

A quasi experimental study tested a contextual teaching and learning model for integrating reading and mathematics competencies through 13 introductory career and technical education (CTE) courses. The treatment group consisted of students in the 13 introductory courses taught by the CTE teachers who designed the units and the control group…

Emulation of rocket trajectory based on a six degree of freedom model

NASA Astrophysics Data System (ADS)

Zhang, Wenpeng; Li, Fan; Wu, Zhong; Li, Rong

2008-10-01

In this paper, a 6-DOF motion mathematical model is discussed. It is consisted of body dynamics and kinematics block, aero dynamics block and atmosphere block. Based on Simulink, the whole rocket trajectory mathematical model is developed. In this model, dynamic system simulation becomes easy and visual. The method of modularization design gives more convenience to transplant. At last, relevant data is given to be validated by Monte Carlo means. Simulation results show that the flight trajectory of the rocket can be simulated preferably by means of this model, and it also supplies a necessary simulating tool for the development of control system.

Cognitive components of a mathematical processing network in 9-year-old children.

PubMed

Szűcs, Dénes; Devine, Amy; Soltesz, Fruzsina; Nobes, Alison; Gabriel, Florence

2014-07-01

We determined how various cognitive abilities, including several measures of a proposed domain-specific number sense, relate to mathematical competence in nearly 100 9-year-old children with normal reading skill. Results are consistent with an extended number processing network and suggest that important processing nodes of this network are phonological processing, verbal knowledge, visuo-spatial short-term and working memory, spatial ability and general executive functioning. The model was highly specific to predicting arithmetic performance. There were no strong relations between mathematical achievement and verbal short-term and working memory, sustained attention, response inhibition, finger knowledge and symbolic number comparison performance. Non-verbal intelligence measures were also non-significant predictors when added to our model. Number sense variables were non-significant predictors in the model and they were also non-significant predictors when entered into regression analysis with only a single visuo-spatial WM measure. Number sense variables were predicted by sustained attention. Results support a network theory of mathematical competence in primary school children and falsify the importance of a proposed modular 'number sense'. We suggest an 'executive memory function centric' model of mathematical processing. Mapping a complex processing network requires that studies consider the complex predictor space of mathematics rather than just focusing on a single or a few explanatory factors.

Cognitive components of a mathematical processing network in 9-year-old children

PubMed Central

Szűcs, Dénes; Devine, Amy; Soltesz, Fruzsina; Nobes, Alison; Gabriel, Florence

2014-01-01

We determined how various cognitive abilities, including several measures of a proposed domain-specific number sense, relate to mathematical competence in nearly 100 9-year-old children with normal reading skill. Results are consistent with an extended number processing network and suggest that important processing nodes of this network are phonological processing, verbal knowledge, visuo-spatial short-term and working memory, spatial ability and general executive functioning. The model was highly specific to predicting arithmetic performance. There were no strong relations between mathematical achievement and verbal short-term and working memory, sustained attention, response inhibition, finger knowledge and symbolic number comparison performance. Non-verbal intelligence measures were also non-significant predictors when added to our model. Number sense variables were non-significant predictors in the model and they were also non-significant predictors when entered into regression analysis with only a single visuo-spatial WM measure. Number sense variables were predicted by sustained attention. Results support a network theory of mathematical competence in primary school children and falsify the importance of a proposed modular ‘number sense’. We suggest an ‘executive memory function centric’ model of mathematical processing. Mapping a complex processing network requires that studies consider the complex predictor space of mathematics rather than just focusing on a single or a few explanatory factors. PMID:25089322

Contributions of Motivation, Early Numeracy Skills, and Executive Functioning to Mathematical Performance. A Longitudinal Study.

PubMed

Mercader, Jessica; Miranda, Ana; Presentación, M Jesús; Siegenthaler, Rebeca; Rosel, Jesús F

2017-01-01

The main goal of this longitudinal study is to examine the power of different variables and its dynamic interactions in predicting mathematical performance. The model proposed in this study includes indicators of motivational constructs (learning motivation and attributions), executive functioning (inhibition and working memory), and early numeracy skills (logical operations, counting, and magnitude comparison abilities), assessed during kindergarten, and mathematical performance in the second year of Primary Education. The sample consisted of 180 subjects assessed in two moments (5-6 and 7-8 years old). The results showed an indirect effect of initial motivation on later mathematical performance. Executive functioning and early numeracy skills mediated the effect of motivation on later mathematic achievement. Practical implications of these findings for mathematics education are discussed.

Contributions of Motivation, Early Numeracy Skills, and Executive Functioning to Mathematical Performance. A Longitudinal Study

PubMed Central

Mercader, Jessica; Miranda, Ana; Presentación, M. Jesús; Siegenthaler, Rebeca; Rosel, Jesús F.

2018-01-01

The main goal of this longitudinal study is to examine the power of different variables and its dynamic interactions in predicting mathematical performance. The model proposed in this study includes indicators of motivational constructs (learning motivation and attributions), executive functioning (inhibition and working memory), and early numeracy skills (logical operations, counting, and magnitude comparison abilities), assessed during kindergarten, and mathematical performance in the second year of Primary Education. The sample consisted of 180 subjects assessed in two moments (5–6 and 7–8 years old). The results showed an indirect effect of initial motivation on later mathematical performance. Executive functioning and early numeracy skills mediated the effect of motivation on later mathematic achievement. Practical implications of these findings for mathematics education are discussed. PMID:29379462

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.

Nonlinear differential system applied of a mechanical plan model of the automotives used for the nonlinear stability analysis

NASA Astrophysics Data System (ADS)

Simniceanu, Loreta; Mihaela, Bogdan; Otat, Victor; Trotea, Mario

2017-10-01

This paper proposes a plan mechanical model for the vehicles with two axles, taking into account the lateral deflection of the tire. For this mechanical model are determined two mathematical models under the nonlinear differential equations systems form without taking into account the action of the driver and taking into account. The analysis of driver-vehicle system consists in the mathematical description of vehicle dynamics, coupled with the possibilities and limits of the human factor. Description seeks to emphasize the significant influence of the driver in handling and stability analyzes of vehicles and vehicle-driver system stability until the advent of skidding. These mathematical models are seen as very useful tools to analyzing the vehicles stability. The paper analyzes the influence of some parameters of the vehicle on its behavior in terms of stability of dynamic systems.

General existence principles for Stieltjes differential equations with applications to mathematical biology

NASA Astrophysics Data System (ADS)

López Pouso, Rodrigo; Márquez Albés, Ignacio

2018-04-01

Stieltjes differential equations, which contain equations with impulses and equations on time scales as particular cases, simply consist on replacing usual derivatives by derivatives with respect to a nondecreasing function. In this paper we prove new existence results for functional and discontinuous Stieltjes differential equations and we show that such general results have real world applications. Specifically, we show that Stieltjes differential equations are specially suitable to study populations which exhibit dormant states and/or very short (impulsive) periods of reproduction. In particular, we construct two mathematical models for the evolution of a silkworm population. Our first model can be explicitly solved, as it consists on a linear Stieltjes equation. Our second model, more realistic, is nonlinear, discontinuous and functional, and we deduce the existence of solutions by means of a result proven in this paper.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Relapse prediction in Graves´ disease: Towards mathematical modeling of clinical, immune and genetic markers.

PubMed

Langenstein, Christoph; Schork, Diana; Badenhoop, Klaus; Herrmann, Eva

2016-12-01

Graves' disease (GD) is an important and prevalent thyroid autoimmune disorder. Standard therapy for GD consists of antithyroid drugs (ATD) with treatment periods of around 12 months but relapse is frequent. Since predictors for relapse are difficult to identify the individual decision making for optimal treatment is often arbitrary. After reviewing the literature on this topic we summarize important factors involved in GD and with respect to their potential for relapse prediction from markers before and after treatment. This information was used to design a mathematical model integrating thyroid hormone parameters, thyroid size, antibody titers and a complex algorithm encompassing genetic predisposition, environmental exposures and current immune activity in order to arrive at a prognostic index for relapse risk after treatment. In the search for a tool to analyze and predict relapse in GD mathematical modeling is a promising approach. In analogy to mathematical modeling approaches in other diseases such as viral infections, we developed a differential equation model on the basis of published clinical trials in patients with GD. Although our model needs further evaluation to be applicable in a clinical context, it provides a perspective for an important contribution to a final statistical prediction 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.

Effects of Singapore Model Method with Explicit Instruction on Math Problem Solving Skills of Students at Risk for or Identified with Learning Disabilities

ERIC Educational Resources Information Center

Preston, Angela Irene

2016-01-01

Over the last two decades, students in Singapore consistently scored above students from other nations on the Trends in International Mathematics and Science Study (TIMSS; Provasnik et al., 2012). In contrast, students in the United States have not performed as well on international and national mathematics assessments and students with…

What Role for Developmental Theories in Mathematics Study Programmes in French-Speaking Belgium? An Analysis of the Geometry Curriculum's Aspects, Framed by Van Hiele's Model

ERIC Educational Resources Information Center

Duroisin, Natacha; Demeuse, Marc

2015-01-01

One possible way of evaluating set curricula is to examine the consistency of study programmes with students' psycho-cognitive development. Three theories were used to evaluate matching between developmental theories and content proposed in the mathematics programmes (geometry section) for primary and the beginning of secondary education. These…

A SIMPLE MODEL FOR THE UPTAKE, TRANSLOCATION, AND ACCUMULATION OF PERCHLORATE IN TOBACCO PLANTS

EPA Science Inventory

A simple mathematical model is being developed to describe the uptake, translocation, and accumulation of perchlorate in tobacco plants. The model defines a plant as a set of compartments, consisting of mass balance differential equations and plant-specific physiological paramet...

Exponential Models of Legislative Turnover. [and] The Dynamics of Political Mobilization, I: A Model of the Mobilization Process, II: Deductive Consequences and Empirical Application of the Model. Applications of Calculus to American Politics. [and] Public Support for Presidents. Applications of Algebra to American Politics. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Units 296-300.

ERIC Educational Resources Information Center

Casstevens, Thomas W.; And Others

This document consists of five units which all view applications of mathematics to American politics. The first three view calculus applications, the last two deal with applications of algebra. The first module is geared to teach a student how to: 1) compute estimates of the value of the parameters in negative exponential models; and draw…

Mathematical models of radiation action on living cells: From the target theory to the modern approaches. A historical and critical review.

PubMed

Bodgi, Larry; Canet, Aurélien; Pujo-Menjouet, Laurent; Lesne, Annick; Victor, Jean-Marc; Foray, Nicolas

2016-04-07

Cell survival is conventionally defined as the capability of irradiated cells to produce colonies. It is quantified by the clonogenic assays that consist in determining the number of colonies resulting from a known number of irradiated cells. Several mathematical models were proposed to describe the survival curves, notably from the target theory. The Linear-Quadratic (LQ) model, which is to date the most frequently used model in radiobiology and radiotherapy, dominates all the other models by its robustness and simplicity. Its usefulness is particularly important because the ratio of the values of the adjustable parameters, α and β, on which it is based, predicts the occurrence of post-irradiation tissue reactions. However, the biological interpretation of these parameters is still unknown. Throughout this review, we revisit and discuss historically, mathematically and biologically, the different models of the radiation action by providing clues for resolving the enigma of the LQ model. Copyright © 2016 Elsevier Ltd. All rights reserved.

A model for closing the inviscid form of the average-passage equation system

NASA Technical Reports Server (NTRS)

Adamczyk, J. J.; Mulac, R. A.; Celestina, M. L.

1985-01-01

A mathematical model is proposed for closing or mathematically completing the system of equations which describes the time average flow field through the blade passages of multistage turbomachinery. These equations referred to as the average passage equation system govern a conceptual model which has proven useful in turbomachinery aerodynamic design and analysis. The closure model is developed so as to insure a consistency between these equations and the axisymmetric through flow equations. The closure model was incorporated into a computer code for use in simulating the flow field about a high speed counter rotating propeller and a high speed fan stage. Results from these simulations are presented.

Theoretical studies of solar lasers and converters

NASA Technical Reports Server (NTRS)

Heinbockel, John H.

1990-01-01

The research described consisted of developing and refining the continuous flow laser model program including the creation of a working model. The mathematical development of a two pass amplifier for an iodine laser is summarized. A computer program for the amplifier's simulation is included with output from the simulation model.

Energy-technological complex with reactor for torrefaction

NASA Astrophysics Data System (ADS)

Kuzmina, J. S.; Director, L. B.; Zaichenko, V. M.

2016-11-01

To eliminate shortcomings of raw plant materials pelletizing process with thermal treatment (low-temperature pyrolysis or torrefaction) can be applied. This paper presents a mathematical model of energy-technological complex (ETC) for combined production of heat, electricity and solid biofuels torrefied pellets. According to the structure the mathematical model consists of mathematical models of main units of ETC and the relationships between them and equations of energy and material balances. The equations describe exhaust gas straining action through a porous medium formed by pellets. Decomposition rate of biomass was calculated by using the gross-reaction diagram, which is responsible for the disintegration of raw material. A mathematical model has been tested according to bench experiments on one reactor module. From nomographs, designed for a particular configuration of ETC it is possible to determine the basic characteristics of torrefied pellets (rate of weight loss, heating value and heat content) specifying only two parameters (temperature and torrefaction time). It is shown that the addition of reactor for torrefaction to gas piston engine can improve the energy efficiency of power plant.

Young-age gender differences in mathematics mediated by independent control or uncontrollability.

PubMed

Zirk-Sadowski, Jan; Lamptey, Charlotte; Devine, Amy; Haggard, Mark; Szűcs, Dénes

2014-05-01

We studied whether the origins of math anxiety can be related to a biologically supported framework of stress induction: (un)controllability perception, here indicated by self-reported independent efforts in mathematics. Math anxiety was tested in 182 children (8- to 11-year-olds). Latent factor modeling was used to test hypotheses on plausible causal processes and mediations within competing models in quasi-experimental contrasts. Uncontrollability perception in mathematics, or (in)dependence of efforts, best fit the data as an antecedent of math anxiety. In addition, the relationship of math anxiety with gender was fully mediated by adaptive perception of control (i.e. controllability). That is, young boys differ from girls in terms of their experience of control in mathematics learning. These differences influence math anxiety. Our findings are consistent with recent suggestions in clinical literature according to which uncontrollability makes women more susceptible to fear and anxiety disorders. © 2014 John Wiley & Sons Ltd.

Evaluating a technical university's placement test using the Rasch measurement model

NASA Astrophysics Data System (ADS)

Salleh, Tuan Salwani; Bakri, Norhayati; Zin, Zalhan Mohd

2016-10-01

This study discusses the process of validating a mathematics placement test at a technical university. The main objective is to produce a valid and reliable test to measure students' prerequisite knowledge to learn engineering technology mathematics. It is crucial to have a valid and reliable test as the results will be used in a critical decision making to assign students into different groups of Technical Mathematics 1. The placement test which consists of 50 mathematics questions were tested on 82 new diplomas in engineering technology students at a technical university. This study employed rasch measurement model to analyze the data through the Winsteps software. The results revealed that there are ten test questions lower than less able students' ability. Nevertheless, all the ten questions satisfied infit and outfit standard values. Thus, all the questions can be reused in the future placement test at the technical university.

Evaluation of the Thermodynamic Consistency of Closure Approximations in Several Models Proposed for the Description of Liquid Crystalline Dynamics

NASA Astrophysics Data System (ADS)

Edwards, Brian J.

2002-05-01

Given the premise that a set of dynamical equations must possess a definite, underlying mathematical structure to ensure local and global thermodynamic stability, as has been well documented, several different models for describing liquid crystalline dynamics are examined with respect to said structure. These models, each derived during the past several years using a specific closure approximation for the fourth moment of the distribution function in Doi's rigid rod theory, are all shown to be inconsistent with this basic mathematical structure. The source of this inconsistency lies in Doi's expressions for the extra stress tensor and temporal evolution of the order parameter, which are rederived herein using a transformation that allows for internal compatibility with the underlying mathematical structure that is present on the distribution function level of description.

Improving students’ mathematical representational ability through RME-based progressive mathematization

NASA Astrophysics Data System (ADS)

Warsito; Darhim; Herman, T.

2018-01-01

This study aims to determine the differences in the improving of mathematical representation ability based on progressive mathematization with realistic mathematics education (PMR-MP) with conventional learning approach (PB). The method of research is quasi-experiments with non-equivalent control group designs. The study population is all students of class VIII SMPN 2 Tangerang consisting of 6 classes, while the sample was taken two classes with purposive sampling technique. The experimental class is treated with PMR-MP while the control class is treated with PB. The instruments used are test of mathematical representation ability. Data analysis was done by t-test, ANOVA test, post hoc test, and descriptive analysis. The result of analysis can be concluded that: 1) there are differences of mathematical representation ability improvement between students treated by PMR-MP and PB, 2) no interaction between learning approach (PMR-MP, PB) and prior mathematics knowledge (PAM) to improve students’ mathematical representation; 3) Students’ mathematical representation improvement in the level of higher PAM is better than medium, and low PAM students. Thus, based on the process of mathematization, it is very important when the learning direction of PMR-MP emphasizes on the process of building mathematics through a mathematical model.

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

NASA Astrophysics Data System (ADS)

Tweney, Ryan D.

2011-07-01

James Clerk Maxwell `translated' Michael Faraday's experimentally-based field theory into the mathematical representation now known as `Maxwell's Equations.' Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday's theory and brought it into consistency with other results in the physics of electricity and magnetism. Examination of Maxwell's procedures opens many issues about the role of mathematical representation in physics and the learning background required for its success. Specifically, Maxwell's training in `Cambridge University' mathematical physics emphasized the use of analogous equations across fields of physics and the repeated solving of extremely difficult problems in physics. Such training develops an array of overlearned mathematical representations supported by highly sophisticated cognitive mechanisms for the retrieval of relevant information from long term memory. For Maxwell, mathematics constituted a new form of representation in physics, enhancing the formal derivational and calculational role of mathematics and opening a cognitive means for the conduct of `experiments in the mind' and for sophisticated representations of theory.

Effect of operational cycle time length on nitrogen removal in an alternating oxidation ditch system.

PubMed

Mantziaras, I D; Stamou, A; Katsiri, A

2011-06-01

This paper refers to nitrogen removal optimization of an alternating oxidation ditch system through the use of a mathematical model and pilot testing. The pilot system where measurements have been made has a total volume of 120 m(3) and consists of two ditches operating in four phases during one cycle and performs carbon oxidation, nitrification, denitrification and settling. The mathematical model consists of one-dimensional mass balance (convection-dispersion) equations based on the IAWPRC ASM 1 model. After the calibration and verification of the model, simulation system performance was made. Optimization is achieved by testing operational cycles and phases with different time lengths. The limits of EU directive 91/271 for nitrogen removal have been used for comparison. The findings show that operational cycles with smaller time lengths can achieve higher nitrogen removals and that an "equilibrium" between phase time percentages in the whole cycle, for a given inflow, must be achieved.

Mathematical model of depolarization mechanism of conducted vasoreactivity

NASA Astrophysics Data System (ADS)

Neganova, Anastasiia Y.; Stiukhina, Elena S.; Postnov, Dmitry E.

2015-03-01

We address the problem of conducted vasodilation, the phenomenon which is also known as functional hyperemia. Specifically, we test the mechanism of nondecremental propagation of electric signals along endothelial cell layer recently hypothesized by Figueroa et al. By means of functional modeling we focus on possible nonlinear mechanisms that can underlie such regenerative pulse transmission (RPT). Since endothelial cells (EC) are generally known as electrically inexcitable, the possible role of ECs in RPT mechanisms is not evident. By means of mathematical modeling we check the dynamical self-consistency of Figueroa's hypothesis, as well as estimate the possible contribution of specific ionic currents to the suggested RPT mechanism.

Validation of the replica trick for simple models

NASA Astrophysics Data System (ADS)

Shinzato, Takashi

2018-04-01

We discuss the replica analytic continuation using several simple models in order to prove mathematically the validity of the replica analysis, which is used in a wide range of fields related to large-scale complex systems. While replica analysis consists of two analytical techniques—the replica trick (or replica analytic continuation) and the thermodynamical limit (and/or order parameter expansion)—we focus our study on replica analytic continuation, which is the mathematical basis of the replica trick. We apply replica analysis to solve a variety of analytical models, and examine the properties of replica analytic continuation. Based on the positive results for these models we propose that replica analytic continuation is a robust procedure in replica analysis.

Stochastic and Deterministic Models for the Metastatic Emission Process: Formalisms and Crosslinks.

PubMed

Gomez, Christophe; Hartung, Niklas

2018-01-01

Although the detection of metastases radically changes prognosis of and treatment decisions for a cancer patient, clinically undetectable micrometastases hamper a consistent classification into localized or metastatic disease. This chapter discusses mathematical modeling efforts that could help to estimate the metastatic risk in such a situation. We focus on two approaches: (1) a stochastic framework describing metastatic emission events at random times, formalized via Poisson processes, and (2) a deterministic framework describing the micrometastatic state through a size-structured density function in a partial differential equation model. Three aspects are addressed in this chapter. First, a motivation for the Poisson process framework is presented and modeling hypotheses and mechanisms are introduced. Second, we extend the Poisson model to account for secondary metastatic emission. Third, we highlight an inherent crosslink between the stochastic and deterministic frameworks and discuss its implications. For increased accessibility the chapter is split into an informal presentation of the results using a minimum of mathematical formalism and a rigorous mathematical treatment for more theoretically interested readers.

An animated depiction of major depression epidemiology.

PubMed

Patten, Scott B

2007-06-08

Epidemiologic estimates are now available for a variety of parameters related to major depression epidemiology (incidence, prevalence, etc.). These estimates are potentially useful for policy and planning purposes, but it is first necessary that they be synthesized into a coherent picture of the epidemiology of the condition. Several attempts to do so have been made using mathematical modeling procedures. However, this information is not easy to communicate to users of epidemiological data (clinicians, administrators, policy makers). In this study, up-to-date data on major depression epidemiology were integrated using a discrete event simulation model. The mathematical model was animated in Virtual Reality Modeling Language (VRML) to create a visual, rather than mathematical, depiction of the epidemiology. Consistent with existing literature, the model highlights potential advantages of population health strategies that emphasize access to effective long-term treatment. The paper contains a web-link to the animation. Visual animation of epidemiological results may be an effective knowledge translation tool. In clinical practice, such animations could potentially assist with patient education and enhanced long-term compliance.

Relational Understanding of the Derivative Concept through Mathematical Modeling: A Case Study

ERIC Educational Resources Information Center

Sahin, Zulal; Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat

2015-01-01

The purpose of this study was to investigate three second-year graduate students' awareness and understanding of the relationships among the "big ideas" that underlie the concept of derivative through modeling tasks and Skemp's distinction between relational and instrumental understanding. The modeling tasks consisting of warm-up,…

Online Professional Development: Combining Best Practices from Teacher, Technology and Distance Education

ERIC Educational Resources Information Center

Signer, Barbara

2008-01-01

This article provides a model of online professional development that is consistent with recommendations from the fields of teacher education, technology staff development and online learning. A graduate mathematics education course designed and implemented using the model is presented to exemplify the model's core components and interactions. The…

Influence of drug-light-interval on photodynamic therapy of port wine stains--simulation and validation of mathematic models.

PubMed

Huang, Naiyan; Cheng, Gang; Li, Xiaosong; Gu, Ying; Liu, Fanguang; Zhong, Qiuhai; Wang, Ying; Zen, Jin; Qiu, Haixia; Chen, Hongxia

2008-06-01

We established mathematical models of photodynamic therapy (PDT) on port wine stains (PWS) to observe the effect of drug-light-interval (DLI) and optimize light dose. The mathematical simulations included determining (1) the distribution of laser light by Monte Carlo model, (2) the change of photosensitizer concentration in PWS vessels by a pharmacokinetics equation, (3) the change of photosensitizer distribution in tissue outside the vessels by a diffuse equation and photobleaching equation, and (4) the change of tissue oxygen concentration by the Fick's law with a consideration of the oxygen consumption during PDT. The concentration of singlet oxygen in the tissue model was calculated by the finite difference method. To validate those models, a PWS lesion of the same patient was divided into two areas and subjected to different DLIs and treated with different energy density. The color of lesion was assessed 8-12 weeks later. The simulation indicated the singlet oxygen concentration of the second treatment area (DLI=40 min) was lower than that of the first treatment area (DLI=0 min). However, it would be increased to a level similar to that of the first treatment area if the light irradiation time of the second treatment area was prolonged from 40 min to 55 min. Clinical results were consistent with the results predicted by the mathematical models. The mathematical models established in this study are helpful to optimize clinical protocol.

Cross-validating a bidimensional mathematics anxiety scale.

PubMed

Haiyan Bai

2011-03-01

The psychometric properties of a 14-item bidimensional Mathematics Anxiety Scale-Revised (MAS-R) were empirically cross-validated with two independent samples consisting of 647 secondary school students. An exploratory factor analysis on the scale yielded strong construct validity with a clear two-factor structure. The results from a confirmatory factor analysis indicated an excellent model-fit (χ(2) = 98.32, df = 62; normed fit index = .92, comparative fit index = .97; root mean square error of approximation = .04). The internal consistency (.85), test-retest reliability (.71), interfactor correlation (.26, p < .001), and positive discrimination power indicated that MAS-R is a psychometrically reliable and valid instrument for measuring mathematics anxiety. Math anxiety, as measured by MAS-R, correlated negatively with student achievement scores (r = -.38), suggesting that MAS-R may be a useful tool for classroom teachers and other educational personnel tasked with identifying students at risk of reduced math achievement because of anxiety.

Recent Advances in the Edge-Function Method 1979-1980

DTIC Science & Technology

1980-07-30

the residuals are within the limits within which an engineer can specify the boundary conditions of the problem, then the corresponding Mathematical ...truncation lvel . The consistent preference shown by the solver routine for verteA functions as opposed to polar functions reinforces the expectations of...Accordingly,each solution zr_.-4_des a Mathematical Model for the given physical problem- R.M.S. values provide a practical criterion for the enai--er to

Consistency Properties for Growth Model Parameters Under an Infill Asymptotics Domain

DTIC Science & Technology

2010-09-01

Gompertz in 1825 [15], was initially used for actuarial projections. Winsor’s 1932 reparameterization of the Gompertz curve in [38] is given by f(t;K, a, b...these assumptions it is possible to construct a pathological example which, while mathematically interesting, is of no practical use to a practitioner...Abramowitz, Milton and Irene A. Stegun. Handbook of Mathematical Functions . Washington D.C.: National Bureau of Standards, 1972. [2] Allgower, E. L

A University Admissions System

ERIC Educational Resources Information Center

Ittig, Peter T.

1977-01-01

Presents a mathematical programming model that will make admit/reject decisions for freshman university applicants. The model is intended to aid reviewers in producing better, more consistent decisions. The author shows that a linear programming formulation will provide an efficient and practical solution for all but a very few applicants.…

Development of guidelines for the definition of the relavant information content in data classes

NASA Technical Reports Server (NTRS)

Schmitt, E.

1973-01-01

The problem of experiment design is defined as an information system consisting of information source, measurement unit, environmental disturbances, data handling and storage, and the mathematical analysis and usage of data. Based on today's concept of effective computability, general guidelines for the definition of the relevant information content in data classes are derived. The lack of a universally applicable information theory and corresponding mathematical or system structure is restricting the solvable problem classes to a small set. It is expected that a new relativity theory of information, generally described by a universal algebra of relations will lead to new mathematical models and system structures capable of modeling any well defined practical problem isomorphic to an equivalence relation at any corresponding level of abstractness.

Malaysian and Singaporean students' affective characteristics and mathematics performance: evidence from PISA 2012.

PubMed

Thien, Lei Mee; Ong, Mei Yean

2015-01-01

This paper attempts to identify the extent to which the affective characteristics of Malaysian and Singaporean students' attainment compared to the OECD average in Programme for International Student Assessment (PISA) 2012, and examine the influence of students' affective characteristics, gender, and their socioeconomic status on mathematics performance at both student and school levels. Sample consisted of 5197 and 5546 15-year-old Malaysian and Singaporean students. Data were analysed using hierarchical linear modelling approach with HLM 7.0 software. Results showed that the Index of economic, social, and cultural status (ESCS), mathematics self-efficacy, and mathematics anxiety have significant effects on mathematics performance in Malaysia and Singapore at the student level. Proportion of boys at the school level has no significant effects on mathematics performance for both Malaysian and Singaporean students. ESCS mean at the school level has positive and significant effects on mathematics performance in Malaysia, but not in Singapore. Limitations, implications, and future studies were discussed.

A theory of drug tolerance and dependence I: a conceptual analysis.

PubMed

Peper, Abraham

2004-08-21

A mathematical model of drug tolerance and its underlying theory is presented. The model extends a first approach, published previously. The model is essentially more complex than the generally used model of homeostasis, which is demonstrated to fail in describing tolerance development to repeated drug administrations. 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 only 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 behavior 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 mathematical model verifies the proposed theory and provides a basis for the implementation of mathematical models of specific physiological processes. In addition, it establishes a relation between the drug dose at any moment, and the resulting drug effect and relates the magnitude of the reactions following withdrawal to the rate of tolerance and other parameters involved in the tolerance process. The present paper analyses the concept behind the model. The next paper discusses the mathematical model.

Validation of instruments to measure students' mathematical knowledge

NASA Astrophysics Data System (ADS)

Khatimin, Nuraini; Zaharim, Azami; Aziz, Azrilah Abd

2015-02-01

This paper describes instruments' validation process to identify the suitability and accuracy of the final examination questions for engineering mathematics. As a compulsory subject for second year students from 4 departments in Faculty of Engineering and Built Environment Universiti Kebangsaan Malaysia, the Differential Equations 1 course (KKKQ2124) was considered in this study. The data used in this study consists of the raw marks for final examination of semester 2, 2012/2013 session. The data then will be run and analyzed using the Rasch measurement model. Rasch model can also examine the ability of students and redundancy of instrument constructs.

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.

Building Academic Skills in Context: Testing the Value of Enhanced Math Learning in CTE

ERIC Educational Resources Information Center

Stone, James R., III; Alfeld, Corinne; Pearson, Donna; Lewis, Morgan V.; Jensen, Susan

2006-01-01

An experimental study tested a model for enhancing mathematics instruction in five high school career and technical education (CTE) programs (agriculture, auto technology, business/marketing, health, and information technology). The model consisted of a pedagogy and intense teacher professional development. Volunteer CTE teachers were randomly…

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

NASA Astrophysics Data System (ADS)

2015-01-01

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

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.

A study of structural properties of gene network graphs for mathematical modeling of integrated mosaic gene networks.

PubMed

Petrovskaya, Olga V; Petrovskiy, Evgeny D; Lavrik, Inna N; Ivanisenko, Vladimir A

2017-04-01

Gene network modeling is one of the widely used approaches in systems biology. It allows for the study of complex genetic systems function, including so-called mosaic gene networks, which consist of functionally interacting subnetworks. We conducted a study of a mosaic gene networks modeling method based on integration of models of gene subnetworks by linear control functionals. An automatic modeling of 10,000 synthetic mosaic gene regulatory networks was carried out using computer experiments on gene knockdowns/knockouts. Structural analysis of graphs of generated mosaic gene regulatory networks has revealed that the most important factor for building accurate integrated mathematical models, among those analyzed in the study, is data on expression of genes corresponding to the vertices with high properties of centrality.

A logic-based dynamic modeling approach to explicate the evolution of the central dogma of molecular biology.

PubMed

Jafari, Mohieddin; Ansari-Pour, Naser; Azimzadeh, Sadegh; Mirzaie, Mehdi

It is nearly half a century past the age of the introduction of the Central Dogma (CD) of molecular biology. This biological axiom has been developed and currently appears to be all the more complex. In this study, we modified CD by adding further species to the CD information flow and mathematically expressed CD within a dynamic framework by using Boolean network based on its present-day and 1965 editions. We show that the enhancement of the Dogma not only now entails a higher level of complexity, but it also shows a higher level of robustness, thus far more consistent with the nature of biological systems. Using this mathematical modeling approach, we put forward a logic-based expression of our conceptual view of molecular biology. Finally, we show that such biological concepts can be converted into dynamic mathematical models using a logic-based approach and thus may be useful as a framework for improving static conceptual models in biology.

A logic-based dynamic modeling approach to explicate the evolution of the central dogma of molecular biology

PubMed Central

Jafari, Mohieddin; Ansari-Pour, Naser; Azimzadeh, Sadegh; Mirzaie, Mehdi

2017-01-01

It is nearly half a century past the age of the introduction of the Central Dogma (CD) of molecular biology. This biological axiom has been developed and currently appears to be all the more complex. In this study, we modified CD by adding further species to the CD information flow and mathematically expressed CD within a dynamic framework by using Boolean network based on its present-day and 1965 editions. We show that the enhancement of the Dogma not only now entails a higher level of complexity, but it also shows a higher level of robustness, thus far more consistent with the nature of biological systems. Using this mathematical modeling approach, we put forward a logic-based expression of our conceptual view of molecular biology. Finally, we show that such biological concepts can be converted into dynamic mathematical models using a logic-based approach and thus may be useful as a framework for improving static conceptual models in biology. PMID:29267315

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.

Invariant characteristics of self-organization modes in Belousov reaction modeling

NASA Astrophysics Data System (ADS)

Glyzin, S. D.; Goryunov, V. E.; Kolesov, A. Yu

2018-01-01

We consider the problem of mathematical modeling of oxidation-reduction oscillatory chemical reactions based on the mechanism of Belousov reaction. The process of the main components interaction in such reaction can be interpreted by a phenomenologically similar to it “predator-prey” model. Thereby, we consider a parabolic boundary value problem consisting of three Volterra-type equations, which is a mathematical model of this reaction. We carry out a local study of the neighborhood of the system’s non-trivial equilibrium state and construct the normal form of the considering system. Finally, we do a numerical analysis of the coexisting chaotic oscillatory modes of the boundary value problem in a flat area, which have different nature and occur as the diffusion coefficient decreases.

A mathematical model for CTL effect on a latently infected cell inclusive HIV dynamics and treatment

NASA Astrophysics Data System (ADS)

Tarfulea, N. E.

2017-10-01

This paper investigates theoretically and numerically the effect of immune effectors, such as the cytotoxic lymphocyte (CTL), in modeling HIV pathogenesis (via a newly developed mathematical model); our results suggest the significant impact of the immune response on the control of the virus during primary infection. Qualitative aspects (including positivity, boundedness, stability, uncertainty, and sensitivity analysis) are addressed. Additionally, by introducing drug therapy, we analyze numerically the model to assess the effect of treatment consisting of a combination of several antiretroviral drugs. Our results show that the inclusion of the CTL compartment produces a higher rebound for an individual's healthy helper T-cell compartment than drug therapy alone. Furthermore, we quantitatively characterize successful drugs or drug combination scenarios.

QMRA for Drinking Water: 1. Revisiting the Mathematical Structure of Single-Hit Dose-Response Models.

PubMed

Nilsen, Vegard; Wyller, John

2016-01-01

Dose-response models are essential to quantitative microbial risk assessment (QMRA), providing a link between levels of human exposure to pathogens and the probability of negative health outcomes. In drinking water studies, the class of semi-mechanistic models known as single-hit models, such as the exponential and the exact beta-Poisson, has seen widespread use. In this work, an attempt is made to carefully develop the general mathematical single-hit framework while explicitly accounting for variation in (1) host susceptibility and (2) pathogen infectivity. This allows a precise interpretation of the so-called single-hit probability and precise identification of a set of statistical independence assumptions that are sufficient to arrive at single-hit models. Further analysis of the model framework is facilitated by formulating the single-hit models compactly using probability generating and moment generating functions. Among the more practically relevant conclusions drawn are: (1) for any dose distribution, variation in host susceptibility always reduces the single-hit risk compared to a constant host susceptibility (assuming equal mean susceptibilities), (2) the model-consistent representation of complete host immunity is formally demonstrated to be a simple scaling of the response, (3) the model-consistent expression for the total risk from repeated exposures deviates (gives lower risk) from the conventional expression used in applications, and (4) a model-consistent expression for the mean per-exposure dose that produces the correct total risk from repeated exposures is developed. © 2016 Society for Risk Analysis.

Analysis and Management of Animal Populations: Modeling, Estimation and Decision Making

USGS Publications Warehouse

Williams, B.K.; Nichols, J.D.; Conroy, M.J.

2002-01-01

This book deals with the processes involved in making informed decisions about the management of animal populations. It covers the modeling of population responses to management actions, the estimation of quantities needed in the modeling effort, and the application of these estimates and models to the development of sound management decisions. The book synthesizes and integrates in a single volume the methods associated with these themes, as they apply to ecological assessment and conservation of animal populations. KEY FEATURES * Integrates population modeling, parameter estimation and * decision-theoretic approaches to management in a single, cohesive framework * Provides authoritative, state-of-the-art descriptions of quantitative * approaches to modeling, estimation and decision-making * Emphasizes the role of mathematical modeling in the conduct of science * and management * Utilizes a unifying biological context, consistent mathematical notation, * and numerous biological examples

Functional versus non-functional intratumor heterogeneity in cancer

PubMed Central

Williams, Marc J.; Werner, Benjamin; Graham, Trevor A.; Sottoriva, Andrea

2016-01-01

ABSTRACT Next-generation sequencing data from human cancers are often difficult to interpret within the context of tumor evolution. We developed a mathematical model describing the accumulation of mutations under neutral evolutionary dynamics and showed that 323/904 cancers (∼30%) from multiple types were consistent with the neutral model of tumor evolution. PMID:27652316

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 object.

ITEMS Project: An online sequence for teaching mathematics and astronomy

NASA Astrophysics Data System (ADS)

Martínez, Bernat; Pérez, Josep

2010-10-01

This work describes an elearning sequence for teaching geometry and astronomy in lower secondary school created inside the ITEMS (Improving Teacher Education in Mathematics and Science) project. It is based on results from the astronomy education research about studentsŠ difficulties in understanding elementary astronomical observations and models. The sequence consists of a set of computer animations embedded in an elearning environment aimed at supporting students in learning about astronomy ideas that require the use of geometrical concepts and visual-spatial reasoning.

The Effects of a Female Role Model on Academic Performance and Persistence of Women in STEM Courses

ERIC Educational Resources Information Center

Herrmann, Sarah D.; Adelman, Robert Mark; Bodford, Jessica E.; Graudejus, Oliver; Okun, Morris A.; Kwan, Virginia S. Y.

2016-01-01

Women are more likely to leave science, technology, engineering, and mathematics compared to men, in part because they lack similar role models such as peers, teaching assistants, and instructors. We examined the effect of a brief, scalable online intervention that consisted of a letter from a female role model who normalized concerns about…

Improving Preservice Field Placements in Secondary Mathematics: A Residency Model for Student Teaching through Lesson Study

ERIC Educational Resources Information Center

Gurl, Theresa

2010-01-01

In response to the recent calls for a residency model for field internships in education, a possible model based on an adaptation of Japanese lesson study is described. Lesson study consists of collaboratively planning, implementing, and discussing lessons after the lesson is taught. Results of a study in which student teachers and cooperating…

An Examination of the Domain of Multivariable Functions Using the Pirie-Kieren Model

ERIC Educational Resources Information Center

Sengul, Sare; Yildiz, Sevda Goktepe

2016-01-01

The aim of this study is to employ the Pirie-Kieren model so as to examine the understandings relating to the domain of multivariable functions held by primary school mathematics preservice teachers. The data obtained was categorized according to Pirie-Kieren model and demonstrated visually in tables and bar charts. The study group consisted of…

Analytical Models for Rotor Test Module, Strut, and Balance Frame Dynamics in the 40 by 80 Ft Wind Tunnel

NASA Technical Reports Server (NTRS)

Johnson, W.

1976-01-01

A mathematical model is developed for the dynamics of a wind tunnel support system consisting of a balance frame, struts, and an aircraft or test module. Data are given for several rotor test modules in the Ames 40 by 80 ft wind tunnel. A model for ground resonance calculations is also described.

Mathematical model of information process of protection of the social sector

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Workshop Physics Activity Guide, Module 3: Heat Temperature and Nuclear Radiation, Thermodynamics, Kinetic Theory, Heat Engines, Nuclear Decay, and Random Monitoring (Units 16 - 18 & 28)

NASA Astrophysics Data System (ADS)

Laws, Priscilla W.

2004-05-01

The Workshop Physics Activity Guide is a set of student workbooks designed to serve as the foundation for a two-semester calculus-based introductory physics course. It consists of 28 units that interweave text materials with activities that include prediction, qualitative observation, explanation, equation derivation, mathematical modeling, quantitative experiments, and problem solving. Students use a powerful set of computer tools to record, display, and analyze data, as well as to develop mathematical models of physical phenomena. The design of many of the activities is based on the outcomes of physics education research.

Modeling the Metabolism of Arabidopsis thaliana: Application of Network Decomposition and Network Reduction in the Context of Petri Nets.

PubMed

Koch, Ina; Nöthen, Joachim; Schleiff, Enrico

2017-01-01

Motivation: Arabidopsis thaliana is a well-established model system for the analysis of the basic physiological and metabolic pathways of plants. Nevertheless, the system is not yet fully understood, although many mechanisms are described, and information for many processes exists. However, the combination and interpretation of the large amount of biological data remain a big challenge, not only because data sets for metabolic paths are still incomplete. Moreover, they are often inconsistent, because they are coming from different experiments of various scales, regarding, for example, accuracy and/or significance. Here, theoretical modeling is powerful to formulate hypotheses for pathways and the dynamics of the metabolism, even if the biological data are incomplete. To develop reliable mathematical models they have to be proven for consistency. This is still a challenging task because many verification techniques fail already for middle-sized models. Consequently, new methods, like decomposition methods or reduction approaches, are developed to circumvent this problem. Methods: We present a new semi-quantitative mathematical model of the metabolism of Arabidopsis thaliana . We used the Petri net formalism to express the complex reaction system in a mathematically unique manner. To verify the model for correctness and consistency we applied concepts of network decomposition and network reduction such as transition invariants, common transition pairs, and invariant transition pairs. Results: We formulated the core metabolism of Arabidopsis thaliana based on recent knowledge from literature, including the Calvin cycle, glycolysis and citric acid cycle, glyoxylate cycle, urea cycle, sucrose synthesis, and the starch metabolism. By applying network decomposition and reduction techniques at steady-state conditions, we suggest a straightforward mathematical modeling process. We demonstrate that potential steady-state pathways exist, which provide the fixed carbon to nearly all parts of the network, especially to the citric acid cycle. There is a close cooperation of important metabolic pathways, e.g., the de novo synthesis of uridine-5-monophosphate, the γ-aminobutyric acid shunt, and the urea cycle. The presented approach extends the established methods for a feasible interpretation of biological network models, in particular of large and complex models.

Modeling the Metabolism of Arabidopsis thaliana: Application of Network Decomposition and Network Reduction in the Context of Petri Nets

PubMed Central

Koch, Ina; Nöthen, Joachim; Schleiff, Enrico

2017-01-01

Motivation: Arabidopsis thaliana is a well-established model system for the analysis of the basic physiological and metabolic pathways of plants. Nevertheless, the system is not yet fully understood, although many mechanisms are described, and information for many processes exists. However, the combination and interpretation of the large amount of biological data remain a big challenge, not only because data sets for metabolic paths are still incomplete. Moreover, they are often inconsistent, because they are coming from different experiments of various scales, regarding, for example, accuracy and/or significance. Here, theoretical modeling is powerful to formulate hypotheses for pathways and the dynamics of the metabolism, even if the biological data are incomplete. To develop reliable mathematical models they have to be proven for consistency. This is still a challenging task because many verification techniques fail already for middle-sized models. Consequently, new methods, like decomposition methods or reduction approaches, are developed to circumvent this problem. Methods: We present a new semi-quantitative mathematical model of the metabolism of Arabidopsis thaliana. We used the Petri net formalism to express the complex reaction system in a mathematically unique manner. To verify the model for correctness and consistency we applied concepts of network decomposition and network reduction such as transition invariants, common transition pairs, and invariant transition pairs. Results: We formulated the core metabolism of Arabidopsis thaliana based on recent knowledge from literature, including the Calvin cycle, glycolysis and citric acid cycle, glyoxylate cycle, urea cycle, sucrose synthesis, and the starch metabolism. By applying network decomposition and reduction techniques at steady-state conditions, we suggest a straightforward mathematical modeling process. We demonstrate that potential steady-state pathways exist, which provide the fixed carbon to nearly all parts of the network, especially to the citric acid cycle. There is a close cooperation of important metabolic pathways, e.g., the de novo synthesis of uridine-5-monophosphate, the γ-aminobutyric acid shunt, and the urea cycle. The presented approach extends the established methods for a feasible interpretation of biological network models, in particular of large and complex models. PMID:28713420

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.

The enhancement of students' mathematical self-efficacy through teaching with metacognitive scaffolding approach

NASA Astrophysics Data System (ADS)

Prabawanto, S.

2018-05-01

This research aims to investigate the enhancement of students’ mathematical self- efficacy through teaching with metacognitive scaffolding approach. This research used a quasi- experimental design with pre-post respon control. The subjects were pre-service elementary school teachers in a state university in Bandung. In this study, there were two groups: experimental and control groups. The experimental group consists of 60 students who acquire teaching mathematics under metacognitive approach, while the control group consists of 58 students who acquire teaching mathematics under direct approach. Students were classified into three categories based on the mathematical prior ability, namely high, middle, and low. Data collection instruments consist of mathematical self-efficacy instruments. By using mean difference test, two conclusions of the research: (1) there is a significant difference in the enhancement of mathematical self-efficacy between the students who attended the course under metacognitive scaffolding approach and students who attended the course under direct approach, and (2) there is no significant interaction effect of teaching approaches and ability level based on the mathematical prior ability toward enhancement of students’ mathematical self-efficacy.

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

PubMed

Boden, Lisa A; McKendrick, Iain J

2017-01-01

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

Modeling of Two-Wheeled Self-Balancing Robot Driven by DC Gearmotors

NASA Astrophysics Data System (ADS)

Frankovský, P.; Dominik, L.; Gmiterko, A.; Virgala, I.; Kurylo, P.; Perminova, O.

2017-08-01

This paper is aimed at modelling a two-wheeled self-balancing robot driven by the geared DC motors. A mathematical model consists of two main parts, the model of robot's mechanical structure and the model of the actuator. Linearized equations of motion are derived and the overall model of the two-wheeled self-balancing robot is represented in state-space realization for the purpose of state feedback controller design.

Modeling and simulation of enzymatic gluconic acid production using immobilized enzyme and CSTR-PFTR circulation reaction system.

PubMed

Li, Can; Lin, Jianqun; Gao, Ling; Lin, Huibin; Lin, Jianqiang

2018-04-01

Production of gluconic acid by using immobilized enzyme and continuous stirred tank reactor-plug flow tubular reactor (CSTR-PFTR) circulation reaction system. A production system is constructed for gluconic acid production, which consists of a continuous stirred tank reactor (CSTR) for pH control and liquid storage and a plug flow tubular reactor (PFTR) filled with immobilized glucose oxidase (GOD) for gluconic acid production. Mathematical model is developed for this production system and simulation is made for the enzymatic reaction process. The pH inhibition effect on GOD is modeled by using a bell-type curve. Gluconic acid can be efficiently produced by using the reaction system and the mathematical model developed for this system can simulate and predict the process well.

A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization.

PubMed

Terrier, Alexandre; Aeberhard, Martin; Michellod, Yvan; Mullhaupt, Philippe; Gillet, Denis; Farron, Alain; Pioletti, Dominique P

2010-11-01

The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa. Copyright © 2010 IPEM. Published by Elsevier Ltd. All rights reserved.

Determination of in vivo mechanical properties of long bones from their impedance response curves

NASA Technical Reports Server (NTRS)

Borders, S. G.

1981-01-01

A mathematical model consisting of a uniform, linear, visco-elastic, Euler-Bernoulli beam to represent the ulna or tibia of the vibrating forearm or leg system is developed. The skin and tissue compressed between the probe and bone is represented by a spring in series with the beam. The remaining skin and tissue surrounding the bone is represented by a visco-elastic foundation with mass. An extensive parametric study is carried out to determine the effect of each parameter of the mathematical model on its impedance response. A system identification algorithm is developed and programmed on a digital computer to determine the parametric values of the model which best simulate the data obtained from an impedance test.

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

NASA Astrophysics Data System (ADS)

2014-03-01

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

Simpler score of routine laboratory tests predicts liver fibrosis in patients with chronic hepatitis B.

PubMed

Zhou, Kun; Gao, Chun-Fang; Zhao, Yun-Peng; Liu, Hai-Lin; Zheng, Rui-Dan; Xian, Jian-Chun; Xu, Hong-Tao; Mao, Yi-Min; Zeng, Min-De; Lu, Lun-Gen

2010-09-01

In recent years, a great interest has been dedicated to the development of noninvasive predictive models to substitute liver biopsy for fibrosis assessment and follow-up. Our aim was to provide a simpler model consisting of routine laboratory markers for predicting liver fibrosis in patients chronically infected with hepatitis B virus (HBV) in order to optimize their clinical management. Liver fibrosis was staged in 386 chronic HBV carriers who underwent liver biopsy and routine laboratory testing. Correlations between routine laboratory markers and fibrosis stage were statistically assessed. After logistic regression analysis, a novel predictive model was constructed. This S index was validated in an independent cohort of 146 chronic HBV carriers in comparison to the SLFG model, Fibrometer, Hepascore, Hui model, Forns score and APRI using receiver operating characteristic (ROC) curves. The diagnostic values of each marker panels were better than single routine laboratory markers. The S index consisting of gamma-glutamyltransferase (GGT), platelets (PLT) and albumin (ALB) (S-index: 1000 x GGT/(PLT x ALB(2))) had a higher diagnostic accuracy in predicting degree of fibrosis than any other mathematical model tested. The areas under the ROC curves (AUROC) were 0.812 and 0.890 for predicting significant fibrosis and cirrhosis in the validation cohort, respectively. The S index, a simpler mathematical model consisting of routine laboratory markers predicts significant fibrosis and cirrhosis in patients with chronic HBV infection with a high degree of accuracy, potentially decreasing the need for liver biopsy.

The use of concrete learning objects taken from the history of mathematics in mathematics education

NASA Astrophysics Data System (ADS)

Bütüner, Suphi Önder

2016-11-01

This study aimed to reveal the effects of teaching with concrete learning objects taken from the history of mathematics on student achievement. Being a quasi-experimental study, it was conducted with two grade 8 classes in a secondary school located in Trabzon. The experimental group consisted of 27 students and the control group consisted of 25. Data were collected by using worksheets, an achievement exam and written opinion forms. The data from the achievement exam were analysed by using the Mann-Whitney U-test while the data from written opinion forms were analysed through content analysis. The Mann-Whitney U-test results showed a significant difference between the mean ranks of the experimental and control groups in favour of the former. Findings from the written opinion forms suggested that the students found the activities to be instructive and fun, enjoyed using concrete models in their classes, and learned from discovering the rules. It was also found that students had previously not engaged in similar activities and had only experienced the history of mathematics through the life stories and works of mathematicians and the representation of ancient numbers at the beginning of each unit.

Mathematical methods in biological dosimetry: the 1996 Iranian accident.

PubMed

Voisin, P; Assaei, R G; Heidary, A; Varzegar, R; Zakeri, F; Durand, V; Sorokine-Durm, I

2000-11-01

To report 18 months of cytogenetic follow-up for an Iranian worker accidentally overexposed to 192Ir, the mathematical extrapolation and comparison with clinical data. Unstable chromosome aberrations were measured using conventional cytogenetic tests by French and Iranian biological dosimetry laboratories on five occasions after the exposure. The decrease in dicentrics over time was analysed mathematically. In addition, Dolphin and Qdr extrapolations were applied to the data to check the exposure estimates. FISH determination of translocation yields was performed twice by the French laboratory and the results compared with the Dolphin and Qdr corrected values. Dose estimates based on dicentrics decreased from 3.1 +/- 0.4 Gy at 5 days after the accident to 0.8 +/- 0.2 Gy at 529 days. This could be fitted by double-exponential regression with an inflexion point between rapid and slow decrease of dicentrics after about 40 days. Dose estimates of 3.4 +/- 0.4 Gy for the Qdr model and 3.6 +/- 0.5 Gy for the Dolphin model were calculated during the post-exposure period and were remarkably stable. FISH translocation data at 26 and 61 days appeared consistent with the Dolphin and Qdr estimates. Dose correction by the Qdr and Dolphin models and translocation scoring appeared consistent with the clinical data and provided better information about the radiation injury than did crude estimates from dicentric scoring alone. Estimation by the Dolphin model of the irradiated fraction of the body seemed unreliable: it correlated better with the fraction of originally irradiated lymphocytes.

A rapid radiative transfer model for reflection of solar radiation

NASA Technical Reports Server (NTRS)

Xiang, X.; Smith, E. A.; Justus, C. G.

1994-01-01

A rapid analytical radiative transfer model for reflection of solar radiation in plane-parallel atmospheres is developed based on the Sobolev approach and the delta function transformation technique. A distinct advantage of this model over alternative two-stream solutions is that in addition to yielding the irradiance components, which turn out to be mathematically equivalent to the delta-Eddington approximation, the radiance field can also be expanded in a mathematically consistent fashion. Tests with the model against a more precise multistream discrete ordinate model over a wide range of input parameters demonstrate that the new approximate method typically produces average radiance differences of less than 5%, with worst average differences of approximately 10%-15%. By the same token, the computational speed of the new model is some tens to thousands times faster than that of the more precise model when its stream resolution is set to generate precise calculations.

A model of yeast glycolysis based on a consistent kinetic characterisation of all its enzymes

PubMed Central

Smallbone, Kieran; Messiha, Hanan L.; Carroll, Kathleen M.; Winder, Catherine L.; Malys, Naglis; Dunn, Warwick B.; Murabito, Ettore; Swainston, Neil; Dada, Joseph O.; Khan, Farid; Pir, Pınar; Simeonidis, Evangelos; Spasić, Irena; Wishart, Jill; Weichart, Dieter; Hayes, Neil W.; Jameson, Daniel; Broomhead, David S.; Oliver, Stephen G.; Gaskell, Simon J.; McCarthy, John E.G.; Paton, Norman W.; Westerhoff, Hans V.; Kell, Douglas B.; Mendes, Pedro

2013-01-01

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a “cycle of knowledge” strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. PMID:23831062

Correlation between multispectral photography and near-surface turbidities

NASA Technical Reports Server (NTRS)

Wertz, D. L.; Mealor, W. T.; Steele, M. L.; Pinson, J. W.

1976-01-01

Four-band multispectral photography obtained from an aerial platform at an altitude of about 10,000 feet has been utilized to measure near-surface turbidity at numerous sampling sites in the Ross Barnett Reservoir, Mississippi. Correlation of the photographs with turbidity measurements has been accomplished via an empirical mathematical model which depends upon visual color recognition when the composited photographs are examined on either an I squared S model 600 or a Spectral Data model 65 color-additive viewer. The mathematical model was developed utilizing least-squares, iterative, and standard statistical methods and includes a time-dependent term related to sun angle. This model is consistent with information obtained from two overflights of the target area - July 30, 1973 and October 30, 1973 - and now is being evaluated with regard to information obtained from a third overflight on November 8, 1974.

Teacher Code Switching Consistency and Precision in a Multilingual Mathematics Classroom

ERIC Educational Resources Information Center

Chikiwa, Clemence; Schäfer, Marc

2016-01-01

This paper reports on a study that investigated teacher code switching consistency and precision in multilingual secondary school mathematics classrooms in South Africa. Data was obtained through interviewing and observing five lessons of each of three mathematics teachers purposively selected from three township schools in the Eastern Cape…

Neurally and mathematically motivated architecture for language and thought.

PubMed

Perlovsky, L I; Ilin, R

2010-01-01

Neural structures of interaction between thinking and language are unknown. This paper suggests a possible architecture motivated by neural and mathematical considerations. A mathematical requirement of computability imposes significant constraints on possible architectures consistent with brain neural structure and with a wealth of psychological knowledge. How language interacts with cognition. Do we think with words, or is thinking independent from language with words being just labels for decisions? Why is language learned by the age of 5 or 7, but acquisition of knowledge represented by learning to use this language knowledge takes a lifetime? This paper discusses hierarchical aspects of language and thought and argues that high level abstract thinking is impossible without language. We discuss a mathematical technique that can model the joint language-thought architecture, while overcoming previously encountered difficulties of computability. This architecture explains a contradiction between human ability for rational thoughtful decisions and irrationality of human thinking revealed by Tversky and Kahneman; a crucial role in this contradiction might be played by language. The proposed model resolves long-standing issues: how the brain learns correct words-object associations; why animals do not talk and think like people. We propose the role played by language emotionality in its interaction with thought. We relate the mathematical model to Humboldt's "firmness" of languages; and discuss possible influence of language grammar on its emotionality. Psychological and brain imaging experiments related to the proposed model are discussed. Future theoretical and experimental research is outlined.

Neurally and Mathematically Motivated Architecture for Language and Thought

PubMed Central

Perlovsky, L.I; Ilin, R

2010-01-01

Neural structures of interaction between thinking and language are unknown. This paper suggests a possible architecture motivated by neural and mathematical considerations. A mathematical requirement of computability imposes significant constraints on possible architectures consistent with brain neural structure and with a wealth of psychological knowledge. How language interacts with cognition. Do we think with words, or is thinking independent from language with words being just labels for decisions? Why is language learned by the age of 5 or 7, but acquisition of knowledge represented by learning to use this language knowledge takes a lifetime? This paper discusses hierarchical aspects of language and thought and argues that high level abstract thinking is impossible without language. We discuss a mathematical technique that can model the joint language-thought architecture, while overcoming previously encountered difficulties of computability. This architecture explains a contradiction between human ability for rational thoughtful decisions and irrationality of human thinking revealed by Tversky and Kahneman; a crucial role in this contradiction might be played by language. The proposed model resolves long-standing issues: how the brain learns correct words-object associations; why animals do not talk and think like people. We propose the role played by language emotionality in its interaction with thought. We relate the mathematical model to Humboldt’s “firmness” of languages; and discuss possible influence of language grammar on its emotionality. Psychological and brain imaging experiments related to the proposed model are discussed. Future theoretical and experimental research is outlined. PMID:21673788

Comparison effectiveness of cooperative learning type STAD with cooperative learning type TPS in terms of mathematical method of Junior High School students

NASA Astrophysics Data System (ADS)

Wahyuni, A.

2018-05-01

This research is aimed to find out whether the model of cooperative learning type Student Team Achievement Division (STAD) is more effective than cooperative learning type Think-Pair-Share in SMP Negeri 7 Yogyakarta. This research was a quasi-experimental research, using two experimental groups. The population of research was all students of 7thclass in SMP Negeri 7 Yogyakarta that consists of 5 Classes. From the population were taken 2 classes randomly which used as sample. The instrument to collect data was a description test. Measurement of instrument validity use content validity and construct validity, while measuring instrument reliability use Cronbach Alpha formula. To investigate the effectiveness of cooperative learning type STAD and cooperative learning type TPS on the aspect of student’s mathematical method, the datas were analyzed by one sample test. Comparing the effectiveness of cooperative learning type STAD and TPS in terms of mathematical communication skills by using t-test. Normality test was not conducted because the sample of research more than 30 students, while homogeneity tested by using Kolmogorov Smirnov test. The analysis was performed at 5% confidence level.The results show as follows : 1) The model of cooperative learning type STAD and TPS are effective in terms of mathematical method of junior high school students. 2). STAD type cooperative learning model is more effective than TPS type cooperative learning model in terms of mathematical methods of junior high school students.

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

PubMed

Pirbodaghi, Tohid

2017-08-01

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

Examining Factors Affecting Science Achievement of Hong Kong in PISA 2006 Using Hierarchical Linear Modeling

ERIC Educational Resources Information Center

Lam, Terence Yuk Ping; Lau, Kwok Chi

2014-01-01

This study uses hierarchical linear modeling to examine the influence of a range of factors on the science performances of Hong Kong students in PISA 2006. Hong Kong has been consistently ranked highly in international science assessments, such as Programme for International Student Assessment and Trends in International Mathematics and Science…

Authentic assessment based showcase portfolio on learning of mathematical problem solving in senior high school

NASA Astrophysics Data System (ADS)

Sukmawati, Zuhairoh, Faihatuz

2017-05-01

The purpose of this research was to develop authentic assessment model based on showcase portfolio on learning of mathematical problem solving. This research used research and development Method (R & D) which consists of four stages of development that: Phase I, conducting a preliminary study. Phase II, determining the purpose of developing and preparing the initial model. Phase III, trial test of instrument for the initial draft model and the initial product. The respondents of this research are the students of SMAN 8 and SMAN 20 Makassar. The collection of data was through observation, interviews, documentation, student questionnaire, and instrument tests mathematical solving abilities. The data were analyzed with descriptive and inferential statistics. The results of this research are authentic assessment model design based on showcase portfolio which involves: 1) Steps in implementing the authentic assessment based Showcase, assessment rubric of cognitive aspects, assessment rubric of affective aspects, and assessment rubric of skill aspect. 2) The average ability of the students' problem solving which is scored by using authentic assessment based on showcase portfolio was in high category and the students' response in good category.

Studies on mathematical modeling of the leaching process in order to efficiently recover lead from the sulfate/oxide lead paste.

PubMed

Buzatu, Traian; Ghica, Gabriel Valeriu; Petrescu, Ionuţ Mircea; Iacob, Gheorghe; Buzatu, Mihai; Niculescu, Florentina

2017-02-01

Increasing global lead consumption has been mainly supported by the acid battery manufacturing industry. As the lead demand will continue to grow, to provide the necessary lead will require an efficient approach to recycling lead acid batteries. In this paper was performed a mathematical modeling of the process parameters for lead recovery from spent lead-acid batteries. The results of the mathematical modeling compare well with the experimental data. The experimental method applied consists in the solubilisation of the sulfate/oxide paste with sodium hydroxide solutions followed by electrolytic processing for lead recovery. The parameters taken into considerations were NaOH molarity (4M, 6M and 8M), solid/liquid ratio - S/L (1/10, 1/30 and 1/50) and temperature (40°C, 60°C and 80°C). The optimal conditions resulted by mathematical modeling of the electrolytic process of lead deposition from alkaline solutions have been established by using a second-order orthogonal program, in order to obtain a maximum efficiency of current without exceeding an imposed energy specific consumption. The optimum value for the leaching recovery efficiency, obtained through mathematical modeling, was 89.647%, with an error of δ y =3.623 which leads to a maximum recovery efficiency of 86.024%. The optimum values for each variable that ensure the lead extraction efficiency equal to 89.647% are the following: 3M - NaOH, 1/35 - S/L, 70°C - temperature. Copyright © 2016 Elsevier Ltd. All rights reserved.

A Cellular Automata Model of Bone Formation

PubMed Central

Van Scoy, Gabrielle K.; George, Estee L.; Asantewaa, Flora Opoku; Kerns, Lucy; Saunders, Marnie M.; Prieto-Langarica, Alicia

2017-01-01

Bone remodeling is an elegantly orchestrated process by which osteocytes, osteoblasts and osteoclasts function as a syncytium to maintain or modify bone. On the microscopic level, bone consists of cells that create, destroy and monitor the bone matrix. These cells interact in a coordinated manner to maintain a tightly regulated homeostasis. It is this regulation that is responsible for the observed increase in bone gain in the dominant arm of a tennis player and the observed increase in bone loss associated with spaceflight and osteoporosis. The manner in which these cells interact to bring about a change in bone quality and quantity has yet to be fully elucidated. But efforts to understand the multicellular complexity can ultimately lead to eradication of metabolic bone diseases such as osteoporosis and improved implant longevity. Experimentally validated mathematical models that simulate functional activity and offer eventual predictive capabilities offer tremendous potential in understanding multicellular bone remodeling. Here we undertake the initial challenge to develop a mathematical model of bone formation validated with in vitro data obtained from osteoblastic bone cells induced to mineralize and quantified at 26 days of culture. A cellular automata model was constructed to simulate the in vitro characterization. Permutation tests were performed to compare the distribution of the mineralization in the cultures and the distribution of the mineralization in the mathematical models. The results of the permutation test show the distribution of mineralization from the characterization and mathematical model come from the same probability distribution, therefore validating the cellular automata model. PMID:28189632

CADLIVE toolbox for MATLAB: automatic dynamic modeling of biochemical networks with comprehensive system analysis.

PubMed

Inoue, Kentaro; Maeda, Kazuhiro; Miyabe, Takaaki; Matsuoka, Yu; Kurata, Hiroyuki

2014-09-01

Mathematical modeling has become a standard technique to understand the dynamics of complex biochemical systems. To promote the modeling, we had developed the CADLIVE dynamic simulator that automatically converted a biochemical map into its associated mathematical model, simulated its dynamic behaviors and analyzed its robustness. To enhance the feasibility by CADLIVE and extend its functions, we propose the CADLIVE toolbox available for MATLAB, which implements not only the existing functions of the CADLIVE dynamic simulator, but also the latest tools including global parameter search methods with robustness analysis. The seamless, bottom-up processes consisting of biochemical network construction, automatic construction of its dynamic model, simulation, optimization, and S-system analysis greatly facilitate dynamic modeling, contributing to the research of systems biology and synthetic biology. This application can be freely downloaded from http://www.cadlive.jp/CADLIVE_MATLAB/ together with an instruction.

MCAID--A Generalized Text Driver.

ERIC Educational Resources Information Center

Ahmed, K.; Dickinson, C. J.

MCAID is a relatively machine-independent technique for writing computer-aided instructional material consisting of descriptive text, multiple choice questions, and the ability to call compiled subroutines to perform extensive calculations. It was specially developed to incorporate test-authoring around complex mathematical models to explore a…

Reduced modeling of signal transduction – a modular approach

PubMed Central

Koschorreck, Markus; Conzelmann, Holger; Ebert, Sybille; Ederer, Michael; Gilles, Ernst Dieter

2007-01-01

Background Combinatorial complexity is a challenging problem in detailed and mechanistic mathematical modeling of signal transduction. This subject has been discussed intensively and a lot of progress has been made within the last few years. A software tool (BioNetGen) was developed which allows an automatic rule-based set-up of mechanistic model equations. In many cases these models can be reduced by an exact domain-oriented lumping technique. However, the resulting models can still consist of a very large number of differential equations. Results We introduce a new reduction technique, which allows building modularized and highly reduced models. Compared to existing approaches further reduction of signal transduction networks is possible. The method also provides a new modularization criterion, which allows to dissect the model into smaller modules that are called layers and can be modeled independently. Hallmarks of the approach are conservation relations within each layer and connection of layers by signal flows instead of mass flows. The reduced model can be formulated directly without previous generation of detailed model equations. It can be understood and interpreted intuitively, as model variables are macroscopic quantities that are converted by rates following simple kinetics. The proposed technique is applicable without using complex mathematical tools and even without detailed knowledge of the mathematical background. However, we provide a detailed mathematical analysis to show performance and limitations of the method. For physiologically relevant parameter domains the transient as well as the stationary errors caused by the reduction are negligible. Conclusion The new layer based reduced modeling method allows building modularized and strongly reduced models of signal transduction networks. Reduced model equations can be directly formulated and are intuitively interpretable. Additionally, the method provides very good approximations especially for macroscopic variables. It can be combined with existing reduction methods without any difficulties. PMID:17854494

The relationship between mathematical problem-solving skills and self-regulated learning through homework behaviours, motivation, and metacognition

NASA Astrophysics Data System (ADS)

Çiğdem Özcan, Zeynep

2016-04-01

Studies highlight that using appropriate strategies during problem solving is important to improve problem-solving skills and draw attention to the fact that using these skills is an important part of students' self-regulated learning ability. Studies on this matter view the self-regulated learning ability as key to improving problem-solving skills. The aim of this study is to investigate the relationship between mathematical problem-solving skills and the three dimensions of self-regulated learning (motivation, metacognition, and behaviour), and whether this relationship is of a predictive nature. The sample of this study consists of 323 students from two public secondary schools in Istanbul. In this study, the mathematics homework behaviour scale was administered to measure students' homework behaviours. For metacognition measurements, the mathematics metacognition skills test for students was administered to measure offline mathematical metacognitive skills, and the metacognitive experience scale was used to measure the online mathematical metacognitive experience. The internal and external motivational scales used in the Programme for International Student Assessment (PISA) test were administered to measure motivation. A hierarchic regression analysis was conducted to determine the relationship between the dependent and independent variables in the study. Based on the findings, a model was formed in which 24% of the total variance in students' mathematical problem-solving skills is explained by the three sub-dimensions of the self-regulated learning model: internal motivation (13%), willingness to do homework (7%), and post-problem retrospective metacognitive experience (4%).

Mathematical Modeling of Cellular Metabolism.

PubMed

Berndt, Nikolaus; Holzhütter, Hermann-Georg

Cellular metabolism basically consists of the conversion of chemical compounds taken up from the extracellular environment into energy (conserved in energy-rich bonds of organic phosphates) and a wide array of organic molecules serving as catalysts (enzymes), information carriers (nucleic acids), and building blocks for cellular structures such as membranes or ribosomes. Metabolic modeling aims at the construction of mathematical representations of the cellular metabolism that can be used to calculate the concentration of cellular molecules and the rates of their mutual chemical interconversion in response to varying external conditions as, for example, hormonal stimuli or supply of essential nutrients. Based on such calculations, it is possible to quantify complex cellular functions as cellular growth, detoxification of drugs and xenobiotic compounds or synthesis of exported molecules. Depending on the specific questions to metabolism addressed, the methodological expertise of the researcher, and available experimental information, different conceptual frameworks have been established, allowing the usage of computational methods to condense experimental information from various layers of organization into (self-) consistent models. Here, we briefly outline the main conceptual frameworks that are currently exploited in metabolism research.

[Stature estimation for Sichuan Han nationality female based on X-ray technology with measurement of lumbar vertebrae].

PubMed

Qing, Si-han; Chang, Yun-feng; Dong, Xiao-ai; Li, Yuan; Chen, Xiao-gang; Shu, Yong-kang; Deng, Zhen-hua

2013-10-01

To establish the mathematical models of stature estimation for Sichuan Han female with measurement of lumbar vertebrae by X-ray to provide essential data for forensic anthropology research. The samples, 206 Sichuan Han females, were divided into three groups including group A, B and C according to the ages. Group A (206 samples) consisted of all ages, group B (116 samples) were 20-45 years old and 90 samples over 45 years old were group C. All the samples were examined lumbar vertebrae through CR technology, including the parameters of five centrums (L1-L5) as anterior border, posterior border and central heights (x1-x15), total central height of lumbar spine (x16), and the real height of every sample. The linear regression analysis was produced using the parameters to establish the mathematical models of stature estimation. Sixty-two trained subjects were tested to verify the accuracy of the mathematical models. The established mathematical models by hypothesis test of linear regression equation model were statistically significant (P<0.05). The standard errors of the equation were 2.982-5.004 cm, while correlation coefficients were 0.370-0.779 and multiple correlation coefficients were 0.533-0.834. The return tests of the highest correlation coefficient and multiple correlation coefficient of each group showed that the highest accuracy of the multiple regression equation, y = 100.33 + 1.489 x3 - 0.548 x6 + 0.772 x9 + 0.058 x12 + 0.645 x15, in group A were 80.6% (+/- lSE) and 100% (+/- 2SE). The established mathematical models in this study could be applied for the stature estimation for Sichuan Han females.

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

NASA Astrophysics Data System (ADS)

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

2017-02-01

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

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.

Mathematic modeling of the method of measurement relative dielectric permeability

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Power Laws in Stochastic Processes for Social Phenomena: An Introductory Review

NASA Astrophysics Data System (ADS)

Kumamoto, Shin-Ichiro; Kamihigashi, Takashi

2018-03-01

Many phenomena with power laws have been observed in various fields of the natural and social sciences, and these power laws are often interpreted as the macro behaviors of systems that consist of micro units. In this paper, we review some basic mathematical mechanisms that are known to generate power laws. In particular, we focus on stochastic processes including the Yule process and the Simon process as well as some recent models. The main purpose of this paper is to explain the mathematical details of their mechanisms in a self-contained manner.

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

PubMed Central

Boden, Lisa A.; McKendrick, Iain J.

2017-01-01

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

Nonlinear analysis of a model of vascular tumour growth and treatment

NASA Astrophysics Data System (ADS)

Tao, Youshan; Yoshida, Norio; Guo, Qian

2004-05-01

We consider a mathematical model describing the evolution of a vascular tumour in response to traditional chemotherapy. The model is a free boundary problem for a system of partial differential equations governing intratumoural drug concentration, cancer cell density and blood vessel density. Tumour cells consist of two types of competitive cells that have different proliferation rates and different sensitivities to drugs. The balance between cell proliferation and death generates a velocity field that drives tumour cell movement. The tumour surface is a moving boundary. The purpose of this paper is to establish a rigorous mathematical analysis of the model for studying the dynamics of intratumoural blood vessels and to explore drug dosage for the successful treatment of a tumour. We also study numerically the competitive effects of the two cell types on tumour growth.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Consistent Chemical Mechanism from Collaborative Data Processing

DOE PAGES

Slavinskaya, Nadezda; Starcke, Jan-Hendrik; Abbasi, Mehdi; ...

2016-04-01

Numerical tool of Process Informatics Model (PrIMe) is mathematically rigorous and numerically efficient approach for analysis and optimization of chemical systems. It handles heterogeneous data and is scalable to a large number of parameters. The Boundto-Bound Data Collaboration module of the automated data-centric infrastructure of PrIMe was used for the systematic uncertainty and data consistency analyses of the H 2/CO reaction model (73/17) and 94 experimental targets (ignition delay times). The empirical rule for evaluation of the shock tube experimental data is proposed. The initial results demonstrate clear benefits of the PrIMe methods for an evaluation of the kinetic datamore » quality and data consistency and for developing predictive kinetic models.« less

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

PubMed Central

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

2017-01-01

ABSTRACT New contributions that aim to accelerate the development or to improve the efficacy and safety of vaccines arise from many different areas of research and technology. One of these areas is computational science, which traditionally participates in the initial steps, such as the pre-screening of active substances that have the potential to become a vaccine antigen. In this work, we present another promising way to use computational science in vaccinology: mathematical and computational models of important cell and protein dynamics of the immune system. A system of Ordinary Differential Equations represents different immune system populations, such as B cells and T cells, antigen presenting cells and antibodies. In this way, it is possible to simulate, in silico, the immune response to vaccines under development or under study. Distinct scenarios can be simulated by varying parameters of the mathematical model. As a proof of concept, we developed a model of the immune response to vaccination against the yellow fever. Our simulations have shown consistent results when compared with experimental data available in the literature. The model is generic enough to represent the action of other diseases or vaccines in the human immune system, such as dengue and Zika virus. PMID:28027002

Vibration of rotating-shaft design spindles with flexible bases

NASA Astrophysics Data System (ADS)

Tseng, Chaw-Wu

The purpose of this study is to demonstrate an accurate mathematical model predicting forced vibration of rotating-shaft HDD spindle motors with flexible stationary parts. The mathematical model consists of three parts: a rotating part, a stationary part, and bearings. The rotating part includes a flexible hub, a flexible shaft press-fit into the hub, and N elastic disks mounted on the hub. The stationary part can include motor bracket (stator), base casting, and top cover. The bearings under consideration can be ball bearings or hydrodynamic bearings (HDB). The rotating disks are modelled through the classical plate theory. The rotating part (except the disks) and the stationary part are modelled through finite element analyses (FEA). With mode shapes and natural frequencies obtained from FEA, the kinetic and potential energies of the rotating and stationary parts are formulated and discretized to compensate for the gyroscopic effects from rotation. Finally, use of Lagrange equation results in the equations of motion. To verify the mathematical model, frequency response functions are measured experimentally for an HDB spindle carrying two identical disks at motor and drive levels. Experimental measurements agree very well with theoretical predictions not only in resonance frequency but also in resonance amplitude.

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

PubMed

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

2017-02-01

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

Potential Costs of Veterans’ Health Care

DTIC Science & Technology

2010-10-01

coverage, there is no rigid mathematical relationship among those proportions because veterans enrolled in Part A may choose to enroll in either Part B or...assumption is consistent with the statistical analysis by an actuarial firm with which VA contracted when developing its model for projecting

Numerical Modeling of Saturated Boiling in a Heated Tube

NASA Technical Reports Server (NTRS)

Majumdar, Alok; LeClair, Andre; Hartwig, Jason

2017-01-01

This paper describes a mathematical formulation and numerical solution of boiling in a heated tube. The mathematical formulation involves a discretization of the tube into a flow network consisting of fluid nodes and branches and a thermal network consisting of solid nodes and conductors. In the fluid network, the mass, momentum and energy conservation equations are solved and in the thermal network, the energy conservation equation of solids is solved. A pressure-based, finite-volume formulation has been used to solve the equations in the fluid network. The system of equations is solved by a hybrid numerical scheme which solves the mass and momentum conservation equations by a simultaneous Newton-Raphson method and the energy conservation equation by a successive substitution method. The fluid network and thermal network are coupled through heat transfer between the solid and fluid nodes which is computed by Chen's correlation of saturated boiling heat transfer. The computer model is developed using the Generalized Fluid System Simulation Program and the numerical predictions are compared with test data.

The Construction of Mathematical Literacy Problems for Geometry

NASA Astrophysics Data System (ADS)

Malasari, P. N.; Herman, T.; Jupri, A.

2017-09-01

The students of junior high school should have mathematical literacy ability to formulate, apply, and interpret mathematics in problem solving of daily life. Teaching these students are not enough by giving them ordinary mathematics problems. Teaching activities for these students brings consequence for teacher to construct mathematical literacy problems. Therefore, the aim of this study is to construct mathematical literacy problems to assess mathematical literacy ability. The steps of this study that consists of analysing, designing, theoretical validation, revising, limited testing to students, and evaluating. The data was collected with written test to 38 students of grade IX at one of state junior high school. Mathematical literacy problems consist of three essays with three indicators and three levels at polyhedron subject. The Indicators are formulating and employing mathematics. The results show that: (1) mathematical literacy problems which are constructed have been valid and practical, (2) mathematical literacy problems have good distinguishing characteristics and adequate distinguishing characteristics, (3) difficulty levels of problems are easy and moderate. The final conclusion is mathematical literacy problems which are constructed can be used to assess mathematical literacy ability.

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

Bastian, Mark; Trigueros, Jose V.

Phoenix is a Java Virtual Machine (JVM) based library for performing mathematical and astrodynamics calculations. It consists of two primary sub-modules, phoenix-math and phoenix-astrodynamics. The mathematics package has a variety of mathematical classes for performing 3D transformations, geometric reasoning, and numerical analysis. The astrodynamics package has various classes and methods for computing locations, attitudes, accesses, and other values useful for general satellite modeling and simulation. Methods for computing celestial locations, such as the location of the Sun and Moon, are also included. Phoenix is meant to be used as a library within the context of a larger application. For example,more » it could be used for a web service, desktop client, or to compute simple values in a scripting environment.« less

Structural Model of the Relationships among Cognitive Processes, Visual Motor Integration, and Academic Achievement in Students with Mild Intellectual Disability (MID)

ERIC Educational Resources Information Center

Taha, Mohamed Mostafa

2016-01-01

This study aimed to test a proposed structural model of the relationships and existing paths among cognitive processes (attention and planning), visual motor integration, and academic achievement in reading, writing, and mathematics. The study sample consisted of 50 students with mild intellectual disability or MID. The average age of these…

Free Fall Misconceptions: Results of a Graph Based Pre-Test of Sophomore Civil Engineering Students

ERIC Educational Resources Information Center

Montecinos, Alicia M.

2014-01-01

A partially unusual behaviour was found among 14 sophomore students of civil engineering who took a pre test for a free fall laboratory session, in the context of a general mechanics course. An analysis contemplating mathematics models and physics models consistency was made. In all cases, the students presented evidence favoring a correct free…

Do the Teacher and School Factors of the Dynamic Model Affect High- and Low-Achieving Student Groups to the Same Extent? A Cross-Country Study

ERIC Educational Resources Information Center

Vanlaar, Gudrun; Kyriakides, Leonidas; Panayiotou, Anastasia; Vandecandelaere, Machteld; McMahon, Léan; De Fraine, Bieke; Van Damme, Jan

2016-01-01

Background: The dynamic model of educational effectiveness (DMEE) is a comprehensive theoretical framework including factors that are important for school learning, based on consistent findings within educational effectiveness research. Purpose: This study investigates the impact of teacher and school factors of DMEE on mathematics and science…

Branch-Based Model for the Diameters of the Pulmonary Airways: Accounting for Departures From Self-Consistency and Registration Errors

PubMed Central

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

2017-01-01

We examine a previously published branch-based approach for modeling airway diameters that is predicated on the assumption of self-consistency across all levels of the tree. We mathematically formulate this assumption, propose a method to test it and develop a more general model to be used when the assumption is violated. We discuss the effect of measurement error on the estimated models and propose methods that take account of error. The methods are illustrated on data from MRI and CT images of silicone casts of two rats, two normal monkeys, and one ozone-exposed monkey. Our results showed substantial departures from self-consistency in all five subjects. When departures from self-consistency exist, we do not recommend using the self-consistency model, even as an approximation, as we have shown that it may likely lead to an incorrect representation of the diameter geometry. The new variance model can be used instead. Measurement error has an important impact on the estimated morphometry models and needs to be addressed in the analysis. PMID:22528468

Pre-Service Science Teachers' Cognitive Structures Regarding Science, Technology, Engineering, Mathematics (STEM) and Science Education

ERIC Educational Resources Information Center

Hacioglu, Yasemin; Yamak, Havva; Kavak, Nusret

2016-01-01

The aim of this study is to reveal pre-service science teachers' cognitive structures regarding Science, Technology, Engineering, Mathematics (STEM) and science education. The study group of the study consisted of 192 pre-service science teachers. A Free Word Association Test (WAT) consisting of science, technology, engineering, mathematics and…

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.

Defining Computational Thinking for Mathematics and Science Classrooms

NASA Astrophysics Data System (ADS)

Weintrop, David; Beheshti, Elham; Horn, Michael; Orton, Kai; Jona, Kemi; Trouille, Laura; Wilensky, Uri

2016-02-01

Science and mathematics are becoming computational endeavors. This fact is reflected in the recently released Next Generation Science Standards and the decision to include "computational thinking" as a core scientific practice. With this addition, and the increased presence of computation in mathematics and scientific contexts, a new urgency has come to the challenge of defining computational thinking and providing a theoretical grounding for what form it should take in school science and mathematics classrooms. This paper presents a response to this challenge by proposing a definition of computational thinking for mathematics and science in the form of a taxonomy consisting of four main categories: data practices, modeling and simulation practices, computational problem solving practices, and systems thinking practices. In formulating this taxonomy, we draw on the existing computational thinking literature, interviews with mathematicians and scientists, and exemplary computational thinking instructional materials. This work was undertaken as part of a larger effort to infuse computational thinking into high school science and mathematics curricular materials. In this paper, we argue for the approach of embedding computational thinking in mathematics and science contexts, present the taxonomy, and discuss how we envision the taxonomy being used to bring current educational efforts in line with the increasingly computational nature of modern science and mathematics.

Biological Aging - Criteria for Modeling and a New Mechanistic Model

NASA Astrophysics Data System (ADS)

Pletcher, Scott D.; Neuhauser, Claudia

To stimulate interaction and collaboration across scientific fields, we introduce a minimum set of biological criteria that theoretical models of aging should satisfy. We review results of several recent experiments that examined changes in age-specific mortality rates caused by genetic and environmental manipulation. The empirical data from these experiments is then used to test mathematical models of aging from several different disciplines, including molecular biology, reliability theory, physics, and evolutionary biology/population genetics. We find that none of the current models are consistent with all of the published experimental findings. To provide an example of how our criteria might be applied in practice, we develop a new conceptual model of aging that is consistent with our observations.

Preservice Mathematics Teachers' Metaphorical Perceptions towards Proof and Proving

ERIC Educational Resources Information Center

Ersen, Zeynep Bahar

2016-01-01

Since mathematical proof and proving are in the center of mathematics; preservice mathematics teachers' perceptions against these concepts have a great importance. Therefore, the study aimed to determine preservice mathematics teachers' perceptions towards proof and proving through metaphors. The participants consisted of 192 preservice…

The enhancement of students' mathematical problem solving ability through teaching with metacognitive scaffolding approach

NASA Astrophysics Data System (ADS)

Prabawanto, Sufyani

2017-05-01

This research aims to investigate the enhancement of students' mathematical problem solving through teaching with metacognitive scaffolding approach. This research used a quasi-experimental design with pretest-posttest control. The subjects were pre-service elementary school teachers in a state university in Bandung. In this study, there were two groups: experimental and control groups. The experimental group consists of 60 studentswho acquire teaching mathematicsunder metacognitive scaffolding approach, while the control group consists of 58 studentswho acquire teaching mathematicsunder direct approach. Students were classified into three categories based on the mathematical prior ability, namely high, middle, and low. Data collection instruments consist of mathematical problem solving test instruments. By usingmean difference test, two conclusions of the research:(1) there is a significant difference in the enhancement of mathematical problem solving between the students who attended the course under metacognitive scaffolding approach and students who attended the course under direct approach, and(2) thereis no significant interaction effect of teaching approaches and ability level based on the mathematical prior ability toward enhancement of students' mathematical problem solving.

A Comparison of Grade Achievement of Students Using a Programmed Mathematics Text Versus Students Using a Traditional Mathematics Text.

ERIC Educational Resources Information Center

Raines, Roy H.

The effectiveness of a basic college mathematics course consisting of lecture-discussion classroom procedures and homework assignments from a traditional text was compared to the effectiveness of a course designed to combat low grade achievement and a high dropout rate by allowing for individual differences. The revised course consisted of…

A cellular automata model of bone formation.

PubMed

Van Scoy, Gabrielle K; George, Estee L; Opoku Asantewaa, Flora; Kerns, Lucy; Saunders, Marnie M; Prieto-Langarica, Alicia

2017-04-01

Bone remodeling is an elegantly orchestrated process by which osteocytes, osteoblasts and osteoclasts function as a syncytium to maintain or modify bone. On the microscopic level, bone consists of cells that create, destroy and monitor the bone matrix. These cells interact in a coordinated manner to maintain a tightly regulated homeostasis. It is this regulation that is responsible for the observed increase in bone gain in the dominant arm of a tennis player and the observed increase in bone loss associated with spaceflight and osteoporosis. The manner in which these cells interact to bring about a change in bone quality and quantity has yet to be fully elucidated. But efforts to understand the multicellular complexity can ultimately lead to eradication of metabolic bone diseases such as osteoporosis and improved implant longevity. Experimentally validated mathematical models that simulate functional activity and offer eventual predictive capabilities offer tremendous potential in understanding multicellular bone remodeling. Here we undertake the initial challenge to develop a mathematical model of bone formation validated with in vitro data obtained from osteoblastic bone cells induced to mineralize and quantified at 26 days of culture. A cellular automata model was constructed to simulate the in vitro characterization. Permutation tests were performed to compare the distribution of the mineralization in the cultures and the distribution of the mineralization in the mathematical models. The results of the permutation test show the distribution of mineralization from the characterization and mathematical model come from the same probability distribution, therefore validating the cellular automata model. Copyright © 2017 Elsevier Inc. All rights reserved.

Does Time Matter in Improving Mathematical Discussions? The Influence of Mathematical Autonomy

ERIC Educational Resources Information Center

Kosko, Karl W.; Wilkins, Jesse L. M.

2015-01-01

Facilitating students' transition from less to more mathematically productive engagement in discussions is an important area of investigation. Research on mathematical whole-class discussions has consistently identified facilitating students' mathematical autonomy as a central component of this transition. Additionally, research commonly infers…

The mathematical properties of the quasi-chemical model for microorganism growth-death kinetics in foods.

PubMed

Ross, E W; Taub, I A; Doona, C J; Feeherry, F E; Kustin, K

2005-03-15

Knowledge of the mathematical properties of the quasi-chemical model [Taub, Feeherry, Ross, Kustin, Doona, 2003. A quasi-chemical kinetics model for the growth and death of Staphylococcus aureus in intermediate moisture bread. J. Food Sci. 68 (8), 2530-2537], which is used to characterize and predict microbial growth-death kinetics in foods, is important for its applications in predictive microbiology. The model consists of a system of four ordinary differential equations (ODEs), which govern the temporal dependence of the bacterial life cycle (the lag, exponential growth, stationary, and death phases, respectively). The ODE system derives from a hypothetical four-step reaction scheme that postulates the activity of a critical intermediate as an antagonist to growth (perhaps through a quorum sensing biomechanism). The general behavior of the solutions to the ODEs is illustrated by several examples. In instances when explicit mathematical solutions to these ODEs are not obtainable, mathematical approximations are used to find solutions that are helpful in evaluating growth in the early stages and again near the end of the process. Useful solutions for the ODE system are also obtained in the case where the rate of antagonist formation is small. The examples and the approximate solutions provide guidance in the parameter estimation that must be done when fitting the model to data. The general behavior of the solutions is illustrated by examples, and the MATLAB programs with worked examples are included in the appendices for use by predictive microbiologists for data collected independently.

Cold-Cap Temperature Profile Comparison between the Laboratory and Mathematical Model

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

Dixon, Derek R.; Schweiger, Michael J.; Riley, Brian J.

2015-06-01

The rate of waste vitrification in an electric melter is connected to the feed-to-glass conversion process, which occurs in the cold cap, a layer of reacting feed on top of molten glass. The cold cap consists of two layers: a low temperature (~100°C – ~800°C) region of unconnected feed and a high temperature (~800°C – ~1100°C) region of foam with gas bubbles and cavities mixed in the connected glass melt. A recently developed mathematical model describes the effect of the cold cap on glass production. For verification of the mathematical model, a laboratory-scale melter was used to produce a coldmore » cap that could be cross-sectioned and polished in order to determine the temperature profile related to position in the cold cap. The cold cap from the laboratory-scale melter exhibited an accumulation of feed ~400°C due to radiant heat from the molten glass creating dry feed conditions in the melter, which was not the case in the mathematical model where wet feed conditions were calculated. Through the temperature range from ~500°C – ~1100°C, there was good agreement between the model and the laboratory cold cap. Differences were observed between the two temperature profiles due to the temperature of the glass melts and the lack of secondary foam, large cavities, and shrinkage of the primary foam bubbles upon the cooling of the laboratory-scale cold cap.« less

Contribution of Auditory Learning Style to Students’ Mathematical Connection Ability

NASA Astrophysics Data System (ADS)

Karlimah; Risfiani, F.

2017-09-01

This paper presents the results of the research on the relation of mathematical concept with mathematics, other subjects, and with everyday life. This research reveals study result of the students who had auditory learning style and correlates it with their ability of mathematical connection. In this research, the researchers used a combination model or sequential exploratory design method, which is the use of qualitative and quantitative research methods in sequence. The result proves that giving learning facilities which are not suitable for the class whose students have the auditory learning style results in the barely sufficient math connection ability. The average mathematical connection ability of the auditory students was initially in the medium level of qualification. Then, the improvement in the form of the varied learning that suited the auditory learning style still showed the average ability of mathematical connection in medium level of qualification. Nevertheless, there was increase in the frequency of students in the medium level of qualification and decrease in the very low and low level of qualification. This suggests that the learning facilities, which are appropriate for the student’s auditory learning style, contribute well enough to the students’ mathematical connection ability. Therefore, the mathematics learning for students who have an auditory learning style should consist of particular activity that is understanding the concepts of mathematics and their relations.

Mathematical modelling of the influenced of diffusion rate on macro nutrient availability in paddy field

NASA Astrophysics Data System (ADS)

Renny; Supriyanto

2018-04-01

Nutrition is the chemical compounds that needed by the organism for the growth process. In plants, nutrients are organic or inorganic compounds that are absorbed from the roots of the soil. It consist of macro and micro nutrient. Macro nutrients are nutrition that needed by plants in large quantities, such as, nitrogen, calcium, pottacium, magnesium, and sulfur. The total soil nutrient is the difference between the input nutrient and the output nutrients. Input nutrients are nutrient that derived from the decomposition of organic substances. Meanwhile, the output nutrient consists of the nutrients that absorbed by plant roots (uptake), the evaporated nutrients (volatilized) and leached nutrients. The nutrient transport can be done through diffusion process. The diffusion process is essential in removing the nutrient from one place to the root surface. It will cause the rate of absorption of nutrient by the roots will be greater. Nutrient concept in paddy filed can be represented into a mathematical modelling, by making compartment models. The rate of concentration change in the compartment model forms a system of homogeneous linear differential equations. In this research, we will use Laplaces transformation to solve the compartment model and determined the dynamics of macro nutrition due to diffusion process.

Oncolytic potency and reduced virus tumor-specificity in oncolytic virotherapy. A mathematical modelling approach.

PubMed

Mahasa, Khaphetsi Joseph; Eladdadi, Amina; de Pillis, Lisette; Ouifki, Rachid

2017-01-01

In the present paper, we address by means of mathematical modeling the following main question: How can oncolytic virus infection of some normal cells in the vicinity of tumor cells enhance oncolytic virotherapy? We formulate a mathematical model describing the interactions between the oncolytic virus, the tumor cells, the normal cells, and the antitumoral and antiviral immune responses. The model consists of a system of delay differential equations with one (discrete) delay. We derive the model's basic reproductive number within tumor and normal cell populations and use their ratio as a metric for virus tumor-specificity. Numerical simulations are performed for different values of the basic reproduction numbers and their ratios to investigate potential trade-offs between tumor reduction and normal cells losses. A fundamental feature unravelled by the model simulations is its great sensitivity to parameters that account for most variation in the early or late stages of oncolytic virotherapy. From a clinical point of view, our findings indicate that designing an oncolytic virus that is not 100% tumor-specific can increase virus particles, which in turn, can further infect tumor cells. Moreover, our findings indicate that when infected tissues can be regenerated, oncolytic viral infection of normal cells could improve cancer treatment.

A two-phase model of plantar tissue: a step toward prediction of diabetic foot ulceration.

PubMed

Sciumè, G; Boso, D P; Gray, W G; Cobelli, C; Schrefler, B A

2014-11-01

A new computational model, based on the thermodynamically constrained averaging theory, has been recently proposed to predict tumor initiation and proliferation. A similar mathematical approach is proposed here as an aid in diabetic ulcer prevention. The common aspects at the continuum level are the macroscopic balance equations governing the flow of the fluid phase, diffusion of chemical species, tissue mechanics, and some of the constitutive equations. The soft plantar tissue is modeled as a two-phase system: a solid phase consisting of the tissue cells and their extracellular matrix, and a fluid one (interstitial fluid and dissolved chemical species). The solid phase may become necrotic depending on the stress level and on the oxygen availability in the tissue. Actually, in diabetic patients, peripheral vascular disease impacts tissue necrosis; this is considered in the model via the introduction of an effective diffusion coefficient that governs transport of nutrients within the microvasculature. The governing equations of the mathematical model are discretized in space by the finite element method and in time domain using the θ-Wilson Method. While the full mathematical model is developed in this paper, the example is limited to the simulation of several gait cycles of a healthy foot. Copyright © 2014 John Wiley & Sons, Ltd.

Time Spent on Homework, Mathematics Anxiety and Mathematics Achievement: Evidence from a US Sample

ERIC Educational Resources Information Center

Cheema, Jehanzeb R.; Sheridan, Kimberly

2015-01-01

This study investigated the effect of time spent on homework and mathematics anxiety on mathematics achievement. Data from a nationally representative US sample consisting of 4,978 cases was used to predict mathematics achievement from time spent on homework and mathematics anxiety while controlling for demographic differences such as gender,…

Bipotential continuum models for granular mechanics

NASA Astrophysics Data System (ADS)

Goddard, Joe

2014-03-01

Most currently popular continuum models for granular media are special cases of a generalized Maxwell fluid model, which describes the evolution of stress and internal variables such as granular particle fraction and fabric,in terms of imposed strain rate. It is shown how such models can be obtained from two scalar potentials, a standard elastic free energy and a ``dissipation potential'' given rigorously by the mathematical theory of Edelen. This allows for a relatively easy derivation of properly invariant continuum models for granular media and fluid-particle suspensions within a thermodynamically consistent framework. The resulting continuum models encompass all the prominent regimes of granular flow, ranging from the quasi-static to rapidly sheared, and are readily extended to include higher-gradient or Cosserat effects. Models involving stress diffusion, such as that proposed recently by Kamrin and Koval (PRL 108 178301), provide an alternative approach that is mentioned in passing. This paper provides a brief overview of a forthcoming review articles by the speaker (The Princeton Companion to Applied Mathematics, and Appl. Mech. Rev.,in the press, 2013).

Effect of Directed Study of Mathematics Vocabulary on Standardized Mathematics Assessment Questions

ERIC Educational Resources Information Center

Waite, Adel Marlane

2017-01-01

The problems under investigation included (a) Did a directed study of mathematics vocabulary significantly affect student performance levels on standardized mathematical questions? and (b) Did the strategies used in this study significantly affect student performance levels on standardized mathematical questions? The population consisted of…

Solving for Irrational Zeros: Whiteness in Mathematics Teacher Education

ERIC Educational Resources Information Center

Warburton, Trevor Thayne

2015-01-01

For many, mathematics and social justice are perceived as incompatible. Several mathematics education researchers have noted resistance to social justice among mathematics teachers. However, mathematics education has a consistently negative impact on the education of students of color. This study seeks to better understand the nature of this…

How do microclimate factors affect the risk for superficial pressure ulcers: a mathematical modeling study.

PubMed

Gefen, Amit

2011-08-01

In this study, a mathematical model is developed for analyzing the effects of the microclimate on skin tolerance to superficial pressure ulcers (SPUs). The modeling identified the following factors as such that decrease the tolerance of skin to SPUs: (i) increase in the skin temperature, (ii) increase in the ambient temperature, (iii) increase in the relative humidity, (iv) increase in the skin-support (or skin-clothing-support) contact pressures, and (v) decrease in permeabilities of the materials contacting the skin or being close to it, e.g. the covering sheet of the support and clothing. The modeling is consistent with relevant empirical findings and clinical observations documented in the literature, explains them from a basic science aspect, and can be further developed for design of interventions, safer patient clothing and supports that consider the optimization of microclimate factors. Copyright © 2010 Tissue Viability Society. Published by Elsevier Ltd. All rights reserved.

Catalytic wet oxidation: mathematical modeling of multicompound destruction.

PubMed

Yang, J; Hand, D W; Hokanson, D R; Crittenden, J C; Oman, E J

2003-01-01

A mathematical model of a three-phase catalytic reactor, CatReac, was developed for analysis and optimization of a catalytic oxidation reactor that is used in the International Space Station potable water processor. The packed-bed catalytic reactor, known as the volatile reactor assembly (VRA), is operated as a three-phase reactor and contains a proprietary catalyst, a pure-oxygen gas phase, and the contaminated water. The contaminated water being fed to the VRA primarily consists of acetic acid, acetone, ethanol, 1-propanol, 2-propanol, and propionic acid ranging in concentration from 1 to 10 mg/L. The Langmuir-Hinshelwood Hougen-Watson (L-H) (Hougen, 1943) expression was used to describe the surface reaction rate for these compounds. Single and multicompound short-column experiments were used to determine the L-H rate parameters and calibrate the model. The model was able to predict steady-state multicomponent effluent profiles for short and full-scale reactor experiments.

A community effort towards a knowledge-base and mathematical model of the human pathogen Salmonella Typhimurium LT2

USDA-ARS?s Scientific Manuscript database

Metabolic reconstructions (MRs) are common denominators in systems biology and represent biochemical, genetic, and genomic (BiGG) knowledge-bases for target organisms by capturing currently available information in a consistent, structured manner. Salmonella enterica subspecies I serovar Typhimurium...

A program to assess a thermal discharge on Trinity Bay, Texas

NASA Technical Reports Server (NTRS)

Zaitzeff, J. B.; Whitehead, V. S.

1972-01-01

The application of a two dimensional mathematical model to the analysis of the thermal discharge to verify its ability to predict the temperature distribution of Trinity Bay in the vicinity of the water outfall. Basic data consist of aerial thermal infrared and in situ measurements.

Semiotic Mediation within an AT Frame

ERIC Educational Resources Information Center

Maracci, Mirko; Mariotti, Maria Alessandra

2013-01-01

This article is meant to present a specific elaboration of the notion of mediation in relation to the use of artefacts to enhance mathematics teaching and learning: the elaboration offered by the Theory of Semiotic Mediation. In particular, it provides an explicit model--consistent with the activity-actions-operations framework--of the actions…

Psychometric properties of the Turkish adaptation of the Mathematics Teacher Efficacy Belief Instrument for in-service teachers.

PubMed

Cetinkaya, Bulent; Erbas, Ayhan Kursat

2011-11-01

Teaching efficacy beliefs have attracted researchers' attention in recent decades because of its close association with and potential impact on the implementation of new ideas and skills in education. In the present study, we have explored the psychometric properties and construct validity of the Turkish adaptation of the Mathematics Teacher Efficacy Belief Instrument developed by Enochs, Smith, & Huinker (2000) for in-service mathematics teachers. The instrument distinguishes between two dimensions of efficacy beliefs for mathematics teachers: personal mathematics teaching efficacy and mathematics teaching outcome expectancy. The sample consisted of 1355 in-service elementary school teachers and middle school mathematics teachers from 368 schools. Exploratory and confirmatory factor analysis revealed a two-factor structure similar to that found in other studies. Also, scores from the two subscales indicated acceptable internal consistency.

The Use of Concrete Learning Objects Taken from the History of Mathematics in Mathematics Education

ERIC Educational Resources Information Center

Bütüner, Suphi Önder

2016-01-01

This study aimed to reveal the effects of teaching with concrete learning objects taken from the history of mathematics on student achievement. Being a quasi-experimental study, it was conducted with two grade 8 classes in a secondary school located in Trabzon. The experimental group consisted of 27 students and the control group consisted of 25.…

The roles of lesson study in the development of mathematics learning instrument based on learning trajectory

NASA Astrophysics Data System (ADS)

Misnasanti; Dien, C. A.; Azizah, F.

2018-03-01

This study is aimed to describe Lesson Study (LS) activity and its roles in the development of mathematics learning instruments based on Learning Trajectory (LT). This study is a narrative study of teacher’s experiences in joining LS activity. Data collecting in this study will use three methods such as observation, documentations, and deep interview. The collected data will be analyzed with Milles and Huberman’s model that consists of reduction, display, and verification. The study result shows that through LS activity, teachers know more about how students think. Teachers also can revise their mathematics learning instrument in the form of lesson plan. It means that LS activity is important to make a better learning instruments and focus on how student learn not on how teacher teach.

Truth, models, model sets, AIC, and multimodel inference: a Bayesian perspective

USGS Publications Warehouse

Barker, Richard J.; Link, William A.

2015-01-01

Statistical inference begins with viewing data as realizations of stochastic processes. Mathematical models provide partial descriptions of these processes; inference is the process of using the data to obtain a more complete description of the stochastic processes. Wildlife and ecological scientists have become increasingly concerned with the conditional nature of model-based inference: what if the model is wrong? Over the last 2 decades, Akaike's Information Criterion (AIC) has been widely and increasingly used in wildlife statistics for 2 related purposes, first for model choice and second to quantify model uncertainty. We argue that for the second of these purposes, the Bayesian paradigm provides the natural framework for describing uncertainty associated with model choice and provides the most easily communicated basis for model weighting. Moreover, Bayesian arguments provide the sole justification for interpreting model weights (including AIC weights) as coherent (mathematically self consistent) model probabilities. This interpretation requires treating the model as an exact description of the data-generating mechanism. We discuss the implications of this assumption, and conclude that more emphasis is needed on model checking to provide confidence in the quality of inference.

New Directions for Mathematics Instruction. 1989 Yearbook.

ERIC Educational Resources Information Center

Blume, Glendon W., Ed.; Heid, M. Kathleen, Ed.

This yearbook discusses instructional approaches that are consistent with the reformulation of the school mathematics curriculum by the National Council of Teachers of Mathematics (NCTM). Articles included cover: (1) Pennsylvania standards for mathematics programs (including goals, curriculum, instruction, evaluation, teachers, and…

Mathematical Abstraction: Constructing Concept of Parallel Coordinates

NASA Astrophysics Data System (ADS)

Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.

2017-09-01

Mathematical abstraction is an important process in teaching and learning mathematics so pre-service mathematics teachers need to understand and experience this process. One of the theoretical-methodological frameworks for studying this process is Abstraction in Context (AiC). Based on this framework, abstraction process comprises of observable epistemic actions, Recognition, Building-With, Construction, and Consolidation called as RBC + C model. This study investigates and analyzes how pre-service mathematics teachers constructed and consolidated concept of Parallel Coordinates in a group discussion. It uses AiC framework for analyzing mathematical abstraction of a group of pre-service teachers consisted of four students in learning Parallel Coordinates concepts. The data were collected through video recording, students’ worksheet, test, and field notes. The result shows that the students’ prior knowledge related to concept of the Cartesian coordinate has significant role in the process of constructing Parallel Coordinates concept as a new knowledge. The consolidation process is influenced by the social interaction between group members. The abstraction process taken place in this group were dominated by empirical abstraction that emphasizes on the aspect of identifying characteristic of manipulated or imagined object during the process of recognizing and building-with.

Numerical approaches to model perturbation fire in turing pattern formations

NASA Astrophysics Data System (ADS)

Campagna, R.; Brancaccio, M.; Cuomo, S.; Mazzoleni, S.; Russo, L.; Siettos, K.; Giannino, F.

2017-11-01

Turing patterns were observed in chemical, physical and biological systems described by coupled reaction-diffusion equations. Several models have been formulated proposing the water as the causal mechanism of vegetation pattern formation, but this isn't an exhaustive hypothesis in some natural environments. An alternative explanation has been related to the plant-soil negative feedback. In Marasco et al. [1] the authors explored the hypothesis that both mechanisms contribute in the formation of regular and irregular vegetation patterns. The mathematical model consists in three partial differential equations (PDEs) that take into account for a dynamic balance between biomass, water and toxic compounds. A numerical approach is mandatory also to investigate on the predictions of this kind of models. In this paper we start from the mathematical model described in [1], set the model parameters such that the biomass reaches a stable spatial pattern (spots) and present preliminary studies about the occurrence of perturbing events, such as wildfire, that can affect the regularity of the biomass configuration.

Elective Drama Course in Mathematics Education: An Assessment of Pre-Service Teachers

ERIC Educational Resources Information Center

Sagirli, Meryem Özturan

2014-01-01

This study aimed to evaluate a newly introduced elective course "Drama in Mathematics Education" into mathematics education curriculum from the viewpoints of pre-service mathematics teachers. A case study was employed in the study. The study group consisted of 37 pre-service mathematics teachers who were enrolled in a Turkish state…

Learning from Math Circles: Providing Underserved Students of Color with Accessibility to Mathematics Education

ERIC Educational Resources Information Center

Winful, Audrey M.

2009-01-01

Consistently high minority failure rates in high school and college mathematics, the noticeable decrease in access to mathematics education for our underserved students of color, and this mathematics educator's genuine belief in the global necessity, desirability, and applicability of engaging our youth in learning mathematics through Math…

Mathematical Aspects of Educating Architecture Designers: A College Study

ERIC Educational Resources Information Center

Verner, I. M.; Maor, S.

2005-01-01

This paper considers a second-year Mathematical Aspects in Architectural Design course, which relies on a first-year mathematics course and offers mathematical learning as part of hands-on practice in architecture design studio. The 16-hour course consisted of seminar presentations of mathematics concepts, their application to covering the plane…

A mathematical model of sentimental dynamics accounting for marital dissolution.

PubMed

Rey, José-Manuel

2010-03-31

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

A Mathematical Model of Sentimental Dynamics Accounting for Marital Dissolution

PubMed Central

Rey, José-Manuel

2010-01-01

Background Marital dissolution is ubiquitous in western societies. It poses major scientific and sociological problems both in theoretical and therapeutic terms. Scholars and therapists agree on the existence of a sort of second law of thermodynamics for sentimental relationships. Effort is required to sustain them. Love is not enough. Methodology/Principal Findings Building on a simple version of the second law we use optimal control theory as a novel approach to model sentimental dynamics. Our analysis is consistent with sociological data. We show that, when both partners have similar emotional attributes, there is an optimal effort policy yielding a durable happy union. This policy is prey to structural destabilization resulting from a combination of two factors: there is an effort gap because the optimal policy always entails discomfort and there is a tendency to lower effort to non-sustaining levels due to the instability of the dynamics. Conclusions/Significance These mathematical facts implied by the model unveil an underlying mechanism that may explain couple disruption in real scenarios. Within this framework the apparent paradox that a union consistently planned to last forever will probably break up is explained as a mechanistic consequence of the second law. PMID:20360987

Kantorovich-Wasserstein Distance for Identifying the Dynamic of Some Compartmental Models in Biology

NASA Astrophysics Data System (ADS)

Pousin, Jérôme

2008-09-01

Determining the influence of a biological species to the evolution of an other one strongly depends on the choice of mathematical models in biology. In this work we consider the case of distribution of lipids (docosahexaenoic acid (DHA)) in two compartments of the plasma, the platelets and the erythrocytes, and we compare three different mathematical approaches. The first one, consists of a system of differential equations the coefficients of which are identified through a least square procedure. The second one is made of a system of differential equations on a graph, the adjacency matrix of which represents the interplay between the species. The third one consists of mapping the provider curves to the target curves. Thus we have a distance between two families of curves, the curves of providers and the curves of targets, and by comparing the distances, we are able to decide which provider delivers preferentially to a target according to cumulative species mass curves. Numerical results are presented, and we show that the ordinary differential least square model provides qualitatively the same result as the Kantorovich-Wasserstein distance strategy. Finally, we discuss the potential ability of the presented Kantorovich-Wasserstein distance to perform the biological properties of a system.

In Vivo Bioluminescence Tomography for Monitoring Breast Tumor Growth and Metastatic Spreading: Comparative Study and Mathematical Modeling

PubMed Central

Mollard, Séverine; Fanciullino, Raphaelle; Giacometti, Sarah; Serdjebi, Cindy; Benzekry, Sebastien; Ciccolini, Joseph

2016-01-01

This study aimed at evaluating the reliability and precision of Diffuse Luminescent Imaging Tomography (DLIT) for monitoring primary tumor and metastatic spreading in breast cancer mice, and to develop a biomathematical model to describe the collected data. Using orthotopic mammary fat pad model of breast cancer (MDAMB231-Luc) in mice, we monitored tumor and metastatic spreading by three-dimensional (3D) bioluminescence and cross-validated it with standard bioluminescence imaging, caliper measurement and necropsy examination. DLIT imaging proved to be reproducible and reliable throughout time. It was possible to discriminate secondary lesions from the main breast cancer, without removing the primary tumor. Preferential metastatic sites were lungs, peritoneum and lymph nodes. Necropsy examinations confirmed DLIT measurements. Marked differences in growth profiles were observed, with an overestimation of the exponential phase when using a caliper as compared with bioluminescence. Our mathematical model taking into account the balance between living and necrotic cells proved to be able to reproduce the experimental data obtained with a caliper or DLIT imaging, because it could discriminate proliferative living cells from a more composite mass consisting of tumor cells, necrotic cell, or inflammatory tissues. DLIT imaging combined with mathematical modeling could be a powerful and informative tool in experimental oncology. PMID:27812027

Abstract Model of the SATS Concept of Operations: Initial Results and Recommendations

NASA Technical Reports Server (NTRS)

Dowek, Gilles; Munoz, Cesar; Carreno, Victor A.

2004-01-01

An abstract mathematical model of the concept of operations for the Small Aircraft Transportation System (SATS) is presented. The Concept of Operations consist of several procedures that describe nominal operations for SATS, Several safety properties of the system are proven using formal techniques. The final goal of the verification effort is to show that under nominal operations, aircraft are safely separated. The abstract model was written and formally verified in the Prototype Verification System (PVS).

Temporal Subtraction of Digital Breast Tomosynthesis Images for Improved Mass Detection

DTIC Science & Technology

2008-10-01

K. Fishman and B. M. W. Tsui, "Development of a computer-generated model for the coronary arterial tree based on multislice CT and morphometric data...mathematical models based on geometric primitives8-22. Bakic et al created synthetic x-ray mammograms using a 3D simulated breast tissue model consisting of...utilized a combination of voxel matrices and geometric primitives to create a breast phantom that includes the breast surface, the duct system, and

Dose conversion coefficients based on the Chinese mathematical phantom and MCNP code for external photon irradiation.

PubMed

Qiu, Rui; Li, Junli; Zhang, Zhan; Liu, Liye; Bi, Lei; Ren, Li

2009-02-01

A set of conversion coefficients from kerma free-in-air to the organ-absorbed dose are presented for external monoenergetic photon beams from 10 keV to 10 MeV based on the Chinese mathematical phantom, a whole-body mathematical phantom model. The model was developed based on the methods of the Oak Ridge National Laboratory mathematical phantom series and data from the Chinese Reference Man and the Reference Asian Man. This work is carried out to obtain the conversion coefficients based on this model, which represents the characteristics of the Chinese population, as the anatomical parameters of the Chinese are different from those of Caucasians. Monte Carlo simulation with MCNP code is carried out to calculate the organ dose conversion coefficients. Before the calculation, the effects from the physics model and tally type are investigated, considering both the calculation efficiency and precision. In the calculation irradiation conditions include anterior-posterior, posterior-anterior, right lateral, left lateral, rotational and isotropic geometries. Conversion coefficients from this study are compared with those recommended in the Publication 74 of International Commission on Radiological Protection (ICRP74) since both the sets of data are calculated with mathematical phantoms. Overall, consistency between the two sets of data is observed and the difference for more than 60% of the data is below 10%. However, significant deviations are also found, mainly for the superficial organs (up to 65.9%) and bone surface (up to 66%). The big difference of the dose conversion coefficients for the superficial organs at high photon energy could be ascribed to kerma approximation for the data in ICRP74. Both anatomical variations between races and the calculation method contribute to the difference of the data for bone surface.

Using LEGO for learning fractions, supporting or distracting?

NASA Astrophysics Data System (ADS)

Rejeki, Sri; Setyaningsih, Nining; Toyib, Muhamad

2017-05-01

The role of games used for learning mathematics is still in debate. However, many research revealed that it gave positive effects on both students' motivation and performance in mathematics. Therefore, this study aims at investigating the effects of using LEGO-as one of games which students are familiar with, for learning mathematics, on both students' conceptual knowledge of fractions and students' attitude in learning mathematics. A set of learning activities consisting three meetings of fractions learning was designed for this study. The activities were mainly about solving word-context problems using LEGO as the model. Thirty students of seven grade with high-ability in mathematics and thirty two students with low-ability in mathematics were involved in this study. The data were collected through students' written works, video registration and field notes during the teaching and learning activities. The results indicate that in general the use of LEGO in learning activities support the conceptual understanding on fractions for both students with high-ability and low-ability in mathematics. Moreover, for students with low-ability in mathematics, it promotes the computational skill of fractions operation. The evidences also suggest that bringing LEGO into classroom activities improve students' motivation and engagement. However, in some cases, students were more focus on playing than learning. Therefore, teachers play important roles on providing clear pedagogical instructions about the way to use LEGO properly.

Mathematics Student Teachers' Epistemological Beliefs about the Nature of Mathematics and the Goals of Mathematics Teaching and Learning in the Beginning of Their Studies

ERIC Educational Resources Information Center

Viholainen, Antti; Asikainen, Mervi; Hirvonen, Pekka E.

2014-01-01

This article examines Finnish mathematics student teachers' epistemological beliefs concerning the nature of mathematics and the goals of mathematics teaching and learning solely in the beginning of their studies at university. A total of 18 students participated in a study consisting of a short questionnaire and interviews. The data was analyzed…

In-vitro development of vitrified-warmed bovine oocytes after activation may be predicted based on mathematical modelling of cooling and warming rates during vitrification, storage and sample removal.

PubMed

Sansinena, Marina; Santos, Maria Victoria; Chirife, Jorge; Zaritzky, Noemi

2018-05-01

Heat transfer during cooling and warming is difficult to measure in cryo-devices; mathematical modelling is an alternative method that can describe these processes. In this study, we tested the validity of one such model by assessing in-vitro development of vitrified and warmed bovine oocytes after parthenogenetic activation and culture. The viability of oocytes vitrified in four different cryo-devices was assessed. Consistent with modelling predictions, oocytes vitrified using cryo-devices with the highest modelled cooling rates had significantly (P < 0.05) better cleavage and blastocyst formation rates. We then evaluated a two-step sample removal process, in which oocytes were held in nitrogen vapour for 15 s to simulate sample identification during clinical application, before being removed completely and warmed. Oocytes exposed to this procedure showed reduced developmental potential, according to the model, owing to thermodynamic instability and devitrification at relatively low temperatures. These findings suggest that cryo-device selection and handling, including method of removal from nitrogen storage, are critical to survival of vitrified oocytes. Limitations of the study include use of parthenogenetically activated rather than fertilized ova and lack of physical measurement of recrystallization. We suggest mathematical modelling could be used to predict the effect of critical steps in cryopreservation. Copyright © 2018 Reproductive Healthcare Ltd. Published by Elsevier Ltd. All rights reserved.

Predicting Drug Combination Index and Simulating the Network-Regulation Dynamics by Mathematical Modeling of Drug-Targeted EGFR-ERK Signaling Pathway

NASA Astrophysics Data System (ADS)

Huang, Lu; Jiang, Yuyang; Chen, Yuzong

2017-01-01

Synergistic drug combinations enable enhanced therapeutics. Their discovery typically involves the measurement and assessment of drug combination index (CI), which can be facilitated by the development and applications of in-silico CI predictive tools. In this work, we developed and tested the ability of a mathematical model of drug-targeted EGFR-ERK pathway in predicting CIs and in analyzing multiple synergistic drug combinations against observations. Our mathematical model was validated against the literature reported signaling, drug response dynamics, and EGFR-MEK drug combination effect. The predicted CIs and combination therapeutic effects of the EGFR-BRaf, BRaf-MEK, FTI-MEK, and FTI-BRaf inhibitor combinations showed consistent synergism. Our results suggest that existing pathway models may be potentially extended for developing drug-targeted pathway models to predict drug combination CI values, isobolograms, and drug-response surfaces as well as to analyze the dynamics of individual and combinations of drugs. With our model, the efficacy of potential drug combinations can be predicted. Our method complements the developed in-silico methods (e.g. the chemogenomic profile and the statistically-inferenced network models) by predicting drug combination effects from the perspectives of pathway dynamics using experimental or validated molecular kinetic constants, thereby facilitating the collective prediction of drug combination effects in diverse ranges of disease systems.

A mathematical model for predicting the life of polymer electrolyte fuel cell membranes subjected to hydration cycling

NASA Astrophysics Data System (ADS)

Burlatsky, S. F.; Gummalla, M.; O'Neill, J.; Atrazhev, V. V.; Varyukhin, A. N.; Dmitriev, D. V.; Erikhman, N. S.

2012-10-01

Under typical Polymer Electrolyte Membrane Fuel Cell (PEMFC) fuel cell operating conditions, part of the membrane electrode assembly is subjected to humidity cycling due to variation of inlet gas RH and/or flow rate. Cyclic membrane hydration/dehydration would cause cyclic swelling/shrinking of the unconstrained membrane. In a constrained membrane, it causes cyclic stress resulting in mechanical failure in the area adjacent to the gas inlet. A mathematical modeling framework for prediction of the lifetime of a PEMFC membrane subjected to hydration cycling is developed in this paper. The model predicts membrane lifetime as a function of RH cycling amplitude and membrane mechanical properties. The modeling framework consists of three model components: a fuel cell RH distribution model, a hydration/dehydration induced stress model that predicts stress distribution in the membrane, and a damage accrual model that predicts membrane lifetime. Short descriptions of the model components along with overall framework are presented in the paper. The model was used for lifetime prediction of a GORE-SELECT membrane.

Comment on "Asymmetric coevolutionary networks facilitate biodiversity maintenance"

USGS Publications Warehouse

Holland, J. Nathaniel; Okuyama, Toshinori; DeAngelis, Donald L.

2006-01-01

Bascompte et al. (Reports, 21 April 2006, p. 431) used network asymmetries to explain mathematical conditions necessary for stability in historic models of mutualism. The Lotka-Volterra equations they used artificially created conditions in which some factor, such as asymmetric interaction strengths, is necessary for community coexistence. We show that a more realistic model incorporating nonlinear functional responses requires no such condition and is consistent with their data.

Energy regeneration model of self-consistent field of electron beams into electric power*

NASA Astrophysics Data System (ADS)

Kazmin, B. N.; Ryzhov, D. R.; Trifanov, I. V.; Snezhko, A. A.; Savelyeva, M. V.

2016-04-01

We consider physic-mathematical models of electric processes in electron beams, conversion of beam parameters into electric power values and their transformation into users’ electric power grid (onboard spacecraft network). We perform computer simulation validating high energy efficiency of the studied processes to be applied in the electric power technology to produce the power as well as electric power plants and propulsion installation in the spacecraft.

Periodicity in cell dynamics in some mathematical models for the treatment of leukemia

NASA Astrophysics Data System (ADS)

Halanay, A.

2012-11-01

A model for the evolution of short-term hematopoietic stem cells and of leukocytes in leucemia under periodic treatment is introduced. It consists of a system of periodic delay differential equations and takes into consideration the asymmetric division. A guiding function is used, together with a theorem of Krasnoselskii, to prove the existence of a strictly positive periodic solution and its stability is investigated.

Personal Epistemology and Mathematics: A Critical Review and Synthesis of Research

ERIC Educational Resources Information Center

Muis, Krista R.

2004-01-01

This review critically examines 33 studies on students' epistemological beliefs about mathematics. Five categories were identified: beliefs about mathematics, development of beliefs, effects of beliefs on behavior, domain differences, and changing beliefs. Studies examining beliefs about mathematics revealed consistent patterns of nonavailing…

Learning to Write about Mathematics

ERIC Educational Resources Information Center

Parker, Renee; Breyfogle, M. Lynn

2011-01-01

Beginning in third grade, Pennsylvania students are required to take the Pennsylvania State Standardized Assessment (PSSA), which presents multiple-choice mathematics questions and open-ended mathematics problems. Consistent with the Communication Standard of the National Council of Teachers of Mathematics, while solving the open-ended problems,…

Development of a model describing the inhibitory effect of selected preservatives on the growth of Listeria monocytogenes in a meat model system.

PubMed

Dussault, Dominic; Vu, Khanh Dang; Lacroix, Monique

2016-02-01

The objective of this study was to evaluate the impact of seven independent factors consisting of sodium nitrite, pH, sodium chloride, sodium acetate, sodium lactate syrup, calcium propionate and a blend of nisin and hop alpha acids on the growth rate of Listeria monocytogenes in ham as a model of ready-to-eat (RTE) meat products. A central composite consisted of seven factors mentioned above was designed and the response surface methodology was applied for creating a mathematic model to predict the growth rate of L. monocytogenes in RTE meat products. Six parameters showed a significant (P ≤ 0.1) influence on the growth rate of L. monocytogenes. Only the blend of nisin and hop alpha acids did not show any significant effect (P > 0.1) in the concentrations used in this study. Increasing concentration of sodium chloride, sodium nitrite, sodium acetate, potassium lactate and calcium propionate in meat reduced bacterial growth rate while increasing pH in meat increased the growth rate of L. monocytogenes. The current mathematical equation will be an important tool in order to reduce the required number of challenge studies performed in order to ensure a safe food product. Copyright © 2015 Elsevier Ltd. All rights reserved.

Attitudes of Mathematics Teachers toward Using Smart Board in Teaching Mathematics

ERIC Educational Resources Information Center

Muhanna, Wafa; Nejem, Khamis Mousa

2013-01-01

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

An Investigation of Teachers' Noticing, Cognitive Demand, and Mathematical Knowledge for Teaching: Video Reflections in an Elementary Mathematics Context

ERIC Educational Resources Information Center

Coddington, Lorelei R.

2014-01-01

In the past decade, mathematics performance by all students, especially minority students in low socioeconomic schools, has shown limited improvement nationwide (NCES, 2011). Traditionally in the United States, mathematics has consisted of arithmetic and computational fluency; however, mathematics researchers widely believe that this method of…

Blending Individual and Group Assessment: A Model for Measuring Student Performance

ERIC Educational Resources Information Center

Reiser, Elana

2017-01-01

Two sections of a college discrete mathematics class were taught using cooperative learning techniques throughout the semester. The 33 students attending these sections were randomly assigned into groups of three. Their final examination consisted of an individual and group blended examination where students worked in their groups and discussed…

An analytical procedure to assist decision-making in a government research organization

Treesearch

H. Dean Claxton; Giuseppe Rensi

1972-01-01

An analytical procedure to help management decision-making in planning government research is described. The objectives, activities, and restrictions of a government research organization are modeled in a consistent analytical framework. Theory and methodology is drawn from economics and mathe-matical programing. The major analytical aspects distinguishing research...

Nested Neural Networks

NASA Technical Reports Server (NTRS)

Baram, Yoram

1992-01-01

Report presents analysis of nested neural networks, consisting of interconnected subnetworks. Analysis based on simplified mathematical models more appropriate for artificial electronic neural networks, partly applicable to biological neural networks. Nested structure allows for retrieval of individual subpatterns. Requires fewer wires and connection devices than fully connected networks, and allows for local reconstruction of damaged subnetworks without rewiring entire network.

Entrepreneur Program. COM-LINK. Competency Based Vocational Curricula with Basic Skills and Academic Linkages.

ERIC Educational Resources Information Center

De Maria, Richard

This competency-based module uses the Ocean County (New Jersey) Vocational-Technical Schools curriculum-infused model for infusing basic skills instruction into vocational education. The document consists of matrices that describe the relationship of vocational skills to basic communication, mathematics, and science skills within the entrepreneur…

Student and high-school characteristics related to completing a science, technology, engineering or mathematics (STEM) major in college

NASA Astrophysics Data System (ADS)

LeBeau, Brandon; Harwell, Michael; Monson, Debra; Dupuis, Danielle; Medhanie, Amanuel; Post, Thomas R.

2012-04-01

Background: The importance of increasing the number of US college students completing degrees in science, technology, engineering or mathematics (STEM) has prompted calls for research to provide a better understanding of factors related to student participation in these majors, including the impact of a student's high-school mathematics curriculum. Purpose: This study examines the relationship between various student and high-school characteristics and completion of a STEM major in college. Of specific interest is the influence of a student's high-school mathematics curriculum on the completion of a STEM major in college. Sample: The sample consisted of approximately 3500 students from 229 high schools. Students were predominantly Caucasian (80%), with slightly more males than females (52% vs 48%). Design and method: A quasi-experimental design with archival data was used for students who enrolled in, and graduated from, a post-secondary institution in the upper Midwest. To be included in the sample, students needed to have completed at least three years of high-school mathematics. A generalized linear mixed model was used with students nested within high schools. The data were cross-sectional. Results: High-school predictors were not found to have a significant impact on the completion of a STEM major. Significant student-level predictors included ACT mathematics score, gender and high-school mathematics GPA. Conclusions: The results provide evidence that on average students are equally prepared for the rigorous mathematics coursework regardless of the high-school mathematics curriculum they completed.

Branch-Based Model for the Diameters of the Pulmonary Airways: Accounting for Departures From Self-Consistency and Registration Errors

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

Neradilek, Moni B.; Polissar, Nayak L.; Einstein, Daniel R.

2012-04-24

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

Assessing adult mortality in HIV-1-afflicted Zimbabwe (1998 -2003).

PubMed Central

Lopman, Ben A.; Barnabas, Ruanne; Hallett, Timothy B.; Nyamukapa, Constance; Mundandi, Costa; Mushati, Phyllis; Garnett, Geoff P.; Gregson, Simon

2006-01-01

OBJECTIVE: To compare alternative methods to vital registration systems for estimating adult mortality, and describe patterns of mortality in Manicaland, Zimbabwe, which has been severely affected by HIV. METHODS: We compared estimates of adult mortality from (1) a single question on household mortality, (2) repeated household censuses, and (3) an adult cohort study with linked HIV testing from Manicaland, with a mathematical model fitted to local age-specific HIV prevalence (1998 -2000). FINDINGS: The crude death rate from the single question (29 per 1000 person-years) was roughly consistent with that from the mathematical model (22 -25 per 1000 person-years), but much higher than that from the household censuses (12 per 1000 person-years). Adult mortality in the household censuses (males 0.65; females 0.51) was lower than in the cohort study (males 0.77; females 0.57), while mathematical models gave a much higher estimate, especially for females (males 0.80 -0.83; females 0.75 -0.80). The population attributable fraction of adult deaths due to HIV was 0.61 for men and 0.70 for women, with life expectancy estimated to be 34.3 years for males and 38.2 years for females. CONCLUSION: Each method for estimating adult mortality had limitations in terms of loss to follow-up (cohort study), under-ascertainment (household censuses), transparency of underlying processes (single question), and sensitivity to parameterization (mathematical model). However, these analyses make clear the advantages of longitudinal cohort data, which provide more complete ascertainment than household censuses, highlight possible inaccuracies in model assumptions, and allow direct quantification of the impact of HIV. PMID:16583077

A Long-Term Mathematical Model for Mining Industries

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

Achdou, Yves, E-mail: achdou@ljll.univ-paris-diderot.fr; Giraud, Pierre-Noel; Lasry, Jean-Michel

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

A Mathematical Modeling Approach to Understanding the Effect of Anti‐Interleukin Therapy on Eosinophils

PubMed Central

Karelina, T; Voronova, V; Demin, O; Colice, G

2016-01-01

Emerging T‐helper type 2 (Th2) cytokine‐based asthma therapies, such as tralokinumab, lebrikizumab (anti‐interleukin (IL)‐13), and mepolizumab (anti‐IL‐5), have shown differences in their blood eosinophil (EOS) response. To better understand these effects, we developed a mathematical model of EOS dynamics. For the anti‐IL‐13 therapies, lebrikizumab and tralokinumab, the model predicted an increase of 30% and 10% in total and activated EOS in the blood, respectively, and a decrease in the total and activated EOS in the airways. The model predicted a rapid decrease in total and activated EOS levels in blood and airways for the anti‐IL‐5 therapy mepolizumab. All model‐based predictions were consistent with published clinical observations. The modeling approach provided insights into EOS response after treatment with Th2‐targeted therapies, and supports the hypothesis that an increase in blood EOS after anti‐IL‐13 therapy is part of the pharmacological action of these therapies. PMID:27885827

Experiment of Enzyme Kinetics Using Guided Inquiry Model for Enhancing Generic Science Skills

NASA Astrophysics Data System (ADS)

Amida, N.; Supriyanti, F. M. T.; Liliasari

2017-02-01

This study aims to enhance generic science skills of students using guided inquiry model through experiments of enzyme kinetics. This study used quasi-experimental methods, with pretest-posttestnonequivalent control group design. Subjects of this study were chemistry students enrolled in biochemistry lab course, consisted of 18 students in experimental class and 19 students in control class. Instrument in this study were essay test that involves 5 indicators of generic science skills (i.e. direct observation, causality, symbolic language, mathematical modeling, and concepts formation) and also student worksheets. The results showed that the experiments of kinetics enzyme using guided inquiry model have been enhance generic science skills in high category with a value of average of 0.77. Four indicators classified in the high category are direct observation, causality, symbolic language, and mathematical modeling with the value of 0,73 0,70; 0,96; dan 0,85. Meanwhile, indicator of concepts formation in the medium category with a value of 0.62

Mathematical model of phase transformations and elastoplastic stress in the water spray quenching of steel bars

NASA Astrophysics Data System (ADS)

Nagasaka, Y.; Brimacombe, J. K.; Hawbolt, E. B.; Samarasekera, I. V.; Hernandez-Morales, B.; Chidiac, S. E.

1993-04-01

A mathematical model, based on the finite-element technique and incorporating thermo-elasto-plastic behavior during the water spray quenching of steel, has been developed. In the model, the kinetics of diffusion-dependent phase transformation and martensitic transformation have been coupled with the transient heat flow to predict the microstructural evolution of the steel. Furthermore, an elasto-plastic constitutive relation has been applied to calculate internal stresses resulting from phase changes as well as temperature variation. The computer code has been verified for internal consistency with previously published results for pure iron bars. The model has been applied to the water spray quenching of two grades of steel bars, 1035 carbon and nickel-chromium alloyed steel; the calculated temperature, hardness, distortion, and residual stresses in the bars agreed well with experimental measurements. The results show that the phase changes occurring during this process affect the internal stresses significantly and must be included in the thermomechanical model.

Wind tunnel tests of a free-wing/free-trimmer model

NASA Technical Reports Server (NTRS)

Sandlin, D. R.

1982-01-01

The riding qualities of an aircraft with low wing loading can be improved by freeing the wing to rotate about its spanwise axis. A trimming surface also free to rotate about its spanwise axis can be added at the wing tips to permit the use of high lift devices. Wind tunnel tests of the free wing/free trimmer model with the trimmer attached to the wing tips aft of the wing chord were conducted to validate a mathematical model developed to predict the dynamic characteristics of a free wing/free trimmer aircraft. A model consisting of a semispan wing with the trimmer mounted on with the wing on an air bearing and the trimmer on a ball bearing was displaced to various angles of attack and released. The damped oscillations of the wing and trimmer were recorded. Real and imaginary parts of the characteristic equations of motion were determined and compared to values predicted using the mathematical model.

Mirror neurons, language, and embodied cognition.

PubMed

Perlovsky, Leonid I; Ilin, Roman

2013-05-01

Basic mechanisms of the mind, cognition, language, its semantic and emotional mechanisms are modeled using dynamic logic (DL). This cognitively and mathematically motivated model leads to a dual-model hypothesis of language and cognition. The paper emphasizes that abstract cognition cannot evolve without language. The developed model is consistent with a joint emergence of language and cognition from a mirror neuron system. The dual language-cognition model leads to the dual mental hierarchy. The nature of cognition embodiment in the hierarchy is analyzed. Future theoretical and experimental research is discussed. Published by Elsevier Ltd.

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…

Optimal design of the rotor geometry of line-start permanent magnet synchronous motor using the bat algorithm

NASA Astrophysics Data System (ADS)

Knypiński, Łukasz

2017-12-01

In this paper an algorithm for the optimization of excitation system of line-start permanent magnet synchronous motors will be presented. For the basis of this algorithm, software was developed in the Borland Delphi environment. The software consists of two independent modules: an optimization solver, and a module including the mathematical model of a synchronous motor with a self-start ability. The optimization module contains the bat algorithm procedure. The mathematical model of the motor has been developed in an Ansys Maxwell environment. In order to determine the functional parameters of the motor, additional scripts in Visual Basic language were developed. Selected results of the optimization calculation are presented and compared with results for the particle swarm optimization algorithm.

Reflective thinking in solving an algebra problem: a case study of field independent-prospective teacher

NASA Astrophysics Data System (ADS)

Agustan, S.; Juniati, Dwi; Yuli Eko Siswono, Tatag

2017-10-01

Nowadays, reflective thinking is one of the important things which become a concern in learning mathematics, especially in solving a mathematical problem. The purpose of this paper is to describe how the student used reflective thinking when solved an algebra problem. The subject of this research is one female student who has field independent cognitive style. This research is a descriptive exploratory study with data analysis using qualitative approach to describe in depth reflective thinking of prospective teacher in solving an algebra problem. Four main categories are used to analyse the reflective thinking in solving an algebra problem: (1) formulation and synthesis of experience, (2) orderliness of experience, (3) evaluating the experience and (4) testing the selected solution based on the experience. The results showed that the subject described the problem by using another word and the subject also found the difficulties in making mathematical modelling. The subject analysed two concepts used in solving problem. For instance, geometry related to point and line while algebra is related to algebra arithmetic operation. The subject stated that solution must have four aspect to get effective solution, specifically the ability to (a) understand the meaning of every words; (b) make mathematical modelling; (c) calculate mathematically; (d) interpret solution obtained logically. To test the internal consistency or error in solution, the subject checked and looked back related procedures and operations used. Moreover, the subject tried to resolve the problem in a different way to compare the answers which had been obtained before. The findings supported the assertion that reflective thinking provides an opportunity for the students in improving their weakness in mathematical problem solving. It can make a grow accuracy and concentration in solving a mathematical problem. Consequently, the students will get the right and logic answer by reflective thinking.

Functional Concept of a Multipurpose Actuator: Design and Analysis

NASA Astrophysics Data System (ADS)

Krivka, Vladimir

2018-05-01

The principles of operation (dynamic characteristics) of electromagnetic devices are discussed using a threephase multifunctional actuator as an example, whose major limitations are associated with the magnetic field nonlinearity and control over the magnetic forces affecting the moving element. The investigation is carried out using the methods of physico-mathematical modeling and a full-scale experiment. A physico-mathematical model is proposed, which is based on acceptable approximations and simplifications, the replacement of a nonlinear (but periodic) magnetic field in a quasi-stationary state by a harmonic magnetic field being the most important among them. The magnetic permeability in every cell of the discretization grid is assumed to be constant and corresponds to the local magnetic flux density. The features and characteristics obtained through this modeling are quite consistent with the observed behavior and measured values. It is shown that the dependence of friction coefficient on its velocity exhibits a hysteresis.

Quantitative analysis of transverse bacterial migration induced by chemotaxis in a packed column with structured physical heterogeneity.

PubMed

Wang, Meng; Ford, Roseanne M

2010-01-15

A two-dimensional mathematical model was developed to simulate transport phenomena of chemotactic bacteria in a sand-packed column designed with structured physical heterogeneity in the presence of a localized chemical source. In contrast to mathematical models in previous research work, in which bacteria were typically treated as immobile colloids, this model incorporated a convective-like chemotaxis term to represent chemotactic migration. Consistency between experimental observation and model prediction supported the assertions that (1) dispersion-induced microbial transfer between adjacent conductive zones occurred at the interface and had little influence on bacterial transport in the bulk flow of the permeable layers and (2) the enhanced transverse bacterial migration in chemotactic experiments relative to nonchemotactic controls was mainly due to directed migration toward the chemical source zone. On the basis of parameter sensitivity analysis, chemotactic parameters determined in bulk aqueous fluid were adequate to predict the microbial transport in our intermediate-scale porous media system. Additionally, the analysis of adsorption coefficient values supported the observation of a previous study that microbial deposition to the surface of porous media might be decreased under the effect of chemoattractant gradients. By quantitatively describing bacterial transport and distribution in a heterogeneous system, this mathematical model serves to advance our understanding of chemotaxis and motility effects in granular media systems and provides insights for modeling microbial transport in in situ microbial processes.

The Effectiveness of Technology Integration in a Metropolitan Elementary Mathematics Program: Mad Dog Math

ERIC Educational Resources Information Center

Cohen, Miriam

2012-01-01

The outcome of American students' performances during international comparisons consistently scoring inadequately in mathematics exposes the crisis of deficient mathematics achievement thus causing deep concerns. Learners who acquire a strong theoretical foundation in mathematics at the primary level thrived later in more advanced level…

Do High Ability Students Have Mathematics Anxiety?

ERIC Educational Resources Information Center

Yeo, Kai Kow Joseph

2004-01-01

This exploratory study investigates the level of mathematics anxiety among 116 high ability Secondary Two students. These students were from the top 10% of the Secondary Two students in Singapore. Mathematics Anxiety was measured using the Fennema-Sherman Mathematics Anxiety Scale (MAS) (Fennema & Sherman, 1978) which consisted of twelve items…

On Pupils' Self-Confidence in Mathematics: Gender Comparisons

ERIC Educational Resources Information Center

Nurmi, Anu; Hannula, Markku; Maijala, Hanna; Pehkonen, Erkki

2003-01-01

In this paper we will concentrate on pupils' self-confidence in mathematics, which belongs to pupils' mathematical beliefs in themselves, and beliefs on achievement in mathematics. Research described consists of a survey of more than 3000 fifth-graders and seventh-graders. Furthermore, 40 pupils participated in a qualitative follow-up study…

Investigative Approaches to Teaching Mathematics and "Getting through the Curriculum": The Example of Pendulums

ERIC Educational Resources Information Center

Beswick, Kim; Muir, Tracey; Callingham, Rosemary

2014-01-01

The benefits of rich tasks, project-based learning, and other inquiry-based approaches in terms of student understanding and engagement with mathematics are well documented. Such pedagogies are consistent with the development of mathematical proficiencies as described in the "Australian Curriculum: Mathematics" (Australian Curriculum…

A MATLAB-Aided Method for Teaching Calculus-Based Business Mathematics

ERIC Educational Resources Information Center

Liang, Jiajuan; Pan, William S. Y.

2009-01-01

MATLAB is a powerful package for numerical computation. MATLAB contains a rich pool of mathematical functions and provides flexible plotting functions for illustrating mathematical solutions. The course of calculus-based business mathematics consists of two major topics: 1) derivative and its applications in business; and 2) integration and its…

Knowledge Concerning the Mathematical Horizon: A Close View

ERIC Educational Resources Information Center

Guberman, Raisa; Gorev, Dvora

2015-01-01

The main objective of this study is to identify components of teachers' mathematical knowledge for teaching, associated with the knowledge of mathematical horizon (KMH) in order to describe this type of knowledge from the viewpoint of elementary school mathematics teachers. The research population of this study consisted of 118 elementary school…

Improving Mathematics Teaching in Kindergarten with Realistic Mathematical Education

ERIC Educational Resources Information Center

Papadakis, Stamatios; Kalogiannakis, Michail; Zaranis, Nicholas

2017-01-01

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

Mathematics for Electronics.

ERIC Educational Resources Information Center

Clary, Joseph R.; Nery, Karen P.

This set of 20 modules was designed for use primarily to help teach and reinforce the basic mathematics skills in electronics classes. The modules are based on electronics competencies that require mathematics skills, as determined by a panel of high school electronics and mathematics teachers. Each module consists of one or two pages of basic…

Self-Regulation of Mathematics Homework Behavior: An Empirical Investigation

ERIC Educational Resources Information Center

Xu, Jianzhong; Du, Jianxia; Fan, Xitao

2017-01-01

The authors examined self-regulation of mathematics homework behavior (i.e., mathematics homework management). The participants consisted of 796 eighth-grade students (46 classes) in China. Multilevel results showed that mathematics homework management was positively associated with value belief at the class and individual level. At the individual…

A Scale for Measuring Teachers' Mathematics-Related Beliefs: A Validity and Reliability Study

ERIC Educational Resources Information Center

Purnomo,Yoppy Wahyu

2017-01-01

The purpose of this study was to develop and validate a scale of teacher beliefs related to mathematics, namely, beliefs about the nature of mathematics, mathematics teaching, and assessment in mathematics learning. A scale development study was used to achieve it. The draft scale consisted of 54 items in which 16 items related to beliefs about…

Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

ERIC Educational Resources Information Center

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

2014-01-01

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

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…

Hydrodynamic water impact. [Apollo spacecraft waterlanding

NASA Technical Reports Server (NTRS)

Kettleborough, C. F.

1972-01-01

The hydrodynamic impact of a falling body upon a viscous incompressible fluid was investigated by numerically solving the equations of motion. Initially the mathematical model simulated the axisymmetric impact of a rigid right circular cylinder upon the initially quiescent free surface of a fluid. A compressible air layer exists between the falling cylinder and the liquid free surface. The mathematical model was developed by applying the Navier-Stokes equations to the incompressible air layer and the incompressible fluid. Assuming the flow to be one dimensional within the air layer, the average velocity, pressure and density distributions were calculated. The liquid free surface was allowed to deform as the air pressure acting on it increases. For the liquid the normalized equations were expressed in two-dimensional cylindrical coordinates. The governing equations for the air layer and the liquid were expressed in finite difference form and solved numerically. For the liquid a modified version of the Marker-and-Cell method was used. The mathematical model has been reexamined and a new approach has recently been initiated. Essentially this consists of examining the impact of an inclined plate onto a quiesent water surface with the equations now formulated in cartesian coordinates.

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…

Design-Tradeoff Model For Space Station

NASA Technical Reports Server (NTRS)

Chamberlain, Robert G.; Smith, Jeffrey L.; Borden, Chester S.; Deshpande, Govind K.; Fox, George; Duquette, William H.; Dilullo, Larry A.; Seeley, Larry; Shishko, Robert

1990-01-01

System Design Tradeoff Model (SDTM) computer program produces information which helps to enforce consistency of design objectives throughout system. Mathematical model of set of possible designs for Space Station Freedom. Program finds particular design enabling station to provide specified amounts of resources to users at lowest total (or life-cycle) cost. Compares alternative design concepts by changing set of possible designs, while holding specified services to users constant, and then comparing costs. Finally, both costs and services varied simultaneously when comparing different designs. Written in Turbo C 2.0.

Mathematical Modelling Approach in Mathematics Education

ERIC Educational Resources Information Center

Arseven, Ayla

2015-01-01

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

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…

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.

Flight and wind-tunnel calibrations of a flush airdata sensor at high angles of attack and sideslip and at supersonic Mach numbers

NASA Technical Reports Server (NTRS)

Moes, Timothy R.; Whitmore, Stephen A.; Jordan, Frank L., Jr.

1993-01-01

A nonintrusive airdata-sensing system was calibrated in flight and wind-tunnel experiments to an angle of attack of 70 deg and to angles of sideslip of +/- 15 deg. Flight-calibration data have also been obtained to Mach 1.2. The sensor, known as the flush airdata sensor, was installed on the nosecap of an F-18 aircraft for flight tests and on a full-scale F-18 forebody for wind-tunnel tests. Flight tests occurred at the NASA Dryden Flight Research Facility, Edwards, California, using the F-18 High Alpha Research Vehicle. Wind-tunnel tests were conducted in the 30- by 60-ft wind tunnel at the NASA LaRC, Hampton, Virginia. The sensor consisted of 23 flush-mounted pressure ports arranged in concentric circles and located within 1.75 in. of the tip of the nosecap. An overdetermined mathematical model was used to relate the pressure measurements to the local airdata quantities. The mathematical model was based on potential flow over a sphere and was empirically adjusted based on flight and wind-tunnel data. For quasi-steady maneuvering, the mathematical model worked well throughout the subsonic, transonic, and low supersonic flight regimes. The model also worked well throughout the angle-of-attack and sideslip regions studied.

Flight and wind-tunnel calibrations of a flush airdata sensor at high angles of attack and sideslip and at supersonic Mach numbers

NASA Technical Reports Server (NTRS)

Moes, Timothy R.; Whitmore, Stephen A.; Jordan, Frank L., Jr.

1993-01-01

A nonintrusive airdata-sensing system was calibrated in flight and wind-tunnel experiments to an angle of attack of 70 deg and to angles of sideslip of +/- 15 deg. Flight-calibration data have also been obtained to Mach 1.2. The sensor, known as the flush airdata sensor, was installed on the nosecap of an F-18 aircraft for flight tests and on a full-scale F-18 forebody for wind-tunnel tests. Flight tests occurred at the NASA Dryden Flight Research Facility, Edwards, California, using the F-18 High Alpha Research Vehicle. Wind-tunnel tests were conducted in the 30- by 60-ft wind tunnel at the NASA LaRC, Hampton, Virginia. The sensor consisted of 23 flush-mounted pressure ports arranged in concentric circles and located within 1.75 in. of the tip of the nosecap. An overdetermined mathematical model was used to relate the pressure measurements to the local airdata quantities. The mathematical model was based on potential flow over a sphere and was empirically adjusted based on flight and wind-tunnel data. For quasi-steady maneuvering, the mathematical model worked well throughout the subsonic, transonic, and low supersonic flight regimes. The model also worked well throughout the angles-of-attack and -sideslip regions studied.

[Chest modelling and automotive accidents].

PubMed

Trosseille, Xavier

2011-11-01

Automobile development is increasingly based on mathematical modeling. Accurate models of the human body are now available and serve to develop new means of protection. These models used to consist of rigid, articulated bodies but are now made of several million finite elements. They are now capable of predicting some risks of injury. To develop these models, sophisticated tests were conducted on human cadavers. For example, chest modeling started with material characterization and led to complete validation in the automobile environment. Model personalization, based on medical imaging, will permit studies of the behavior and tolerances of the entire population.

A Multiple Items EPQ/EOQ Model for a Vendor and Multiple Buyers System with Considering Continuous and Discrete Demand Simultaneously

NASA Astrophysics Data System (ADS)

Jonrinaldi; Rahman, T.; Henmaidi; Wirdianto, E.; Zhang, D. Z.

2018-03-01

This paper proposed a mathematical model for multiple items Economic Production and Order Quantity (EPQ/EOQ) with considering continuous and discrete demand simultaneously in a system consisting of a vendor and multiple buyers. This model is used to investigate the optimal production lot size of the vendor and the number of shipments policy of orders to multiple buyers. The model considers the multiple buyers’ holding cost as well as transportation cost, which minimize the total production and inventory costs of the system. The continuous demand from any other customers can be fulfilled anytime by the vendor while the discrete demand from multiple buyers can be fulfilled by the vendor using the multiple delivery policy with a number of shipments of items in the production cycle time. A mathematical model is developed to illustrate the system based on EPQ and EOQ model. Solution procedures are proposed to solve the model using a Mixed Integer Non Linear Programming (MINLP) and algorithm methods. Then, the numerical example is provided to illustrate the system and results are discussed.

Modeling of the Competitive Growth of Listeria monocytogenes and Lactococcus lactis in Vegetable Broth

PubMed Central

Breidt, Frederick; Fleming, Henry P.

1998-01-01

Current mathematical models used by food microbiologists do not address the issue of competitive growth in mixed cultures of bacteria. We developed a mathematical model which consists of a system of nonlinear differential equations describing the growth of competing bacterial cell cultures. In this model, bacterial cell growth is limited by the accumulation of protonated lactic acid and decreasing pH. In our experimental system, pure and mixed cultures of Lactococcus lactis and Listeria monocytogenes were grown in a vegetable broth medium. Predictions of the model indicate that pH is the primary factor that limits the growth of L. monocytogenes in competition with a strain of L. lactis which does not produce the bacteriocin nisin. The model also predicts the values of parameters that affect the growth and death of the competing populations. Further development of this model will incorporate the effects of additional inhibitors, such as bacteriocins, and may aid in the selection of lactic acid bacterium cultures for use in competitive inhibition of pathogens in minimally processed foods. PMID:9726854

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 like to thank the members of the International Scientific Committee and the members of the Organizing Committee. Conference Chairmen Theocharis Kosmas Department of Physics, University of Ioannina Elias Vagenas RCAAM, Academy of Athens Dimitrios Vlachos Department of Computer Science and Technology, University of Peloponnese The PDF also contains a list of members of the International Scientific Committes and details of the Keynote and Invited Speakers.

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…

Age-dependent Fourier model of the shape of the isolated ex vivo human crystalline lens.

PubMed

Urs, Raksha; Ho, Arthur; Manns, Fabrice; Parel, Jean-Marie

2010-06-01

To develop an age-dependent mathematical model of the zero-order shape of the isolated ex vivo human crystalline lens, using one mathematical function, that can be subsequently used to facilitate the development of other models for specific purposes such as optical modeling and analytical and numerical modeling of the lens. Profiles of whole isolated human lenses (n=30) aged 20-69, were measured from shadow-photogrammetric images. The profiles were fit to a 10th-order Fourier series consisting of cosine functions in polar-co-ordinate system that included terms for tilt and decentration. The profiles were corrected using these terms and processed in two ways. In the first, each lens was fit to a 10th-order Fourier series to obtain thickness and diameter, while in the second, all lenses were simultaneously fit to a Fourier series equation that explicitly include linear terms for age to develop an age-dependent mathematical model for the whole lens shape. Thickness and diameter obtained from Fourier series fits exhibited high correlation with manual measurements made from shadow-photogrammetric images. The root-mean-squared-error of the age-dependent fit was 205 microm. The age-dependent equations provide a reliable lens model for ages 20-60 years. The contour of the whole human crystalline lens can be modeled with a Fourier series. Shape obtained from the age-dependent model described in this paper can be used to facilitate the development of other models for specific purposes such as optical modeling and analytical and numerical modeling of the lens. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

DigitalHuman (DH): An Integrative Mathematical Model ofHuman Physiology

NASA Technical Reports Server (NTRS)

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

2010-01-01

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

An Earth Albedo Model: A Mathematical Model for the Radiant Energy Input to an Orbiting Spacecraft Due to the Diffuse Reflectance of Solar Radiation from the Earth Below

NASA Technical Reports Server (NTRS)

Flatley, Thomas W.; Moore, Wendy A.

1994-01-01

Past missions have shown that the earth's albedo can have a significant effect on the sun sensors used for spacecraft attitude control information. In response to this concern, an algorithm was developed to simulate this phenomenon, consisting of two parts, the physical model of albedo and its effect on the sun sensors. This paper contains the theoretical development of this model, practical operational notes, and its implementation in a FORTRAN subroutine.

Galactic chemical evolution and nucleocosmochronology - Standard model with terminated infall

NASA Technical Reports Server (NTRS)

Clayton, D. D.

1984-01-01

Some exactly soluble families of models for the chemical evolution of the Galaxy are presented. The parameters considered include gas mass, the age-metallicity relation, the star mass vs. metallicity, the age distribution, and the mean age of dwarfs. A short BASIC program for calculating these parameters is given. The calculation of metallicity gradients, nuclear cosmochronology, and extinct radioactivities is addressed. An especially simple, mathematically linear model is recommended as a standard model of galaxies with truncated infall due to its internal consistency and compact display of the physical effects of the parameters.

Metaphor Perceptions of Pre-Service Teachers towards Mathematics and Mathematics Education in Preschool Education

ERIC Educational Resources Information Center

Keles, Oguz; Tas, Isil; Aslan, Durmus

2016-01-01

The aim of this study was to identify the thoughts of pre-service teachers, who play an important role in the early preschool experience of children in mathematics, towards the concepts of mathematics and education of mathematics with the help of metaphors. The study group of the research consists of a total of 227 pre-service teachers at the…

Mathematics and Economics: Connections for Life, 9-12.

ERIC Educational Resources Information Center

MacDonald, Rich; Breidenbach, Lisa; Doetschman, Evelyn L.

Bringing mathematics and economics together to connect them in students' minds gives students very important skills they can use in their lives. This book is intended for high school mathematics teachers, with lessons designed to reinforce the mathematics concepts and processes taught by using examples from economics. The book consists of 15…

The Origins of Liberal Arts Mathematics

ERIC Educational Resources Information Center

George, Michael

2010-01-01

"Liberal arts mathematics" differs from traditional mathematics courses in that it consists of a disparate collection of topics, rather than being organized around a single mathematical subject. As a result, the educational rationale for and purpose of the course may be vague both to instructors and students. The purpose of this study is to…

Mathematics Education in Lebanon: Gender Differences in Attitudes and Achievement

ERIC Educational Resources Information Center

Sarouphim, Ketty M.; Chartouny, Madona

2017-01-01

The purpose of this study was to investigate gender differences in students' mathematics achievement and in their attitudes toward mathematics. Another purpose was to examine mathematics teachers' beliefs and their perceptions of their male and female students' ability. The sample consisted of 692 students (353 girls, 339 boys) between the ages of…

First-Year Students' Beliefs about Context Problems in Mathematics in University Science Programmes

ERIC Educational Resources Information Center

Drobnic Vidic, Andreja

2015-01-01

Mathematics-related beliefs play an important role in the willingness to engage in academic activities in mathematics education. Such beliefs might not be consistent with the beliefs students hold about context problems that require sufficient mathematical knowledge and the application of such knowledge to various real-life situations. This study…

Consistent three-equation model for thin films

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

[Forced Oscillations of DNA Bases].

PubMed

Yakushevich, L V; Krasnobaeva, L A

2016-01-01

This paper presents the results of the studying of forced angular oscillations of the DNA bases with the help of the mathematical model consisting of two coupled nonlinear differential equations that take into account the effects of dissipation and the influence of an external periodic field. The calculation results are illustrated for sequence of gene encoding interferon alpha 17 (IFNA 17).

Predicting Statistical Response and Extreme Events in Uncertainty Quantification through Reduced-Order Models

NASA Astrophysics Data System (ADS)

Qi, D.; Majda, A.

2017-12-01

A low-dimensional reduced-order statistical closure model is developed for quantifying the uncertainty in statistical sensitivity and intermittency in principal model directions with largest variability in high-dimensional turbulent system and turbulent transport models. Imperfect model sensitivity is improved through a recent mathematical strategy for calibrating model errors in a training phase, where information theory and linear statistical response theory are combined in a systematic fashion to achieve the optimal model performance. The idea in the reduced-order method is from a self-consistent mathematical framework for general systems with quadratic nonlinearity, where crucial high-order statistics are approximated by a systematic model calibration procedure. Model efficiency is improved through additional damping and noise corrections to replace the expensive energy-conserving nonlinear interactions. Model errors due to the imperfect nonlinear approximation are corrected by tuning the model parameters using linear response theory with an information metric in a training phase before prediction. A statistical energy principle is adopted to introduce a global scaling factor in characterizing the higher-order moments in a consistent way to improve model sensitivity. Stringent models of barotropic and baroclinic turbulence are used to display the feasibility of the reduced-order methods. Principal statistical responses in mean and variance can be captured by the reduced-order models with accuracy and efficiency. Besides, the reduced-order models are also used to capture crucial passive tracer field that is advected by the baroclinic turbulent flow. It is demonstrated that crucial principal statistical quantities like the tracer spectrum and fat-tails in the tracer probability density functions in the most important large scales can be captured efficiently with accuracy using the reduced-order tracer model in various dynamical regimes of the flow field with distinct statistical structures.

Analysis of the impact of trap-neuter-return programs on populations of feral cats.

PubMed

Foley, Patrick; Foley, Janet E; Levy, Julie K; Paik, Terry

2005-12-01

To evaluate 2 county trap-neuter-return (TNR) programs for feral cat population management via mathematical modeling. Theoretical population model. Feral cats assessed from 1992 to 2003 in San Diego County, California (n = 14,452), and from 1998 to 2004 in Alachua County, Florida (11,822). Data were analyzed with a mathematical Ricker model to describe population dynamics of the feral cats and modifications to the dynamics that occurred as a result of the TNR programs. In both counties, results of analyses did not indicate a consistent reduction in per capita growth, the population multiplier, or the proportion of female cats that were pregnant. Success of feral cat management programs that use TNR can be monitored with an easily collected set of data and statistical analyses facilitated by population modeling techniques. Results may be used to suggest possible future monitoring and modification of TNR programs, which could result in greater success controlling and reducing feral cat populations.

A mathematical model for foreign body reactions in 2D.

PubMed

Su, Jianzhong; Gonzales, Humberto Perez; Todorov, Michail; Kojouharov, Hristo; Tang, Liping

2011-02-01

The foreign body reactions are commonly referred to the network of immune and inflammatory reactions of human or animals to foreign objects placed in tissues. They are basic biological processes, and are also highly relevant to bioengineering applications in implants, as fibrotic tissue formations surrounding medical implants have been found to substantially reduce the effectiveness of devices. Despite of intensive research on determining the mechanisms governing such complex responses, few mechanistic mathematical models have been developed to study such foreign body reactions. This study focuses on a kinetics-based predictive tool in order to analyze outcomes of multiple interactive complex reactions of various cells/proteins and biochemical processes and to understand transient behavior during the entire period (up to several months). A computational model in two spatial dimensions is constructed to investigate the time dynamics as well as spatial variation of foreign body reaction kinetics. The simulation results have been consistent with experimental data and the model can facilitate quantitative insights for study of foreign body reaction process in general.

Shoreline as a controlling factor in commercial shrimp production

NASA Technical Reports Server (NTRS)

Faller, K. H. (Principal Investigator)

1978-01-01

An ecological model was developed that relates marsh detritus export and shrimp production, based on the hypothesis that the shoreline is a controlling factor in the production of shrimp through regulation of detritus export from the marsh. LANDSAT data were used to develop measurements of shoreline length and area of marsh having more than 5.0 km shoreline/sq km for the coast of Louisiana, demonstrating the capability of remote sensing to provide important geographic information. These factors were combined with published tidal ranges and salinities to develop a mathematical model that predicted shrimp production for nine geographic units of the Louisiana coast, as indicated by the long term average commercial shrimp yield. The mathematical model relating these parameters and the shrimp production is consistent with an energy flow model describing the interaction of detritus producing marshlands with shrimp nursery grounds and inshore shrimping areas. The analysis supports the basic hypothesis and further raises the possibility of applications to coastal zone management requirements.

Monte Carlo Modeling-Based Digital Loop-Mediated Isothermal Amplification on a Spiral Chip for Absolute Quantification of Nucleic Acids.

PubMed

Xia, Yun; Yan, Shuangqian; Zhang, Xian; Ma, Peng; Du, Wei; Feng, Xiaojun; Liu, Bi-Feng

2017-03-21

Digital loop-mediated isothermal amplification (dLAMP) is an attractive approach for absolute quantification of nucleic acids with high sensitivity and selectivity. Theoretical and numerical analysis of dLAMP provides necessary guidance for the design and analysis of dLAMP devices. In this work, a mathematical model was proposed on the basis of the Monte Carlo method and the theories of Poisson statistics and chemometrics. To examine the established model, we fabricated a spiral chip with 1200 uniform and discrete reaction chambers (9.6 nL) for absolute quantification of pathogenic DNA samples by dLAMP. Under the optimized conditions, dLAMP analysis on the spiral chip realized quantification of nucleic acids spanning over 4 orders of magnitude in concentration with sensitivity as low as 8.7 × 10 -2 copies/μL in 40 min. The experimental results were consistent with the proposed mathematical model, which could provide useful guideline for future development of dLAMP devices.

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…

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

ERIC Educational Resources Information Center

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

2016-01-01

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

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

Du, Qiang

The rational design of materials, the development of accurate and efficient material simulation algorithms, and the determination of the response of materials to environments and loads occurring in practice all require an understanding of mechanics at disparate spatial and temporal scales. The project addresses mathematical and numerical analyses for material problems for which relevant scales range from those usually treated by molecular dynamics all the way up to those most often treated by classical elasticity. The prevalent approach towards developing a multiscale material model couples two or more well known models, e.g., molecular dynamics and classical elasticity, each of whichmore » is useful at a different scale, creating a multiscale multi-model. However, the challenges behind such a coupling are formidable and largely arise because the atomistic and continuum models employ nonlocal and local models of force, respectively. The project focuses on a multiscale analysis of the peridynamics materials model. Peridynamics can be used as a transition between molecular dynamics and classical elasticity so that the difficulties encountered when directly coupling those two models are mitigated. In addition, in some situations, peridynamics can be used all by itself as a material model that accurately and efficiently captures the behavior of materials over a wide range of spatial and temporal scales. Peridynamics is well suited to these purposes because it employs a nonlocal model of force, analogous to that of molecular dynamics; furthermore, at sufficiently large length scales and assuming smooth deformation, peridynamics can be approximated by classical elasticity. The project will extend the emerging mathematical and numerical analysis of peridynamics. One goal is to develop a peridynamics-enabled multiscale multi-model that potentially provides a new and more extensive mathematical basis for coupling classical elasticity and molecular dynamics, thus enabling next generation atomistic-to-continuum multiscale simulations. In addition, a rigorous studyof nite element discretizations of peridynamics will be considered. Using the fact that peridynamics is spatially derivative free, we will also characterize the space of admissible peridynamic solutions and carry out systematic analyses of the models, in particular rigorously showing how peridynamics encompasses fracture and other failure phenomena. Additional aspects of the project include the mathematical and numerical analysis of peridynamics applied to stochastic peridynamics models. In summary, the project will make feasible mathematically consistent multiscale models for the analysis and design of advanced materials.« less

A mathematical model for the effects of radiation to the induced cancer in mice

NASA Astrophysics Data System (ADS)

Wada, Takahiro; Manabe, Yuichiro; Bando, Masako

We have been studying biological effects of radiation in terms of mathematical models. There are two main objects that we need to study: mutation and cancer. We proposed the Whack-A-Mole (WAM) model which takes account of the repair effects to study radiation induced mutations. We applied it to the mutation of several species including Drosophila and mice, and succeeded to reproduce the dose and dose-rate dependence of the mutation rates. Here, as a next step, we study the effects of low dose-rate radiation to an induced cancer in mice. In the experiment, they divided their mice in four groups and kept them under constant gamma-ray radiations with different dose rate for each group since the birth. On the 35th day, chemical carcinogen was given to each mouse and they observed the occurrence and the growth of cancer for one year. Our mathematical model consists of two stages. The first stage describes a multiple-step carcinogenesis and the second stage describes its growth. We assume that the carcinogenesis starts with the chemical carcinogen and that the rate of the following processes depends on the dose rate as it does in the WAM model. We found some irregularities in the data, however, the overall fit is satisfactory. This work was supported by JSPS KAKENHI Grant Number JP16H04637.

Which preparatory curriculum for the International Baccalaureate Diploma Programme is best? The challenge for international schools with regard to mathematics and science

NASA Astrophysics Data System (ADS)

Corlu, M. Sencer

2014-12-01

There are two mainstream curricula for international school students at the junior high level: the International Baccalaureate (IB) Middle Years Programme (MYP) and the Cambridge International General Certificate of Secondary Education (IGCSE). The former was developed in the mid-1990s and is currently being relaunched in a 21st-century approach. The latter programme of study was developed by University of Cambridge International Examinations in 1985 and has become popular in recent years among British domestic and international schools worldwide due to the clarity of its learning content. The prevailing uncertainty about which curriculum is best to prepare students for the IB Diploma Programme represents a challenge for international schools. The purpose of the current study is to develop a methodology through causal models which can explain the relationship between student performance in the IGCSE and the Diploma Programme with regard to mathematics and science. The data evaluated here consisted of external examination scores of students who attended a private international high school between the years 2005 and 2012. Two structural equation models were developed. The first model employed a maximum likelihood estimation, while the second model used a Bayesian estimation with a Markov Chain Monte Carlo method. Both models fit the data well. The evidence suggests that the IGCSE provides a good foundational preparation for the Diploma Programme in mathematics and science.

A mathematical model of the passage of an asteroid-comet body through the Earth’s atmosphere

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

Shaydurov, V., E-mail: shaidurov04@mail.ru; Siberian Federal University, 79 Svobodny pr., 660041 Krasnoyarsk; Shchepanovskaya, G.

In the paper, a mathematical model and a numerical algorithm are proposed for modeling the complex of phenomena which accompany the passage of a friable asteroid-comet body through the Earth’s atmosphere: the material ablation, the dissociation of molecules, and the radiation. The proposed model is constructed on the basis of the Navier-Stokes equations for viscous heat-conducting gas with an additional equation for the motion and propagation of a friable lumpy-dust material in air. The energy equation is modified for the relation between two its kinds: the usual energy of the translation of molecules (which defines the temperature and pressure) andmore » the combined energy of their rotation, oscillation, electronic excitation, dissociation, and radiation. For the mathematical model of atmosphere, the distribution of density, pressure, and temperature in height is taken as for the standard atmosphere. An asteroid-comet body is taken initially as a round body consisting of a friable lumpy-dust material with corresponding density and significant viscosity which far exceed those for the atmosphere gas. A numerical algorithm is proposed for solving the initial-boundary problem for the extended system of Navier-Stokes equations. The algorithm is the combination of the semi-Lagrangian approximation for Lagrange transport derivatives and the conforming finite element method for other terms. The implementation of these approaches is illustrated by a numerical example.« less

Physical consistency of subgrid-scale models for large-eddy simulation of incompressible turbulent flows

NASA Astrophysics Data System (ADS)

Silvis, Maurits H.; Remmerswaal, Ronald A.; Verstappen, Roel

2017-01-01

We study the construction of subgrid-scale models for large-eddy simulation of incompressible turbulent flows. In particular, we aim to consolidate a systematic approach of constructing subgrid-scale models, based on the idea that it is desirable that subgrid-scale models are consistent with the mathematical and physical properties of the Navier-Stokes equations and the turbulent stresses. To that end, we first discuss in detail the symmetries of the Navier-Stokes equations, and the near-wall scaling behavior, realizability and dissipation properties of the turbulent stresses. We furthermore summarize the requirements that subgrid-scale models have to satisfy in order to preserve these important mathematical and physical properties. In this fashion, a framework of model constraints arises that we apply to analyze the behavior of a number of existing subgrid-scale models that are based on the local velocity gradient. We show that these subgrid-scale models do not satisfy all the desired properties, after which we explain that this is partly due to incompatibilities between model constraints and limitations of velocity-gradient-based subgrid-scale models. However, we also reason that the current framework shows that there is room for improvement in the properties and, hence, the behavior of existing subgrid-scale models. We furthermore show how compatible model constraints can be combined to construct new subgrid-scale models that have desirable properties built into them. We provide a few examples of such new models, of which a new model of eddy viscosity type, that is based on the vortex stretching magnitude, is successfully tested in large-eddy simulations of decaying homogeneous isotropic turbulence and turbulent plane-channel flow.

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…

Interplay of Determinism and Randomness: From Irreversibility to Chaos, Fractals, and Stochasticity

NASA Astrophysics Data System (ADS)

Tsonis, A.

2017-12-01

We will start our discussion into randomness by looking exclusively at our formal mathematical system to show that even in this pure and strictly logical system one cannot do away with randomness. By employing simple mathematical models, we will identify the three possible sources of randomness: randomness due to inability to find the rules (irreversibility), randomness due to inability to have infinite power (chaos), and randomness due to stochastic processes. Subsequently we will move from the mathematical system to our physical world to show that randomness, through the quantum mechanical character of small scales, through chaos, and because of the second law of thermodynamics, is an intrinsic property of nature as well. We will subsequently argue that the randomness in the physical world is consistent with the three sources of randomness suggested from the study of simple mathematical systems. Many examples ranging from purely mathematical to natural processes will be presented, which clearly demonstrate how the combination of rules and randomness produces the world we live in. Finally, the principle of least effort or the principle of minimum energy consumption will be suggested as the underlying principle behind this symbiosis between determinism and randomness.

Topologically Consistent Models for Efficient Big Geo-Spatio Data Distribution

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

A mathematical framework for modelling cambial surface evolution using a level set method

PubMed Central

Sellier, Damien; Plank, Michael J.; Harrington, Jonathan J.

2011-01-01

Background and Aims During their lifetime, tree stems take a series of successive nested shapes. Individual tree growth models traditionally focus on apical growth and architecture. However, cambial growth, which is distributed over a surface layer wrapping the whole organism, equally contributes to plant form and function. This study aims at providing a framework to simulate how organism shape evolves as a result of a secondary growth process that occurs at the cellular scale. Methods The development of the vascular cambium is modelled as an expanding surface using the level set method. The surface consists of multiple compartments following distinct expansion rules. Growth behaviour can be formulated as a mathematical function of surface state variables and independent variables to describe biological processes. Key Results The model was coupled to an architectural model and to a forest stand model to simulate cambium dynamics and wood formation at the scale of the organism. The model is able to simulate competition between cambia, surface irregularities and local features. Predicting the shapes associated with arbitrarily complex growth functions does not add complexity to the numerical method itself. Conclusions Despite their slenderness, it is sometimes useful to conceive of trees as expanding surfaces. The proposed mathematical framework provides a way to integrate through time and space the biological and physical mechanisms underlying cambium activity. It can be used either to test growth hypotheses or to generate detailed maps of wood internal structure. PMID:21470972

Development of dynamic Bayesian models for web application test management

NASA Astrophysics Data System (ADS)

Azarnova, T. V.; Polukhin, P. V.; Bondarenko, Yu V.; Kashirina, I. L.

2018-03-01

The mathematical apparatus of dynamic Bayesian networks is an effective and technically proven tool that can be used to model complex stochastic dynamic processes. According to the results of the research, mathematical models and methods of dynamic Bayesian networks provide a high coverage of stochastic tasks associated with error testing in multiuser software products operated in a dynamically changing environment. Formalized representation of the discrete test process as a dynamic Bayesian model allows us to organize the logical connection between individual test assets for multiple time slices. This approach gives an opportunity to present testing as a discrete process with set structural components responsible for the generation of test assets. Dynamic Bayesian network-based models allow us to combine in one management area individual units and testing components with different functionalities and a direct influence on each other in the process of comprehensive testing of various groups of computer bugs. The application of the proposed models provides an opportunity to use a consistent approach to formalize test principles and procedures, methods used to treat situational error signs, and methods used to produce analytical conclusions based on test results.

Modeling compressible multiphase flows with dispersed particles in both dense and dilute regimes

NASA Astrophysics Data System (ADS)

McGrath, T.; St. Clair, J.; Balachandar, S.

2018-05-01

Many important explosives and energetics applications involve multiphase formulations employing dispersed particles. While considerable progress has been made toward developing mathematical models and computational methodologies for these flows, significant challenges remain. In this work, we apply a mathematical model for compressible multiphase flows with dispersed particles to existing shock and explosive dispersal problems from the literature. The model is cast in an Eulerian framework, treats all phases as compressible, is hyperbolic, and satisfies the second law of thermodynamics. It directly applies the continuous-phase pressure gradient as a forcing function for particle acceleration and thereby retains relaxed characteristics for the dispersed particle phase that remove the constituent material sound velocity from the eigenvalues. This is consistent with the expected characteristics of dispersed particle phases and can significantly improve the stable time-step size for explicit methods. The model is applied to test cases involving the shock and explosive dispersal of solid particles and compared to data from the literature. Computed results compare well with experimental measurements, providing confidence in the model and computational methods applied.

Analysis of satellite multibeam antennas’ performances

NASA Astrophysics Data System (ADS)

Sterbini, Guido

2006-07-01

In this work, we discuss the application of frequency reuse's concept in satellite communications, stressing the importance for a design-oriented mathematical model as first step for dimensioning antenna systems. We consider multibeam reflector antennas. The first part of the work consists in reorganizing, making uniform and completing the models already developed in the scientific literature. In doing it, we adopt the multidimensional Taylor development formalism. For computing the spillover efficiency of the antenna, we consider different feed's illuminations and we propose a completely original mathematical model, obtained by the interpolation of simulator results. The second part of the work is dedicated to characterize the secondary far field pattern. Combining this model together with the information on the cellular coverage geometry is possible to evaluate the isolation and the minimum directivity on the cell. As third part, in order to test the model and its analysis and synthesis capabilities, we implement a software tool that helps the designer in the rapid tuning of the fundamental quantities for the optimization of the performance: the proposed model shows an optimum agreement with the results of the simulations.

Using Mathematical Transmission Modelling to Investigate Drivers of Respiratory Syncytial Virus Seasonality in Children in the Philippines

PubMed Central

Paynter, Stuart; Yakob, Laith; Simões, Eric A. F.; Lucero, Marilla G.; Tallo, Veronica; Nohynek, Hanna; Ware, Robert S.; Weinstein, Philip; Williams, Gail; Sly, Peter D.

2014-01-01

We used a mathematical transmission model to estimate when ecological drivers of respiratory syncytial virus (RSV) transmissibility would need to act in order to produce the observed seasonality of RSV in the Philippines. We estimated that a seasonal peak in transmissibility would need to occur approximately 51 days prior to the observed peak in RSV cases (range 49 to 67 days). We then compared this estimated seasonal pattern of transmissibility to the seasonal patterns of possible ecological drivers of transmissibility: rainfall, humidity and temperature patterns, nutritional status, and school holidays. The timing of the seasonal patterns of nutritional status and rainfall were both consistent with the estimated seasonal pattern of transmissibility and these are both plausible drivers of the seasonality of RSV in this setting. PMID:24587222

Optimal back-extrapolation method for estimating plasma volume in humans using the indocyanine green dilution method.

PubMed

Polidori, David; Rowley, Clarence

2014-07-22

The indocyanine green dilution method is one of the methods available to estimate plasma volume, although some researchers have questioned the accuracy of this method. We developed a new, physiologically based mathematical model of indocyanine green kinetics that more accurately represents indocyanine green kinetics during the first few minutes postinjection than what is assumed when using the traditional mono-exponential back-extrapolation method. The mathematical model is used to develop an optimal back-extrapolation method for estimating plasma volume based on simulated indocyanine green kinetics obtained from the physiological model. Results from a clinical study using the indocyanine green dilution method in 36 subjects with type 2 diabetes indicate that the estimated plasma volumes are considerably lower when using the traditional back-extrapolation method than when using the proposed back-extrapolation method (mean (standard deviation) plasma volume = 26.8 (5.4) mL/kg for the traditional method vs 35.1 (7.0) mL/kg for the proposed method). The results obtained using the proposed method are more consistent with previously reported plasma volume values. Based on the more physiological representation of indocyanine green kinetics and greater consistency with previously reported plasma volume values, the new back-extrapolation method is proposed for use when estimating plasma volume using the indocyanine green dilution method.

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…

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…

Student’s rigorous mathematical thinking based on cognitive style

NASA Astrophysics Data System (ADS)

Fitriyani, H.; Khasanah, U.

2017-12-01

The purpose of this research was to determine the rigorous mathematical thinking (RMT) of mathematics education students in solving math problems in terms of reflective and impulsive cognitive styles. The research used descriptive qualitative approach. Subjects in this research were 4 students of the reflective and impulsive cognitive style which was each consisting male and female subjects. Data collection techniques used problem-solving test and interview. Analysis of research data used Miles and Huberman model that was reduction of data, presentation of data, and conclusion. The results showed that impulsive male subjects used three levels of the cognitive function required for RMT that were qualitative thinking, quantitative thinking with precision, and relational thinking completely while the other three subjects were only able to use cognitive function at qualitative thinking level of RMT. Therefore the subject of impulsive male has a better RMT ability than the other three research subjects.

Reflective Modeling in Teacher Education.

ERIC Educational Resources Information Center

Shealy, Barry E.

This paper describes mathematical modeling activities from a secondary mathematics teacher education course taken by fourth-year university students. Experiences with mathematical modeling are viewed as important in helping teachers develop a more intuitive understanding of mathematics, generate and evaluate mathematical interpretations, and…

Business Mathematics Curriculum.

ERIC Educational Resources Information Center

EASTCONN Regional Educational Services Center, North Windham, CT.

This curriculum guide for teaching business mathematics in the Connecticut Vocational-Technical School System is based on the latest thinking of instructors in the field, suggestions from mathematics authorities, and current instructional approaches in education. The curriculum guide consists of six sections: (1) career relationships and…

The Effect of Video-Based Approach on Prospective Teachers' Ability to Analyze Mathematics Teaching

ERIC Educational Resources Information Center

Alsawaie, Othman N.; Alghazo, Iman M.

2010-01-01

This is an intervention study that explored the effect of using video lesson analysis methodology (VLAM) on the ability of prospective middle/high school mathematics teachers to analyze mathematics teaching. The sample of the study consisted of 26 female prospective mathematics teachers enrolled in a methods course at the United Arab Emirates…

Which Advanced Mathematics Courses Influence ACT Score? A State Level Analysis of the Iowa Class of 2012

ERIC Educational Resources Information Center

Grinstead, Mary L.

2013-01-01

This study explores the relationship between specific advanced mathematics courses and college readiness (as determined by ACT score). The ACT organization has found a consistent relationship between taking a minimum core number of mathematics courses and higher ACT scores (mathematics and composite) (ACT, Inc., 2012c). However, the extent to…

When Mathematics Works in Black: A Case Study of Effective Mathematics Instruction for African American Children

ERIC Educational Resources Information Center

Hakim, Khalel

2014-01-01

The purpose of this study was to describe and explain the 5th grade mathematics teaching practice of an African American female teacher in a predominantly African American classroom that consistently meets and/or exceeds Michigan's mathematics proficiency standards. Using multiple emancipatory lenses, and a single case study method that employed…

Structure and Typical Profiles of Elementary Teacher Students' View of Mathematics

ERIC Educational Resources Information Center

Hannula, Markku S.; Kaasila, Raimo; Laine, Anu; Pehkonen, Erkki

2005-01-01

The elementary school teachers' view of mathematics is important because it will influence the way they will teach mathematics. Based on a survey study in three Finnish universities we explored the structure of student teachers view of mathematics and also the different belief profiles that they had. The core of student teachers' view consisted of…

The Effect of the Success in Teaching Geometry of Basic Level Education Mathematics

ERIC Educational Resources Information Center

Yavuz, Ayse; Aydin, Bünyamin; Avci, Musa

2016-01-01

The purpose of this study was to investigate primary and secondary mathematics teachers' candidates' effect of the success in geometry education. The sample of the study consists of students first and last class preservice primary mathematics teachers which are enrolled program education at department of mathematics and students first and last…

A COMPARISON OF MATHEMATICS PROGRAMS FOR ABLE JUNIOR HIGH SCHOOL STUDENTS, VOLUME 1 - FINAL REPORT.

ERIC Educational Resources Information Center

GOLDBERG, MIRIAM L.; AND OTHERS

THE TALENTED YOUTH PROJECT (TYP) MATHEMATICS STUDY WAS DESIGNED AS A STUDY TO COMPARE THE EFFECTIVENESS OF VARIOUS CURRICULUM PATTERNS AND PRACTICES IN MATHEMATICS EDUCATION CURRENTLY USED WITH ACADEMICALLY TALENTED JUNIOR HIGH SCHOOL STUDENTS. THE SAMPLE CONSISTED OF 51 CLASSES AND 6 MATHEMATICS PROGRAMS. THE LORGE-THORNDIKE VERBAL INTELLIGENCE…

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…

An Incidence Loss Model for Wave Rotors with Axially Aligned Passages

NASA Technical Reports Server (NTRS)

Paxson, Daniel E.

1998-01-01

A simple mathematical model is described to account for the losses incurred when the flow in the duct (port) of a wave rotor is not aligned with the passages. The model, specifically for wave rotors with axially aligned passages, describes a loss mechanism which is sensitive to incident flow angle and Mach number. Implementation of the model in a one-dimensional CFD based wave rotor simulation is presented. Comparisons with limited experimental results are consistent with the model. Sensitivity studies are presented which highlight the significance of the incidence loss relative to other loss mechanisms in the wave rotor.

The implementation of multiple intelligences based teaching model to improve mathematical problem solving ability for student of junior high school

NASA Astrophysics Data System (ADS)

Fasni, Nurli; Fatimah, Siti; Yulanda, Syerli

2017-05-01

This research aims to achieve some purposes such as: to know whether mathematical problem solving ability of students who have learned mathematics using Multiple Intelligences based teaching model is higher than the student who have learned mathematics using cooperative learning; to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using Multiple Intelligences based teaching model., to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using cooperative learning; to know the attitude of the students to Multiple Intelligences based teaching model. The method employed here is quasi-experiment which is controlled by pre-test and post-test. The population of this research is all of VII grade in SMP Negeri 14 Bandung even-term 2013/2014, later on two classes of it were taken for the samples of this research. A class was taught using Multiple Intelligences based teaching model and the other one was taught using cooperative learning. The data of this research were gotten from the test in mathematical problem solving, scale questionnaire of the student attitudes, and observation. The results show the mathematical problem solving of the students who have learned mathematics using Multiple Intelligences based teaching model learning is higher than the student who have learned mathematics using cooperative learning, the mathematical problem solving ability of the student who have learned mathematics using cooperative learning and Multiple Intelligences based teaching model are in intermediate level, and the students showed the positive attitude in learning mathematics using Multiple Intelligences based teaching model. As for the recommendation for next author, Multiple Intelligences based teaching model can be tested on other subject and other ability.

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

ERIC Educational Resources Information Center

Mumcu, Hayal Yavuz

2016-01-01

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

Self-consistent radiation-based simulation of electric arcs: II. Application to gas circuit breakers

NASA Astrophysics Data System (ADS)

Iordanidis, A. A.; Franck, C. M.

2008-07-01

An accurate and robust method for radiative heat transfer simulation for arc applications was presented in the previous paper (part I). In this paper a self-consistent mathematical model based on computational fluid dynamics and a rigorous radiative heat transfer model is described. The model is applied to simulate switching arcs in high voltage gas circuit breakers. The accuracy of the model is proven by comparison with experimental data for all arc modes. The ablation-controlled arc model is used to simulate high current PTFE arcs burning in cylindrical tubes. Model accuracy for the lower current arcs is evaluated using experimental data on the axially blown SF6 arc in steady state and arc resistance measurements close to current zero. The complete switching process with the arc going through all three phases is also simulated and compared with the experimental data from an industrial circuit breaker switching test.

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…

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 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…

Differential roles of two delayed rectifier potassium currents in regulation of ventricular action potential duration and arrhythmia susceptibility.

PubMed

Devenyi, Ryan A; Ortega, Francis A; Groenendaal, Willemijn; Krogh-Madsen, Trine; Christini, David J; Sobie, Eric A

2017-04-01

Arrhythmias result from disruptions to cardiac electrical activity, although the factors that control cellular action potentials are incompletely understood. We combined mathematical modelling with experiments in heart cells from guinea pigs to determine how cellular electrical activity is regulated. A mismatch between modelling predictions and the experimental results allowed us to construct an improved, more predictive mathematical model. The balance between two particular potassium currents dictates how heart cells respond to perturbations and their susceptibility to arrhythmias. Imbalances of ionic currents can destabilize the cardiac action potential and potentially trigger lethal cardiac arrhythmias. In the present study, we combined mathematical modelling with information-rich dynamic clamp experiments to determine the regulation of action potential morphology in guinea pig ventricular myocytes. Parameter sensitivity analysis was used to predict how changes in ionic currents alter action potential duration, and these were tested experimentally using dynamic clamp, a technique that allows for multiple perturbations to be tested in each cell. Surprisingly, we found that a leading mathematical model, developed with traditional approaches, systematically underestimated experimental responses to dynamic clamp perturbations. We then re-parameterized the model using a genetic algorithm, which allowed us to estimate ionic current levels in each of the cells studied. This unbiased model adjustment consistently predicted an increase in the rapid delayed rectifier K + current and a drastic decrease in the slow delayed rectifier K + current, and this prediction was validated experimentally. Subsequent simulations with the adjusted model generated the clinically relevant prediction that the slow delayed rectifier is better able to stabilize the action potential and suppress pro-arrhythmic events than the rapid delayed rectifier. In summary, iterative coupling of simulations and experiments enabled novel insight into how the balance between cardiac K + currents influences ventricular arrhythmia susceptibility. © 2016 The Authors. The Journal of Physiology © 2016 The Physiological Society.

Seeking mathematics success for college students: a randomized field trial of an adapted approach

NASA Astrophysics Data System (ADS)

Gula, Taras; Hoessler, Carolyn; Maciejewski, Wes

2015-11-01

Many students enter the Canadian college system with insufficient mathematical ability and leave the system with little improvement. Those students who enter with poor mathematics ability typically take a developmental mathematics course as their first and possibly only mathematics course. The educational experiences that comprise a developmental mathematics course vary widely and are, too often, ineffective at improving students' ability. This trend is concerning, since low mathematics ability is known to be related to lower rates of success in subsequent courses. To date, little attention has been paid to the selection of an instructional approach to consistently apply across developmental mathematics courses. Prior research suggests that an appropriate instructional method would involve explicit instruction and practising mathematical procedures linked to a mathematical concept. This study reports on a randomized field trial of a developmental mathematics approach at a college in Ontario, Canada. The new approach is an adaptation of the JUMP Math program, an explicit instruction method designed for primary and secondary school curriculae, to the college learning environment. In this study, a subset of courses was assigned to JUMP Math and the remainder was taught in the same style as in the previous years. We found consistent, modest improvement in the JUMP Math sections compared to the non-JUMP sections, after accounting for potential covariates. The findings from this randomized field trial, along with prior research on effective education for developmental mathematics students, suggest that JUMP Math is a promising way to improve college student outcomes.

Manipulatives Implementation For Supporting Learning Of Mathematics For Prospective Teachers

NASA Astrophysics Data System (ADS)

Sulistyaningsih, D.; Mawarsari, V. D.; Hidayah, I.; Dwijanto

2017-04-01

Manipulatives are needed by teachers to facilitate students understand of mathematics which is abstract. As a prospective mathematics teacher, the student must have good skills in making manipulatives. Aims of this study is to describe the implementation of learning courses of manipulative workshop in mathematics education courses by lecturer at Universitas Muhammadiyah Semarang which includes the preparation of learning, general professional ability, the professional capacity specifically, ability of self-development, development class managing, planning and implementation of learning, a way of delivering the material, and evaluation of learning outcomes. Data collection techniques used were questionnaires, interviews, and observation. The research instrument consisted of a questionnaire sheet, sheet observation and interview guides. Validity is determined using data triangulation and triangulation methods. Data were analyzed using an interactive model. The results showed that the average value of activities in preparation for learning, fosters capabilities of general professional, specialized professional, self-development, manage the classroom, implementing the learning, how to deliver the material, and how to evaluate learning outcomes are 79%, 73%, 67%, 75%, 83%, 72%, 64%, and 54%, respectively

Mathematical Modeling and Pure Mathematics

ERIC Educational Resources Information Center

Usiskin, Zalman

2015-01-01

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

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…

Report of the Graduate Medical Education National Advisory Committee to the Secretary, Department of Health and Human Services. Volume 1: Summary.

ERIC Educational Resources Information Center

Health Resources Administration (DHHS/PHS), Hyattsville Md. Office of Graduate Medical Education.

Results of a three-year study to estimate the future supply and requirements for physicians, which was conducted by the Graduate Medical Education National Advisory Committee (GMENAC), are summarized. The research methodology, which consisted of three mathematical models to project physician supply and requirements, is described, and 40…

Proposing a Model Assessment and Intervention Program for Learning Disabled Adolescents in a Typical School Population.

ERIC Educational Resources Information Center

Currie, Winifred

Reported are results of screening over 1,000 eighth or ninth grade students for learning disabilities, and suggested is an intervention program utilizing available local resources. The Currie-Milonas Screening Test is described as consisting of eight subtests to identify problems in the basic skills of reading, writing, language, or mathematics.…

Haldane and Mayr: a response to Rao and Nanjundiah.

PubMed

Sarkar, Sahotra

2016-04-01

The discussion with Rao and Nanjundiah about the history of interactions between J. B. S. Haldane and Ernst Mayr is further extended in this note. The nature of the dispute about beanbag genetics is explicated as consisting of two separate issues, one about the role of mathematical analysis in evolutionary biology, and the other about the value of single-locus genic models.

A generic biogeochemical module for earth system models

NASA Astrophysics Data System (ADS)

Fang, Y.; Huang, M.; Liu, C.; Li, H.-Y.; Leung, L. R.

2013-06-01

Physical and biogeochemical processes regulate soil carbon dynamics and CO2 flux to and from the atmosphere, influencing global climate changes. Integration of these processes into earth system models (e.g. community land models - CLM), however, currently faces three major challenges: (1) extensive efforts are required to modify modeling structures and to rewrite computer programs to incorporate new or updated processes as new knowledge is being generated, (2) computational cost is prohibitively expensive to simulate biogeochemical processes in land models due to large variations in the rates of biogeochemical processes, and (3) various mathematical representations of biogeochemical processes exist to incorporate different aspects of fundamental mechanisms, but systematic evaluation of the different mathematical representations is difficult, if not impossible. To address these challenges, we propose a new computational framework to easily incorporate physical and biogeochemical processes into land models. The new framework consists of a new biogeochemical module with a generic algorithm and reaction database so that new and updated processes can be incorporated into land models without the need to manually set up the ordinary differential equations to be solved numerically. The reaction database consists of processes of nutrient flow through the terrestrial ecosystems in plants, litter and soil. This framework facilitates effective comparison studies of biogeochemical cycles in an ecosystem using different conceptual models under the same land modeling framework. The approach was first implemented in CLM and benchmarked against simulations from the original CLM-CN code. A case study was then provided to demonstrate the advantages of using the new approach to incorporate a phosphorus cycle into the CLM model. To our knowledge, the phosphorus-incorporated CLM is a new model that can be used to simulate phosphorus limitation on the productivity of terrestrial ecosystems.

A Contemporary Analysis of the Content of Mathematics for Liberal Education at the College Level

ERIC Educational Resources Information Center

Sporn, Howard Bruce

2010-01-01

The purpose of this study is to determine whether educators believe mathematics should be taught to liberal arts students, what topics are taught in liberal arts mathematics courses, and what the motivation is for teaching such topics. The study consists of two parts, a review of the opinions of educators regarding liberal arts mathematics, and a…

The State of Proof in Finnish and Swedish Mathematics Textbooks--Capturing Differences in Approaches to Upper-Secondary Integral Calculus

ERIC Educational Resources Information Center

Bergwall, Andreas; Hemmi, Kirsti

2017-01-01

Students' difficulties with proof, scholars' calls for proof to be a consistent part of K-12 mathematics, and the extensive use of textbooks in mathematics classrooms motivate investigations on how proof-related items are addressed in mathematics textbooks. We contribute to textbook research by focusing on opportunities to learn proof-related…

The Impacts of Student-, Teacher- and School-Level Factors on Mathematics Achievement: An Exploratory Comparative Investigation of Singaporean Students and the USA Students

ERIC Educational Resources Information Center

Ker, H. W.

2016-01-01

Reports from the Trends in International Mathematics and Science Study (TIMSS) consistently show that there is a substantial gap in average mathematics achievement between Singapore and the USA. This study conducts an exploratory comparative investigation on the multilevel factors influencing the mathematics achievement of students from these two…

Derivation of an applied nonlinear Schroedinger equation

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

Pitts, Todd Alan; Laine, Mark Richard; Schwarz, Jens

We derive from first principles a mathematical physics model useful for understanding nonlinear optical propagation (including filamentation). All assumptions necessary for the development are clearly explained. We include the Kerr effect, Raman scattering, and ionization (as well as linear and nonlinear shock, diffraction and dispersion). We explain the phenomenological sub-models and each assumption required to arrive at a complete and consistent theoretical description. The development includes the relationship between shock and ionization and demonstrates why inclusion of Drude model impedance effects alters the nature of the shock operator. Unclassified Unlimited Release

System identification of propagating wave segments in excitable media and its application to advanced control

NASA Astrophysics Data System (ADS)

Katsumata, Hisatoshi; Konishi, Keiji; Hara, Naoyuki

2018-04-01

The present paper proposes a scheme for controlling wave segments in excitable media. This scheme consists of two phases: in the first phase, a simple mathematical model for wave segments is derived using only the time series data of input and output signals for the media; in the second phase, the model derived in the first phase is used in an advanced control technique. We demonstrate with numerical simulations of the Oregonator model that this scheme performs better than a conventional control scheme.

Evaluation of the mathematical and economic basis for conversion processes in the LEAP energy-economy model

NASA Astrophysics Data System (ADS)

Oblow, E. M.

1982-10-01

An evaluation was made of the mathematical and economic basis for conversion processes in the Long-term Energy Analysis Program (LEAP) energy economy model. Conversion processes are the main modeling subunit in LEAP used to represent energy conversion industries and are supposedly based on the classical economic theory of the firm. Questions about uniqueness and existence of LEAP solutions and their relation to classical equilibrium economic theory prompted the study. An analysis of classical theory and LEAP model equations was made to determine their exact relationship. The conclusions drawn from this analysis were that LEAP theory is not consistent with the classical theory of the firm. Specifically, the capacity factor formalism used by LEAP does not support a classical interpretation in terms of a technological production function for energy conversion processes. The economic implications of this inconsistency are suboptimal process operation and short term negative profits in years where plant operation should be terminated. A new capacity factor formalism, which retains the behavioral features of the original model, is proposed to resolve these discrepancies.

Mathematical modeling on T-cell mediated adaptive immunity in primary dengue infections.

PubMed

Sasmal, Sourav Kumar; Dong, Yueping; Takeuchi, Yasuhiro

2017-09-21

At present, dengue is the most common mosquito-borne viral disease in the world, and the global dengue incidence is increasing day by day due to climate changing. Here, we present a mathematical model of dengue viruses (DENVs) dynamics in micro-environment (cellular level) consisting of healthy cells, infected cells, virus particles and T-cell mediated adaptive immunity. We have considered the explicit role of cytokines and antibody in our model. We find that the virus load goes down to zero within 6 days as it is common for DENV infection. From our analysis, we have identified the important model parameters and done the numerical simulation with respect to such important parameters. We have shown that the cytokine mediated virus clearance plays a very important role in dengue dynamics. It can change the dynamical behavior of the system and causes essential extinction of the virus. Finally, we have incorporated the antiviral treatment for dengue in our model and shown that the basic reproduction number is directly proportional to the antiviral treatment effects. Copyright © 2017 Elsevier Ltd. All rights reserved.

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…

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.…

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…

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)…

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…

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…

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 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…

Experimentation of cooperative learning model Numbered Heads Together (NHT) type by concept maps and Teams Games Tournament (TGT) by concept maps in terms of students logical mathematics intellegences

NASA Astrophysics Data System (ADS)

Irawan, Adi; Mardiyana; Retno Sari Saputro, Dewi

2017-06-01

This research is aimed to find out the effect of learning model towards learning achievement in terms of students’ logical mathematics intelligences. The learning models that were compared were NHT by Concept Maps, TGT by Concept Maps, and Direct Learning model. This research was pseudo experimental by factorial design 3×3. The population of this research was all of the students of class XI Natural Sciences of Senior High School in all regency of Karanganyar in academic year 2016/2017. The conclusions of this research were: 1) the students’ achievements with NHT learning model by Concept Maps were better than students’ achievements with TGT model by Concept Maps and Direct Learning model. The students’ achievements with TGT model by Concept Maps were better than the students’ achievements with Direct Learning model. 2) The students’ achievements that exposed high logical mathematics intelligences were better than students’ medium and low logical mathematics intelligences. The students’ achievements that exposed medium logical mathematics intelligences were better than the students’ low logical mathematics intelligences. 3) Each of student logical mathematics intelligences with NHT learning model by Concept Maps has better achievement than students with TGT learning model by Concept Maps, students with NHT learning model by Concept Maps have better achievement than students with the direct learning model, and the students with TGT by Concept Maps learning model have better achievement than students with Direct Learning model. 4) Each of learning model, students who have logical mathematics intelligences have better achievement then students who have medium logical mathematics intelligences, and students who have medium logical mathematics intelligences have better achievement than students who have low logical mathematics intelligences.

Modeling and simulation of protein elution in linear pH and salt gradients on weak, strong and mixed cation exchange resins applying an extended Donnan ion exchange model.

PubMed

Wittkopp, Felix; Peeck, Lars; Hafner, Mathias; Frech, Christian

2018-04-13

Process development and characterization based on mathematic modeling provides several advantages and has been applied more frequently over the last few years. In this work, a Donnan equilibrium ion exchange (DIX) model is applied for modelling and simulation of ion exchange chromatography of a monoclonal antibody in linear chromatography. Four different cation exchange resin prototypes consisting of weak, strong and mixed ligands are characterized using pH and salt gradient elution experiments applying the extended DIX model. The modelling results are compared with the results using a classic stoichiometric displacement model. The Donnan equilibrium model is able to describe all four prototype resins while the stoichiometric displacement model fails for the weak and mixed weak/strong ligands. Finally, in silico chromatogram simulations of pH and pH/salt dual gradients are performed to verify the results and to show the consistency of the developed model. Copyright © 2018 Elsevier B.V. All rights reserved.

Mathematical modeling of the fermentation of acid-hydrolyzed pyrolytic sugars to ethanol by the engineered strain Escherichia coli ACCC 11177.

PubMed

Chang, Dongdong; Yu, Zhisheng; Islam, Zia Ul; Zhang, Hongxun

2015-05-01

Pyrolysate from waste cotton was acid hydrolyzed and detoxified to yield pyrolytic sugars, which were fermented to ethanol by the strain Escherichia coli ACCC 11177. Mathematical models based on the fermentation data were also constructed. Pyrolysate containing an initial levoglucosan concentration of 146.34 g/L gave a glucose yield of 150 % after hydrolysis, suggesting that other compounds were hydrolyzed to glucose as well. Ethyl acetate-based extraction of bacterial growth inhibitors with an ethyl acetate/hydrolysate ratio of 1:0.5 enabled hydrolysate fermentation by E. coli ACCC 11177, without a standard absorption treatment. Batch processing in a fermenter exhibited a maximum ethanol yield and productivity of 0.41 g/g and 0.93 g/L·h(-1), respectively. The cell growth rate (r x ) was consistent with a logistic equation [Formula: see text], which was determined as a function of cell growth (X). Glucose consumption rate (r s ) and ethanol formation rate (r p ) were accurately validated by the equations [Formula: see text] and [Formula: see text], respectively. Together, our results suggest that combining mathematical models with fermenter fermentation processes can enable optimized ethanol production from cellulosic pyrolysate with E. coli. Similar approaches may facilitate the production of other commercially important organic substances.

Mathematical modelling of the maternal cardiovascular system in the three stages of pregnancy.

PubMed

Corsini, Chiara; Cervi, Elena; Migliavacca, Francesco; Schievano, Silvia; Hsia, Tain-Yen; Pennati, Giancarlo

2017-09-01

In this study, a mathematical model of the female circulation during pregnancy is presented in order to investigate the hemodynamic response to the cardiovascular changes associated with each trimester of pregnancy. First, a preliminary lumped parameter model of the circulation of a non-pregnant female was developed, including the heart, the systemic circulation with a specific block for the uterine district and the pulmonary circulation. The model was first tested at rest; then heart rate and vascular resistances were individually varied to verify the correct response to parameter alterations characterising pregnancy. In order to simulate hemodynamics during pregnancy at each trimester, the main changes applied to the model consisted in reducing vascular resistances, and simultaneously increasing heart rate and ventricular wall volumes. Overall, reasonable agreement was found between model outputs and in vivo data, with the trends of the cardiac hemodynamic quantities suggesting correct response of the heart model throughout pregnancy. Results were reported for uterine hemodynamics, with flow tracings resembling typical Doppler velocity waveforms at each stage, including pulsatility indexes. Such a model may be used to explore the changes that happen during pregnancy in female with cardiovascular diseases. Crown Copyright © 2017. Published by Elsevier Ltd. All rights reserved.

Patterns of interactions at grade 5 classroom in learning the topic of statistics viewed from cognitive load theory

NASA Astrophysics Data System (ADS)

Setianingsih, R.

2018-01-01

The nature of interactions that occurs among teacher, students, learning sources, and learning environment creates different settings to enhance learning. Any setting created by a teacher is affected by 3 (three) types of cognitive load: intrinsic cognitive load, extraneous cognitive load, and germane cognitive load. This study is qualitative in nature, aims to analyse the patterns of interaction that are constituted in mathematics instructions by taking into account the cognitive load theory. The subjects of this study are 21 fifth-grade students who learn mathematics in small groups and whole-class interactive lessons. The data were collected through classroom observations which were videotaped, while field notes were also taken. The data analysis revealed that students engaged in productive interaction and inquiry while they were learning mathematics in small groups or in whole class setting, in which there was a different type of cognitive load that dominantly affecting the learning processes at each setting. During learning mathematics in whole class setting, the most frequently found interaction patterns were to discuss and compare solution based on self-developed models, followed by expressing opinions. This is consistent with the principles of mathematics learning, which gives students wide opportunities to construct mathematical knowledge through individual learning, learning in small groups as well as learning in whole class settings. It means that by participating in interactive learning, the students are habitually engaged in productive interactions and high level of mathematical thinking.

Pre-Service Teachers' Modelling Processes through Engagement with Model Eliciting Activities with a Technological Tool

ERIC Educational Resources Information Center

Daher, Wajeeh M.; Shahbari, Juhaina Awawdeh

2015-01-01

Engaging mathematics students with modelling activities helps them learn mathematics meaningfully. This engagement, in the case of model eliciting activities, helps the students elicit mathematical models by interpreting real-world situation in mathematical ways. This is especially true when the students utilize technology to build the models.…

An Efficacy Study of Interleaved Mathematics Practice. Revised

ERIC Educational Resources Information Center

Rohrer, Doug; Dedrick, Robert F.; Burgess, Kaleena

2013-01-01

In a typical mathematics course, the material is divided into many lessons, and each lesson is followed by an assignment consisting of practice problems. Most commonly, each assignment consists solely of problems on the preceding lesson. For example, a lesson on ratios might be followed by an assignment with 12 problems on ratios. In other words,…

AGAMA: Action-based galaxy modeling framework

NASA Astrophysics Data System (ADS)

Vasiliev, Eugene

2018-05-01

The AGAMA library models galaxies. It computes gravitational potential and forces, performs orbit integration and analysis, and can convert between position/velocity and action/angle coordinates. It offers a framework for finding best-fit parameters of a model from data and self-consistent multi-component galaxy models, and contains useful auxiliary utilities such as various mathematical routines. The core of the library is written in C++, and there are Python and Fortran interfaces. AGAMA may be used as a plugin for the stellar-dynamical software packages galpy (ascl:1411.008), AMUSE (ascl:1107.007), and NEMO (ascl:1010.051).

Modeling the effects of inflammation in bone fracture healing

NASA Astrophysics Data System (ADS)

Kojouharov, H. V.; Trejo, I.; Chen-Charpentier, B. M.

2017-10-01

A new mathematical model is presented to study the early inflammatory effects in bone healing. It consists of a system of nonlinear ordinary differential equations that represents the interactions among macrophages, mesenchymal stem cells, and osteoblasts. A qualitative analysis of the model is performed to determine the equilibria and their corresponding stability properties. A set of numerical simulations is performed to support the theoretical results. The model is also used to numerically monitor the evolution of a broken bone for different types of fractures and to explore possible treatments to accelerate bone healing by administrating anti-inflammatory drugs.

Vibration isolation of a ship's seat

NASA Astrophysics Data System (ADS)

Agahi, Maryam; Samani, Mehrdad B.; Behzad, Mehdi

2005-05-01

Different factors cause vibration. These vibrations make the voyages difficult and reduce comfort and convenience in passenger ships. In this paper, the creating factors of vibration have discussed first, then with mathematical modelling it will be attempted to minimize the vibration over the crew's seat. The modelling consists of a system with two degrees of freedom and by using vibrationisolation with passive method of Tuned Mass Damper (TMD) it will be tried to reduce the vibration over personnel. Moreover using active control systems will be compared with passive systems.

Blood circulation in the lower limbs

NASA Astrophysics Data System (ADS)

Pen'kovskiy, V. I.; Korsakova, N. K.

2018-03-01

Blood circulation process in inferior limbs is considered in the terms of the previously proposed mathematical model of sanguimotion in living organism tissues. The model includes the equations of homogeneous fluid flower in heterogeneous medium that consists of two or more interpenetrating continua. The continua (distributing net of arteries and collecting net of veins) interact through ramified capillary net. A volume of blood flowering from arterial net to venous one is proportional to pressure (head) difference in the nets. Some analytical solutions and numerical results are given.

Local-global analysis of crack growth in continuously reinfoced ceramic matrix composites

NASA Technical Reports Server (NTRS)

Ballarini, Roberto; Ahmed, Shamim

1989-01-01

This paper describes the development of a mathematical model for predicting the strength and micromechanical failure characteristics of continuously reinforced ceramic matrix composites. The local-global analysis models the vicinity of a propagating crack tip as a local heterogeneous region (LHR) consisting of spring-like representation of the matrix, fibers and interfaces. Parametric studies are conducted to investigate the effects of LHR size, component properties, and interface conditions on the strength and sequence of the failure processes in the unidirectional composite system.

MAA Placement Test Newsletter. 1978-87.

ERIC Educational Resources Information Center

Harvey, John G., Ed.

1987-01-01

This document consists of volumes 1-9 of the Mathematics Association of America's (MAA) Placement Test Program Newsletter. The MAA is the professional association primarily concerned with undergraduate education in mathematics. It has responded to the increasingly difficult problem of placing freshmen students in mathematics courses by developing…

Core Skills Assessment to Improve Mathematical Competency

ERIC Educational Resources Information Center

Carr, Michael; Bowe, Brian; Ní Fhloinn, Eabhnat

2013-01-01

Many engineering undergraduates begin third-level education with significant deficiencies in their core mathematical skills. Every year, in the Dublin Institute of Technology, a diagnostic test is given to incoming first-year students, consistently revealing problems in basic mathematics. It is difficult to motivate students to address these…

Mathematics and Computer Science: Exploring a Symbiotic Relationship

ERIC Educational Resources Information Center

Bravaco, Ralph; Simonson, Shai

2004-01-01

This paper describes a "learning community" designed for sophomore computer science majors who are simultaneously studying discrete mathematics. The learning community consists of three courses: Discrete Mathematics, Data Structures and an Integrative Seminar/Lab. The seminar functions as a link that integrates the two disciplines. Participation…

Conceptualizing "Homework" in Flipped Mathematics Classes

ERIC Educational Resources Information Center

de Araujo, Zandra; Otten, Samuel; Birisci, Salih

2017-01-01

Flipped instruction is becoming more common in the United States, particularly in mathematics classes. One of the defining characteristics of this increasingly popular instructional format is the homework teachers assign. In contrast to traditional mathematics classes in which homework consists of problem sets, homework in flipped classes often…

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.

Routing and Scheduling Optimization Model of Sea Transportation

NASA Astrophysics Data System (ADS)

barus, Mika debora br; asyrafy, Habib; nababan, Esther; mawengkang, Herman

2018-01-01

This paper examines the routing and scheduling optimization model of sea transportation. One of the issues discussed is about the transportation of ships carrying crude oil (tankers) which is distributed to many islands. The consideration is the cost of transportation which consists of travel costs and the cost of layover at the port. Crude oil to be distributed consists of several types. This paper develops routing and scheduling model taking into consideration some objective functions and constraints. The formulation of the mathematical model analyzed is to minimize costs based on the total distance visited by the tanker and minimize the cost of the ports. In order for the model of the problem to be more realistic and the cost calculated to be more appropriate then added a parameter that states the multiplier factor of cost increases as the charge of crude oil is filled.

The Development of Proofs in Analytical Mathematics for Undergraduate Students

NASA Astrophysics Data System (ADS)

Ali, Maselan; Sufahani, Suliadi; Hasim, Nurnazifa; Saifullah Rusiman, Mohd; Roslan, Rozaini; Mohamad, Mahathir; Khalid, Kamil

2018-04-01

Proofs in analytical mathematics are essential parts of mathematics, difficult to learn because its underlying concepts are not visible. This research consists of problems involving logic and proofs. In this study, a short overview was provided on how proofs in analytical mathematics were used by university students. From the results obtained, excellent students obtained better scores compared to average and poor students. The research instruments used in this study consisted of two parts: test and interview. In this way, analysis of students’ actual performances can be obtained. The result of this study showed that the less able students have fragile conceptual and cognitive linkages but the more able students use their strong conceptual linkages to produce effective solutions

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…

Leaning on Mathematical Habits of Mind

ERIC Educational Resources Information Center

Sword, Sarah; Matsuura, Ryota; Cuoco, Al; Kang, Jane; Gates, Miriam

2018-01-01

Mathematical modeling has taken on increasing curricular importance in the past decade due in no small measure to the Common Core State Standards in Mathematics (CCSSM) identifying modeling as one of the Standards for Mathematical Practice (SMP 4, CCSSI 2010, p. 7). Although researchers have worked on mathematical modeling (Lesh and Doerr 2003;…

An objective function exploiting suboptimal solutions in metabolic networks

PubMed Central

2013-01-01

Background Flux Balance Analysis is a theoretically elegant, computationally efficient, genome-scale approach to predicting biochemical reaction fluxes. Yet FBA models exhibit persistent mathematical degeneracy that generally limits their predictive power. Results We propose a novel objective function for cellular metabolism that accounts for and exploits degeneracy in the metabolic network to improve flux predictions. In our model, regulation drives metabolism toward a region of flux space that allows nearly optimal growth. Metabolic mutants deviate minimally from this region, a function represented mathematically as a convex cone. Near-optimal flux configurations within this region are considered equally plausible and not subject to further optimizing regulation. Consistent with relaxed regulation near optimality, we find that the size of the near-optimal region predicts flux variability under experimental perturbation. Conclusion Accounting for suboptimal solutions can improve the predictive power of metabolic FBA models. Because fluctuations of enzyme and metabolite levels are inevitable, tolerance for suboptimality may support a functionally robust metabolic network. PMID:24088221

The Development of Statistics Textbook Supported with ICT and Portfolio-Based Assessment

NASA Astrophysics Data System (ADS)

Hendikawati, Putriaji; Yuni Arini, Florentina

2016-02-01

This research was development research that aimed to develop and produce a Statistics textbook model that supported with information and communication technology (ICT) and Portfolio-Based Assessment. This book was designed for students of mathematics at the college to improve students’ ability in mathematical connection and communication. There were three stages in this research i.e. define, design, and develop. The textbooks consisted of 10 chapters which each chapter contains introduction, core materials and include examples and exercises. The textbook developed phase begins with the early stages of designed the book (draft 1) which then validated by experts. Revision of draft 1 produced draft 2 which then limited test for readability test book. Furthermore, revision of draft 2 produced textbook draft 3 which simulated on a small sample to produce a valid model textbook. The data were analysed with descriptive statistics. The analysis showed that the Statistics textbook model that supported with ICT and Portfolio-Based Assessment valid and fill up the criteria of practicality.

V/STOL tilt rotor study. Volume 5: A mathematical model for real time flight simulation of the Bell model 301 tilt rotor research aircraft

NASA Technical Reports Server (NTRS)

Harendra, P. B.; Joglekar, M. J.; Gaffey, T. M.; Marr, R. L.

1973-01-01

A mathematical model for real-time flight simulation of a tilt rotor research aircraft was developed. The mathematical model was used to support the aircraft design, pilot training, and proof-of-concept aspects of the development program. The structure of the mathematical model is indicated by a block diagram. The mathematical model differs from that for a conventional fixed wing aircraft principally in the added requirement to represent the dynamics and aerodynamics of the rotors, the interaction of the rotor wake with the airframe, and the rotor control and drive systems. The constraints imposed on the mathematical model are defined.

COLD-SAT dynamic model

NASA Technical Reports Server (NTRS)

Adams, Neil S.; Bollenbacher, Gary

1992-01-01

This report discusses the development and underlying mathematics of a rigid-body computer model of a proposed cryogenic on-orbit liquid depot storage, acquisition, and transfer spacecraft (COLD-SAT). This model, referred to in this report as the COLD-SAT dynamic model, consists of both a trajectory model and an attitudinal model. All disturbance forces and torques expected to be significant for the actual COLD-SAT spacecraft are modeled to the required degree of accuracy. Control and experimental thrusters are modeled, as well as fluid slosh. The model also computes microgravity disturbance accelerations at any specified point in the spacecraft. The model was developed by using the Boeing EASY5 dynamic analysis package and will run on Apollo, Cray, and other computing platforms.

Examination of the Relationship between the Preschool Teachers' Attitudes towards Mathematics and the Mathematical Development in 6-Year-Old Preschool Children

ERIC Educational Resources Information Center

Çelik, Meryem

2017-01-01

This study was carried out to determine whether there is a relationship between the preschool teachers' attitudes towards mathematics and mathematical development in 6-year-old preschool children. The sampling of the study was consisted of 30 teachers working with 6 years old children and their 120 students in public kindergartens and independent…

Attitudinal and Motivational Variables Related to Mathematics Achievement in Jordan: Findings from the Third International Mathematics and Science Study (TIMSS)

ERIC Educational Resources Information Center

Hammouri, Hind

2004-01-01

The purpose of the present study was to examine the effects of student-related variables on achievement in mathematics. The sample consisted of 3736 13-year-old Jordanian 8th-graders who participated in the Third International Mathematics and Science Study (TIMSS). The participants completed a student questionnaire and participated in the…

Imbedded-Fracture Formulation of THMC Processes in Fractured Media

NASA Astrophysics Data System (ADS)

Yeh, G. T.; Tsai, C. H.; Sung, R.

2016-12-01

Fractured media consist of porous materials and fracture networks. There exist four approaches to mathematically formulating THMC (Thermal-Hydrology-Mechanics-Chemistry) processes models in the system: (1) Equivalent Porous Media, (2) Dual Porosity or Dual Continuum, (3) Heterogeneous Media, and (4) Discrete Fracture Network. The first approach cannot explicitly explore the interactions between porous materials and fracture networks. The second approach introduces too many extra parameters (namely, exchange coefficients) between two media. The third approach may make the problems too stiff because the order of material heterogeneity may be too much. The fourth approach ignore the interaction between porous materials and fracture networks. This talk presents an alternative approach in which fracture networks are modeled with a lower dimension than the surrounding porous materials. Theoretical derivation of mathematical formulations will be given. An example will be illustrated to show the feasibility of this approach.

The pressure distribution for biharmonic transmitting array: theoretical study

NASA Astrophysics Data System (ADS)

Baranowska, A.

2005-03-01

The aim of the paper is theoretical analysis of the finite amplitude waves interaction problem for the biharmonic transmitting array. We assume that the array consists of 16 circular pistons of the same dimensions that regrouped in two sections. Two different arrangements of radiating elements were considered. In this situation the radiating surface is non-continuous without axial symmetry. The mathematical model was built on the basis of the Khokhlov - Zabolotskaya - Kuznetsov (KZK) equation. To solve the problem the finite-difference method was applied. On-axis pressure amplitude for different frequency waves as a function of distance from the source, transverse pressure distribution of these waves at fixed distances from the source and pressure amplitude distribution for them at fixed planes were examined. Especially changes of normalized pressure amplitude for difference frequency were studied. The paper presents mathematical model and some results of theoretical investigations obtained for different values of source parameters.

An Intuitionistic Fuzzy Logic Models for Multicriteria Decision Making Under Uncertainty

NASA Astrophysics Data System (ADS)

Jana, Biswajit; Mohanty, Sachi Nandan

2017-04-01

The purpose of this paper is to enhance the applicability of the fuzzy sets for developing mathematical models for decision making under uncertainty, In general a decision making process consist of four stages, namely collection of information from various sources, compile the information, execute the information and finally take the decision/action. Only fuzzy sets theory is capable to quantifying the linguistic expression to mathematical form in complex situation. Intuitionistic fuzzy set (IFSs) which reflects the fact that the degree of non membership is not always equal to one minus degree of membership. There may be some degree of hesitation. Thus, there are some situations where IFS theory provides a more meaningful and applicable to cope with imprecise information present for solving multiple criteria decision making problem. This paper emphasis on IFSs, which is help for solving real world problem in uncertainty situation.

Working Characteristics of Variable Intake Valve in Compressed Air Engine

PubMed Central

Yu, Qihui; Shi, Yan; Cai, Maolin

2014-01-01

A new camless compressed air engine is proposed, which can make the compressed air energy reasonably distributed. Through analysis of the camless compressed air engine, a mathematical model of the working processes was set up. Using the software MATLAB/Simulink for simulation, the pressure, temperature, and air mass of the cylinder were obtained. In order to verify the accuracy of the mathematical model, the experiments were conducted. Moreover, performance analysis was introduced to design compressed air engine. Results show that, firstly, the simulation results have good consistency with the experimental results. Secondly, under different intake pressures, the highest output power is obtained when the crank speed reaches 500 rpm, which also provides the maximum output torque. Finally, higher energy utilization efficiency can be obtained at the lower speed, intake pressure, and valve duration angle. This research can refer to the design of the camless valve of compressed air engine. PMID:25379536

Working characteristics of variable intake valve in compressed air engine.

PubMed

Yu, Qihui; Shi, Yan; Cai, Maolin

2014-01-01

A new camless compressed air engine is proposed, which can make the compressed air energy reasonably distributed. Through analysis of the camless compressed air engine, a mathematical model of the working processes was set up. Using the software MATLAB/Simulink for simulation, the pressure, temperature, and air mass of the cylinder were obtained. In order to verify the accuracy of the mathematical model, the experiments were conducted. Moreover, performance analysis was introduced to design compressed air engine. Results show that, firstly, the simulation results have good consistency with the experimental results. Secondly, under different intake pressures, the highest output power is obtained when the crank speed reaches 500 rpm, which also provides the maximum output torque. Finally, higher energy utilization efficiency can be obtained at the lower speed, intake pressure, and valve duration angle. This research can refer to the design of the camless valve of compressed air engine.

The analytical solution for drug delivery system with nonhomogeneous moving boundary condition

NASA Astrophysics Data System (ADS)

Saudi, Muhamad Hakimi; Mahali, Shalela Mohd; Harun, Fatimah Noor

2017-08-01

This paper discusses the development and the analytical solution of a mathematical model based on drug release system from a swelling delivery device. The mathematical model is represented by a one-dimensional advection-diffusion equation with nonhomogeneous moving boundary condition. The solution procedures consist of three major steps. Firstly, the application of steady state solution method, which is used to transform the nonhomogeneous moving boundary condition to homogeneous boundary condition. Secondly, the application of the Landau transformation technique that gives a significant impact in removing the advection term in the system of equation and transforming the moving boundary condition to a fixed boundary condition. Thirdly, the used of separation of variables method to find the analytical solution for the resulted initial boundary value problem. The results show that the swelling rate of delivery device and drug release rate is influenced by value of growth factor r.

On Two-Scale Modelling of Heat and Mass Transfer

NASA Astrophysics Data System (ADS)

Vala, J.; Št'astník, S.

2008-09-01

Modelling of macroscopic behaviour of materials, consisting of several layers or components, whose microscopic (at least stochastic) analysis is available, as well as (more general) simulation of non-local phenomena, complicated coupled processes, etc., requires both deeper understanding of physical principles and development of mathematical theories and software algorithms. Starting from the (relatively simple) example of phase transformation in substitutional alloys, this paper sketches the general formulation of a nonlinear system of partial differential equations of evolution for the heat and mass transfer (useful in mechanical and civil engineering, etc.), corresponding to conservation principles of thermodynamics, both at the micro- and at the macroscopic level, and suggests an algorithm for scale-bridging, based on the robust finite element techniques. Some existence and convergence questions, namely those based on the construction of sequences of Rothe and on the mathematical theory of two-scale convergence, are discussed together with references to useful generalizations, required by new technologies.

[Quality assurance of the renal applications software].

PubMed

del Real Núñez, R; Contreras Puertas, P I; Moreno Ortega, E; Mena Bares, L M; Maza Muret, F R; Latre Romero, J M

2007-01-01

The need for quality assurance of all technical aspects of nuclear medicine studies is widely recognised. However, little attention has been paid to the quality assurance of the applications software. Our work reported here aims at verifying the analysis software for processing of renal nuclear medicine studies (renograms). The software tools were used to build a synthetic dynamic model of renal system. The model consists of two phases: perfusion and function. The organs of interest (kidneys, bladder and aortic artery) were simple geometric forms. The uptake of the renal structures was described by mathematic functions. Curves corresponding to normal or pathological conditions were simulated for kidneys, bladder and aortic artery by appropriate selection of parameters. There was no difference between the parameters of the mathematic curves and the quantitative data produced by the renal analysis program. Our test procedure is simple to apply, reliable, reproducible and rapid to verify the renal applications software.

Developing Students' Reflections on the Function and Status of Mathematical Modeling in Different Scientific Practices: History as a Provider of Cases

ERIC Educational Resources Information Center

Kjeldsen, Tinne Hoff; Blomhøj, Morten

2013-01-01

Mathematical models and mathematical modeling play different roles in the different areas and problems in which they are used. The function and status of mathematical modeling and models in the different areas depend on the scientific practice as well as the underlying philosophical and theoretical position held by the modeler(s) and the…

How Ordinary Meaning Underpins the Meaning of Mathematics.

ERIC Educational Resources Information Center

Ormell, Christopher

1991-01-01

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

Estimating the production, consumption and export of cannabis: The Dutch case.

PubMed

van der Giessen, Mark; van Ooyen-Houben, Marianne M J; Moolenaar, Debora E G

2016-05-01

Quantifying an illegal phenomenon like a drug market is inherently complex due to its hidden nature and the limited availability of reliable information. This article presents findings from a recent estimate of the production, consumption and export of Dutch cannabis and discusses the opportunities provided by, and limitations of, mathematical models for estimating the illegal cannabis market. The data collection consisted of a comprehensive literature study, secondary analyses on data from available registrations (2012-2014) and previous studies, and expert opinion. The cannabis market was quantified with several mathematical models. The data analysis included a Monte Carlo simulation to come to a 95% interval estimate (IE) and a sensitivity analysis to identify the most influential indicators. The annual production of Dutch cannabis was estimated to be between 171 and 965tons (95% IE of 271-613tons). The consumption was estimated to be between 28 and 119tons, depending on the inclusion or exclusion of non-residents (95% IE of 51-78tons or 32-49tons respectively). The export was estimated to be between 53 and 937tons (95% IE of 206-549tons or 231-573tons, respectively). Mathematical models are valuable tools for the systematic assessment of the size of illegal markets and determining the uncertainty inherent in the estimates. The estimates required the use of many assumptions and the availability of reliable indicators was limited. This uncertainty is reflected in the wide ranges of the estimates. The estimates are sensitive to 10 of the 45 indicators. These 10 account for 86-93% of the variation found. Further research should focus on improving the variables and the independence of the mathematical models. Copyright © 2016 Elsevier B.V. All rights reserved.

Systems biology of the modified branched Entner-Doudoroff pathway in Sulfolobus solfataricus

PubMed Central

Figueiredo, Ana Sofia; Esser, Dominik; Haferkamp, Patrick; Wieloch, Patricia; Schomburg, Dietmar; Siebers, Bettina; Schaber, Jörg

2017-01-01

Sulfolobus solfataricus is a thermoacidophilic Archaeon that thrives in terrestrial hot springs (solfatares) with optimal growth at 80°C and pH 2–4. It catabolizes specific carbon sources, such as D-glucose, to pyruvate via the modified Entner-Doudoroff (ED) pathway. This pathway has two parallel branches, the semi-phosphorylative and the non-phosphorylative. However, the strategy of S.solfataricus to endure in such an extreme environment in terms of robustness and adaptation is not yet completely understood. Here, we present the first dynamic mathematical model of the ED pathway parameterized with quantitative experimental data. These data consist of enzyme activities of the branched pathway at 70°C and 80°C and of metabolomics data at the same temperatures for the wild type and for a metabolic engineered knockout of the semi-phosphorylative branch. We use the validated model to address two questions: 1. Is this system more robust to perturbations at its optimal growth temperature? 2. Is the ED robust to deletion and perturbations? We employed a systems biology approach to answer these questions and to gain further knowledge on the emergent properties of this biological system. Specifically, we applied deterministic and stochastic approaches to study the sensitivity and robustness of the system, respectively. The mathematical model we present here, shows that: 1. Steady state metabolite concentrations of the ED pathway are consistently more robust to stochastic internal perturbations at 80°C than at 70°C; 2. These metabolite concentrations are highly robust when faced with the knockout of either branch. Connected with this observation, these two branches show different properties at the level of metabolite production and flux control. These new results reveal how enzyme kinetics and metabolomics synergizes with mathematical modelling to unveil new systemic properties of the ED pathway in S.solfataricus in terms of its adaptation and robustness. PMID:28692669

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…

Water-discharge determinations for the tidal reach of the Willamette River from Ross Island Bridge to Mile 10.3, Portland, Oregon

USGS Publications Warehouse

Dempster, G.R.; Lutz, Gale A.

1968-01-01

Water-discharge, velocity, and slope variations for a 3.7-mile-Iong tidal reach of the Willamette River at Portland, Oreg., were defined from discharge measurements and river stage data collected between July 1962 and January 1965. Observed water discharge during tide-affected flows, during floods, and during backwater from the Columbia River and recorded stages at each end of the river reach were used to determine water discharge from two mathematical models. These models use a finite-difference method to solve the equations of moderately unsteady open-channel streamflow, and discharges are computed by an electronic digital computer. Discharges computed by using the mathematical models compare satisfactorily with observed discharges, except during the period of backwater from the annual flood of the Columbia River. The flow resistance coefficients used in the models vary with discharge; for one model, the coefficients for discharges above 30,000 cfs (cubic feet per second) are 12 and 24 percent less than the coefficient used for discharges below 30,000 cfs. Daily mean discharges were determined by use of one mathematical model for approximately two-thirds of the water year, October 1963 through September 1964. Agreement of computed with routed daily mean discharges is fair; above 30,000 cfs, average differences between the two discharges are about 10 percent, and below 30,000 cfs, computed daily discharges are consistently greater (by as much as 25 percent) than routed discharges. The other model was used to compute discharges for the unusually high flood flows of December 1964.

A new mathematical model for nitrogen gas production with special emphasis on the role of attached growth media in anammox hybrid reactor.

PubMed

Tomar, Swati; Gupta, Sunil Kumar

2015-11-01

The present study emphasised on the development of new mathematical models based on mass balance and stoichiometry of nitrogen removal in anammox hybrid reactor (AHR). The performance of AHR at varying hydraulic retention times (HRTs) and nitrogen loading rates (NLRs) revealed that nitrogen removal efficiency (NRE) increases with increase in HRT and was found optimal (89 %) at HRT of 2 days. Mass balance of nitrogen revealed that major fraction (74.1 %) of input nitrogen is converted into N2 gas followed by 11.2 % utilised in biomass synthesis. Attached growth media (AGM) in AHR contributed to an additional 15.4 % ammonium removal and reduced the sludge washout rate by 29 %. This also enhanced the sludge retention capacity of AHR and thus minimised the formation of nitrate in the treated effluent, which is one of the bottlenecks of anammox process. Process kinetics was also studied using various mathematical models. The mass balance model derived from total nitrogen was found most precise and predicted N2 gas with least error (1.68 ± 4.44 %). Model validation for substrate removal kinetics dictated comparatively higher correlation for Grau second-order model (0.952) than modified Stover-Kincannon model (0.920). The study concluded that owing to features of high biomass retention, less nitrate formation and consistently higher nitrogen removal efficiency, this reactor configuration is techno-economically most efficient and viable. The study opens the door for researchers and scientists for pilot-scale testing of AHR leading to its wide industrial application.

Utilizing the National Research Council's (NRC) Conceptual Framework for the Next Generation Science Standards (NGSS): A Self-Study in My Science, Engineering, and Mathematics Classroom

NASA Astrophysics Data System (ADS)

Corvo, Arthur Francis

Given the reality that active and competitive participation in the 21 st century requires American students to deepen their scientific and mathematical knowledge base, the National Research Council (NRC) proposed a new conceptual framework for K--12 science education. The framework consists of an integration of what the NRC report refers to as the three dimensions: scientific and engineering practices, crosscutting concepts, and core ideas in four disciplinary areas (physical, life and earth/spaces sciences, and engineering/technology). The Next Generation Science Standards (NGSS ), which are derived from this new framework, were released in April 2013 and have implications on teacher learning and development in Science, Technology, Engineering, and Mathematics (STEM). Given the NGSS's recent introduction, there is little research on how teachers can prepare for its release. To meet this research need, I implemented a self-study aimed at examining my teaching practices and classroom outcomes through the lens of the NRC's conceptual framework and the NGSS. The self-study employed design-based research (DBR) methods to investigate what happened in my secondary classroom when I designed, enacted, and reflected on units of study for my science, engineering, and mathematics classes. I utilized various best practices including Learning for Use (LfU) and Understanding by Design (UbD) models for instructional design, talk moves as a tool for promoting discourse, and modeling instruction for these designed units of study. The DBR strategy was chosen to promote reflective cycles, which are consistent with and in support of the self-study framework. A multiple case, mixed-methods approach was used for data collection and analysis. The findings in the study are reported by study phase in terms of unit planning, unit enactment, and unit reflection. The findings have implications for science teaching, teacher professional development, and teacher education.

Identification of line-specific strategies for improving carotenoid production in synthetic maize through data-driven mathematical modeling.

PubMed

Comas, Jorge; Benfeitas, Rui; Vilaprinyo, Ester; Sorribas, Albert; Solsona, Francesc; Farré, Gemma; Berman, Judit; Zorrilla, Uxue; Capell, Teresa; Sandmann, Gerhard; Zhu, Changfu; Christou, Paul; Alves, Rui

2016-09-01

Plant synthetic biology is still in its infancy. However, synthetic biology approaches have been used to manipulate and improve the nutritional and health value of staple food crops such as rice, potato and maize. With current technologies, production yields of the synthetic nutrients are a result of trial and error, and systematic rational strategies to optimize those yields are still lacking. Here, we present a workflow that combines gene expression and quantitative metabolomics with mathematical modeling to identify strategies for increasing production yields of nutritionally important carotenoids in the seed endosperm synthesized through alternative biosynthetic pathways in synthetic lines of white maize, which is normally devoid of carotenoids. Quantitative metabolomics and gene expression data are used to create and fit parameters of mathematical models that are specific to four independent maize lines. Sensitivity analysis and simulation of each model is used to predict which gene activities should be further engineered in order to increase production yields for carotenoid accumulation in each line. Some of these predictions (e.g. increasing Zmlycb/Gllycb will increase accumulated β-carotenes) are valid across the four maize lines and consistent with experimental observations in other systems. Other predictions are line specific. The workflow is adaptable to any other biological system for which appropriate quantitative information is available. Furthermore, we validate some of the predictions using experimental data from additional synthetic maize lines for which no models were developed. © 2016 The Authors The Plant Journal © 2016 John Wiley & Sons Ltd.

Researching Research: Mathematics Education in the Political

ERIC Educational Resources Information Center

Pais, Alexandre; Valero, Paola

2012-01-01

We discuss contemporary theories in mathematics education in order to do research on research. Our strategy consists of analysing discursively and ideologically recent key publications addressing the role of theory in mathematics education research. We examine how the field fabricates its object of research by deploying Foucault's notion of…

BIBLIOGRAPHIES, HIGH SCHOOL MATHEMATICS.

ERIC Educational Resources Information Center

WOODS, PAUL E.

THIS ANNOTATED BIBLIOGRAPHY IS A COMPILATION OF A NUMBER OF HIGHLY REGARDED BOOK LISTS CONSISTING OF LIBRARY BOOKS AND TEXTBOOKS FOR GRADES 7-12. THE BOOKS IN THIS LIST ARE CURRENTLY IN PRINT AND THE CONTENT IS REPRESENTATIVE OF THE FOLLOWING AREAS OF MATHEMATICS--MATHEMATICAL RECREATION, COMPUTERS, ARITHMETIC, ALGEBRA, EUCLIDEAN GEOMETRY,…

Teaching and Learning Mathematics in the 1990s: 1990 Yearbook.

ERIC Educational Resources Information Center

Cooney, Thomas J., Ed.; Hirsch, Christian R., Ed.

This yearbook includes 28 articles related to teachers and students of mathematics education and their changing roles. Part 1, "New Perspectives on Teaching and Learning," focuses on the relationship between research and practice and suggests a perspective based on the belief that mathematical learning consists of students constructing…

Visual Processing in Generally Gifted and Mathematically Excelling Adolescents

ERIC Educational Resources Information Center

Paz-Baruch, Nurit; Leikin, Roza; Leikin, Mark

2016-01-01

Little empirical data are available concerning the cognitive abilities of gifted individuals in general and especially those who excel in mathematics. We examined visual processing abilities distinguishing between general giftedness (G) and excellence in mathematics (EM). The research population consisted of 190 students from four groups of 10th-…

Secondary School Teachers' Conceptions and Their Teaching Practices Using Graphing Calculators

ERIC Educational Resources Information Center

Lee, Jane A.; McDougall, Douglas E.

2010-01-01

This article investigates secondary school teachers' conceptions of mathematics and their teaching practices in the use of graphing calculators in their mathematics classrooms. Case studies on three teacher participants were developed using quantitative and qualitative data that consisted of self-assessments on beliefs in mathematics,…

Students' Conceptions of a Mathematical Definition

ERIC Educational Resources Information Center

Zaslavsky, Orit; Shir, Karni

2005-01-01

This article deals with 12th-grade students' conceptions of a mathematical definition. Their conceptions of a definition were revealed through individual and group activities in which they were asked to consider a number of possible definitions of four mathematical concepts: two geometric and two analytic. Data consisted of written responses to…

Handbook for Spoken Mathematics: (Larry's Speakeasy).

ERIC Educational Resources Information Center

Chang, Lawrence A.; And Others

This handbook is directed toward those who have to deal with spoken mathematics, yet have insufficient background to know the correct verbal expression for the written symbolic one. It compiles consistent and well-defined ways of uttering mathematical expressions so listeners will receive clear, unambiguous, and well-pronounced representations.…

Understanding Mathematics and Science Matters. Studies in Mathematical Thinking and Learning Series

ERIC Educational Resources Information Center

Romberg, Thomas A., Ed.; Carpenter, Thomas P., Ed.; Dremock, Fae, Ed.

2005-01-01

The research reported in this book provides reliable evidence on and knowledge about mathematics and science instruction that emphasizes student understanding--instruction consistent with the needs of students who will be citizens in an increasingly demanding technological world. The National Center for Improving Student Learning in Mathematics…

Internal consistency reliability and validity of the Arabic translation of the Mathematics Teaching Efficacy Beliefs Instrument.

PubMed

Alkhateeb, Haitham M

2004-06-01

The Arabic translation of the Mathematics Teaching Efficacy Beliefs was completed by 144 undergraduate students (M age=20.6) in Jordan. The findings support the internal reliability of the Arabic translation of the Mathematics Teaching Efficacy Beliefs as well as its construct validity.

An Investigation of Elementary Preservice Teachers' Self-Efficacy for Teaching Mathematics

ERIC Educational Resources Information Center

Giles, Rebecca McMahon; Byrd, Kelly O.; Bendolph, Angelia

2016-01-01

Research has consistently shown that teacher efficacy is related to a variety of desirable student outcomes, thus, making teacher efficacy an important factor in high quality mathematics instruction. The purpose of this study was to determine elementary preservice teachers' self-efficacy beliefs related to teaching mathematics. Forty-one…

Amplitude and frequency modulation control of sound production in a mechanical model of the avian syrinx.

PubMed

Elemans, Coen P H; Muller, Mees; Larsen, Ole Naesbye; van Leeuwen, Johan L

2009-04-01

Birdsong has developed into one of the important models for motor control of learned behaviour and shows many parallels with speech acquisition in humans. However, there are several experimental limitations to studying the vocal organ - the syrinx - in vivo. The multidisciplinary approach of combining experimental data and mathematical modelling has greatly improved the understanding of neural control and peripheral motor dynamics of sound generation in birds. Here, we present a simple mechanical model of the syrinx that facilitates detailed study of vibrations and sound production. Our model resembles the 'starling resistor', a collapsible tube model, and consists of a tube with a single membrane in its casing, suspended in an external pressure chamber and driven by various pressure patterns. With this design, we can separately control 'bronchial' pressure and tension in the oscillating membrane and generate a wide variety of 'syllables' with simple sweeps of the control parameters. We show that the membrane exhibits high frequency, self-sustained oscillations in the audio range (>600 Hz fundamental frequency) using laser Doppler vibrometry, and systematically explore the conditions for sound production of the model in its control space. The fundamental frequency of the sound increases with tension in three membranes with different stiffness and mass. The lower-bound fundamental frequency increases with membrane mass. The membrane vibrations are strongly coupled to the resonance properties of the distal tube, most likely because of its reflective properties to sound waves. Our model is a gross simplification of the complex morphology found in birds, and more closely resembles mathematical models of the syrinx. Our results confirm several assumptions underlying existing mathematical models in a complex geometry.

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…

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…

Multiple Scales in Fluid Dynamics and Meteorology: The DFG Priority Programme 1276 MetStröm

NASA Astrophysics Data System (ADS)

von Larcher, Th; Klein, R.

2012-04-01

Geophysical fluid motions are characterized by a very wide range of length and time scales, and by a rich collection of varying physical phenomena. The mathematical description of these motions reflects this multitude of scales and mechanisms in that it involves strong non-linearities and various scale-dependent singular limit regimes. Considerable progress has been made in recent years in the mathematical modelling and numerical simulation of such flows in detailed process studies, numerical weather forecasting, and climate research. One task of outstanding importance in this context has been and will remain for the foreseeable future the subgrid scale parameterization of the net effects of non-resolved processes that take place on spacio-temporal scales not resolvable even by the largest most recent supercomputers. Since the advent of numerical weather forecasting some 60 years ago, one simple but efficient means to achieve improved forecasting skills has been increased spacio-temporal resolution. This seems quite consistent with the concept of convergence of numerical methods in Applied Mathematics and Computational Fluid Dynamics (CFD) at a first glance. Yet, the very notion of increased resolution in atmosphere-ocean science is very different from the one used in Applied Mathematics: For the mathematician, increased resolution provides the benefit of getting closer to the ideal of a converged solution of some given partial differential equations. On the other hand, the atmosphere-ocean scientist would naturally refine the computational grid and adjust his mathematical model, such that it better represents the relevant physical processes that occur at smaller scales. This conceptual contradiction remains largely irrelevant as long as geophysical flow models operate with fixed computational grids and time steps and with subgrid scale parameterizations being optimized accordingly. The picture changes fundamentally when modern techniques from CFD involving spacio-temporal grid adaptivity get invoked in order to further improve the net efficiency in exploiting the given computational resources. In the setting of geophysical flow simulation one must then employ subgrid scale parameterizations that dynamically adapt to the changing grid sizes and time steps, implement ways to judiciously control and steer the newly available flexibility of resolution, and invent novel ways of quantifying the remaining errors. The DFG priority program MetStröm covers the expertise of Meteorology, Fluid Dynamics, and Applied Mathematics to develop model- as well as grid-adaptive numerical simulation concepts in multidisciplinary projects. The goal of this priority programme is to provide simulation models which combine scale-dependent (mathematical) descriptions of key physical processes with adaptive flow discretization schemes. Deterministic continuous approaches and discrete and/or stochastic closures and their possible interplay are taken into consideration. Research focuses on the theory and methodology of multiscale meteorological-fluid mechanics modelling. Accompanying reference experiments support model validation.

Steady state phosphorus mass balance model during hemodialysis based on a pseudo one-compartment kinetic model.

PubMed

Leypoldt, John K; Agar, Baris U; Akonur, Alp; Gellens, Mary E; Culleton, Bruce F

2012-11-01

Mathematical models of phosphorus kinetics and mass balance during hemodialysis are in early development. We describe a theoretical phosphorus steady state mass balance model during hemodialysis based on a novel pseudo one-compartment kinetic model. The steady state mass balance model accounted for net intestinal absorption of phosphorus and phosphorus removal by both dialysis and residual kidney function. Analytical mathematical solutions were derived to describe time-dependent intradialytic and interdialytic serum phosphorus concentrations assuming hemodialysis treatments were performed symmetrically throughout a week. Results from the steady state phosphorus mass balance model are described for thrice weekly hemodialysis treatment prescriptions only. The analysis predicts 1) a minimal impact of dialyzer phosphorus clearance on predialysis serum phosphorus concentration using modern, conventional hemodialysis technology, 2) variability in the postdialysis-to-predialysis phosphorus concentration ratio due to differences in patient-specific phosphorus mobilization, and 3) the importance of treatment time in determining the predialysis serum phosphorus concentration. We conclude that a steady state phosphorus mass balance model can be developed based on a pseudo one-compartment kinetic model and that predictions from this model are consistent with previous clinical observations. The predictions from this mass balance model are theoretical and hypothesis-generating only; additional prospective clinical studies will be required for model confirmation.

Developing self-concept instrument for pre-service mathematics teachers

NASA Astrophysics Data System (ADS)

Afgani, M. W.; Suryadi, D.; Dahlan, J. A.

2018-01-01

This study aimed to develop self-concept instrument for undergraduate students of mathematics education in Palembang, Indonesia. Type of this study was development research of non-test instrument in questionnaire form. A Validity test of the instrument was performed with construct validity test by using Pearson product moment and factor analysis, while reliability test used Cronbach’s alpha. The instrument was tested by 65 undergraduate students of mathematics education in one of the universities at Palembang, Indonesia. The instrument consisted of 43 items with 7 aspects of self-concept, that were the individual concern, social identity, individual personality, view of the future, the influence of others who become role models, the influence of the environment inside or outside the classroom, and view of the mathematics. The result of validity test showed there was one invalid item because the value of Pearson’s r was 0.107 less than the critical value (0.244; α = 0.05). The item was included in social identity aspect. After the invalid item was removed, Construct validity test with factor analysis generated only one factor. The Kaiser-Meyer-Olkin (KMO) coefficient was 0.846 and reliability coefficient was 0.91. From that result, we concluded that the self-concept instrument for undergraduate students of mathematics education in Palembang, Indonesia was valid and reliable with 42 items.

Exploring mathematics anxiety and attitude: Mathematics students' experiences

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

A New Model of Special Relativity and the Relationship between the Time Warps of General and Special Relativity

ERIC Educational Resources Information Center

Stannard, Warren B.

2018-01-01

Einstein's two theories of relativity were introduced over 100 years ago. High school science students are seldom exposed to these revolutionary ideas as they are often perceived to be too difficult conceptually and mathematically. This paper brings together the two theories of relativity in a way that is logical and consistent and enables the…

Learning Partners: Escribamos! Leamos! Juguemos a las Ciencias! Juguemos a las Matematicas! (Learning Partners: Let's Write! Let's Read! Let's Play Mathematics! Let's Play Science!)

ERIC Educational Resources Information Center

Office of Educational Research and Improvement (ED), Washington, DC.

This Spanish-language document consists of four single-sheet sets of guidelines developed by the Family Involvement Partnership for Learning to assist parents in facilitating their children's elementary school success. The front part of the sheets describes general ways parents can support their children, including modeling writing, reading aloud,…

Evaluation and Assessment in Mathematics Education. Science and Technology Education Document Series No. 32.

ERIC Educational Resources Information Center

Robitaille, David F.

This document contains 15 papers selected from 47 papers presented at a theme group of the Sixth International Congress on Mathematical Education. The papers included have been divided into four groups. The first group consists of a survey paper, which discusses the history of assessment and evaluation. The second section consists of six papers…

Rigorous Model Reduction for a Damped-Forced Nonlinear Beam Model: An Infinite-Dimensional Analysis

NASA Astrophysics Data System (ADS)

Kogelbauer, Florian; Haller, George

2018-06-01

We use invariant manifold results on Banach spaces to conclude the existence of spectral submanifolds (SSMs) in a class of nonlinear, externally forced beam oscillations. SSMs are the smoothest nonlinear extensions of spectral subspaces of the linearized beam equation. Reduction in the governing PDE to SSMs provides an explicit low-dimensional model which captures the correct asymptotics of the full, infinite-dimensional dynamics. Our approach is general enough to admit extensions to other types of continuum vibrations. The model-reduction procedure we employ also gives guidelines for a mathematically self-consistent modeling of damping in PDEs describing structural vibrations.

Numerical Modeling of Nonlinear Thermodynamics in SMA Wires

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

Reynolds, D R; Kloucek, P

We present a mathematical model describing the thermodynamic behavior of shape memory alloy wires, as well as a computational technique to solve the resulting system of partial differential equations. The model consists of conservation equations based on a new Helmholtz free energy potential. The computational technique introduces a viscosity-based continuation method, which allows the model to handle dynamic applications where the temporally local behavior of solutions is desired. Computational experiments document that this combination of modeling and solution techniques appropriately predicts the thermally- and stress-induced martensitic phase transitions, as well as the hysteretic behavior and production of latent heat associatedmore » with such materials.« less

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.

Associating Mathematical Stories That Are Written by the 8th Grade Students Who Are Studying at Advantageous and Disadvantageous Regions' Schools with Their Mathematical Perceptions: Istanbul Case

ERIC Educational Resources Information Center

Bahadir, Elif

2017-01-01

In this study, mathematical stories written by 50 middle school students were analyzed. The study group consisted of two different student groups who were living in advantageous and disadvantageous regions in Istanbul. At the first stage, the students were presented a mathematical story called "My Fractal Tree", then told about what the…

Multidisciplinary approaches to understanding collective cell migration in developmental biology.

PubMed

Schumacher, Linus J; Kulesa, Paul M; McLennan, Rebecca; Baker, Ruth E; Maini, Philip K

2016-06-01

Mathematical models are becoming increasingly integrated with experimental efforts in the study of biological systems. Collective cell migration in developmental biology is a particularly fruitful application area for the development of theoretical models to predict the behaviour of complex multicellular systems with many interacting parts. In this context, mathematical models provide a tool to assess the consistency of experimental observations with testable mechanistic hypotheses. In this review, we showcase examples from recent years of multidisciplinary investigations of neural crest cell migration. The neural crest model system has been used to study how collective migration of cell populations is shaped by cell-cell interactions, cell-environmental interactions and heterogeneity between cells. The wide range of emergent behaviours exhibited by neural crest cells in different embryonal locations and in different organisms helps us chart out the spectrum of collective cell migration. At the same time, this diversity in migratory characteristics highlights the need to reconcile or unify the array of currently hypothesized mechanisms through the next generation of experimental data and generalized theoretical descriptions. © 2016 The Authors.

Equilibria of perceptrons for simple contingency problems.

PubMed

Dawson, Michael R W; Dupuis, Brian

2012-08-01

The contingency between cues and outcomes is fundamentally important to theories of causal reasoning and to theories of associative learning. Researchers have computed the equilibria of Rescorla-Wagner models for a variety of contingency problems, and have used these equilibria to identify situations in which the Rescorla-Wagner model is consistent, or inconsistent, with normative models of contingency. Mathematical analyses that directly compare artificial neural networks to contingency theory have not been performed, because of the assumed equivalence between the Rescorla-Wagner learning rule and the delta rule training of artificial neural networks. However, recent results indicate that this equivalence is not as straightforward as typically assumed, suggesting a strong need for mathematical accounts of how networks deal with contingency problems. One such analysis is presented here, where it is proven that the structure of the equilibrium for a simple network trained on a basic contingency problem is quite different from the structure of the equilibrium for a Rescorla-Wagner model faced with the same problem. However, these structural differences lead to functionally equivalent behavior. The implications of this result for the relationships between associative learning, contingency theory, and connectionism are discussed.

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…

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…

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…

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).

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.

Optimal back-extrapolation method for estimating plasma volume in humans using the indocyanine green dilution method

PubMed Central

2014-01-01

Background The indocyanine green dilution method is one of the methods available to estimate plasma volume, although some researchers have questioned the accuracy of this method. Methods We developed a new, physiologically based mathematical model of indocyanine green kinetics that more accurately represents indocyanine green kinetics during the first few minutes postinjection than what is assumed when using the traditional mono-exponential back-extrapolation method. The mathematical model is used to develop an optimal back-extrapolation method for estimating plasma volume based on simulated indocyanine green kinetics obtained from the physiological model. Results Results from a clinical study using the indocyanine green dilution method in 36 subjects with type 2 diabetes indicate that the estimated plasma volumes are considerably lower when using the traditional back-extrapolation method than when using the proposed back-extrapolation method (mean (standard deviation) plasma volume = 26.8 (5.4) mL/kg for the traditional method vs 35.1 (7.0) mL/kg for the proposed method). The results obtained using the proposed method are more consistent with previously reported plasma volume values. Conclusions Based on the more physiological representation of indocyanine green kinetics and greater consistency with previously reported plasma volume values, the new back-extrapolation method is proposed for use when estimating plasma volume using the indocyanine green dilution method. PMID:25052018

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

Stories from the Classroom: The Developing Beliefs and Practices of Beginning Primary Mathematics Teachers

ERIC Educational Resources Information Center

Brady, Kathy

2012-01-01

This study examines the developing beliefs and practices of six beginning primary teachers. Their accounts reveal practices indicative of contemporary approaches to teaching and learning in mathematics. Additionally, a consistency appears to exist between the beliefs and practices of the beginning teachers, and the ideals for mathematics teaching…

Beliefs about Using Technology in the Mathematics Classroom: Interviews with Pre-Service Elementary Teachers

ERIC Educational Resources Information Center

Lin, Cheng-Yao

2008-01-01

This study explored the efficacy of web-based workshops in topics in elementary school mathematics in fostering teachers' confidence and competence in using instructional technology, and thereby promoting more positive attitudes toward using computers and Internet resources in the mathematics classroom. It consisted of in-depth interviews of…

Preschool Teachers' Perceived Math Anxiety and Self-Efficacy for Teaching Mathematics

ERIC Educational Resources Information Center

Cook, Carolyn D.

2017-01-01

This study explored the relationship between math anxiety and perceived self-efficacy for teaching mathematics in preschool teachers. Perceptions of and attributions for the teachers' perceived math anxiety and perceived self-efficacy for teaching mathematics were also explored. The study employed a mixed-method design consisting of both…

Strategies to Recruit and Retain Students in Physical Science and Mathematics on a Diverse College Campus

ERIC Educational Resources Information Center

Chang, Jen-Mei; Kwon, Chuhee; Stevens, Lora; Buonora, Paul

2016-01-01

This article presents implementation details and findings of a National Science Foundation Scholarship in Science, Technology, Engineering, and Mathematics Program (S-STEM) consisting of many high-impact practices to recruit and retain students in the physical sciences and mathematics programs, particularly first-generation and underrepresented…

Solving Common Mathematical Problems

NASA Technical Reports Server (NTRS)

Luz, Paul L.

2005-01-01

Mathematical Solutions Toolset is a collection of five software programs that rapidly solve some common mathematical problems. The programs consist of a set of Microsoft Excel worksheets. The programs provide for entry of input data and display of output data in a user-friendly, menu-driven format, and for automatic execution once the input data has been entered.

Mathematics Anxiety and Beliefs of Turkish Pre-Service Elementary Teachers

ERIC Educational Resources Information Center

Uysal, Figen; Dede, Yüksel

2016-01-01

The purpose of this study was to investigate the relationship between pre-service elementary teachers' mathematics teaching beliefs and mathematics anxiety. The participants of the study consist of 96 pre-service elementary teachers from a department of primary education in a state university in Turkey during the 2010-2011 spring term. Mathematics…

Mathematics and Global Perspectives: A Working Team.

ERIC Educational Resources Information Center

Schwartz, Richard H.

1980-01-01

Ways in which mathematics and global education can be combined are described. Following a discussion of the need for having a citizenry capable of analyzing global issues, methods of infusing global education into the mathematics curriculum and math into the social studies curriculum are offered. Half of the document consists of eight sample…

Improving Mastery of Basic Mathematics Facts in Elementary School through Various Learning Strategies.

ERIC Educational Resources Information Center

Haught, Laurie; Kunce, Christine; Pratt, Phyllis; Werneske, Roberta; Zemel, Susan

This report describes the intervention programs used to improve student proficiency in learning, recalling, and retaining basic mathematics facts. The targeted population consisted of first, second, third, and fifth grades in four suburban midwestern schools. The problems of recalling basic mathematics facts is documented through teacher surveys,…

Student Teachers' Views about Assessment and Evaluation Methods in Mathematics

ERIC Educational Resources Information Center

Dogan, Mustafa

2011-01-01

This study aimed to find out assessment and evaluation approaches in a Mathematics Teacher Training Department based on the views and experiences of student teachers. The study used a descriptive survey method, with the research sample consisting of 150 third- and fourth-year Primary Mathematics student teachers. Data were collected using a…

Turkish High School Teachers' Conceptions of Creativity in Mathematics

ERIC Educational Resources Information Center

Aktas, Meral Cansiz

2016-01-01

The aim of this research is to explore Turkish high school teachers' conceptions of creativity in mathematics. The research was carried out using qualitative research methods. The sample consisted of seven mathematics teachers, and semi-structured interviews were used as a data collection tool. Analysis of the responses indicated that mathematics…

Perceptual Preferences of Mathematically Deficient Elementary Students: Implications for Instruction.

ERIC Educational Resources Information Center

McCoy, Leah P.

Two groups of elementary school students were tested and compared on learning style perceptual preference. One group was comprised of 11 students identified as being in need of remedial instruction in mathematics. The other group consisted of eight average/above average students experiencing slight or no difficulties in mathematics. Grade levels…

Selected Aspects of Mathematics Education in the People's Republic of China.

ERIC Educational Resources Information Center

Swetz, Frank

This paper consists of three articles: (1) "Chinese Mathematics Revision in Accordance with the Teachings of Mao Tse-tung," which shows that Chinese teachers are making concerted efforts to improve both their teaching and curriculum; (2) "Training of Mathematics Teachers in the People's Republic of China," which describes the…

Emergency response to an anthrax attack

PubMed Central

Wein, Lawrence M.; Craft, David L.; Kaplan, Edward H.

2003-01-01

We developed a mathematical model to compare various emergency responses in the event of an airborne anthrax attack. The system consists of an atmospheric dispersion model, an age-dependent dose–response model, a disease progression model, and a set of spatially distributed two-stage queueing systems consisting of antibiotic distribution and hospital care. Our results underscore the need for the extremely aggressive and timely use of oral antibiotics by all asymptomatics in the exposure region, distributed either preattack or by nonprofessionals postattack, and the creation of surge capacity for supportive hospital care via expanded training of nonemergency care workers at the local level and the use of federal and military resources and nationwide medical volunteers. The use of prioritization (based on disease stage and/or age) at both queues, and the development and deployment of modestly rapid and sensitive biosensors, while helpful, produce only second-order improvements. PMID:12651951

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

PubMed

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

2012-12-11

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

Point spread function and depth-invariant focal sweep point spread function for plenoptic camera 2.0.

PubMed

Jin, Xin; Liu, Li; Chen, Yanqin; Dai, Qionghai

2017-05-01

This paper derives a mathematical point spread function (PSF) and a depth-invariant focal sweep point spread function (FSPSF) for plenoptic camera 2.0. Derivation of PSF is based on the Fresnel diffraction equation and image formation analysis of a self-built imaging system which is divided into two sub-systems to reflect the relay imaging properties of plenoptic camera 2.0. The variations in PSF, which are caused by changes of object's depth and sensor position variation, are analyzed. A mathematical model of FSPSF is further derived, which is verified to be depth-invariant. Experiments on the real imaging systems demonstrate the consistency between the proposed PSF and the actual imaging results.

Simulation and Verification of Synchronous Set Relations in Rewriting Logic

NASA Technical Reports Server (NTRS)

Rocha, Camilo; Munoz, Cesar A.

2011-01-01

This paper presents a mathematical foundation and a rewriting logic infrastructure for the execution and property veri cation of synchronous set relations. The mathematical foundation is given in the language of abstract set relations. The infrastructure consists of an ordersorted rewrite theory in Maude, a rewriting logic system, that enables the synchronous execution of a set relation provided by the user. By using the infrastructure, existing algorithm veri cation techniques already available in Maude for traditional asynchronous rewriting, such as reachability analysis and model checking, are automatically available to synchronous set rewriting. The use of the infrastructure is illustrated with an executable operational semantics of a simple synchronous language and the veri cation of temporal properties of a synchronous system.

Preservice Secondary Teachers' Conceptions from a Mathematical Modeling Activity and Connections to the Common Core State Standards

ERIC Educational Resources Information Center

Stohlmann, Micah; Maiorca, Cathrine; Olson, Travis A.

2015-01-01

Mathematical modeling is an essential integrated piece of the Common Core State Standards. However, researchers have shown that mathematical modeling activities can be difficult for teachers to implement. Teachers are more likely to implement mathematical modeling activities if they have their own successful experiences with such activities. This…

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-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.

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…

Making the Most of Modeling Tasks

ERIC Educational Resources Information Center

Wernet, Jamie L.; Lawrence, Kevin A.; Gilbertson, Nicholas J.

2015-01-01

While there is disagreement among mathematics educators about some aspects of its meaning, mathematical modeling generally involves taking a real-world scenario and translating it into the mathematical world (Niss, Blum, and Galbraith 2007). The complete modeling process involves describing situations posed in problems with mathematical concepts,…

Strengthening programs in science, engineering and mathematics. Third annual progress report

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

Sandhu, S.S.

1997-09-30

The Division of Natural Sciences and Mathematics at Claflin College consists of the Departments of Biology, Chemistry, Computer Science, Physics, Engineering and Mathematics. It offers a variety of major and minor academic programs designed to meet the mission and objectives of the college. The division`s pursuit to achieve excellence in science education is adversely impacted by the poor academic preparation of entering students and the lack of equipment, facilities and research participation, required to impart adequate academic training and laboratory skills to the students. Funds were received from the US Department of Energy to improve the divisional facilities and laboratorymore » equipment and establish mechanism at pre-college and college levels to increase (1) the pool of high school students who will enroll in Science and Mathematics courses (2) the pool of well qualified college freshmen who will seek careers in Science, Engineering and Mathematics (3) the graduation rate in Science,engineering and Mathematics at the undergraduate level and (4) the pool of well-qualified students who can successfully compete to enter the graduate schools of their choice in the fields of science, engineering, and mathematics. The strategies that were used to achieve the mentioned objectives include: (1) Improved Mentoring and Advisement, (2) Summer Science Camp for 7th and 8th graders, (3) Summer Research Internships for Claflin SEM Seniors, (4) Summer Internships for Rising High School Seniors, (5) Development of Mathematical Skills at Pre-college/Post-secondary Levels, (6) Expansion of Undergraduate Seminars, (7) Exposure of Undergraduates to Guest Speakers/Roll Models, (8) Visitations by Undergraduate Students to Graduate Schools, and (9) Expanded Academic Program in Environmental Chemistry.« less

Influence of structural parameters of deep groove ball bearings on vibration

NASA Astrophysics Data System (ADS)

Yu, Guangwei; Wu, Rui; Xia, Wei

2018-04-01

Taking 6201 bearing as the research object, a dynamic model of 4 degrees of freedom is established to solve the vibration characteristics such as the displacement, velocity and acceleration of deep groove ball bearings by MATLAB and Runge-Kutta method. By calculating the theoretical value of the frequency of the rolling element passing through the outer ring and the simulation value of the model, it can be known that the theoretical calculation value and the simulation value have good consistency. By the experiments, the measured values and simulation values are consistent. Using the mathematical model, the effect of structural parameters on vibration is obtained. The method in the paper is testified to be feasible and the results can be used as references for the design, manufacturing and testing of deep groove ball bearings.

Standards in C.S.E. and G.C.E.: English and Mathematics. Working Paper No. 9.

ERIC Educational Resources Information Center

Schools Council, London (England).

Attainment tests in English and mathematics were administered to a total sample of 2,011/15-year old students. The English test consisted of a composition and a test battery of objective items. Marking of the composition was made by the test designer on a rapid first-impression reading. The objective test battery consisted of a comprehension test,…

Model Based Targeting of IL-6-Induced Inflammatory Responses in Cultured Primary Hepatocytes to Improve Application of the JAK Inhibitor Ruxolitinib

PubMed Central

Sobotta, Svantje; Raue, Andreas; Huang, Xiaoyun; Vanlier, Joep; Jünger, Anja; Bohl, Sebastian; Albrecht, Ute; Hahnel, Maximilian J.; Wolf, Stephanie; Mueller, Nikola S.; D'Alessandro, Lorenza A.; Mueller-Bohl, Stephanie; Boehm, Martin E.; Lucarelli, Philippe; Bonefas, Sandra; Damm, Georg; Seehofer, Daniel; Lehmann, Wolf D.; Rose-John, Stefan; van der Hoeven, Frank; Gretz, Norbert; Theis, Fabian J.; Ehlting, Christian; Bode, Johannes G.; Timmer, Jens; Schilling, Marcel; Klingmüller, Ursula

2017-01-01

IL-6 is a central mediator of the immediate induction of hepatic acute phase proteins (APP) in the liver during infection and after injury, but increased IL-6 activity has been associated with multiple pathological conditions. In hepatocytes, IL-6 activates JAK1-STAT3 signaling that induces the negative feedback regulator SOCS3 and expression of APPs. While different inhibitors of IL-6-induced JAK1-STAT3-signaling have been developed, understanding their precise impact on signaling dynamics requires a systems biology approach. Here we present a mathematical model of IL-6-induced JAK1-STAT3 signaling that quantitatively links physiological IL-6 concentrations to the dynamics of IL-6-induced signal transduction and expression of target genes in hepatocytes. The mathematical model consists of coupled ordinary differential equations (ODE) and the model parameters were estimated by a maximum likelihood approach, whereas identifiability of the dynamic model parameters was ensured by the Profile Likelihood. Using model simulations coupled with experimental validation we could optimize the long-term impact of the JAK-inhibitor Ruxolitinib, a therapeutic compound that is quickly metabolized. Model-predicted doses and timing of treatments helps to improve the reduction of inflammatory APP gene expression in primary mouse hepatocytes close to levels observed during regenerative conditions. The concept of improved efficacy of the inhibitor through multiple treatments at optimized time intervals was confirmed in primary human hepatocytes. Thus, combining quantitative data generation with mathematical modeling suggests that repetitive treatment with Ruxolitinib is required to effectively target excessive inflammatory responses without exceeding doses recommended by the clinical guidelines. PMID:29062282

Model Based Targeting of IL-6-Induced Inflammatory Responses in Cultured Primary Hepatocytes to Improve Application of the JAK Inhibitor Ruxolitinib.

PubMed

Sobotta, Svantje; Raue, Andreas; Huang, Xiaoyun; Vanlier, Joep; Jünger, Anja; Bohl, Sebastian; Albrecht, Ute; Hahnel, Maximilian J; Wolf, Stephanie; Mueller, Nikola S; D'Alessandro, Lorenza A; Mueller-Bohl, Stephanie; Boehm, Martin E; Lucarelli, Philippe; Bonefas, Sandra; Damm, Georg; Seehofer, Daniel; Lehmann, Wolf D; Rose-John, Stefan; van der Hoeven, Frank; Gretz, Norbert; Theis, Fabian J; Ehlting, Christian; Bode, Johannes G; Timmer, Jens; Schilling, Marcel; Klingmüller, Ursula

2017-01-01

IL-6 is a central mediator of the immediate induction of hepatic acute phase proteins (APP) in the liver during infection and after injury, but increased IL-6 activity has been associated with multiple pathological conditions. In hepatocytes, IL-6 activates JAK1-STAT3 signaling that induces the negative feedback regulator SOCS3 and expression of APPs. While different inhibitors of IL-6-induced JAK1-STAT3-signaling have been developed, understanding their precise impact on signaling dynamics requires a systems biology approach. Here we present a mathematical model of IL-6-induced JAK1-STAT3 signaling that quantitatively links physiological IL-6 concentrations to the dynamics of IL-6-induced signal transduction and expression of target genes in hepatocytes. The mathematical model consists of coupled ordinary differential equations (ODE) and the model parameters were estimated by a maximum likelihood approach, whereas identifiability of the dynamic model parameters was ensured by the Profile Likelihood. Using model simulations coupled with experimental validation we could optimize the long-term impact of the JAK-inhibitor Ruxolitinib, a therapeutic compound that is quickly metabolized. Model-predicted doses and timing of treatments helps to improve the reduction of inflammatory APP gene expression in primary mouse hepatocytes close to levels observed during regenerative conditions. The concept of improved efficacy of the inhibitor through multiple treatments at optimized time intervals was confirmed in primary human hepatocytes. Thus, combining quantitative data generation with mathematical modeling suggests that repetitive treatment with Ruxolitinib is required to effectively target excessive inflammatory responses without exceeding doses recommended by the clinical guidelines.

Thermomechanical Fractional Model of TEMHD Rotational Flow

PubMed Central

Hamza, F.; Abd El-Latief, A.; Khatan, W.

2017-01-01

In this work, the fractional mathematical model of an unsteady rotational flow of Xanthan gum (XG) between two cylinders in the presence of a transverse magnetic field has been studied. This model consists of two fractional parameters α and β representing thermomechanical effects. The Laplace transform is used to obtain the numerical solutions. The fractional parameter influence has been discussed graphically for the functions field distribution (temperature, velocity, stress and electric current distributions). The relationship between the rotation of both cylinders and the fractional parameters has been discussed on the functions field distribution for small and large values of time. PMID:28045941

Improving mathematical problem solving ability through problem-based learning and authentic assessment for the students of Bali State Polytechnic

NASA Astrophysics Data System (ADS)

Darma, I. K.

2018-01-01

This research is aimed at determining: 1) the differences of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) the differences of mathematical problem solving ability between the students facilitated with authentic and conventional assessment model, and 3) interaction effect between learning and assessment model on mathematical problem solving. The research was conducted in Bali State Polytechnic, using the 2x2 experiment factorial design. The samples of this research were 110 students. The data were collected using a theoretically and empirically-validated test. Instruments were validated by using Aiken’s approach of technique content validity and item analysis, and then analyzed using anova stylistic. The result of the analysis shows that the students facilitated with problem-based learning and authentic assessment models get the highest score average compared to the other students, both in the concept understanding and mathematical problem solving. The result of hypothesis test shows that, significantly: 1) there is difference of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) there is difference of mathematical problem solving ability between the students facilitated with authentic assessment model and conventional assessment model, and 3) there is interaction effect between learning model and assessment model on mathematical problem solving. In order to improve the effectiveness of mathematics learning, collaboration between problem-based learning model and authentic assessment model can be considered as one of learning models in class.

Influence of Problem-Based Learning Model of Learning to the Mathematical Communication Ability of Students of Grade XI IPA SMAN 14 Padang

NASA Astrophysics Data System (ADS)

Nisa, I. M.

2018-04-01

The ability of mathematical communication is one of the goals of learning mathematics expected to be mastered by students. However, reality in the field found that the ability of mathematical communication the students of grade XI IPA SMA Negeri 14 Padang have not developed optimally. This is evident from the low test results of communication skills mathematically done. One of the factors that causes this happens is learning that has not been fully able to facilitate students to develop mathematical communication skills well. By therefore, to improve students' mathematical communication skills required a model in the learning activities. One of the models learning that can be used is Problem Based learning model Learning (PBL). The purpose of this study is to see whether the ability the students' mathematical communication using the PBL model better than the students' mathematical communication skills of the learning using conventional learning in Class XI IPA SMAN 14 Padang. This research type is quasi experiment with design Randomized Group Only Design. Population in this research that is student of class XI IPA SMAN 14 Padang with sample class XI IPA 3 and class XI IPA 4. Data retrieval is done by using communication skill test mathematically shaped essay. To test the hypothesis used U-Mann test Whitney. Based on the results of data analysis, it can be concluded that the ability mathematical communication of students whose learning apply more PBL model better than the students' mathematical communication skills of their learning apply conventional learning in class XI IPA SMA 14 Padang at α = 0.05. This indicates that the PBL learning model effect on students' mathematical communication ability.

The development of a valid discovery-based learning module to improve students' mathematical connection

NASA Astrophysics Data System (ADS)

Kuneni, Erna; Mardiyana, Pramudya, Ikrar

2017-08-01

Geometry is the most important branch in mathematics. The purpose of teaching this material is to develop students' level of thinking for a better understanding. Otherwise, geometry in particular, has contributed students' failure in mathematics examinations. This problem occurs due to special feature in geometry which has complexity of correlation among its concept. This relates to mathematical connection. It is still difficult for students to improve this ability. This is because teachers' lack in facilitating students towards it. Eventhough, facilitating students can be in the form of teaching material. A learning module can be a solution because it consists of series activities that should be taken by students to achieve a certain goal. A series activities in this case is adopted by the phases of discovery-based learning model. Through this module, students are facilitated to discover concept by deep instruction and guidance. It can build the mathematical habits of mind and also strengthen the mathematical connection. Method used in this research was ten stages of research and development proposed by Bord and Gall. The research purpose is to create a valid learning module to improve students' mathematical connection in teaching quadrilateral. The retrieved valid module based on media expert judgment is 2,43 for eligibility chart aspect, 2,60 for eligibility presentation aspect, and 3,00 for eligibility contents aspect. Then the retrieved valid module based on material expert judgment is 3,10 for eligibility content aspect, 2,87 for eligibility presentation aspect, and 2,80 for eligibility language and legibility aspect.

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 necessity of using such models may change the nature of mathematical modeling in science and, thus, the nature of science, as it happened in the case of Q-models, which not only led to a revolutionary transformation of physics but also opened new possibilities for scientific thinking and mathematical modeling beyond physics.

Exploring individual differences in children's mathematical skills: a correlational and dimensional approach.

PubMed

Sigmundsson, H; Polman, R C J; Lorås, H

2013-08-01

Individual differences in mathematical skills are typically explained by an innate capability to solve mathematical tasks. At the behavioural level this implies a consistent level of mathematical achievement that can be captured by strong relationships between tasks, as well as by a single statistical dimension that underlies performance on all mathematical tasks. To investigate this general assumption, the present study explored interrelations and dimensions of mathematical skills. For this purpose, 68 ten-year-old children from two schools were tested using nine mathematics tasks from the Basic Knowledge in Mathematics Test. Relatively low-to-moderate correlations between the mathematics tasks indicated most tasks shared less than 25% of their variance. There were four principal components, accounting for 70% of the variance in mathematical skill across tasks and participants. The high specificity in mathematical skills was discussed in relation to the principle of task specificity of learning.

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…

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…

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…

Mathematical model simulation of a diesel spill in the Potomac River

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

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

1995-12-31

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

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…

Multilane Traffic Flow Modeling Using Cellular Automata Theory

NASA Astrophysics Data System (ADS)

Chechina, Antonina; Churbanova, Natalia; Trapeznikova, Marina

2018-02-01

The paper deals with the mathematical modeling of traffic flows on urban road networks using microscopic approach. The model is based on the cellular automata theory and presents a generalization of the Nagel-Schreckenberg model to a multilane case. The created program package allows to simulate traffic on various types of road fragments (T or X type intersection, strait road elements, etc.) and on road networks that consist of these elements. Besides that, it allows to predict the consequences of various decisions regarding road infrastructure changes, such as: number of lanes increasing/decreasing, putting new traffic lights into operation, building new roads, entrances/exits, road junctions.

Modelling of thermal field and point defect dynamics during silicon single crystal growth using CZ technique

NASA Astrophysics Data System (ADS)

Sabanskis, A.; Virbulis, J.

2018-05-01

Mathematical modelling is employed to numerically analyse the dynamics of the Czochralski (CZ) silicon single crystal growth. The model is axisymmetric, its thermal part describes heat transfer by conduction and thermal radiation, and allows to predict the time-dependent shape of the crystal-melt interface. Besides the thermal field, the point defect dynamics is modelled using the finite element method. The considered process consists of cone growth and cylindrical phases, including a short period of a reduced crystal pull rate, and a power jump to avoid large diameter changes. The influence of the thermal stresses on the point defects is also investigated.

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…

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.…

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.

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.

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.

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.

Improving High-Level Thinking Skills by Development of Learning PBL Approach on the Learning Mathematics for Senior High School Students

ERIC Educational Resources Information Center

Surya, Edy; Syahputra, Edi

2017-01-01

This study aims to improve the ability of high-level thinking by developing learning models based on problems in senior high school students. The type study is research development. The subject of dissemination consists in 3 district/city in North Sumatera, namely: SMK Negeri 6 Medan, MAN Deli Serdang Distric and SMA Yapim Taruna Langkat Distric,…

Evaluation of the effect of elastic joints on the auto-oscillation of spacecraft with gas-reactive direction systems

NASA Technical Reports Server (NTRS)

Sasin, G. G.

1979-01-01

A mathematical model was obtained, on the basis of the method of mixed coordinates, of a generalized flexible spacecraft at one end of which was appended the directive action of a system of gas reactive nozzles. Various structural forms were obtained functionally describing flexible spacecraft, as systems consisting of a solid central body with flexible structural elements joined to it.

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

Thangavelu, Pulari U.; Gupta, Vipul; Dixit, Narendra M., E-mail: narendra@chemeng.iisc.ernet.in

The contest between the host factor APOBEC3G (A3G) and the HIV-1 protein Vif presents an attractive target of intervention. The extent to which the A3G–Vif interaction must be suppressed to tilt the balance in favor of A3G remains unknown. We employed stochastic simulations and mathematical modeling of the within-host dynamics and evolution of HIV-1 to estimate the fraction of progeny virions that must incorporate A3G to render productive infection unsustainable. Using three different approaches, we found consistently that a transition from sustained infection to suppression of productive infection occurred when the latter fraction exceeded ∼0.8. The transition was triggered bymore » A3G-induced hypermutations that led to premature stop codons compromising viral production and was consistent with driving the basic reproductive number, R{sub 0}, below unity. The fraction identified may serve as a quantitative guideline for strategies targeting the A3G–Vif axis. - Highlights: • We perform simulations and mathematical modeling of the role of APOBEC3G in suppressing HIV-1 infection. • In three distinct ways, we estimate that when over 80% of progeny virions carry APOBEC3G, productive HIV-1 infection would be suppressed. • Our estimate of this critical fraction presents quantitative guidelines for strategies targeting the APOBEC3G–Vif axis.« less

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.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Towards the Construction of a Framework to Deal with Routine Problems to Foster Mathematical Inquiry

ERIC Educational Resources Information Center

Santos-Trigo, Manuel; Camacho-Machin, Matias

2009-01-01

To what extent does the process of solving textbook problems help students develop a way of thinking that is consistent with mathematical practice? Can routine problems be transformed into problem solving activities that promote students' mathematical reflection? These questions are used to outline and discuss features of an inquiry framework…

Language and Mathematical Performance: A Comparison of Lower Secondary School Students with Different Level of Mathematical Skills

ERIC Educational Resources Information Center

Korhonen, Johan; Linnanmaki, Karin; Aunio, Pirjo

2012-01-01

This study investigated the connection between language (i.e., word comprehension, reading comprehension and spelling skills) and mathematical performance. The sample consisted of grade nine students (N = 810) in 14 lower secondary schools in the Swedish speaking areas of Finland. Standardized tests for reading and writing skills, and mathematical…

Logical-Mathematical Constructions in an Initial Course at the University: A View of Their Syntactic, Semantic and Pragmatic Aspects

ERIC Educational Resources Information Center

Falsetti, Marcela; Alvarez, Marisa

2015-01-01

We present an analysis of students' formal constructions in mathematics regarding to syntactic, semantic and pragmatic aspects. The analyzed tasks correspond to students of the Course of Mathematics for the admission to the university. Our study was qualitative, consisted in the identification, analysis and interpretation, focused in logic…

Analysis of Mathematics Teachers' Self-Efficacy Levels Concerning the Teaching Process

ERIC Educational Resources Information Center

Ünsal, Serkan; Korkmaz, Fahrettin; Perçin, Safiye

2016-01-01

The purpose of this study is to identify mathematics teachers' opinions on the teaching process self-efficacy levels; and to examine mathematics teachers' teaching process self-efficacy beliefs with regards to specific variables. The study was conducted in Turkey during the second term of the 2015-2016 academic year. The study sample consisted of…

Matriculation Mathematics, Pure Mathematics - Test Papers. Circular of Information to Secondary Schools.

ERIC Educational Resources Information Center

Victoria Education Dept. (Australia).

This document consists of test questions used in three state high schools teaching the new Matriculation pure mathematics course (approximately grade 12). This material was circulated to all schools teaching this course as a teacher resource. The questions are arranged in 14 papers of varying structure and length. Most questions are of the essay…

What's Happening in the Mathematical Sciences, 1993-1994.

ERIC Educational Resources Information Center

Cipra, Barry

1993-01-01

This document consists of the first two volumes of a new annual serial devoted to surveying some of the important developments in the mathematical sciences in the previous year or so. Mathematics is constantly growing and changing, reaching out to other areas of science and helping to solve some of the major problems facing society. Volumes 1 and…

Understanding of Prospective Mathematics Teachers of the Concept of Diagonal

ERIC Educational Resources Information Center

Ayvaz, Ülkü; Gündüz, Nazan; Bozkus, Figen

2017-01-01

This study aims to investigate the concept images of prospective mathematics teachers about the concept of diagonal. With this aim, case study method was used in the study. The participants of the study were consisted of 7 prospective teachers educating at the Department of Mathematics Education. Criterion sampling method was used to select the…

Test Anxiety in Mathematics among Early Undergraduate Students in a British University in Malaysia

ERIC Educational Resources Information Center

Karjanto, Natanael; Yong, Su Ting

2013-01-01

The level of test anxiety in mathematics subjects among early undergraduate students at the University of Nottingham Malaysia Campus is studied in this article. The sample consists of 206 students taking several mathematics modules who completed the questionnaires on test anxiety just before they entered the venue for midterm examinations. The…

Self-Contained versus Departmentalized Settings in Urban Elementary Schools: An Analysis of Fifth-Grade Student Mathematics Performance

ERIC Educational Resources Information Center

Jack, Diamond Marie

2014-01-01

Student achievement in mathematics, particularly in urban areas, is a consistent concern in the United States. Research suggests that teachers either are under qualified or have a negative perception of themselves as mathematics teachers. Departmentalization on the elementary level is an organizational structure that may benefit urban students and…

And Still I See No Changes: Enduring Views of Students of Color in Science and Mathematics Education Policy Reports

ERIC Educational Resources Information Center

Basile, Vincent; Lopez, Enrique

2015-01-01

Federal education policy reports in science and mathematics education have treated Students of Color consistently over the past two decades, addressing the underrepresentation of minorities in science, technology, engineering, and mathematics (STEM) fields with little regard to actual issues of race and ethnicity. We examine how 17 federal…

Finnish Mathematics Teaching from a Reform Perspective: A Video-Based Case-Study Analysis

ERIC Educational Resources Information Center

Andrews, Paul

2013-01-01

This article offers a qualitative analysis of videotaped mathematics lessons taught by four teachers in a provincial university city in Finland. My study is framed not only by Finnish success on Programme for International Student Assessment (PISA) but also by the objectives of current mathematics education reform, which are consistent with PISA's…

A Conceptual Analysis of the Knowledge of Prospective Mathematics Teachers about Degree and Radian

ERIC Educational Resources Information Center

Tuna, Abdulkadir

2013-01-01

This study examined the knowledge levels of prospective mathematics teachers about the concepts of degree and radian, which are among the angle measuring units that constitute the basis of trigonometry, and the relationships between those concepts. The study group consisted of 93 prospective mathematics teachers attending a state university in…

Relationships among Preservice Primary Mathematics Teachers' Gender, Academic Success and Spatial Ability

ERIC Educational Resources Information Center

Turgut, Melih; Yilmaz, Suha

2012-01-01

The aim of this work is to investigate relationships among pre-service primary mathematics teachers' gender, academic success and spatial ability. The study was conducted in Izmir with 193 pre-service primary mathematics teachers of Dokuz Eylul University. In the work, spatial ability test, which consists of two main sub-tests measuring spatial…

A Case Study on Mathematical Literacy of Prospective Elementary School Teachers

ERIC Educational Resources Information Center

Suharta, I. Gusti Putu; Suarjana, I. Made

2018-01-01

The purpose of this study is to describe Mathematical Literacy (ML) of Prospective Elementary School Teachers with attention to aspects of mathematical skills and gender. The type of research is qualitative with the research design of Case Study. Respondents are assigned 12 Prospective Elementary School Teachers, consisting of 6 men and 6 women.…

Mathematics. Unit 6: A Core Curriculum of Related Instruction for Apprentices.

ERIC Educational Resources Information Center

New York State Education Dept., Albany. Bureau of Occupational and Career Curriculum Development.

The mathematics unit is presented to assist apprentices to acquire a general knowledge of mathematic skills. The unit consists of nine modules: (1) basic addition, subtraction, multiplication, and division; (2) conventional linear measure; (3) using the metric system, (4) steps to take in solving problems, (5) how to calculate areas and volumes,…

Gifted Students' Metaphor Images about Mathematics

ERIC Educational Resources Information Center

Arikan, Elif Esra; Unal, Hasan

2015-01-01

The aim of this study is to investigate the metaphors images of gifted students about mathematics. The sample of the study consists of 82 gifted students, which are 2, 3, 4, 5, 6, 7 graders, from Istanbul. Data were collected by asking students to complete the sentence: "Mathematics is as …, because…". In the study content analysis was…

Longitudinal Effects of Technology Integration and Teacher Professional Development on Students' Mathematics Achievement

ERIC Educational Resources Information Center

Bicer, Ali; Capraro, Robert M.

2017-01-01

MathForward is a program that provides teacher professional development and integrates the use of technology as a tool in the classroom. The present study examined students' mathematics growth from 2012 to 2013 and observed how students' mathematics scores changed after their school implemented the MathForward program. The sample consisted of two…

An imaging-based stochastic model for simulation of tumour vasculature

NASA Astrophysics Data System (ADS)

Adhikarla, Vikram; Jeraj, Robert

2012-10-01

A mathematical model which reconstructs the structure of existing vasculature using patient-specific anatomical, functional and molecular imaging as input was developed. The vessel structure is modelled according to empirical vascular parameters, such as the mean vessel branching angle. The model is calibrated such that the resultant oxygen map modelled from the simulated microvasculature stochastically matches the input oxygen map to a high degree of accuracy (R2 ≈ 1). The calibrated model was successfully applied to preclinical imaging data. Starting from the anatomical vasculature image (obtained from contrast-enhanced computed tomography), a representative map of the complete vasculature was stochastically simulated as determined by the oxygen map (obtained from hypoxia [64Cu]Cu-ATSM positron emission tomography). The simulated microscopic vasculature and the calculated oxygenation map successfully represent the imaged hypoxia distribution (R2 = 0.94). The model elicits the parameters required to simulate vasculature consistent with imaging and provides a key mathematical relationship relating the vessel volume to the tissue oxygen tension. Apart from providing an excellent framework for visualizing the imaging gap between the microscopic and macroscopic imagings, the model has the potential to be extended as a tool to study the dynamics between the tumour and the vasculature in a patient-specific manner and has an application in the simulation of anti-angiogenic therapies.

Towards a Rational Model for the Triple Velocity Correlations of Turbulence

NASA Technical Reports Server (NTRS)

Younis, B. A.; Gatski, T. B.; Speziale, C. G.

1999-01-01

This paper presents a rational approach to modelling the triple velocity correlations that appear in the transport equations for the Reynolds stresses. All existing models of these correlations have largely been formulated on phenomenological grounds and are defective in one important aspect: they all neglect to allow for the dependence of these correlations on the local gradients of mean velocity. The mathematical necessity for this dependence will be demonstrated in the paper. The present contribution lies in the novel use of Group Representation Theory to determine the most general tensorial form of these correlations in terms of all the second- and third-order tensor quantities that appear in the exact equations that govern their evolution. The requisite representation did not exist in the literature and therefore had to be developed specifically for this purpose by Professor G. F. Smith. The outcome of this work is a mathematical framework for the construction of algebraic, explicit, and rational models for the triple velocity correlations that are theoretically consistent and include all the correct dependencies. Previous models are reviewed, and all are shown to be an incomplete subset of this new representation, even to lowest order.