The image of mathematics held by Irish post-primary students

NASA Astrophysics Data System (ADS)

Lane, Ciara; Stynes, Martin; O'Donoghue, John

2014-08-01

The image of mathematics held by Irish post-primary students was examined and a model for the image found was constructed. Initially, a definition for 'image of mathematics' was adopted with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. Research focused on students studying ordinary level mathematics for the Irish Leaving Certificate examination - the final examination for students in second-level or post-primary education. Students were aged between 15 and 18 years. A questionnaire was constructed with both quantitative and qualitative aspects. The questionnaire survey was completed by 356 post-primary students. Responses were analysed quantitatively using Statistical Package for the Social Sciences (SPSS) and qualitatively using the constant comparative method of analysis and by reviewing individual responses. Findings provide an insight into Irish post-primary students' images of mathematics and offer a means for constructing a theoretical model of image of mathematics which could be beneficial for future research.

Mathematics and Measurement.

PubMed

Boisvert, R F; Donahue, M J; Lozier, D W; McMichael, R; Rust, B W

2001-01-01

In this paper we describe the role that mathematics plays in measurement science at NIST. We first survey the history behind NIST's current work in this area, starting with the NBS Math Tables project of the 1930s. We then provide examples of more recent efforts in the application of mathematics to measurement science, including the solution of ill-posed inverse problems, characterization of the accuracy of software for micromagnetic modeling, and in the development and dissemination of mathematical reference data. Finally, we comment on emerging issues in measurement science to which mathematicians will devote their energies in coming years.

Validation of a multi-phase plant-wide model for the description of the aeration process in a WWTP.

PubMed

Lizarralde, I; Fernández-Arévalo, T; Beltrán, S; Ayesa, E; Grau, P

2018-02-01

This paper introduces a new mathematical model built under the PC-PWM methodology to describe the aeration process in a full-scale WWTP. This methodology enables a systematic and rigorous incorporation of chemical and physico-chemical transformations into biochemical process models, particularly for the description of liquid-gas transfer to describe the aeration process. The mathematical model constructed is able to reproduce biological COD and nitrogen removal, liquid-gas transfer and chemical reactions. The capability of the model to describe the liquid-gas mass transfer has been tested by comparing simulated and experimental results in a full-scale WWTP. Finally, an exploration by simulation has been undertaken to show the potential of the mathematical model. Copyright © 2017 Elsevier Ltd. All rights reserved.

Towards predictive models of the human gut microbiome

PubMed Central

2014-01-01

The intestinal microbiota is an ecosystem susceptible to external perturbations such as dietary changes and antibiotic therapies. Mathematical models of microbial communities could be of great value in the rational design of microbiota-tailoring diets and therapies. Here, we discuss how advances in another field, engineering of microbial communities for wastewater treatment bioreactors, could inspire development of mechanistic mathematical models of the gut microbiota. We review the current state-of-the-art in bioreactor modeling and current efforts in modeling the intestinal microbiota. Mathematical modeling could benefit greatly from the deluge of data emerging from metagenomic studies, but data-driven approaches such as network inference that aim to predict microbiome dynamics without explicit mechanistic knowledge seem better suited to model these data. Finally, we discuss how the integration of microbiome shotgun sequencing and metabolic modeling approaches such as flux balance analysis may fulfill the promise of a mechanistic model of the intestinal microbiota. PMID:24727124

Final Report

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

Stinis, Panos

2016-08-07

This is the final report for the work conducted at the University of Minnesota (during the period 12/01/12-09/18/14) by PI Panos Stinis as part of the "Collaboratory on Mathematics for Mesoscopic Modeling of Materials" (CM4). CM4 is a multi-institution DOE-funded project whose aim is to conduct basic and applied research in the emerging field of mesoscopic modeling of materials.

A Model Program in Science, Mathematics, and Technology. Final Report TP87-9.

ERIC Educational Resources Information Center

McDowell, Ceasar; And Others

Over the past 5 years parents, industry leaders, and policy makers have called repeatedly for the improvement of mathematics and science education in urban schools and for measures to insure that all students are "technologically literate." Various efforts at the national, state, and local levels have emerged in response to these calls, with…

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

NASA Astrophysics Data System (ADS)

Hamid, H.

2018-01-01

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

Introducing Seismic Tomography with Computational Modeling

NASA Astrophysics Data System (ADS)

Neves, R.; Neves, M. L.; Teodoro, V.

2011-12-01

Learning seismic tomography principles and techniques involves advanced physical and computational knowledge. In depth learning of such computational skills is a difficult cognitive process that requires a strong background in physics, mathematics and computer programming. The corresponding learning environments and pedagogic methodologies should then involve sets of computational modelling activities with computer software systems which allow students the possibility to improve their mathematical or programming knowledge and simultaneously focus on the learning of seismic wave propagation and inverse theory. To reduce the level of cognitive opacity associated with mathematical or programming knowledge, several computer modelling systems have already been developed (Neves & Teodoro, 2010). Among such systems, Modellus is particularly well suited to achieve this goal because it is a domain general environment for explorative and expressive modelling with the following main advantages: 1) an easy and intuitive creation of mathematical models using just standard mathematical notation; 2) the simultaneous exploration of images, tables, graphs and object animations; 3) the attribution of mathematical properties expressed in the models to animated objects; and finally 4) the computation and display of mathematical quantities obtained from the analysis of images and graphs. Here we describe virtual simulations and educational exercises which enable students an easy grasp of the fundamental of seismic tomography. The simulations make the lecture more interactive and allow students the possibility to overcome their lack of advanced mathematical or programming knowledge and focus on the learning of seismological concepts and processes taking advantage of basic scientific computation methods and tools.

Editorial: Mathematical Methods and Modeling in Machine Fault Diagnosis

DOE PAGES

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

2014-12-18

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

Mathematics and Measurement

PubMed Central

Boisvert, Ronald F.; Donahue, Michael J.; Lozier, Daniel W.; McMichael, Robert; Rust, Bert W.

2001-01-01

In this paper we describe the role that mathematics plays in measurement science at NIST. We first survey the history behind NIST’s current work in this area, starting with the NBS Math Tables project of the 1930s. We then provide examples of more recent efforts in the application of mathematics to measurement science, including the solution of ill-posed inverse problems, characterization of the accuracy of software for micromagnetic modeling, and in the development and dissemination of mathematical reference data. Finally, we comment on emerging issues in measurement science to which mathematicians will devote their energies in coming years. PMID:27500024

Respiratory protective device design using control system techniques

NASA Technical Reports Server (NTRS)

Burgess, W. A.; Yankovich, D.

1972-01-01

The feasibility of a control system analysis approach to provide a design base for respiratory protective devices is considered. A system design approach requires that all functions and components of the system be mathematically identified in a model of the RPD. The mathematical notations describe the operation of the components as closely as possible. The individual component mathematical descriptions are then combined to describe the complete RPD. Finally, analysis of the mathematical notation by control system theory is used to derive compensating component values that force the system to operate in a stable and predictable manner.

Mathematical models of the simplest fuzzy PI/PD controllers with skewed input and output fuzzy sets.

PubMed

Mohan, B M; Sinha, Arpita

2008-07-01

This paper unveils mathematical models for fuzzy PI/PD controllers which employ two skewed fuzzy sets for each of the two-input variables and three skewed fuzzy sets for the output variable. The basic constituents of these models are Gamma-type and L-type membership functions for each input, trapezoidal/triangular membership functions for output, intersection/algebraic product triangular norm, maximum/drastic sum triangular conorm, Mamdani minimum/Larsen product/drastic product inference method, and center of sums defuzzification method. The existing simplest fuzzy PI/PD controller structures derived via symmetrical fuzzy sets become special cases of the mathematical models revealed in this paper. Finally, a numerical example along with its simulation results are included to demonstrate the effectiveness of the simplest fuzzy PI controllers.

Self-charging of identical grains in the absence of an external field.

PubMed

Yoshimatsu, R; Araújo, N A M; Wurm, G; Herrmann, H J; Shinbrot, T

2017-01-06

We investigate the electrostatic charging of an agitated bed of identical grains using simulations, mathematical modeling, and experiments. We simulate charging with a discrete-element model including electrical multipoles and find that infinitesimally small initial charges can grow exponentially rapidly. We propose a mathematical Turing model that defines conditions for exponential charging to occur and provides insights into the mechanisms involved. Finally, we confirm the predicted exponential growth in experiments using vibrated grains under microgravity, and we describe novel predicted spatiotemporal states that merit further study.

Self-charging of identical grains in the absence of an external field

NASA Astrophysics Data System (ADS)

Yoshimatsu, R.; Araújo, N. A. M.; Wurm, G.; Herrmann, H. J.; Shinbrot, T.

2017-01-01

We investigate the electrostatic charging of an agitated bed of identical grains using simulations, mathematical modeling, and experiments. We simulate charging with a discrete-element model including electrical multipoles and find that infinitesimally small initial charges can grow exponentially rapidly. We propose a mathematical Turing model that defines conditions for exponential charging to occur and provides insights into the mechanisms involved. Finally, we confirm the predicted exponential growth in experiments using vibrated grains under microgravity, and we describe novel predicted spatiotemporal states that merit further study.

Something from nothing: self-charging of identical grains

NASA Astrophysics Data System (ADS)

Shinbrot, Troy; Yoshimatsu, Ryuta; Nuno Araujo, Nuno; Wurm, Gerhard; Herrmann, Hans

We investigate the electrostatic charging of an agitated bed of identical grains using simulations, mathematical modeling, and experiments. We simulate charging with a discrete-element model including electrical multipoles and find that infinitesimally small initial charges can grow exponentially rapidly. We propose a mathematical Turing model that defines conditions for exponential charging to occur and provides insights into the mechanisms involved. Finally, we confirm the predicted exponential growth in experiments using vibrated grains under microgravity, and we describe novel predicted spatiotemporal states that merit further study. I acknowledge support from NSF/DMR, award 1404792.

Mathematical and computational modelling of skin biophysics: a review

PubMed Central

2017-01-01

The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, through anelasticity, including growth, to thermoelasticity. Microstructural and phenomenological approaches combining imaging techniques are also discussed. Finally, recent research applications on skin wrinkles will be presented to highlight the potential of physics-based modelling of skin in tackling global challenges such as ageing of the population and the associated skin degradation, diseases and traumas. PMID:28804267

Mathematical and computational modelling of skin biophysics: a review

NASA Astrophysics Data System (ADS)

Limbert, Georges

2017-07-01

The objective of this paper is to provide a review on some aspects of the mathematical and computational modelling of skin biophysics, with special focus on constitutive theories based on nonlinear continuum mechanics from elasticity, through anelasticity, including growth, to thermoelasticity. Microstructural and phenomenological approaches combining imaging techniques are also discussed. Finally, recent research applications on skin wrinkles will be presented to highlight the potential of physics-based modelling of skin in tackling global challenges such as ageing of the population and the associated skin degradation, diseases and traumas.

The mathematical modeling of rapid solidification processing. Ph.D. Thesis. Final Report

NASA Technical Reports Server (NTRS)

Gutierrez-Miravete, E.

1986-01-01

The detailed formulation of and the results obtained from a continuum mechanics-based mathematical model of the planar flow melt spinning (PFMS) rapid solidification system are presented and discussed. The numerical algorithm proposed is capable of computing the cooling and freezing rates as well as the fluid flow and capillary phenomena which take place inside the molten puddle formed in the PFMS process. The FORTRAN listings of some of the most useful computer programs and a collection of appendices describing the basic equations used for the modeling are included.

Self-charging of identical grains in the absence of an external field

PubMed Central

Yoshimatsu, R.; Araújo, N. A. M.; Wurm, G.; Herrmann, H. J.; Shinbrot, T.

2017-01-01

We investigate the electrostatic charging of an agitated bed of identical grains using simulations, mathematical modeling, and experiments. We simulate charging with a discrete-element model including electrical multipoles and find that infinitesimally small initial charges can grow exponentially rapidly. We propose a mathematical Turing model that defines conditions for exponential charging to occur and provides insights into the mechanisms involved. Finally, we confirm the predicted exponential growth in experiments using vibrated grains under microgravity, and we describe novel predicted spatiotemporal states that merit further study. PMID:28059124

Computer modeling of heat pipe performance

NASA Technical Reports Server (NTRS)

Peterson, G. P.

1983-01-01

A parametric study of the defining equations which govern the steady state operational characteristics of the Grumman monogroove dual passage heat pipe is presented. These defining equations are combined to develop a mathematical model which describes and predicts the operational and performance capabilities of a specific heat pipe given the necessary physical characteristics and working fluid. Included is a brief review of the current literature, a discussion of the governing equations, and a description of both the mathematical and computer model. Final results of preliminary test runs of the model are presented and compared with experimental tests on actual prototypes.

On the Modeling of Vacuum Arc Remelting Process in Titanium Alloys

NASA Astrophysics Data System (ADS)

Patel, Ashish; Fiore, Daniel

2016-07-01

Mathematical modeling is routinely used in the process development and production of advanced aerospace alloys to gain greater insight into the effect of process parameters on final properties. This article describes the application of a 2-D mathematical VAR model presented at previous LMPC meetings. The impact of process parameters on melt pool geometry, solidification behavior, fluid-flow and chemistry in a Ti-6Al-4V ingot is discussed. Model predictions are validated against published data from a industrial size ingot, and results of a parametric study on particle dissolution are also discussed.

Taguchi method for partial differential equations with application in tumor growth.

PubMed

Ilea, M; Turnea, M; Rotariu, M; Arotăriţei, D; Popescu, Marilena

2014-01-01

The growth of tumors is a highly complex process. To describe this process, mathematical models are needed. A variety of partial differential mathematical models for tumor growth have been developed and studied. Most of those models are based on the reaction-diffusion equations and mass conservation law. A variety of modeling strategies have been developed, each focusing on tumor growth. Systems of time-dependent partial differential equations occur in many branches of applied mathematics. The vast majority of mathematical models in tumor growth are formulated in terms of partial differential equations. We propose a mathematical model for the interactions between these three cancer cell populations. The Taguchi methods are widely used by quality engineering scientists to compare the effects of multiple variables, together with their interactions, with a simple and manageable experimental design. In Taguchi's design of experiments, variation is more interesting to study than the average. First, Taguchi methods are utilized to search for the significant factors and the optimal level combination of parameters. Except the three parameters levels, other factors levels other factors levels would not be considered. Second, cutting parameters namely, cutting speed, depth of cut, and feed rate are designed using the Taguchi method. Finally, the adequacy of the developed mathematical model is proved by ANOVA. According to the results of ANOVA, since the percentage contribution of the combined error is as small. Many mathematical models can be quantitatively characterized by partial differential equations. The use of MATLAB and Taguchi method in this article illustrates the important role of informatics in research in mathematical modeling. The study of tumor growth cells is an exciting and important topic in cancer research and will profit considerably from theoretical input. Interpret these results to be a permanent collaboration between math's and medical oncologists.

Latent transition analysis of pre-service teachers' efficacy in mathematics and science

NASA Astrophysics Data System (ADS)

Ward, Elizabeth Kennedy

This study modeled changes in pre-service teacher efficacy in mathematics and science over the course of the final year of teacher preparation using latent transition analysis (LTA), a longitudinal form of analysis that builds on two modeling traditions (latent class analysis (LCA) and auto-regressive modeling). Data were collected using the STEBI-B, MTEBI-r, and the ABNTMS instruments. The findings suggest that LTA is a viable technique for use in teacher efficacy research. Teacher efficacy is modeled as a construct with two dimensions: personal teaching efficacy (PTE) and outcome expectancy (OE). Findings suggest that the mathematics and science teaching efficacy (PTE) of pre-service teachers is a multi-class phenomena. The analyses revealed a four-class model of PTE at the beginning and end of the final year of teacher training. Results indicate that when pre-service teachers transition between classes, they tend to move from a lower efficacy class into a higher efficacy class. In addition, the findings suggest that time-varying variables (attitudes and beliefs) and time-invariant variables (previous coursework, previous experiences, and teacher perceptions) are statistically significant predictors of efficacy class membership. Further, analyses suggest that the measures used to assess outcome expectancy are not suitable for LCA and LTA procedures.

Interventions in Early Mathematics: Avoiding Pollution and Dilution.

PubMed

Sarama, Julie; Clements, Douglas H

2017-01-01

Although specific interventions in early mathematics have been successful, few have been brought to scale successfully, especially across the challenging diversity of populations and contexts in the early childhood system in the United States. In this chapter, we analyze a theoretically based scale-up model for early mathematics that was designed to avoid the pollution and dilution that often plagues efforts to achieve broad success. We elaborate the theoretical framework by noting the junctures that are susceptible to dilution or pollution. Then we expatiate the model's guidelines to describe specifically how they were designed and implemented to mitigate pollution and dilution. Finally, we provide evidence regarding the success of these efforts. © 2017 Elsevier Inc. All rights reserved.

Nonlinear-programming mathematical modeling of coal blending for power plant

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

Tang Longhua; Zhou Junhu; Yao Qiang

At present most of the blending works are guided by experience or linear-programming (LP) which can not reflect the coal complicated characteristics properly. Experimental and theoretical research work shows that most of the coal blend properties can not always be measured as a linear function of the properties of the individual coals in the blend. The authors introduced nonlinear functions or processes (including neural network and fuzzy mathematics), established on the experiments directed by the authors and other researchers, to quantitatively describe the complex coal blend parameters. Finally nonlinear-programming (NLP) mathematical modeling of coal blend is introduced and utilized inmore » the Hangzhou Coal Blending Center. Predictions based on the new method resulted in different results from the ones based on LP modeling. The authors concludes that it is very important to introduce NLP modeling, instead of NL modeling, into the work of coal blending.« less

Trade-offs mathematical modelling of 3DCE in new product development: real three dimensions and directions for development

NASA Astrophysics Data System (ADS)

Ilhami, M. A.; Subagyo; Masruroh, N. A.

2018-04-01

In the last two decades, coordinating product, process, and supply chain has become the main focus in recent years as a growing body of research, which mathematical modelling is leading technique used in the early phase design. In this paper, we aim to conduct a comprehensive literature review of published paper and propose directions for future research, especially in mathematical modelling. Our findings exhibit fact that evidently there are only a few papers coordinate “real three dimensions”. The other papers, in fact, show simply two dimensions. Finally, some suggestions are proposed such as paying more attention to “real three dimensions” research-based and more focus on minimizing time to market, product life cycle consideration, and product rollover.

Teaching using moodle in mathematics education

NASA Astrophysics Data System (ADS)

Handayanto, A.; Supandi, S.; Ariyanto, L.

2018-05-01

The aim of this study is to determine the effect of Learning Modeling System (LMS) Moodle in learning. The population is taken from all students of Mathematics Education, University of PGRI Semarang. The sample was randomly selected from five different course groups. The initial score is taken from the semester test, and the final score is taken through the semester test after the five groups are taught using Moodle. The results of both test results are compared to find out the increase in learning outcomes. Meanwhile, the student's attitude toward learning is taken through his mathematical disposition through questionnaire. The results show that there was a significant increase in exam results on the final exam of the semester. This result is supported by student learning interest which increases on average after using LMS Moodle taken from disposition data.

Current advances in mathematical modeling of anti-cancer drug penetration into tumor tissues.

PubMed

Kim, Munju; Gillies, Robert J; Rejniak, Katarzyna A

2013-11-18

Delivery of anti-cancer drugs to tumor tissues, including their interstitial transport and cellular uptake, is a complex process involving various biochemical, mechanical, and biophysical factors. Mathematical modeling provides a means through which to understand this complexity better, as well as to examine interactions between contributing components in a systematic way via computational simulations and quantitative analyses. In this review, we present the current state of mathematical modeling approaches that address phenomena related to drug delivery. We describe how various types of models were used to predict spatio-temporal distributions of drugs within the tumor tissue, to simulate different ways to overcome barriers to drug transport, or to optimize treatment schedules. Finally, we discuss how integration of mathematical modeling with experimental or clinical data can provide better tools to understand the drug delivery process, in particular to examine the specific tissue- or compound-related factors that limit drug penetration through tumors. Such tools will be important in designing new chemotherapy targets and optimal treatment strategies, as well as in developing non-invasive diagnosis to monitor treatment response and detect tumor recurrence.

Modeling birds on wires.

PubMed

Aydoğdu, A; Frasca, P; D'Apice, C; Manzo, R; Thornton, J M; Gachomo, B; Wilson, T; Cheung, B; Tariq, U; Saidel, W; Piccoli, B

2017-02-21

In this paper we introduce a mathematical model to study the group dynamics of birds resting on wires. The model is agent-based and postulates attraction-repulsion forces between the interacting birds: the interactions are "topological", in the sense that they involve a given number of neighbors irrespective of their distance. The model is first mathematically analyzed and then simulated to study its main properties: we observe that the model predicts birds to be more widely spaced near the borders of each group. We compare the results from the model with experimental data, derived from the analysis of pictures of pigeons and starlings taken in New Jersey: two different image elaboration protocols allow us to establish a good agreement with the model and to quantify its main parameters. We also discuss the potential handedness of the birds, by analyzing the group organization features and the group dynamics at the arrival of new birds. Finally, we propose a more refined mathematical model that describes landing and departing birds by suitable stochastic processes. Copyright © 2016 Elsevier Ltd. All rights reserved.

Modelling the effect of the physical and chemical characteristics of the materials used as casing layers on the production parameters of Agaricus bisporus.

PubMed

Pardo, Arturo; Emilio Pardo, J; de Juan, J Arturo; Zied, Diego Cunha

2010-12-01

The aim of this research was to show the mathematical data obtained through the correlations found between the physical and chemical characteristics of casing layers and the final mushrooms' properties. For this purpose, 8 casing layers were used: soil, soil + peat moss, soil + black peat, soil + composted pine bark, soil + coconut fibre pith, soil + wood fibre, soil + composted vine shoots and, finally, the casing of La Rioja subjected to the ruffling practice. The conclusion that interplays in the fructification process with only the physical and chemical characteristics of casing are complicated was drawn. The mathematical data obtained in earliness could be explained in non-ruffled cultivation. The variability observed for the mushroom weight and the mushroom diameter variables could be explained in both ruffled and non-ruffled cultivations. Finally, the properties of the final quality of mushrooms were established by regression analysis.

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

PubMed

Djuris, Jelena; Djuric, Zorica

2017-11-30

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

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.

1993-1994 Final technical report for establishing the SECME Model in the District of Columbia

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

Vickers, R.G.

1995-12-31

This is the final report for a program to establish the SECME Model in the District of Columbia. This program has seen the development of a partnership between the District of Columbia Public Schools, the University of the District of Columbia, the Department of Energy, and SECME. This partnership has demonstrated positive achievement in mathematics and science education and learning in students within the District of Columbia.

A predictive mathematical model for the calculation of the final mass of Graves' disease thyroids treated with 131I

NASA Astrophysics Data System (ADS)

Traino, Antonio C.; Di Martino, Fabio; Grosso, Mariano; Monzani, Fabio; Dardano, Angela; Caraccio, Nadia; Mariani, Giuliano; Lazzeri, Mauro

2005-05-01

Substantial reductions in thyroid volume (up to 70-80%) after radioiodine therapy of Graves' hyperthyroidism are common and have been reported in the literature. A relationship between thyroid volume reduction and outcome of 131I therapy of Graves' disease has been reported by some authors. This important result could be used to decide individually the optimal radioiodine activity A0 (MBq) to administer to the patient, but a predictive model relating the change in gland volume to A0 is required. Recently, a mathematical model of thyroid mass reduction during the clearance phase (30-35 days) after 131I administration to patients with Graves' disease has been published and used as the basis for prescribing the therapeutic thyroid absorbed dose. It is well known that the thyroid volume reduction goes on until 1 year after therapy. In this paper, a mathematical model to predict the final mass of Graves' diseased thyroids submitted to 131I therapy is presented. This model represents a tentative explanation of what occurs macroscopically after the end of the clearance phase of radioiodine in the gland (the so-called second-order effects). It is shown that the final thyroid mass depends on its basal mass, on the radiation dose absorbed by the gland and on a constant value α typical of thyroid tissue. α has been evaluated based on a set of measurements made in 15 reference patients affected by Graves' disease and submitted to 131I therapy. A predictive equation for the calculation of the final mass of thyroid is presented. It is based on macroscopic parameters measurable after a diagnostic 131I capsule administration (0.37-1.85 MBq), before giving the therapy. The final mass calculated using this equation is compared to the final mass of thyroid measured 1 year after therapy administration in 22 Graves' diseased patients. The final masses calculated and measured 1 year after therapy are in fairly good agreement (R = 0.81). The possibility, for the physician, to decide a therapeutic activity based on the desired decrease of thyroid mass instead of on a fixed thyroid absorbed dose could be a new opportunity to cure Graves' disease.

The Modulus of Rupture from a Mathematical Point of View

NASA Astrophysics Data System (ADS)

Quintela, P.; Sánchez, M. T.

2007-04-01

The goal of this work is to present a complete mathematical study about the three-point bending experiments and the modulus of rupture of brittle materials. We will present the mathematical model associated to three-point bending experiments and we will use the asymptotic expansion method to obtain a new formula to calculate the modulus of rupture. We will compare the modulus of rupture of porcelain obtained with the previous formula with that obtained by using the classic theoretical formula. Finally, we will also present one and three-dimensional numerical simulations to compute the modulus of rupture.

Mathematical modeling to predict residential solid waste generation.

PubMed

Benítez, Sara Ojeda; Lozano-Olvera, Gabriela; Morelos, Raúl Adalberto; Vega, Carolina Armijo de

2008-01-01

One of the challenges faced by waste management authorities is determining the amount of waste generated by households in order to establish waste management systems, as well as trying to charge rates compatible with the principle applied worldwide, and design a fair payment system for households according to the amount of residential solid waste (RSW) they generate. The goal of this research work was to establish mathematical models that correlate the generation of RSW per capita to the following variables: education, income per household, and number of residents. This work was based on data from a study on generation, quantification and composition of residential waste in a Mexican city in three stages. In order to define prediction models, five variables were identified and included in the model. For each waste sampling stage a different mathematical model was developed, in order to find the model that showed the best linear relation to predict residential solid waste generation. Later on, models to explore the combination of included variables and select those which showed a higher R(2) were established. The tests applied were normality, multicolinearity and heteroskedasticity. Another model, formulated with four variables, was generated and the Durban-Watson test was applied to it. Finally, a general mathematical model is proposed to predict residential waste generation, which accounts for 51% of the total.

Optimization Research of Generation Investment Based on Linear Programming Model

NASA Astrophysics Data System (ADS)

Wu, Juan; Ge, Xueqian

Linear programming is an important branch of operational research and it is a mathematical method to assist the people to carry out scientific management. GAMS is an advanced simulation and optimization modeling language and it will combine a large number of complex mathematical programming, such as linear programming LP, nonlinear programming NLP, MIP and other mixed-integer programming with the system simulation. In this paper, based on the linear programming model, the optimized investment decision-making of generation is simulated and analyzed. At last, the optimal installed capacity of power plants and the final total cost are got, which provides the rational decision-making basis for optimized investments.

Incorporating heterogeneity into the transmission dynamics of a waterborne disease model.

PubMed

Collins, O C; Govinder, K S

2014-09-07

We formulate a mathematical model that captures the essential dynamics of waterborne disease transmission to study the effects of heterogeneity on the spread of the disease. The effects of heterogeneity on some important mathematical features of the model such as the basic reproduction number, type reproduction number and final outbreak size are analysed accordingly. We conduct a real-world application of this model by using it to investigate the heterogeneity in transmission in the recent cholera outbreak in Haiti. By evaluating the measure of heterogeneity between the administrative departments in Haiti, we discover a significant difference in the dynamics of the cholera outbreak between the departments. Copyright © 2014 Elsevier Ltd. All rights reserved.

Foundations for Success: The Final Report of the National Mathematics Advisory Panel

ERIC Educational Resources Information Center

US Department of Education, 2008

2008-01-01

On March 13, 2008, the National Mathematics Advisory Panel submitted its Final Report to the President of the United States and the Secretary of Education, and it was officially released to the public on that date, as well. The Panel agrees that the delivery system in mathematics education--the system that translates mathematical knowledge into…

Mathematical Modeling of Early Cellular Innate and Adaptive Immune Responses to Ischemia/Reperfusion Injury and Solid Organ Allotransplantation

PubMed Central

Day, Judy D.; Metes, Diana M.; Vodovotz, Yoram

2015-01-01

A mathematical model of the early inflammatory response in transplantation is formulated with ordinary differential equations. We first consider the inflammatory events associated only with the initial surgical procedure and the subsequent ischemia/reperfusion (I/R) events that cause tissue damage to the host as well as the donor graft. These events release damage-associated molecular pattern molecules (DAMPs), thereby initiating an acute inflammatory response. In simulations of this model, resolution of inflammation depends on the severity of the tissue damage caused by these events and the patient’s (co)-morbidities. We augment a portion of a previously published mathematical model of acute inflammation with the inflammatory effects of T cells in the absence of antigenic allograft mismatch (but with DAMP release proportional to the degree of graft damage prior to transplant). Finally, we include the antigenic mismatch of the graft, which leads to the stimulation of potent memory T cell responses, leading to further DAMP release from the graft and concomitant increase in allograft damage. Regulatory mechanisms are also included at the final stage. Our simulations suggest that surgical injury and I/R-induced graft damage can be well-tolerated by the recipient when each is present alone, but that their combination (along with antigenic mismatch) may lead to acute rejection, as seen clinically in a subset of patients. An emergent phenomenon from our simulations is that low-level DAMP release can tolerize the recipient to a mismatched allograft, whereas different restimulation regimens resulted in an exaggerated rejection response, in agreement with published studies. We suggest that mechanistic mathematical models might serve as an adjunct for patient- or sub-group-specific predictions, simulated clinical studies, and rational design of immunosuppression. PMID:26441988

What is behind the priority heuristic? A mathematical analysis and comment on Brandstätter, Gigerenzer, and Hertwig (2006).

PubMed

Rieger, Marc Oliver; Wang, Mei

2008-01-01

Comments on the article by E. Brandstätter, G. Gigerenzer, and R. Hertwig. The authors discuss the priority heuristic, a recent model for decisions under risk. They reanalyze the experimental validity of this approach and discuss how these results compare with cumulative prospect theory, the currently most established model in behavioral economics. They also discuss how general models for decisions under risk based on a heuristic approach can be understood mathematically to gain some insight in their limitations. They finally consider whether the priority heuristic model can lead to some understanding of the decision process of individuals or whether it is better seen as an as-if model. (c) 2008 APA, all rights reserved

Mathematical, numerical and experimental analysis of the swirling flow at a Kaplan runner outlet

NASA Astrophysics Data System (ADS)

Muntean, S.; Ciocan, T.; Susan-Resiga, R. F.; Cervantes, M.; Nilsson, H.

2012-11-01

The paper presents a novel mathematical model for a-priori computation of the swirling flow at Kaplan runners outlet. The model is an extension of the initial version developed by Susan-Resiga et al [1], to include the contributions of non-negligible radial velocity and of the variable rothalpy. Simple analytical expressions are derived for these additional data from three-dimensional numerical simulations of the Kaplan turbine. The final results, i.e. velocity components profiles, are validated against experimental data at two operating points, with the same Kaplan runner blades opening, but variable discharge.

Infrared band absorptance correlations and applications to nongray radiation. [mathematical models of absorption spectra for nongray atmospheres in order to study air pollution

NASA Technical Reports Server (NTRS)

Tiwari, S. N.; Manian, S. V. S.

1976-01-01

Various mathematical models for infrared radiation absorption spectra for atmospheric gases are reviewed, and continuous correlations for the total absorptance of a wide band are presented. Different band absorptance correlations were employed in two physically realistic problems (radiative transfer in gases with internal heat source, and heat transfer in laminar flow of absorbing-emitting gases between parallel plates) to study their influence on final radiative transfer results. This information will be applied to the study of atmospheric pollutants by infrared radiation measurement.

Management of California Oak Woodlands: Uncertainties and Modeling

Treesearch

Jay E. Noel; Richard P. Thompson

1995-01-01

A mathematical policy model of oak woodlands is presented. The model illustrates the policy uncertainties that exist in the management of oak woodlands. These uncertainties include: (1) selection of a policy criterion function, (2) woodland dynamics, (3) initial and final state of the woodland stock. The paper provides a review of each of the uncertainty issues. The...

The Eye of a Mathematical Physicist

NASA Astrophysics Data System (ADS)

Hepp, Klaus

2009-03-01

In this essay we are searching for neural correlates of `doing mathematical physics'. We introduce a toy model of a mathematical physicist, a brain connected with the outside world only by vision and saccadic eye movements and interacting with a computer screen. First, we describe the neuroanatomy of the visuo-saccadic system and Listing's law, which binds saccades and the optics of the eye. Then we explain space-time transformations in the superior colliculus, the performance of a canonical cortical circuit in the frontal eye field and finally the recurrent interaction of both areas, which leads to a coherent percept of space in spite of saccades. This sets the stage in the brain for doing mathematical physics, which is analyzed in simple examples.

International note: Are Emirati parents' attitudes toward mathematics linked to their adolescent children's attitudes toward mathematics and mathematics achievement?

PubMed

Areepattamannil, Shaljan; Khine, Myint Swe; Melkonian, Michael; Welch, Anita G; Al Nuaimi, Samira Ahmed; Rashad, Fatimah F

2015-10-01

Drawing on data from the 2012 Program for International Student Assessment (PISA) and employing multilevel modeling as an analytic strategy, this study examined the relations of adolescent children's perceptions of their parents' attitudes towards mathematics to their own attitudes towards mathematics and mathematics achievement among a sample of 5116 adolescents from 384 schools in the United Arab Emirates. The results of this cross-sectional study revealed that adolescents who perceived that their parents liked mathematics and considered mathematics was important for their children not only to study but also for their career tended to report higher levels of intrinsic and instrumental motivation to learn mathematics, mathematics self-concept and self-efficacy, and mathematics work ethic. Moreover, adolescents who perceived that their parents liked mathematics and considered mathematics was important for their children's career tended to report positive intentions and behaviors toward mathematics. However, adolescents who perceived that their parents considered mathematics was important for their children's career tended to report higher levels of mathematics anxiety. Finally, adolescents who perceived that their parents considered mathematics was important for their children to study performed significantly better on the mathematics assessment than did their peers whose parents disregarded the importance of learning mathematics. Copyright © 2015 The Foundation for Professionals in Services for Adolescents. Published by Elsevier Ltd. All rights reserved.

Long-term response to recombinant human growth hormone treatment: a new predictive mathematical method.

PubMed

Migliaretti, G; Ditaranto, S; Guiot, C; Vannelli, S; Matarazzo, P; Cappello, N; Stura, I; Cavallo, F

2018-07-01

Recombinant GH has been offered to GH-deficient (GHD) subjects for more than 30 years, in order to improve height and growth velocity in children and to enhance metabolic effects in adults. The aim of our work is to describe the long-term effect of rhGH treatment in GHD pediatric patients, suggesting a growth prediction model. A homogeneous database is defined for diagnosis and treatment modalities, based on GHD patients afferent to Hospital Regina Margherita in Turin (Italy). In this study, 232 GHD patients are selected (204 idiopathic GHD and 28 organic GHD). Each measure is shown in terms of mean with relative standard deviations (SD) and 95% confidence interval (95% CI). To estimate the final height of each patient on the basis of few measures, a mathematical growth prediction model [based on Gompertzian function and a mixed method based on the radial basis functions (RBFs) and the particle swarm optimization (PSO) models] was performed. The results seem to highlight the benefits of an early start of treatment, further confirming what is suggested by the literature. Generally, the RBF-PSO method shows a good reliability in the prediction of the final height. Indeed, RMSE is always lower than 4, i.e., in average the forecast will differ at most of 4 cm to the real value. In conclusion, the large and accurate database of Italian GHD patients allowed us to assess the rhGH treatment efficacy and compare the results with those obtained in other Countries. Moreover, we proposed and validated a new mathematical model forecasting the expected final height after therapy which was validated on our cohort.

Predicting introductory programming performance: A multi-institutional multivariate study

NASA Astrophysics Data System (ADS)

Bergin, Susan; Reilly, Ronan

2006-12-01

A model for predicting student performance on introductory programming modules is presented. The model uses attributes identified in a study carried out at four third-level institutions in the Republic of Ireland. Four instruments were used to collect the data and over 25 attributes were examined. A data reduction technique was applied and a logistic regression model using 10-fold stratified cross validation was developed. The model used three attributes: Leaving Certificate Mathematics result (final mathematics examination at second level), number of hours playing computer games while taking the module and programming self-esteem. Prediction success was significant with 80% of students correctly classified. The model also works well on a per-institution level. A discussion on the implications of the model is provided and future work is outlined.

Modeling the microstructural changes during hot tandem rolling of AA5 XXX aluminum alloys: Part I. Microstructural evolution

NASA Astrophysics Data System (ADS)

Wells, M. A.; Samarasekera, I. V.; Brimacombe, J. K.; Hawbolt, E. B.; Lloyd, D. J.

1998-06-01

A comprehensive mathematical model of the hot tandem rolling process for aluminum alloys has been developed. Reflecting the complex thermomechanical and microstructural changes effected in the alloys during rolling, the model incorporated heat flow, plastic deformation, kinetics of static recrystallization, final recrystallized grain size, and texture evolution. The results of this microstructural engineering study, combining computer modeling, laboratory tests, and industrial measurements, are presented in three parts. In this Part I, laboratory measurements of static recrystallization kinetics and final recrystallized grain size are described for AA5182 and AA5052 aluminum alloys and expressed quantitatively by semiempirical equations. In Part II, laboratory measurements of the texture evolution during static recrystallization are described for each of the alloys and expressed mathematically using a modified form of the Avrami equation. Finally, Part III of this article describes the development of an overall mathematical model for an industrial aluminum hot tandem rolling process which incorporates the microstructure and texture equations developed and the model validation using industrial data. The laboratory measurements for the microstructural evolution were carried out using industrially rolled material and a state-of-the-art plane strain compression tester at Alcan International. Each sample was given a single deformation and heat treated in a salt bath at 400 °C for various lengths of time to effect different levels of recrystallization in the samples. The range of hot-working conditions used for the laboratory study was chosen to represent conditions typically seen in industrial aluminum hot tandem rolling processes, i.e., deformation temperatures of 350 °C to 500 °C, strain rates of 0.5 to 100 seconds and total strains of 0.5 to 2.0. The semiempirical equations developed indicated that both the recrystallization kinetics and the final recrystallized grain size were dependent on the deformation history of the material i.e., total strain and Zener-Hollomon parameter ( Z), where Z = dot \\varepsilon exp left( {{Q_{def} }/{RT_{def }}} right) and time at the recrystallization temperature.

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 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

The Effects of Measurement Error on Statistical Models for Analyzing Change. Final Report.

ERIC Educational Resources Information Center

Dunivant, Noel

The results of six major projects are discussed including a comprehensive mathematical and statistical analysis of the problems caused by errors of measurement in linear models for assessing change. In a general matrix representation of the problem, several new analytic results are proved concerning the parameters which affect bias in…

Formal Models of Word Recognition. Final Report.

ERIC Educational Resources Information Center

Travers, Jeffrey R.

Existing mathematical models of word recognition are reviewed and a new theory is proposed in this research. The new theory integrates earlier proposals within a single framework, sacrificing none of the predictive power of the earlier proposals, but offering a gain in theoretical economy. The theory holds that word recognition is accomplished by…

CSMP Mathematics for the Upper Primary Grades Part II, Teacher's Guide [and] Worksheets. General Introduction. The World of Numbers. Final Experimental Version.

ERIC Educational Resources Information Center

Heidema, Clare; Schweitzer, Janis

This guide represents the final experimental version of a pilot project conducted in the United States between 1973 and 1976. The ideas and manner of presentation are based on the works of Georges and Frederique Papy. They are recognized as having introduced colored arrow drawings ("papygrams") and models of our numeration system (the…

CSMP Mathematics for the Upper Primary Grades Part I, Teacher's Guide [and] Worksheets. General Introduction. The World of Numbers. Final Experimental Version.

ERIC Educational Resources Information Center

Heidema, Clare; Schweitzer, Janis

This guide represents the final experimental version of a pilot project conducted in the United States between 1973 and 1976. The ideas and manner of presentation are based on the works of Georges and Frederique Papy. They are recognized as having introduced colored arrow drawings ("papygrams") and models of our numeration system (the…

SATA II - Stochastic Algebraic Topology and Applications

DTIC Science & Technology

2017-01-30

AFRL-AFOSR-UK-TR-2017-0018 SATA II - Stochastic Algebraic Topology and Applications 150032 Robert Adler TECHNION ISRAEL INSTITUTE OF TECHNOLOGY Final...REPORT TYPE Final 3. DATES COVERED (From - To) 15 Dec 2014 to 14 Dec 2016 4. TITLE AND SUBTITLE SATA II - Stochastic Algebraic Topology and Applications ...has recently been submitted to AFOSR. 15. SUBJECT TERMS Network Theory, Sensor Technology, Mathematical Modeling, EOARD 16. SECURITY CLASSIFICATION OF

Decoding the Principles of Emergence and Resiliency in Biological Collective Systems - A Multi-Scale Approach: Final Report

DTIC Science & Technology

2018-02-15

models and approaches are also valid using other invasive and non - invasive technologies. Finally, we illustrate and experimentally evaluate this...2017 Project Outline q  Pattern formation diversity in wild microbial societies q  Experimental and mathematical analysis methodology q  Skeleton...chemotaxis, nutrient degradation, and the exchange of amino acids between cells. Using both quantitative experimental methods and several theoretical

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

Yan, Ruqiang; Chen, Xuefeng; Li, Weihua

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

Digital Avionics Information System (DAIS): Life Cycle Cost Impact Modeling System Reliability, Maintainability, and Cost Model (RMCM)--Description. Users Guide. Final Report.

ERIC Educational Resources Information Center

Goclowski, John C.; And Others

The Reliability, Maintainability, and Cost Model (RMCM) described in this report is an interactive mathematical model with a built-in sensitivity analysis capability. It is a major component of the Life Cycle Cost Impact Model (LCCIM), which was developed as part of the DAIS advanced development program to be used to assess the potential impacts…

Validation of an instrument for mathematics enhancement teaching efficacy of Pacific Northwest agricultural educators

NASA Astrophysics Data System (ADS)

Jansen, Daniel J.

Teacher efficacy continues to be an important area of study in educational research. This study tested an instrument designed to assess the perceived efficacy of agricultural education teachers when engaged in lessons involving mathematics instruction. The study population of Oregon and Washington agricultural educators utilized in the validation of the instrument revealed important demographic findings and specific results related to teacher efficacy for the study population. An instrument was developed from the assimilation of three scales previously used and validated in efficacy research. Participants' mathematics teaching efficacy was assessed using a portion of the Mathematics Teaching Efficacy Beliefs Instrument (MTEBI), and personal mathematics efficacy was evaluated by the mathematics self-belief instrument which was derived from the Betz and Hackett's Mathematics Self-Efficacy Scale. The final scale, the Teachers' Sense of Efficacy Scale (TSES) created by Tschannen-Moran and Woolfolk Hoy, examined perceived personal teaching efficacy. Structural equation modeling was used as the statistical analyses tool to validate the instrument and examine correlations between efficacy constructs used to determine potential professional development needs of the survey population. As part of the data required for validation of the Mathematics Enhancement Teaching Efficacy instrument, demographic information defining the population of Oregon and Washington agricultural educators was obtained and reported. A hypothetical model derived from teacher efficacy literature was found to be an acceptable model to verify construct validity and determine strength of correlations between the scales that defined the instrument. The instrument produced an alpha coefficient of .905 for reliability. Both exploratory and confirmatory factor analyses were used to verify construct and discriminate validity. Specifics results related to the survey population of agricultural educators concluded that personal mathematics efficacy has a stronger correlation with mathematics teaching efficacy than personal teaching efficacy of teachers for this population. The implications of such findings suggest that professional development and pre-service preparation should be more focused on mathematics content knowledge rather than pedagogical knowledge when the objective is to enhance mathematics in interdisciplinary lessons.

Personality, Motivation, and Math Achievement Among Turkish Students.

PubMed

Akben-Selcuk, Elif

2017-04-01

Using the Turkish portion of the Programme for International Student Assessment dataset ( N = 4,848; 51% boys, 49% girls; age, M = 15.81 years, SD = 0.28), this study investigated factors associated with mathematics achievement among Turkish students. Three different models were estimated using the method of balanced repeated replication with Fay's method and taking into account the presence of five plausible values of the dependent variable. Results showed that male students and older students had better mathematics proficiency. Socio-economic status and school resources also played a significant role in explaining student achievement in mathematics. Finally, students who were more open to problem solving, who attributed their failure to external factors, and who were intrinsically motivated to learn mathematics achieved higher scores. Policy implications are provided.

Use of open-ended problems as the basis for the mathematical creativity growth disclosure of student

NASA Astrophysics Data System (ADS)

Suyitno, A.; Suyitno, H.; Rochmad; Dwijanto

2018-03-01

Mathematical creativity is the essence of learning in mathematics. However, mathematical creativity had not yet grown among students. Means there was a gap between needs and reality. This gap must be bridged through by scientific studies, and there were novelty findings, namely the discovery of stages to cultivate of Mathematical Creativity. The problem formulation: How to use of open-ended problems as the basis for the mathematical creativity growth disclosure of student? The goal was to use of open issues as the basis for the mathematical creativity growth disclosure of student. Research method with a qualitative approach. After data was collected then activity in data analysis, include data reduction, data presentation, data interpretation, and conclusion/verification. The results of the research: After the learning by applying the modification of RTTW learning model, then the students were trained to do the open-ended problems and by looking at the UTS and UAS values then qualitatively the results: (1) There was a significant increase of the student's final score. (2) The category of the growth of mathematical creativity of students, the Very Good there were three students, the Good there were six students, There were 17 students, and there were six students. The validation of these results was reinforced by interviews and triangulation. (3) Stage to cultivate mathematical creativity: lecturers should need to provide inputs on student work; Apply an appropriate learning model, and train students to work on the continuing problems.

An analytic model for footprint dispersions and its application to mission design

NASA Technical Reports Server (NTRS)

Rao, J. R. Jagannatha; Chen, Yi-Chao

1992-01-01

This is the final report on our recent research activities that are complementary to those conducted by our colleagues, Professor Farrokh Mistree and students, in the context of the Taguchi method. We have studied the mathematical model that forms the basis of the Simulation and Optimization of Rocket Trajectories (SORT) program and developed an analytic method for determining mission reliability with a reduced number of flight simulations. This method can be incorporated in a design algorithm to mathematically optimize different performance measures of a mission, thus leading to a robust and easy-to-use methodology for mission planning and design.

Mathematical and Numerical Techniques in Energy and Environmental Modeling

NASA Astrophysics Data System (ADS)

Chen, Z.; Ewing, R. E.

Mathematical models have been widely used to predict, understand, and optimize many complex physical processes, from semiconductor or pharmaceutical design to large-scale applications such as global weather models to astrophysics. In particular, simulation of environmental effects of air pollution is extensive. Here we address the need for using similar models to understand the fate and transport of groundwater contaminants and to design in situ remediation strategies. Three basic problem areas need to be addressed in the modeling and simulation of the flow of groundwater contamination. First, one obtains an effective model to describe the complex fluid/fluid and fluid/rock interactions that control the transport of contaminants in groundwater. This includes the problem of obtaining accurate reservoir descriptions at various length scales and modeling the effects of this heterogeneity in the reservoir simulators. Next, one develops accurate discretization techniques that retain the important physical properties of the continuous models. Finally, one develops efficient numerical solution algorithms that utilize the potential of the emerging computing architectures. We will discuss recent advances and describe the contribution of each of the papers in this book in these three areas. Keywords: reservoir simulation, mathematical models, partial differential equations, numerical algorithms

The (kinetic) theory of active particles applied to learning dynamics. Comment on "Collective learning modeling based on the kinetic theory of active particles" by D. Burini et al.

NASA Astrophysics Data System (ADS)

Nieto, J.

2016-03-01

The learning phenomena, their complexity, concepts, structure, suitable theories and models, have been extensively treated in the mathematical literature in the last century, and [4] contains a very good introduction to the literature describing the many approaches and lines of research developed about them. Two main schools have to be pointed out [5] in order to understand the two -not exclusive- kinds of existing models: the stimulus sampling models and the stochastic learning models. Also [6] should be mentioned as a survey where two methods of learning are pointed out, the cognitive and the social, and where the knowledge looks like a mathematical unknown. Finally, as the authors do, we refer to the works [9,10], where the concept of population thinking was introduced and which motivate the game theory rules as a tool (both included in [4] to develop their theory) and [7], where the ideas of developing a mathematical kinetic theory of perception and learning were proposed.

Information Dynamics in Networks: Models and Algorithms

DTIC Science & Technology

2016-09-13

Twitter ; we investigated how to detect spam accounts on Facebook and other social networks by graph analytics; and finally we investigated how to design...networks. We investigated the appropriateness of existing mathematical models for explaining the structure of retweet cascades on Twitter ; we investigated...Received Paper 1.00 2.00 3.00 . A Note on Modeling Retweet Cascades on Twitter , Workshop on Algorithms and Models for the Web Graph. 09-DEC-15

CSMP Mathematics for the Upper Primary Grades Part I, Teacher's Guide. The Languages of Strings and Arrows. Geometry and Measurement. Workbooks. Final Experimental Version.

ERIC Educational Resources Information Center

CEMREL, Inc., St. Ann, MO.

This guide represents the final experimental version of a pilot project conducted in the Unites States between 1973 and 1976. The ideas and manner of presentation are based on the works of Georges and Frederique Papy. They are recognized as having introduced colored arrow drawings ("papygrams") and models of our numeration system (the…

High pressure common rail injection system modeling and control.

PubMed

Wang, H P; Zheng, D; Tian, Y

2016-07-01

In this paper modeling and common-rail pressure control of high pressure common rail injection system (HPCRIS) is presented. The proposed mathematical model of high pressure common rail injection system which contains three sub-systems: high pressure pump sub-model, common rail sub-model and injector sub-model is a relative complicated nonlinear system. The mathematical model is validated by the software Matlab and a virtual detailed simulation environment. For the considered HPCRIS, an effective model free controller which is called Extended State Observer - based intelligent Proportional Integral (ESO-based iPI) controller is designed. And this proposed method is composed mainly of the referred ESO observer, and a time delay estimation based iPI controller. Finally, to demonstrate the performances of the proposed controller, the proposed ESO-based iPI controller is compared with a conventional PID controller and ADRC. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Modeling and Simulation Environment for Critical Infrastructure Protection

DTIC Science & Technology

2006-06-20

address at the triennial International Symposium on Mathematical Programming, held in Copenhagen, Denmark in August 2003. Finally, in very recent work... Teleworking - The human and organizational issues of computer and information security. Paper presented at the 11th Annual Conference on Human

Examinations in the Final Year of Transition to Mathematical Methods Computer Algebra System (CAS)

ERIC Educational Resources Information Center

Leigh-Lancaster, David; Les, Magdalena; Evans, Michael

2010-01-01

2009 was the final year of parallel implementation for Mathematical Methods Units 3 and 4 and Mathematical Methods (CAS) Units 3 and 4. From 2006-2009 there was a common technology-free short answer examination that covered the same function, algebra, calculus and probability content for both studies with corresponding expectations for key…

A new instrument to measure pre-service primary teachers' attitudes to teaching mathematics

NASA Astrophysics Data System (ADS)

Nisbet, Steven

1991-06-01

This article outlines the development of an instrument to measure pre-service primary teachers' attitudes to teaching mathematics. A trial questionnaire was devised using the set of Fennema-Sherman scales on students' attitudes to the subject mathematics as a model. Analysis of the responses to the questionnaire by 155 student teachers was carried out to develop meaningful attitude scales and to refine the instrument. The end-product is a new instrument which can be used to monitor the attitudes of student teachers. The attitude scales identified in the analysis and built into the final form of the questionnaire are (i) anxiety, (ii) confidence and enjoyment, (iii) desire for recognition and (iv) pressure to conform.

Mathematical modeling of the process of filling a mold during injection molding of ceramic products

NASA Astrophysics Data System (ADS)

Kulkov, S. N.; Korobenkov, M. V.; Bragin, N. A.

2015-10-01

Using the software package Fluent it have been predicted of the filling of a mold in injection molding of ceramic products is of great importance, because the strength of the final product is directly related to the presence of voids in the molding, making possible early prediction of inaccuracies in the mold prior to manufacturing. The calculations were performed in the formulation of mathematical modeling of hydrodynamic turbulent process of filling a predetermined volume of a viscous liquid. The model used to determine the filling forms evaluated the influence of density and viscosity of the feedstock, and the injection pressure on the mold filling process to predict the formation of voids in the area caused by the shape defect geometry.

Understanding the dynamics of sustainable social-ecological systems: human behavior, institutions, and regulatory feedback networks.

PubMed

Anderies, John M

2015-02-01

I present a general mathematical modeling framework that can provide a foundation for the study of sustainability in social- ecological systems (SESs). Using basic principles from feedback control and a sequence of specific models from bioeconomics and economic growth, I outline several mathematical and empirical challenges associated with the study of sustainability of SESs. These challenges are categorized into three classes: (1) the social choice of performance measures, (2) uncertainty, and (3) collective action. Finally, I present some opportunities for combining stylized dynamical systems models with empirical data on human behavior and biophysical systems to address practical challenges for the design of effective governance regimes (policy feedbacks) for highly uncertain natural resource systems.

Tapered Screened Channel PMD for Cryogenic Liquids

NASA Astrophysics Data System (ADS)

Dodge, Franklin T.; Green, Steve T.; Walter, David B.

2004-02-01

If a conventional spacecraft propellant management device (PMD) of the screened channel type were employed with a cryogenic liquid, vapor bubbles generated within the channel by heat transfer could ``dry out'' the channel screens and thereby cause the channels to admit large amounts of vapor from the tank into the liquid outflow. This paper describes a new tapered channel design that passively `pumps' bubbles away from the outlet port and vents them into the tank. A predictive mathematical model of the operating principle is presented and discussed. Scale-model laboratory tests were conducted and the mathematical model agreed well with the measured rates of bubble transport velocity. Finally, an example of the use of the predictive model for a realistic spacecraft application is presented. The model predicts that bubble clearing rates are acceptable even in tanks up to 2 m in length.

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.

Theoretical Mathematics

NASA Astrophysics Data System (ADS)

Stöltzner, Michael

Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.

Accelerated biodegradation of a herbicide applied to the roadside environment using adapted soil microorganisms : final report.

DOT National Transportation Integrated Search

1994-06-01

The extent and duration of pollution from herbicide spills and deliberate applications is related to properties of the herbicide and soil. Objectives of this study included the development of experimental procedures and mathematical models to determi...

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.

Pattern of mathematic representation ability in magnetic electricity problem

NASA Astrophysics Data System (ADS)

Hau, R. R. H.; Marwoto, P.; Putra, N. M. D.

2018-03-01

The mathematic representation ability in solving magnetic electricity problem gives information about the way students understand magnetic electricity. Students have varied mathematic representation pattern ability in solving magnetic electricity problem. This study aims to determine the pattern of students' mathematic representation ability in solving magnet electrical problems.The research method used is qualitative. The subject of this study is the fourth semester students of UNNES Physics Education Study Program. The data collection is done by giving a description test that refers to the test of mathematical representation ability and interview about field line topic and Gauss law. The result of data analysis of student's mathematical representation ability in solving magnet electric problem is categorized into high, medium and low category. The ability of mathematical representations in the high category tends to use a pattern of making known and asked symbols, writing equations, using quantities of physics, substituting quantities into equations, performing calculations and final answers. The ability of mathematical representation in the medium category tends to use several patterns of writing the known symbols, writing equations, using quantities of physics, substituting quantities into equations, performing calculations and final answers. The ability of mathematical representations in the low category tends to use several patterns of making known symbols, writing equations, substituting quantities into equations, performing calculations and final answer.

Radiolytic and thermolytic bubble gas hydrogen composition

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

Woodham, W.

This report describes the development of a mathematical model for the estimation of the hydrogen composition of gas bubbles trapped in radioactive waste. The model described herein uses a material balance approach to accurately incorporate the rates of hydrogen generation by a number of physical phenomena and scale the aforementioned rates in a manner that allows calculation of the final hydrogen composition.

Road simulation for four-wheel vehicle whole input power spectral density

NASA Astrophysics Data System (ADS)

Wang, Jiangbo; Qiang, Baomin

2017-05-01

As the vibration of running vehicle mainly comes from road and influence vehicle ride performance. So the road roughness power spectral density simulation has great significance to analyze automobile suspension vibration system parameters and evaluate ride comfort. Firstly, this paper based on the mathematical model of road roughness power spectral density, established the integral white noise road random method. Then in the MATLAB/Simulink environment, according to the research method of automobile suspension frame from simple two degree of freedom single-wheel vehicle model to complex multiple degrees of freedom vehicle model, this paper built the simple single incentive input simulation model. Finally the spectrum matrix was used to build whole vehicle incentive input simulation model. This simulation method based on reliable and accurate mathematical theory and can be applied to the random road simulation of any specified spectral which provides pavement incentive model and foundation to vehicle ride performance research and vibration simulation.

Mathematical Modeling and Optimization of Gaseous Fuel Processing as a Basic Technology for Long-distance Energy Transportation: The Use of Methanol and Dimethyl Ether as Energy Carriers.

NASA Astrophysics Data System (ADS)

Tyurina, E. A.; Mednikov, A. S.

2017-11-01

The paper presents the results of studies on the perspective technologies of natural gas conversion to synthetic liquid fuel (SLF) at energy-technology installations for combined production of SLF and electricity based on their detailed mathematical models. The technologies of the long-distance transport of energy of natural gas from large fields to final consumers are compared in terms of their efficiency. This work was carried out at Melentiev Energy Systems Institute of Siberian Branch of the Russian Academy of Sciences and supported by Russian Science Foundation via grant No 16-19-10174

The Mathematical Modeling and Computer Simulation of Electrochemical Micromachining Using Ultrashort Pulses

NASA Astrophysics Data System (ADS)

Kozak, J.; Gulbinowicz, D.; Gulbinowicz, Z.

2009-05-01

The need for complex and accurate three dimensional (3-D) microcomponents is increasing rapidly for many industrial and consumer products. Electrochemical machining process (ECM) has the potential of generating desired crack-free and stress-free surfaces of microcomponents. This paper reports a study of pulse electrochemical micromachining (PECMM) using ultrashort (nanoseconds) pulses for generating complex 3-D microstructures of high accuracy. A mathematical model of the microshaping process with taking into consideration unsteady phenomena in electrical double layer has been developed. The software for computer simulation of PECM has been developed and the effects of machining parameters on anodic localization and final shape of machined surface are presented.

A MATHEMATICAL MODEL OF PHYTOREMEDIATION FOR PETROLEUM CONTAMINATED SOIL: SENSITIVITY ANALYSIS. (R827015C018)

EPA Science Inventory

The perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Concl...

Advanced statistics: linear regression, part II: multiple linear regression.

PubMed

Marill, Keith A

2004-01-01

The applications of simple linear regression in medical research are limited, because in most situations, there are multiple relevant predictor variables. Univariate statistical techniques such as simple linear regression use a single predictor variable, and they often may be mathematically correct but clinically misleading. Multiple linear regression is a mathematical technique used to model the relationship between multiple independent predictor variables and a single dependent outcome variable. It is used in medical research to model observational data, as well as in diagnostic and therapeutic studies in which the outcome is dependent on more than one factor. Although the technique generally is limited to data that can be expressed with a linear function, it benefits from a well-developed mathematical framework that yields unique solutions and exact confidence intervals for regression coefficients. Building on Part I of this series, this article acquaints the reader with some of the important concepts in multiple regression analysis. These include multicollinearity, interaction effects, and an expansion of the discussion of inference testing, leverage, and variable transformations to multivariate models. Examples from the first article in this series are expanded on using a primarily graphic, rather than mathematical, approach. The importance of the relationships among the predictor variables and the dependence of the multivariate model coefficients on the choice of these variables are stressed. Finally, concepts in regression model building are discussed.

The B-dot Earth Average Magnetic Field

NASA Technical Reports Server (NTRS)

Capo-Lugo, Pedro A.; Rakoczy, John; Sanders, Devon

2013-01-01

The average Earth's magnetic field is solved with complex mathematical models based on mean square integral. Depending on the selection of the Earth magnetic model, the average Earth's magnetic field can have different solutions. This paper presents a simple technique that takes advantage of the damping effects of the b-dot controller and is not dependent of the Earth magnetic model; but it is dependent on the magnetic torquers of the satellite which is not taken into consideration in the known mathematical models. Also the solution of this new technique can be implemented so easily that the flight software can be updated during flight, and the control system can have current gains for the magnetic torquers. Finally, this technique is verified and validated using flight data from a satellite that it has been in orbit for three years.

Impulsive control of a continuous-culture and flocculation harvest chemostat model

NASA Astrophysics Data System (ADS)

Zhang, Tongqian; Ma, Wanbiao; Meng, Xinzhu

2017-12-01

In this paper, a new mathematical model describing the process of continuous culture and harvest of microalgaes is proposed. By inputting medium and flocculant at two different fixed moments periodically, continuous culture and harvest of microalgaes is implemented. The mathematical analysis is conducted and the whole dynamics of model is investigated by using theory of impulsive differential equations. We find that the model has a microalgaes-extinction periodic solution and it is globally asymptotically stable when some certain threshold value is less than the unit. And the model is permanent when some certain threshold value is larger than the unit. Then, according to the threshold, the control strategies of continuous culture and harvest of microalgaes are discussed. The results show that continuous culture and harvest of microalgaes can be archived by adjusting suitable input time, input amount of medium or flocculant. Finally, some numerical simulations are carried out to verify the control strategy.

CFD Modeling of Flow, Temperature, and Concentration Fields in a Pilot-Scale Rotary Hearth Furnace

NASA Astrophysics Data System (ADS)

Liu, Ying; Su, Fu-Yong; Wen, Zhi; Li, Zhi; Yong, Hai-Quan; Feng, Xiao-Hong

2014-01-01

A three-dimensional mathematical model for simulation of flow, temperature, and concentration fields in a pilot-scale rotary hearth furnace (RHF) has been developed using a commercial computational fluid dynamics software, FLUENT. The layer of composite pellets under the hearth is assumed to be a porous media layer with CO source and energy sink calculated by an independent mathematical model. User-defined functions are developed and linked to FLUENT to process the reduction process of the layer of composite pellets. The standard k-ɛ turbulence model in combination with standard wall functions is used for modeling of gas flow. Turbulence-chemistry interaction is taken into account through the eddy-dissipation model. The discrete ordinates model is used for modeling of radiative heat transfer. A comparison is made between the predictions of the present model and the data from a test of the pilot-scale RHF, and a reasonable agreement is found. Finally, flow field, temperature, and CO concentration fields in the furnace are investigated by the model.

A multi-objective programming model for assessment the GHG emissions in MSW management

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

Mavrotas, George, E-mail: mavrotas@chemeng.ntua.gr; Skoulaxinou, Sotiria; Gakis, Nikos

2013-09-15

Highlights: • The multi-objective multi-period optimization model. • The solution approach for the generation of the Pareto front with mathematical programming. • The very detailed description of the model (decision variables, parameters, equations). • The use of IPCC 2006 guidelines for landfill emissions (first order decay model) in the mathematical programming formulation. - Abstract: In this study a multi-objective mathematical programming model is developed for taking into account GHG emissions for Municipal Solid Waste (MSW) management. Mathematical programming models are often used for structure, design and operational optimization of various systems (energy, supply chain, processes, etc.). The last twenty yearsmore » they are used all the more often in Municipal Solid Waste (MSW) management in order to provide optimal solutions with the cost objective being the usual driver of the optimization. In our work we consider the GHG emissions as an additional criterion, aiming at a multi-objective approach. The Pareto front (Cost vs. GHG emissions) of the system is generated using an appropriate multi-objective method. This information is essential to the decision maker because he can explore the trade-offs in the Pareto curve and select his most preferred among the Pareto optimal solutions. In the present work a detailed multi-objective, multi-period mathematical programming model is developed in order to describe the waste management problem. Apart from the bi-objective approach, the major innovations of the model are (1) the detailed modeling considering 34 materials and 42 technologies, (2) the detailed calculation of the energy content of the various streams based on the detailed material balances, and (3) the incorporation of the IPCC guidelines for the CH{sub 4} generated in the landfills (first order decay model). The equations of the model are described in full detail. Finally, the whole approach is illustrated with a case study referring to the application of the model in a Greek region.« less

Mathematical formalisms based on approximated kinetic representations for modeling genetic and metabolic pathways.

PubMed

Alves, Rui; Vilaprinyo, Ester; Hernádez-Bermejo, Benito; Sorribas, Albert

2008-01-01

There is a renewed interest in obtaining a systemic understanding of metabolism, gene expression and signal transduction processes, driven by the recent research focus on Systems Biology. From a biotechnological point of view, such a systemic understanding of how a biological system is designed to work can facilitate the rational manipulation of specific pathways in different cell types to achieve specific goals. Due to the intrinsic complexity of biological systems, mathematical models are a central tool for understanding and predicting the integrative behavior of those systems. Particularly, models are essential for a rational development of biotechnological applications and in understanding system's design from an evolutionary point of view. Mathematical models can be obtained using many different strategies. In each case, their utility will depend upon the properties of the mathematical representation and on the possibility of obtaining meaningful parameters from available data. In practice, there are several issues at stake when one has to decide which mathematical model is more appropriate for the study of a given problem. First, one needs a model that can represent the aspects of the system one wishes to study. Second, one must choose a mathematical representation that allows an accurate analysis of the system with respect to different aspects of interest (for example, robustness of the system, dynamical behavior, optimization of the system with respect to some production goal, parameter value determination, etc). Third, before choosing between alternative and equally appropriate mathematical representations for the system, one should compare representations with respect to easiness of automation for model set-up, simulation, and analysis of results. Fourth, one should also consider how to facilitate model transference and re-usability by other researchers and for distinct purposes. Finally, one factor that is important for all four aspects is the regularity in the mathematical structure of the equations because it facilitates computational manipulation. This regularity is a mark of kinetic representations based on approximation theory. The use of approximation theory to derive mathematical representations with regular structure for modeling purposes has a long tradition in science. In most applied fields, such as engineering and physics, those approximations are often required to obtain practical solutions to complex problems. In this paper we review some of the more popular mathematical representations that have been derived using approximation theory and are used for modeling in molecular systems biology. We will focus on formalisms that are theoretically supported by the Taylor Theorem. These include the Power-law formalism, the recently proposed (log)linear and Lin-log formalisms as well as some closely related alternatives. We will analyze the similarities and differences between these formalisms, discuss the advantages and limitations of each representation, and provide a tentative "road map" for their potential utilization for different problems.

Mathematical Models for Camouflage Pattern Assessment

DTIC Science & Technology

2013-04-01

Matemático Facultad de Ciencias F́ısicas y Matemáticas http://www.cmm.uchile.cl DISTRIBUTION A: Distribution approved for public release University of Chile...Centro de Modelamiento Matemático Facultad de Ciencias Físicas y Matemáticas Final Report: Camouage Assessment January 2013 Abstract The main

Software Partitioning Schemes for Advanced Simulation Computer Systems. Final Report.

ERIC Educational Resources Information Center

Clymer, S. J.

Conducted to design software partitioning techniques for use by the Air Force to partition a large flight simulator program for optimal execution on alternative configurations, this study resulted in a mathematical model which defines characteristics for an optimal partition, and a manually demonstrated partitioning algorithm design which…

Spreadsheets and Bulgarian Goats

ERIC Educational Resources Information Center

Sugden, Steve

2012-01-01

We consider a problem appearing in an Australian Mathematics Challenge in 2003. This article considers whether a spreadsheet might be used to model this problem, thus allowing students to explore its structure within the spreadsheet environment. It then goes on to reflect on some general principles of problem decomposition when the final goal is a…

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 modelling as a proof of concept for MPNs as a human inflammation model for cancer development.

PubMed

Andersen, Morten; Sajid, Zamra; Pedersen, Rasmus K; Gudmand-Hoeyer, Johanne; Ellervik, Christina; Skov, Vibe; Kjær, Lasse; Pallisgaard, Niels; Kruse, Torben A; Thomassen, Mads; Troelsen, Jesper; Hasselbalch, Hans Carl; Ottesen, Johnny T

2017-01-01

The chronic Philadelphia-negative myeloproliferative neoplasms (MPNs) are acquired stem cell neoplasms which ultimately may transform to acute myelogenous leukemia. Most recently, chronic inflammation has been described as an important factor for the development and progression of MPNs in the biological continuum from early cancer stage to the advanced myelofibrosis stage, the MPNs being described as "A Human Inflammation Model for Cancer Development". This novel concept has been built upon clinical, experimental, genomic, immunological and not least epidemiological studies. Only a few studies have described the development of MPNs by mathematical models, and none have addressed the role of inflammation for clonal evolution and disease progression. Herein, we aim at using mathematical modelling to substantiate the concept of chronic inflammation as an important trigger and driver of MPNs.The basics of the model describe the proliferation from stem cells to mature cells including mutations of healthy stem cells to become malignant stem cells. We include a simple inflammatory coupling coping with cell death and affecting the basic model beneath. First, we describe the system without feedbacks or regulatory interactions. Next, we introduce inflammatory feedback into the system. Finally, we include other feedbacks and regulatory interactions forming the inflammatory-MPN model. Using mathematical modeling, we add further proof to the concept that chronic inflammation may be both a trigger of clonal evolution and an important driving force for MPN disease progression. Our findings support intervention at the earliest stage of cancer development to target the malignant clone and dampen concomitant inflammation.

Modeling, design, and control of flexible manipulator arms: Status and trends

NASA Technical Reports Server (NTRS)

Book, Wayne J.

1989-01-01

The desire for higher performance manipulators has lead to dynamic behavior in which the flexibility is an essential aspect. The mathematical representations commonly used in modeling flexible arms and arms with flexible drives are examined first. Then design considerations directly arising from the flexible nature of the arm are discussed. Finally, controls of joints for general and tip motion are discussed.

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

Preserving privacy whilst maintaining robust epidemiological predictions.

PubMed

Werkman, Marleen; Tildesley, Michael J; Brooks-Pollock, Ellen; Keeling, Matt J

2016-12-01

Mathematical models are invaluable tools for quantifying potential epidemics and devising optimal control strategies in case of an outbreak. State-of-the-art models increasingly require detailed individual farm-based and sensitive data, which may not be available due to either lack of capacity for data collection or privacy concerns. However, in many situations, aggregated data are available for use. In this study, we systematically investigate the accuracy of predictions made by mathematical models initialised with varying data aggregations, using the UK 2001 Foot-and-Mouth Disease Epidemic as a case study. We consider the scenario when the only data available are aggregated into spatial grid cells, and develop a metapopulation model where individual farms in a single subpopulation are assumed to behave uniformly and transmit randomly. We also adapt this standard metapopulation model to capture heterogeneity in farm size and composition, using farm census data. Our results show that homogeneous models based on aggregated data overestimate final epidemic size but can perform well for predicting spatial spread. Recognising heterogeneity in farm sizes improves predictions of the final epidemic size, identifying risk areas, determining the likelihood of epidemic take-off and identifying the optimal control strategy. In conclusion, in cases where individual farm-based data are not available, models can still generate meaningful predictions, although care must be taken in their interpretation and use. Copyright © 2016. Published by Elsevier B.V.

SeSBench - An initiative to benchmark reactive transport models for environmental subsurface processes

NASA Astrophysics Data System (ADS)

Jacques, Diederik

2017-04-01

As soil functions are governed by a multitude of interacting hydrological, geochemical and biological processes, simulation tools coupling mathematical models for interacting processes are needed. Coupled reactive transport models are a typical example of such coupled tools mainly focusing on hydrological and geochemical coupling (see e.g. Steefel et al., 2015). Mathematical and numerical complexity for both the tool itself or of the specific conceptual model can increase rapidly. Therefore, numerical verification of such type of models is a prerequisite for guaranteeing reliability and confidence and qualifying simulation tools and approaches for any further model application. In 2011, a first SeSBench -Subsurface Environmental Simulation Benchmarking- workshop was held in Berkeley (USA) followed by four other ones. The objective is to benchmark subsurface environmental simulation models and methods with a current focus on reactive transport processes. The final outcome was a special issue in Computational Geosciences (2015, issue 3 - Reactive transport benchmarks for subsurface environmental simulation) with a collection of 11 benchmarks. Benchmarks, proposed by the participants of the workshops, should be relevant for environmental or geo-engineering applications; the latter were mostly related to radioactive waste disposal issues - excluding benchmarks defined for pure mathematical reasons. Another important feature is the tiered approach within a benchmark with the definition of a single principle problem and different sub problems. The latter typically benchmarked individual or simplified processes (e.g. inert solute transport, simplified geochemical conceptual model) or geometries (e.g. batch or one-dimensional, homogeneous). Finally, three codes should be involved into a benchmark. The SeSBench initiative contributes to confidence building for applying reactive transport codes. Furthermore, it illustrates the use of those type of models for different environmental and geo-engineering applications. SeSBench will organize new workshops to add new benchmarks in a new special issue. Steefel, C. I., et al. (2015). "Reactive transport codes for subsurface environmental simulation." Computational Geosciences 19: 445-478.

Crypt dynamics and colorectal cancer: advances in mathematical modelling.

PubMed

van Leeuwen, I M M; Byrne, H M; Jensen, O E; King, J R

2006-06-01

Mathematical modelling forms a key component of systems biology, offering insights that complement and stimulate experimental studies. In this review, we illustrate the role of theoretical models in elucidating the mechanisms involved in normal intestinal crypt dynamics and colorectal cancer. We discuss a range of modelling approaches, including models that describe cell proliferation, migration, differentiation, crypt fission, genetic instability, APC inactivation and tumour heterogeneity. We focus on the model assumptions, limitations and applications, rather than on the technical details. We also present a new stochastic model for stem-cell dynamics, which predicts that, on average, APC inactivation occurs more quickly in the stem-cell pool in the absence of symmetric cell division. This suggests that natural niche succession may protect stem cells against malignant transformation in the gut. Finally, we explain how we aim to gain further understanding of the crypt system and of colorectal carcinogenesis with the aid of multiscale models that cover all levels of organization from the molecular to the whole organ.

MAX meets ADAM: a dosimetric comparison between a voxel-based and a mathematical model for external exposure to photons

NASA Astrophysics Data System (ADS)

Kramer, R.; Vieira, J. W.; Khoury, H. J.; Lima, F. de Andrade

2004-03-01

The International Commission on Radiological Protection intends to revise the organ and tissue equivalent dose conversion coefficients published in various reports. For this purpose the mathematical human medical internal radiation dose (MIRD) phantoms, actually in use, have to be replaced by recently developed voxel-based phantoms. This study investigates the dosimetric consequences, especially with respect to the effective male dose, if not only a MIRD phantom is replaced by a voxel phantom, but also if the tissue compositions and the radiation transport codes are changed. This task will be resolved by systematically replacing in the mathematical ADAM/GSF exposure model, first the radiation transport code, then the tissue composition and finally the phantom anatomy, in order to arrive at the voxel-based MAX/EGS4 exposure model. The results show that the combined effect of these replacements can decrease the effective male dose by up to 25% for external exposures to photons for incident energies above 30 keV for different field geometries, mainly because of increased shielding by a heterogeneous skeleton and by the overlying adipose and muscle tissue, and also because of the positions internal organs have in a realistically designed human body compared to their positions in the mathematically constructed phantom.

Algorithm for solving of two-level hierarchical minimax program control problem of final state the regional socio-economic system in the presence of risks

NASA Astrophysics Data System (ADS)

Shorikov, A. F.

2017-10-01

In this paper we study the problem of optimization of guaranteed result for program control by the final state of regional social and economic system in the presence of risks. For this problem we propose a mathematical model in the form of two-level hierarchical minimax program control problem of the final state of this process with incomplete information. For solving of its problem we constructed the common algorithm that has a form of a recurrent procedure of solving a linear programming and a finite optimization problems.

Deflection angle detecting system for the large-angle and high-linearity fast steering mirror using quadrant detector

NASA Astrophysics Data System (ADS)

Ni, Yingxue; Wu, Jiabin; San, Xiaogang; Gao, Shijie; Ding, Shaohang; Wang, Jing; Wang, Tao

2018-02-01

A deflection angle detecting system (DADS) using a quadrant detector (QD) is developed to achieve the large deflection angle and high linearity for the fast steering mirror (FSM). The mathematical model of the DADS is established by analyzing the principle of position detecting and error characteristics of the QD. Based on this mathematical model, the method of optimizing deflection angle and linearity of FSM is demonstrated, which is proved feasible by simulation and experimental results. Finally, a QD-based FSM is designed and tested. The results show that it achieves 0.72% nonlinearity, ±2.0 deg deflection angle, and 1.11-μrad resolution. Therefore, the application of this method will be beneficial to design the FSM.

Designing a multistage supply chain in cross-stage reverse logistics environments: application of particle swarm optimization algorithms.

PubMed

Chiang, Tzu-An; Che, Z H; Cui, Zhihua

2014-01-01

This study designed a cross-stage reverse logistics course for defective products so that damaged products generated in downstream partners can be directly returned to upstream partners throughout the stages of a supply chain for rework and maintenance. To solve this reverse supply chain design problem, an optimal cross-stage reverse logistics mathematical model was developed. In addition, we developed a genetic algorithm (GA) and three particle swarm optimization (PSO) algorithms: the inertia weight method (PSOA_IWM), V(Max) method (PSOA_VMM), and constriction factor method (PSOA_CFM), which we employed to find solutions to support this mathematical model. Finally, a real case and five simulative cases with different scopes were used to compare the execution times, convergence times, and objective function values of the four algorithms used to validate the model proposed in this study. Regarding system execution time, the GA consumed more time than the other three PSOs did. Regarding objective function value, the GA, PSOA_IWM, and PSOA_CFM could obtain a lower convergence value than PSOA_VMM could. Finally, PSOA_IWM demonstrated a faster convergence speed than PSOA_VMM, PSOA_CFM, and the GA did.

Designing a Multistage Supply Chain in Cross-Stage Reverse Logistics Environments: Application of Particle Swarm Optimization Algorithms

PubMed Central

Chiang, Tzu-An; Che, Z. H.

2014-01-01

This study designed a cross-stage reverse logistics course for defective products so that damaged products generated in downstream partners can be directly returned to upstream partners throughout the stages of a supply chain for rework and maintenance. To solve this reverse supply chain design problem, an optimal cross-stage reverse logistics mathematical model was developed. In addition, we developed a genetic algorithm (GA) and three particle swarm optimization (PSO) algorithms: the inertia weight method (PSOA_IWM), V Max method (PSOA_VMM), and constriction factor method (PSOA_CFM), which we employed to find solutions to support this mathematical model. Finally, a real case and five simulative cases with different scopes were used to compare the execution times, convergence times, and objective function values of the four algorithms used to validate the model proposed in this study. Regarding system execution time, the GA consumed more time than the other three PSOs did. Regarding objective function value, the GA, PSOA_IWM, and PSOA_CFM could obtain a lower convergence value than PSOA_VMM could. Finally, PSOA_IWM demonstrated a faster convergence speed than PSOA_VMM, PSOA_CFM, and the GA did. PMID:24772026

Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Aziz, Taha; Fatima, Aeeman; Khalique, Chaudry Masood

2018-03-01

The optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.

Allocation of surgical procedures to operating rooms.

PubMed

Ozkarahan, I

1995-08-01

Reduction of health care costs is of paramount importance in our time. This paper is a part of the research which proposes an expert hospital decision support system for resource scheduling. The proposed system combines mathematical programming, knowledge base, and database technologies, and what is more, its friendly interface is suitable for any novice user. Operating rooms in hospitals represent big investments and must be utilized efficiently. In this paper, first a mathematical model similar to job shop scheduling models is developed. The model loads surgical cases to operating rooms by maximizing room utilization and minimizing overtime in a multiple operating room setting. Then a prototype expert system which replaces the expertise of the operations research analyst for the model, drives the modelbase, database, and manages the user dialog is developed. Finally, an overview of the sequencing procedures for operations within an operating room is also presented.

Bioprocess systems engineering: transferring traditional process engineering principles to industrial biotechnology.

PubMed

Koutinas, Michalis; Kiparissides, Alexandros; Pistikopoulos, Efstratios N; Mantalaris, Athanasios

2012-01-01

The complexity of the regulatory network and the interactions that occur in the intracellular environment of microorganisms highlight the importance in developing tractable mechanistic models of cellular functions and systematic approaches for modelling biological systems. To this end, the existing process systems engineering approaches can serve as a vehicle for understanding, integrating and designing biological systems and processes. Here, we review the application of a holistic approach for the development of mathematical models of biological systems, from the initial conception of the model to its final application in model-based control and optimisation. We also discuss the use of mechanistic models that account for gene regulation, in an attempt to advance the empirical expressions traditionally used to describe micro-organism growth kinetics, and we highlight current and future challenges in mathematical biology. The modelling research framework discussed herein could prove beneficial for the design of optimal bioprocesses, employing rational and feasible approaches towards the efficient production of chemicals and pharmaceuticals.

Bioprocess systems engineering: transferring traditional process engineering principles to industrial biotechnology

PubMed Central

Koutinas, Michalis; Kiparissides, Alexandros; Pistikopoulos, Efstratios N.; Mantalaris, Athanasios

2013-01-01

The complexity of the regulatory network and the interactions that occur in the intracellular environment of microorganisms highlight the importance in developing tractable mechanistic models of cellular functions and systematic approaches for modelling biological systems. To this end, the existing process systems engineering approaches can serve as a vehicle for understanding, integrating and designing biological systems and processes. Here, we review the application of a holistic approach for the development of mathematical models of biological systems, from the initial conception of the model to its final application in model-based control and optimisation. We also discuss the use of mechanistic models that account for gene regulation, in an attempt to advance the empirical expressions traditionally used to describe micro-organism growth kinetics, and we highlight current and future challenges in mathematical biology. The modelling research framework discussed herein could prove beneficial for the design of optimal bioprocesses, employing rational and feasible approaches towards the efficient production of chemicals and pharmaceuticals. PMID:24688682

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

An advanced model framework for solid electrolyte intercalation batteries.

PubMed

Landstorfer, Manuel; Funken, Stefan; Jacob, Timo

2011-07-28

Recent developments of solid electrolytes, especially lithium ion conductors, led to all solid state batteries for various applications. In addition, mathematical models sprout for different electrode materials and battery types, but are missing for solid electrolyte cells. We present a mathematical model for ion flux in solid electrolytes, based on non-equilibrium thermodynamics and functional derivatives. Intercalated ion diffusion within the electrodes is further considered, allowing the computation of the ion concentration at the electrode/electrolyte interface. A generalized Frumkin-Butler-Volmer equation describes the kinetics of (de-)intercalation reactions and is here extended to non-blocking electrodes. Using this approach, numerical simulations were carried out to investigate the space charge region at the interface. Finally, discharge simulations were performed to study different limitations of an all solid state battery cell. This journal is © the Owner Societies 2011

Problems of Mathematical Finance by Stochastic Control Methods

NASA Astrophysics Data System (ADS)

Stettner, Łukasz

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

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).

Mathematical modeling and spectrum analysis of the physiological patello-femoral pulse train produced by slow knee movement.

PubMed

Zhang, Y T; Frank, C B; Rangayyan, R M; Bell, G D

1992-09-01

Analysis of vibration signals emitted by the knee joint has the potential for the development of a noninvasive procedure for the diagnosis and monitoring of knee pathology. In order to obtain as much information as possible from the power density spectrum of the knee vibration signal, it is necessary to identify the physiological factors (or physiologically relevant parameters) that shape the spectrum. This paper presents a mathematical model for knee vibration signals, in particular the physiological patello-femoral pulse (PFP) train produced by slow knee movement. It demonstrates through the mathematical model that the repetition rate of the physiological PFP train introduces repeated peaks in the power spectrum, and that it affects the spectrum mainly at low frequencies. The theoretical results also show that the spectral peaks at multiples of the PFP repetition rate become more evident when the variance of the interpulse interval (IPI) is small, and that these spectral peaks shift toward higher frequencies with increasing PFP repetition rates. To evaluate the mathematical model, a simulation algorithm was developed, which generates PFP signals with adjustable repetition rate and IPI variance. Signals generated by simulation were seen to possess representative spectral characteristics typically observed in physiological PFP signals. This simulation procedure allows an interactive examination of several factors which affect the PFP train spectrum. Finally, in vivo measurements of physiological PFP signals of normal volunteers are presented. Results of simulations and analysis of signals recorded from human subjects support the mathematical model's prediction that the IPI statistics play a very significant role in determining the low-end power spectrum of the physiological PFP signal.(ABSTRACT TRUNCATED AT 250 WORDS)

Measuring and modeling the oxygen profile in a nitrifying Moving Bed Biofilm Reactor.

PubMed

Masić, Alma; Bengtsson, Jessica; Christensson, Magnus

2010-09-01

In this paper we determine the oxygen profile in a biofilm on suspended carriers in two ways: firstly by microelectrode measurements and secondly by a simple mathematical model. The Moving Bed Biofilm Reactor is well-established for wastewater treatment where bacteria grow as a biofilm on the protective surfaces of suspended carriers. The flat shaped BiofilmChip P was developed to allow good conditions for transport of substrates into the biofilm. The oxygen profile was measured in situ the nitrifying biofilm with a microelectrode and it was simulated with a one-dimensional mathematical model. We extended the model by adding a CSTR equation, to connect the reactor to the biofilm through the boundary conditions. We showed the dependence of the thickness of the mass transfer boundary layer on the bulk flow rate. Finally, we estimated the erosion parameter lambda to increase the concordance between the measured and simulated profiles. This lead to a simple empirical relationship between lambda and the flow rate. The data gathered by in situ microelectrode measurements can, together with the mathematical model, be used in predictive modeling and give more insight in the design of new carriers, with the ambition of making process operation more energy efficient. Copyright 2010 Elsevier Inc. All rights reserved.

Mathematical modelling of prostate cancer growth and its application to hormone therapy.

PubMed

Tanaka, Gouhei; Hirata, Yoshito; Goldenberg, S Larry; Bruchovsky, Nicholas; Aihara, Kazuyuki

2010-11-13

Hormone therapy in the form of androgen deprivation is a major treatment for advanced prostate cancer. However, if such therapy is overly prolonged, tumour cells may become resistant to this treatment and result in recurrent fatal disease. Long-term hormone deprivation also is associated with side effects poorly tolerated by patients. In contrast, intermittent hormone therapy with alternating on- and off-treatment periods is a possible clinical strategy to delay progression to hormone-refractory disease with the advantage of reduced side effects during the off-treatment periods. In this paper, we first overview previous studies on mathematical modelling of prostate tumour growth under intermittent hormone therapy. The model is categorized into a hybrid dynamical system because switching between on-treatment and off-treatment intervals is treated in addition to continuous dynamics of tumour growth. Next, we present an extended model of stochastic differential equations and examine how well the model is able to capture the characteristics of authentic serum prostate-specific antigen (PSA) data. We also highlight recent advances in time-series analysis and prediction of changes in serum PSA concentrations. Finally, we discuss practical issues to be considered towards establishment of mathematical model-based tailor-made medicine, which defines how to realize personalized hormone therapy for individual patients based on monitored serum PSA levels.

Linear Mathematical Model for Seam Tracking with an Arc Sensor in P-GMAW Processes

PubMed Central

Liu, Wenji; Li, Liangyu; Hong, Ying; Yue, Jianfeng

2017-01-01

Arc sensors have been used in seam tracking and widely studied since the 80s and commercial arc sensing products for T and V shaped grooves have been developed. However, it is difficult to use these arc sensors in narrow gap welding because the arc stability and sensing accuracy are not satisfactory. Pulse gas melting arc welding (P-GMAW) has been successfully applied in narrow gap welding and all position welding processes, so it is worthwhile to research P-GMAW arc sensing technology. In this paper, we derived a linear mathematical P-GMAW model for arc sensing, and the assumptions for the model are verified through experiments and finite element methods. Finally, the linear characteristics of the mathematical model were investigated. In torch height changing experiments, uphill experiments, and groove angle changing experiments the P-GMAW arc signals all satisfied the linear rules. In addition, the faster the welding speed, the higher the arc signal sensitivities; the smaller the groove angle, the greater the arc sensitivities. The arc signal variation rate needs to be modified according to the welding power, groove angles, and weaving or rotate speed. PMID:28335425

Linear Mathematical Model for Seam Tracking with an Arc Sensor in P-GMAW Processes.

PubMed

Liu, Wenji; Li, Liangyu; Hong, Ying; Yue, Jianfeng

2017-03-14

Arc sensors have been used in seam tracking and widely studied since the 80s and commercial arc sensing products for T and V shaped grooves have been developed. However, it is difficult to use these arc sensors in narrow gap welding because the arc stability and sensing accuracy are not satisfactory. Pulse gas melting arc welding (P-GMAW) has been successfully applied in narrow gap welding and all position welding processes, so it is worthwhile to research P-GMAW arc sensing technology. In this paper, we derived a linear mathematical P-GMAW model for arc sensing, and the assumptions for the model are verified through experiments and finite element methods. Finally, the linear characteristics of the mathematical model were investigated. In torch height changing experiments, uphill experiments, and groove angle changing experiments the P-GMAW arc signals all satisfied the linear rules. In addition, the faster the welding speed, the higher the arc signal sensitivities; the smaller the groove angle, the greater the arc sensitivities. The arc signal variation rate needs to be modified according to the welding power, groove angles, and weaving or rotate speed.

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…

"I Finally Get It!": Developing Mathematical Understanding during Teacher Education

ERIC Educational Resources Information Center

Holm, Jennifer; Kajander, Ann

2012-01-01

A deep conceptual understanding of elementary mathematics as appropriate for teaching is increasingly thought to be an important aspect of elementary teacher capacity. This study explores preservice teachers' initial mathematical understandings and how these understandings developed during a mathematics methods course for upper elementary…

[Fluorescent signal detection of chromatographic chip by algorithms of pyramid connection and Gaussian mixture model].

PubMed

Hu, Beibei; Zhang, Xueqing; Chen, Haopeng; Cui, Daxiang

2011-03-01

We proposed a new algorithm for automatic identification of fluorescent signal. Based on the features of chromatographic chips, mathematic morphology in RGB color space was used to filter and enhance the images, pyramid connection was used to segment the areas of fluorescent signal, and then the method of Gaussian Mixture Model was used to detect the fluorescent signal. Finally we calculated the average fluorescent intensity in obtained fluorescent areas. Our results show that the algorithm has a good efficacy to segment the fluorescent areas, can detect the fluorescent signal quickly and accurately, and finally realize the quantitative detection of fluorescent signal in chromatographic chip.

Mathematical modeling on obligate mutualism: Interactions between leaf-cutter ants and their fungus garden.

PubMed

Kang, Yun; Clark, Rebecca; Makiyama, Michael; Fewell, Jennifer

2011-11-21

We propose a simple mathematical model by applying Michaelis-Menton equations of enzyme kinetics to study the mutualistic interaction between the leaf cutter ant and its fungus garden at the early stage of colony expansion. We derive sufficient conditions on the extinction and coexistence of these two species. In addition, we give a region of initial condition that leads to the extinction of two species when the model has an interior attractor. Our global analysis indicates that the division of labor by worker ants and initial conditions are two important factors that determine whether leaf cutter ants' colonies and their fungus garden can survive and grow or not. We validate the model by comparing model simulations and data on fungal and ant colony growth rates under laboratory conditions. We perform sensitive analysis of the model based on the experimental data to gain more biological insights on ecological interactions between leaf-cutter ants and their fungus garden. Finally, we give conclusions and discuss potential future work. Published by Elsevier Ltd.

Sensory neural pathways revisited to unravel the temporal dynamics of the Simon effect: A model-based cognitive neuroscience approach.

PubMed

Salzer, Yael; de Hollander, Gilles; Forstmann, Birte U

2017-06-01

The Simon task is one of the most prominent interference tasks and has been extensively studied in experimental psychology and cognitive neuroscience. Despite years of research, the underlying mechanism driving the phenomenon and its temporal dynamics are still disputed. Within the framework of the review, we adopt a model-based cognitive neuroscience approach. We first go over key findings in the literature of the Simon task, discuss competing qualitative cognitive theories and the difficulty of testing them empirically. We then introduce sequential sampling models, a particular class of mathematical cognitive process models. Finally, we argue that the brain architecture accountable for the processing of spatial ('where') and non-spatial ('what') information, could constrain these models. We conclude that there is a clear need to bridge neural and behavioral measures, and that mathematical cognitive models may facilitate the construction of this bridge and work towards revealing the underlying mechanisms of the Simon effect. Copyright © 2017 Elsevier Ltd. All rights reserved.

Optimization and Control of Agent-Based Models in Biology: A Perspective.

PubMed

An, G; Fitzpatrick, B G; Christley, S; Federico, P; Kanarek, A; Neilan, R Miller; Oremland, M; Salinas, R; Laubenbacher, R; Lenhart, S

2017-01-01

Agent-based models (ABMs) have become an increasingly important mode of inquiry for the life sciences. They are particularly valuable for systems that are not understood well enough to build an equation-based model. These advantages, however, are counterbalanced by the difficulty of analyzing and using ABMs, due to the lack of the type of mathematical tools available for more traditional models, which leaves simulation as the primary approach. As models become large, simulation becomes challenging. This paper proposes a novel approach to two mathematical aspects of ABMs, optimization and control, and it presents a few first steps outlining how one might carry out this approach. Rather than viewing the ABM as a model, it is to be viewed as a surrogate for the actual system. For a given optimization or control problem (which may change over time), the surrogate system is modeled instead, using data from the ABM and a modeling framework for which ready-made mathematical tools exist, such as differential equations, or for which control strategies can explored more easily. Once the optimization problem is solved for the model of the surrogate, it is then lifted to the surrogate and tested. The final step is to lift the optimization solution from the surrogate system to the actual system. This program is illustrated with published work, using two relatively simple ABMs as a demonstration, Sugarscape and a consumer-resource ABM. Specific techniques discussed include dimension reduction and approximation of an ABM by difference equations as well systems of PDEs, related to certain specific control objectives. This demonstration illustrates the very challenging mathematical problems that need to be solved before this approach can be realistically applied to complex and large ABMs, current and future. The paper outlines a research program to address them.

Do Prospective Mathematics Teachers Teach Who They Say They Are?

ERIC Educational Resources Information Center

van Putten, Sonja; Stols, Gerrit; Howie, Sarah

2014-01-01

In this case study, the professional mathematics teacher identity (PMTI) of final year mathematics education students is investigated in terms of their self-perceived and actualised identity. These prospective teachers were required to discuss and describe their own PMTI in terms of three aspects: mathematics specialisation, teaching-and-learning…

Confidence in Teaching Mathematics among Malaysian Pre-Service Teachers

ERIC Educational Resources Information Center

Yunus, Aida Suraya Md.; Hamzah, Ramlah; Ismail, Habsah; Husain, Sharifah Kartini Said; Ismail, Mat Rofa

2006-01-01

This study focuses on the confidence level of mathematics education students in teaching school mathematics. Respondents were 165 final year students from four Malaysian universities. It was found that the respondents showed a strong foundation in mathematics upon entrance to the university. In spite of their strong background in school…

SECONDARY SCHOOL MATHEMATICS CURRICULUM IMPROVEMENT STUDY. FINAL REPORT.

ERIC Educational Resources Information Center

FEHR, HOWARD F.

THIS SECONDARY SCHOOL MATHEMATICS CURRICULUM IMPROVEMENT STUDY GROUP (SSMCIS), COMPOSED OF BOTH AMERICAN AND EUROPEAN EDUCATORS, WAS GUIDED BY TWO MAIN OBJECTIVES--(1) TO CONSTRUCT AND EVALUATE A UNIFIED SECONDARY SCHOOL MATHEMATICS PROGRAM FOR GRADES 7-12 THAT WOULD TAKE THE CAPABLE STUDENT WELL INTO CURRENT COLLEGE MATHEMATICS, AND (2) DETERMINE…

Modeling pressure rise in gas targets

NASA Astrophysics Data System (ADS)

Jahangiri, P.; Lapi, S. E.; Publicover, J.; Buckley, K.; Martinez, D. M.; Ruth, T. J.; Hoehr, C.

2017-05-01

The purpose of this work is to introduce a universal mathematical model to explain a gas target behaviour at steady-state time scale. To obtain our final goal, an analytical model is proposed to study the pressure rise in the targets used to produce medical isotopes on low-energy cyclotrons. The model is developed based on the assumption that during irradiation the system reaches steady-state. The model is verified by various experiments performed at different beam currents, gas type, and initial pressures at 13 MeV cyclotron at TRIUMF. Excellent agreement is achieved.

Multiplicity of Mathematical Modeling Strategies to Search for Molecular and Cellular Insights into Bacteria Lung Infection

PubMed Central

Cantone, Martina; Santos, Guido; Wentker, Pia; Lai, Xin; Vera, Julio

2017-01-01

Even today two bacterial lung infections, namely pneumonia and tuberculosis, are among the 10 most frequent causes of death worldwide. These infections still lack effective treatments in many developing countries and in immunocompromised populations like infants, elderly people and transplanted patients. The interaction between bacteria and the host is a complex system of interlinked intercellular and the intracellular processes, enriched in regulatory structures like positive and negative feedback loops. Severe pathological condition can emerge when the immune system of the host fails to neutralize the infection. This failure can result in systemic spreading of pathogens or overwhelming immune response followed by a systemic inflammatory response. Mathematical modeling is a promising tool to dissect the complexity underlying pathogenesis of bacterial lung infection at the molecular, cellular and tissue levels, and also at the interfaces among levels. In this article, we introduce mathematical and computational modeling frameworks that can be used for investigating molecular and cellular mechanisms underlying bacterial lung infection. Then, we compile and discuss published results on the modeling of regulatory pathways and cell populations relevant for lung infection and inflammation. Finally, we discuss how to make use of this multiplicity of modeling approaches to open new avenues in the search of the molecular and cellular mechanisms underlying bacterial infection in the lung. PMID:28912729

Multiplicity of Mathematical Modeling Strategies to Search for Molecular and Cellular Insights into Bacteria Lung Infection.

PubMed

Cantone, Martina; Santos, Guido; Wentker, Pia; Lai, Xin; Vera, Julio

2017-01-01

Even today two bacterial lung infections, namely pneumonia and tuberculosis, are among the 10 most frequent causes of death worldwide. These infections still lack effective treatments in many developing countries and in immunocompromised populations like infants, elderly people and transplanted patients. The interaction between bacteria and the host is a complex system of interlinked intercellular and the intracellular processes, enriched in regulatory structures like positive and negative feedback loops. Severe pathological condition can emerge when the immune system of the host fails to neutralize the infection. This failure can result in systemic spreading of pathogens or overwhelming immune response followed by a systemic inflammatory response. Mathematical modeling is a promising tool to dissect the complexity underlying pathogenesis of bacterial lung infection at the molecular, cellular and tissue levels, and also at the interfaces among levels. In this article, we introduce mathematical and computational modeling frameworks that can be used for investigating molecular and cellular mechanisms underlying bacterial lung infection. Then, we compile and discuss published results on the modeling of regulatory pathways and cell populations relevant for lung infection and inflammation. Finally, we discuss how to make use of this multiplicity of modeling approaches to open new avenues in the search of the molecular and cellular mechanisms underlying bacterial infection in the lung.

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.

Rapid Design and Testing of Novel Gas/liquid Contacting Devices for Post-Combustion CO 2 Capture via 3D Printing - Phase II Final Technical Report

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

Panaccione, Charles; Staab, Greg; Meuleman, Erik

ION has developed a mathematically driven model for a contacting device incorporating mass transfer, heat transfer, and computational fluid dynamics. This model is based upon a parametric structure for purposes of future commercialization. The most promising design from modeling was 3D printed and tested in a bench scale CO 2 capture unit and compared to commercially available structured packing tested in the same unit.

Modelling Of Flotation Processes By Classical Mathematical Methods - A Review

NASA Astrophysics Data System (ADS)

Jovanović, Ivana; Miljanović, Igor

2015-12-01

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

Analysing of critical force effects of aircraft seat belt using truss elements

NASA Astrophysics Data System (ADS)

Klemenc, Marek; Markopoulos, Alexandros; Maršálek, Pavel

2017-07-01

This paper deals with the mathematical modelling of an aircraft seat belt crash test. The main goal is determination of a time course of the reactions in a lap belt anchoring points and their maximum values. This work was created on the basis of practical requirements from industry. Results are going to be reflected in developing a new type of aircraft seats. We mainly focus on the mathematical modelling of dynamic problems using the finite element method (FEM). Derived procedures are implemented in the Python programming language and are verified by several examples. A final calculation algorithm is applied on the analysis of the safety belt. We consider that a seat belt bending stiffness is very small compared to a tensile stiffness, therefore we used a 2D plane truss element.

A mathematical model of diffusion from a steady source of short duration in a finite mixing layer

NASA Astrophysics Data System (ADS)

Bianconi, Roberto; Tamponi, Matteo

This paper presents an analytical unsteady-state solution to the atmospheric dispersion equation for substances subject to chemical-physical decay in a finite mixing layer for releases of short duration. This solution is suitable for describing critical events relative to accidental release of toxic, flammable or explosive substances. To implement the solution, the Modello per Rilasci a Breve Termine (MRBT) code has been developed, for some characteristics parameters of which the results of the sensitivity analysis are presented. Moreover some examples of application to the calculation of exposure to toxic substances and to the determination of the ignition field of flammable substances are described. Finally, the mathematical model described can be used to interpret the phenomenon of pollutant accumulation.

A new mathematical modeling approach for the energy of threonine molecule

NASA Astrophysics Data System (ADS)

Sahiner, Ahmet; Kapusuz, Gulden; Yilmaz, Nurullah

2017-07-01

In this paper, we propose an improved new methodology in energy conformation problems for finding optimum energy values. First, we construct the Bezier surfaces near local minimizers based on the data obtained from Density Functional Theory (DFT) calculations. Second, we blend the constructed surfaces in order to obtain a single smooth model. Finally, we apply the global optimization algorithm to find two torsion angles those make the energy of the molecule minimum.

On Mathematical Proving

NASA Astrophysics Data System (ADS)

Stefaneas, Petros; Vandoulakis, Ioannis M.

2015-12-01

This paper outlines a logical representation of certain aspects of the process of mathematical proving that are important from the point of view of Artificial Intelligence. Our starting-point is the concept of proof-event or proving, introduced by Goguen, instead of the traditional concept of mathematical proof. The reason behind this choice is that in contrast to the traditional static concept of mathematical proof, proof-events are understood as processes, which enables their use in Artificial Intelligence in such contexts, in which problem-solving procedures and strategies are studied. We represent proof-events as problem-centered spatio-temporal processes by means of the language of the calculus of events, which captures adequately certain temporal aspects of proof-events (i.e. that they have history and form sequences of proof-events evolving in time). Further, we suggest a "loose" semantics for the proof-events, by means of Kolmogorov's calculus of problems. Finally, we expose the intented interpretations for our logical model from the fields of automated theorem-proving and Web-based collective proving.

Using the Fennema-Sherman Mathematics Attitude Scales with lower-primary teachers

NASA Astrophysics Data System (ADS)

Ren, Lixin; Green, Jennifer L.; Smith, Wendy M.

2016-06-01

The Fennema-Sherman Mathematics Attitude Scales (FSMAS) are among the most popular instruments used in studies of attitudes toward mathematics. However, the FSMAS has been mainly used among student populations and rarely used with teachers. In the present study, three scales from the FSMAS— Confidence, Effectance Motivation, and Anxiety—were revised and used with lower-primary (kindergarten to third grade) teachers. This study includes three parts: (1) a pilot study to ensure the modifications made to the FSMAS were appropriate to use with teachers, (2) confirmatory factor analyses to assess the factor structure of the revised FSMAS with 225 lower-primary teachers, and (3) measurement invariance analyses using data from a similar sample of 171 lower-primary teachers to examine whether the revised FSMAS measures each construct in the same way as in the previous sample. The final three-factor model, after removing three problematic items, achieves acceptable model fit, with each construct meeting all conditions for strict measurement invariance. Additionally, repeated measures analyses were performed on data collected from 39 in-service lower-primary teachers who participated in an elementary mathematics specialist program to examine the use of the revised FSMAS in program evaluation. Overall results suggest that researchers and program evaluators may use the revised FSMAS to reliably measure lower-primary teachers' mathematical attitudes, and it can be a valuable tool for evaluating the effectiveness of professional development programs.

Mathematics Learning Styles of Chinese Immigrant Students. Final Research Report.

ERIC Educational Resources Information Center

Tsang, Sau-Lim

Major revision in the U.S. mathematics curriculum since the 1960s have led to significant differences between the mathematics curriculum of the United States and those of many other countries. This study explored how eight Chinese immigrant students, with different cultural backgrounds, mathematics knowledge, and learning styles, learned in an…

Final Report of Cambridge Conference on School Mathematics, January 1962 - August 1970.

ERIC Educational Resources Information Center

Cambridge Conference on School Mathematics, Newton, MA.

The Cambridge Conference on School Mathematics (CCSM) was an association of prominent mathematicians who had a concern for mathematics education at school level, from kindergarten through grade twelve. These mathematicians organized three main conferences in three areas of mathematics education, and have carried on activities related to the…

A mathematical representation of an advanced helicopter for piloted simulator investigations of control system and display variations

NASA Technical Reports Server (NTRS)

Aiken, E. W.

1980-01-01

A mathematical model of an advanced helicopter is described. The model is suitable for use in control/display research involving piloted simulation. The general design approach for the six degree of freedom equations of motion is to use the full set of nonlinear gravitational and inertial terms of the equations and to express the aerodynamic forces and moments as the reference values and first order terms of a Taylor series expansion about a reference trajectory defined as a function of longitudinal airspeed. Provisions for several different specific and generic flight control systems are included in the model. The logic required to drive various flight control and weapon delivery symbols on a pilot's electronic display is also provided. Finally, the model includes a simplified representation of low altitude wind and turbulence effects. This model was used in a piloted simulator investigation of the effects of control system and display variations for an attack helicopter mission.

Simulating an underwater vehicle self-correcting guidance system with Simulink

NASA Astrophysics Data System (ADS)

Fan, Hui; Zhang, Yu-Wen; Li, Wen-Zhe

2008-09-01

Underwater vehicles have already adopted self-correcting directional guidance algorithms based on multi-beam self-guidance systems, not waiting for research to determine the most effective algorithms. The main challenges facing research on these guidance systems have been effective modeling of the guidance algorithm and a means to analyze the simulation results. A simulation structure based on Simulink that dealt with both issues was proposed. Initially, a mathematical model of relative motion between the vehicle and the target was developed, which was then encapsulated as a subsystem. Next, steps for constructing a model of the self-correcting guidance algorithm based on the Stateflow module were examined in detail. Finally, a 3-D model of the vehicle and target was created in VRML, and by processing mathematical results, the model was shown moving in a visual environment. This process gives more intuitive results for analyzing the simulation. The results showed that the simulation structure performs well. The simulation program heavily used modularization and encapsulation, so has broad applicability to simulations of other dynamic systems.

An Analysis of Final Course Grades in Two Different Entry Level Mathematics Courses between and among First Year College Students with Different Levels of High School Mathematics Preparation

ERIC Educational Resources Information Center

Muir, Carrie

2012-01-01

The purpose of this study was to compare the performance of first year college students with similar high school mathematics backgrounds in two introductory level college mathematics courses, "Fundamentals and Techniques of College Algebra and Quantitative Reasoning and Mathematical Skills," and to compare the performance of students…

Study of Adaptive Mathematical Models for Deriving Automated Pilot Performance Measurement Techniques. Volume II. Appendices. Final Report.

ERIC Educational Resources Information Center

Connelly, E. M.; And Others

A new approach to deriving human performance measures and criteria for use in automatically evaluating trainee performance is described. Ultimately, this approach will allow automatic measurement of pilot performance in a flight simulator or from recorded in-flight data. An efficient method of representing performance data within a computer is…

Recovering metabolic pathways via optimization.

PubMed

Beasley, John E; Planes, Francisco J

2007-01-01

A metabolic pathway is a coherent set of enzyme catalysed biochemical reactions by which a living organism transforms an initial (source) compound into a final (target) compound. Some of the different metabolic pathways adopted within organisms have been experimentally determined. In this paper, we show that a number of experimentally determined metabolic pathways can be recovered by a mathematical optimization model.

Head Start for Learning Disabled Students. Final Report 1990-1991.

ERIC Educational Resources Information Center

Reading Area Community Coll., PA.

A project was conducted at Reading Area Community College (Pennsylvania) to develop the basic reading, writing, and mathematics skills of students with learning disabilities, to develop the self-esteem of these students, to motivate them, and to develop a model program that could be used by other adult education providers. The project featured a…

Multi-Jurisdictional Behaviorally-Based In-Service Program for Elementary School Teachers in Mathematics. Final Report.

ERIC Educational Resources Information Center

Maryland Univ., College Park.

A project was designed to develop and validate a model for inservice education which could reach a large number of elementary school teachers. The thesis explored was whether this research, development, dissemination, and implementation could be effectively accomplished through the pooled competencies of a university-based staff, a state education…

Spreadsheets and Bulgarian goats

NASA Astrophysics Data System (ADS)

Sugden, Steve

2012-10-01

We consider a problem appearing in an Australian Mathematics Challenge in 2003. This article considers whether a spreadsheet might be used to model this problem, thus allowing students to explore its structure within the spreadsheet environment. It then goes on to reflect on some general principles of problem decomposition when the final goal is a successful and lucid spreadsheet implementation.

Catch as Catch Can: The History of the Theory of Gravitational Capture.

ERIC Educational Resources Information Center

Osipov, Y.

1992-01-01

Traces cosmogonic history of solar system from Laplace's hypothesis of revolving gas nebulae, to Newton's two-body problem with its mathematical impossibility of gravitational capture, to the isosceles three-body problem of Schmidt and Sitnikov with its notion of partial capture, and finally to the total capture model of Alexeyev verified by the…

Super-Hopf realizations of Lie superalgebras: Braided Paraparticle extensions of the Jordan-Schwinger map

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

Kanakoglou, K.; School of Physics, Nuclear and Elementary Particle Physics Department, Aristotle University of Thessaloniki; Daskaloyannis, C.

The mathematical structure of a mixed paraparticle system (combining both parabosonic and parafermionic degrees of freedom) commonly known as the Relative Parabose Set, will be investigated and a braided group structure will be described for it. A new family of realizations of an arbitrary Lie superalgebra will be presented and it will be shown that these realizations possess the valuable representation-theoretic property of transferring invariably the super-Hopf structure. Finally two classes of virtual applications will be outlined: The first is of interest for both mathematics and mathematical physics and deals with the representation theory of infinite dimensional Lie superalgebras, whilemore » the second is of interest in theoretical physics and has to do with attempts to determine specific classes of solutions of the Skyrme model.« less

The adventures of climate science in the sweet land of idle arguments

NASA Astrophysics Data System (ADS)

Winsberg, Eric; Goodwin, William Mark

2016-05-01

In a recent series of papers Roman Frigg, Leonard Smith, and several coauthors have developed a general epistemological argument designed to cast doubt on the capacity of a broad range of mathematical models to generate "decision relevant predictions." The presumptive targets of their argument are at least some of the modeling projects undertaken in contemporary climate science. In this paper, we trace and contrast two very different readings of the scope of their argument. We do this by considering the very different implications for climate science that these interpretations would have. Then, we lay out the structure of their argument-an argument by analogy-with an eye to identifying points at which certain epistemically significant distinctions might limit the force of the analogy. Finally, some of these epistemically significant distinctions are introduced and defended as relevant to a great many of the predictive mathematical modeling projects employed in contemporary climate science.

An experimental investigation of the unsteady response of a stator located downstream of a propeller ingesting broadband turbulence

NASA Astrophysics Data System (ADS)

Lynch, Denis Aloysius, III

This experimental investigation examined the unsteady response of a stator located downstream of a four- or ten-bladed propeller encountering broadband turbulence. The response is manifested in a radiated acoustic field which can be directly attributed to the unsteady surface pressure loading on the stator by the turbulent flowfield. In order to characterize the unsteady response of the stator, a thorough analysis of the turbulent flowfield downstream of the propeller was completed. The analysis of the turbulent flowfield is organized in a manner which reflects the causal relationship between influences on the flowfield and the evolution of the flowfield itself. Mathematical models for each of these contributions, including the broadband and periodic contributions of the propeller wakes and modification of the inflow turbulence by the propeller, are presented and analyzed. A further mathematical model involving the prediction of correlation length scale aids in the accurate prediction of the radiated acoustic pressure based solely on fundamental turbulent flowfield measurements. Unsteady surface pressure measurements, originally intended to provide additional information about the response of the stator as it relates to the incoming flowfield, were found to be heavily contaminated by vibrational effects. Therefore, techniques involving cross-correlation measurements are developed to mathematically isolate the unsteady pressure signal. The success of these techniques suggests the strong possibility of future application in this area. Finally, the mathematical models developed to describe the flowfield downstream of the propeller are applied to the case of a twenty-bladed propeller. This case was selected due to the anticipated increased levels of modification of the inflow turbulence. Results provide further evidence that this complex flowfield may be fully and accurately represented using simple mathematical models supported by baseline empirical information.

Validation of mathematical model for CZ process using small-scale laboratory crystal growth furnace

NASA Astrophysics Data System (ADS)

Bergfelds, Kristaps; Sabanskis, Andrejs; Virbulis, Janis

2018-05-01

The present material is focused on the modelling of small-scale laboratory NaCl-RbCl crystal growth furnace. First steps towards fully transient simulations are taken in the form of stationary simulations that deal with the optimization of material properties to match the model to experimental conditions. For this purpose, simulation software primarily used for the modelling of industrial-scale silicon crystal growth process was successfully applied. Finally, transient simulations of the crystal growth are presented, giving a sufficient agreement to experimental results.

Modeling and simulation of high dimensional stochastic multiscale PDE systems at the exascale

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

Zabaras, Nicolas J.

2016-11-08

Predictive Modeling of multiscale and Multiphysics systems requires accurate data driven characterization of the input uncertainties, and understanding of how they propagate across scales and alter the final solution. This project develops a rigorous mathematical framework and scalable uncertainty quantification algorithms to efficiently construct realistic low dimensional input models, and surrogate low complexity systems for the analysis, design, and control of physical systems represented by multiscale stochastic PDEs. The work can be applied to many areas including physical and biological processes, from climate modeling to systems biology.

Modeling Cell Size Regulation: From Single-Cell-Level Statistics to Molecular Mechanisms and Population-Level Effects.

PubMed

Ho, Po-Yi; Lin, Jie; Amir, Ariel

2018-05-20

Most microorganisms regulate their cell size. In this article, we review some of the mathematical formulations of the problem of cell size regulation. We focus on coarse-grained stochastic models and the statistics that they generate. We review the biologically relevant insights obtained from these models. We then describe cell cycle regulation and its molecular implementations, protein number regulation, and population growth, all in relation to size regulation. Finally, we discuss several future directions for developing understanding beyond phenomenological models of cell size regulation.

Persistence and ergodicity of plant disease model with markov conversion and impulsive toxicant input

NASA Astrophysics Data System (ADS)

Zhao, Wencai; Li, Juan; Zhang, Tongqian; Meng, Xinzhu; Zhang, Tonghua

2017-07-01

Taking into account of both white and colored noises, a stochastic mathematical model with impulsive toxicant input is formulated. Based on this model, we investigate dynamics, such as the persistence and ergodicity, of plant infectious disease model with Markov conversion in a polluted environment. The thresholds of extinction and persistence in mean are obtained. By using Lyapunov functions, we prove that the system is ergodic and has a stationary distribution under certain sufficient conditions. Finally, numerical simulations are employed to illustrate our theoretical analysis.

SANDERLING Final Report: Parts A and B, A Research Study into KBS for Command and Control in Naval and TMD Applications

DTIC Science & Technology

1990-04-01

focus of attention ). The inherent local control in the FA/C model allows it to achieve just that, since it only requires a global goal to become...Computing Terms Agent Modelling : is concerned with modelling actor’s intentions and plans, and their modification in the light of information... model or program that is based on a mathematical system of logic. B-tree : or "binary-tree" is a self organising storage mechanism that works by taking

Preface.

PubMed

Friedman, Avner; Lachowicz, Mirosław; Ledzewicz, Urszula; Piotrowska, Monika Joanna; Szymanska, Zuzanna

2017-02-01

This volume was inspired by the topics presented at the international conference "Micro and Macro Systems in Life Sciences" which was held on Jun 8-12, 2015 in Będlewo, Poland. System biology is an approach which tries to understand how micro systems, at the molecular and cellular levels, affect macro systems such as organs, tissue and populations. Thus it is not surprising that a major theme of this volume evolves around cancer and its treatment. Articles on this topic include models for tumor induced angiogenesis, without and with delays, metastatic niche of the bone marrow, drug resistance and metronomic chemotherapy, and virotherapy of glioma. Methods range from dynamical systems to optimal control. Another well represented topic of this volume is mathematical modeling in epidemiology. Mathematical approaches to modeling and control of more specific diseases like malaria, Ebola or human papillomavirus are discussed as well as a more general approaches to the SEIR, and even more general class of models in epidemiology, by using the tools of optimal control and optimization. The volume also brings up challenges in mathematical modeling of other diseases such as tuberculosis. Partial differential equations combined with numerical approaches are becoming important tools in modeling not only tumor growth and treatment, but also other diseases, such as fibrosis of the liver, and atherosclerosis and its associated blood flow dynamics, and our volume presents a state of the art approach on these topics. Understanding mathematics behind the cell motion, appearance of the special patterns in various cell populations, and age structured mutations are among topics addressed inour volume. A spatio-temporal models of synthetic genetic oscillators brings the analysis to the gene level which is the focus of much of current biological research. Mathematics can help biologists to explain the collective behavior of bacterial, a topic that is also presented here. Finally some more across the discipline topics are being addresses, which can appear as a challenge in studying problems in systems biology on all, macro, meso and micro levels. They include numerical approaches to stochastic wave equation arising in modeling Brownian motion, discrete velocity models, many particle approximations as well as very important aspect on the connection between discrete measurement and the construction of the models for various phenomena, particularly the one involving delays. With the variety of biological topics and their mathematical approaches we very much hope that the reader of the Mathematical Biosciences and Engineering will find this volume interesting and inspirational for their own research.

Simulating carbon capture by enhanced weathering with croplands: an overview of key processes highlighting areas of future model development

PubMed Central

Quegan, Shaun; Banwart, Steven A.

2017-01-01

Enhanced weathering (EW) aims to amplify a natural sink for CO2 by incorporating powdered silicate rock with high reactive surface area into agricultural soils. The goal is to achieve rapid dissolution of minerals and release of alkalinity with accompanying dissolution of CO2 into soils and drainage waters. EW could counteract phosphorus limitation and greenhouse gas (GHG) emissions in tropical soils, and soil acidification, a common agricultural problem studied with numerical process models over several decades. Here, we review the processes leading to soil acidification in croplands and how the soil weathering CO2 sink is represented in models. Mathematical models capturing the dominant processes and human interventions governing cropland soil chemistry and GHG emissions neglect weathering, while most weathering models neglect agricultural processes. We discuss current approaches to modelling EW and highlight several classes of model having the potential to simulate EW in croplands. Finally, we argue for further integration of process knowledge in mathematical models to capture feedbacks affecting both longer-term CO2 consumption and crop growth and yields. PMID:28381633

A multidimensional model of the effect of gravity on the spatial orientation of the monkey

NASA Technical Reports Server (NTRS)

Merfeld, D. M.; Young, L. R.; Oman, C. M.; Shelhamer, M. J.

1993-01-01

A "sensory conflict" model of spatial orientation was developed. This mathematical model was based on concepts derived from observer theory, optimal observer theory, and the mathematical properties of coordinate rotations. The primary hypothesis is that the central nervous system of the squirrel monkey incorporates information about body dynamics and sensory dynamics to develop an internal model. The output of this central model (expected sensory afference) is compared to the actual sensory afference, with the difference defined as "sensory conflict." The sensory conflict information is, in turn, used to drive central estimates of angular velocity ("velocity storage"), gravity ("gravity storage"), and linear acceleration ("acceleration storage") toward more accurate values. The model successfully predicts "velocity storage" during rotation about an earth-vertical axis. The model also successfully predicts that the time constant of the horizontal vestibulo-ocular reflex is reduced and that the axis of eye rotation shifts toward alignment with gravity following postrotatory tilt. Finally, the model predicts the bias, modulation, and decay components that have been observed during off-vertical axis rotations (OVAR).

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

PubMed

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

2018-05-31

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

Mathematics in Colleges and Universities. A Comprehensive Survey of Graduate and Undergraduate Programs. Final Report

ERIC Educational Resources Information Center

Lindquist, Clarence B.

Presented is a comprehensive survey of graduate and undergraduate programs in mathematics in effect during Winter and Spring of 1961. Questionnaires were mailed to 1,069 institutions which awarded degrees in mathematics or offered substantial programs in mathematics. Junior colleges and such specialized schools as Bible Colleges and seminaries,…

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…

Effects of the Connected Mathematics Project 2 (CMP2) on the Mathematics Achievement of Grade 6 Students in the Mid-Atlantic Region. Final Report. NCEE 2012-4017

ERIC Educational Resources Information Center

Martin, Taylor; Brasiel, Sarah J.; Turner, Herb; Wise, John C.

2012-01-01

This study examines the effects of Connected Mathematics Project 2 (CMP2) on grade 6 student mathematics achievement and engagement using a cluster randomized controlled trial (RCT) design. It responds to a need to improve mathematics learning in the Mid-Atlantic Region (Delaware, Maryland, New Jersey, Pennsylvania, and Washington, DC). Findings…

Relation between Approximate Number System Acuity and Mathematical Achievement: The Influence of Fluency

PubMed Central

Wang, Li; Sun, Yuhua; Zhou, Xinlin

2016-01-01

Previous studies have observed inconsistent relations between the acuity of the Approximate Number System (ANS) and mathematical achievement. In this paper, we hypothesize that the relation between ANS acuity and mathematical achievement is influenced by fluency; that is, the mathematical achievement test covering a greater expanse of mathematical fluency may better reflect the relation between ANS acuity and mathematics skills. We explored three types of mathematical achievement tests utilized in this study: Subtraction, graded, and semester-final examination. The subtraction test was designed to measure the mathematical fluency. The graded test was more fluency-based than the semester-final examination, but both involved the same mathematical knowledge from the class curriculum. A total of 219 fifth graders from primary schools were asked to perform all three tests, then given a numerosity comparison task, a visual form perception task (figure matching), and a series of other tasks to assess general cognitive processes (mental rotation, non-verbal matrix reasoning, and choice reaction time). The findings were consistent with our expectations. The relation between ANS acuity and mathematical achievement was particularly clearly reflected in the participants’ performance on the visual form perception task, which supports the domain-general explanations for the underlying mechanisms of the relation between ANS acuity and math achievement. PMID:28066291

A Nonlinear differential equation model of Asthma effect of environmental pollution using LHAM

NASA Astrophysics Data System (ADS)

Joseph, G. Arul; Balamuralitharan, S.

2018-04-01

In this paper, we investigated a nonlinear differential equation mathematical model to study the spread of asthma in the environmental pollutants from industry and mainly from tobacco smoke from smokers in different type of population. Smoking is the main cause to spread Asthma in the environment. Numerical simulation is also discussed. Finally by using Liao’s Homotopy analysis Method (LHAM), we found that the approximate analytical solution of Asthmatic disease in the environmental.

Evaluation of Professional Development in the Use of Arts-Integrated Activities with Mathematics Content: Findings from the Evaluation of the Wolf Trap Arts in Education Model Development and Dissemination Grant. Final Grant Report

ERIC Educational Resources Information Center

Ludwig, Meredith; Song, Mengli

2015-01-01

In 2010, the Wolf Trap Foundation for the Performing Arts, Institute for Early Learning Through the Arts (Wolf Trap), was awarded a U.S. Department of Education Arts in Education Model Development and Dissemination (AEMDD) grant. The purpose of the AEMDD grant was to develop, implement, and disseminate a research-based program of professional…

How to make mathematics relevant to first-year engineering students: perceptions of students on student-produced resources

NASA Astrophysics Data System (ADS)

Loch, Birgit; Lamborn, Julia

2016-01-01

Many approaches to make mathematics relevant to first-year engineering students have been described. These include teaching practical engineering applications, or a close collaboration between engineering and mathematics teaching staff on unit design and teaching. In this paper, we report on a novel approach where we gave higher year engineering and multimedia students the task to 'make maths relevant' for first-year students. This approach is novel as we moved away from the traditional thinking that staff should produce these resources to students producing the same. These students have more recently undertaken first-year mathematical study themselves and can also provide a more mature student perspective to the task than first-year students. Two final-year engineering students and three final-year multimedia students worked on this project over the Australian summer term and produced two animated videos showing where concepts taught in first-year mathematics are applied by professional engineers. It is this student perspective on how to make mathematics relevant to first-year students that we investigate in this paper. We analyse interviews with higher year students as well as focus groups with first-year students who had been shown the videos in class, with a focus on answering the following three research questions: (1) How would students demonstrate the relevance of mathematics in engineering? (2) What are first-year students' views on the resources produced for them? (3) Who should produce resources to demonstrate the relevance of mathematics? There seemed to be some disagreement between first- and final-year students as to how the importance of mathematics should be demonstrated in a video. We therefore argue that it should ideally be a collaboration between higher year students and first-year students, with advice from lecturers, to produce such resources.

The Origin of Mathematics and Number Sense in the Cerebellum: with Implications for Finger Counting and Dyscalculia.

PubMed

Vandervert, Larry

2017-01-01

Mathematicians and scientists have struggled to adequately describe the ultimate foundations of mathematics. Nobel laureates Albert Einstein and Eugene Wigner were perplexed by this issue, with Wigner concluding that the workability of mathematics in the real world is a mystery we cannot explain. In response to this classic enigma, the major purpose of this article is to provide a theoretical model of the ultimate origin of mathematics and "number sense" (as defined by S. Dehaene) that is proposed to involve the learning of inverse dynamics models through the collaboration of the cerebellum and the cerebral cortex (but prominently cerebellum-driven). This model is based upon (1) the modern definition of mathematics as the "science of patterns," (2) cerebellar sequence (pattern) detection, and (3) findings that the manipulation of numbers is automated in the cerebellum. This cerebro-cerebellar approach does not necessarily conflict with mathematics or number sense models that focus on brain functions associated with especially the intraparietal sulcus region of the cerebral cortex. A direct corollary purpose of this article is to offer a cerebellar inner speech explanation for difficulty in developing "number sense" in developmental dyscalculia. It is argued that during infancy the cerebellum learns (1) a first tier of internal models for a primitive physics that constitutes the foundations of visual-spatial working memory, and (2) a second (and more abstract) tier of internal models based on (1) that learns "number" and relationships among dimensions across the primitive physics of the first tier. Within this context it is further argued that difficulty in the early development of the second tier of abstraction (and "number sense") is based on the more demanding attentional requirements imposed on cerebellar inner speech executive control during the learning of cerebellar inverse dynamics models. Finally, it is argued that finger counting improves (does not originate) "number sense" by extending focus of attention in executive control of silent cerebellar inner speech. It is suggested that (1) the origin of mathematics has historically been an enigma only because it is learned below the level of conscious awareness in cerebellar internal models, (2) understandings of the development of "number sense" and developmental dyscalculia can be advanced by first understanding the ultimate foundations of number and mathematics do not simply originate in the cerebral cortex, but rather in cerebro-cerebellar collaboration (predominately driven by the cerebellum). It is concluded that difficulty with "number sense" results from the extended demands on executive control in learning inverse dynamics models associated with cerebellar inner speech related to the second tier of abstraction (numbers) of the infant's primitive physics.

Tacit Beginnings Towards a Model of Scientific Thinking

NASA Astrophysics Data System (ADS)

Glass, Rory J.

2013-10-01

The purpose of this paper is to provide an examination of the role tacit knowledge plays in understanding, and to provide a model to make such knowledge identifiable. To do this I first consider the needs of society, the ubiquity of information in our world and the future demands of the science classroom. I propose the use of more implicit or tacit understandings as foundational elements for the development of student knowledge. To justify this proposition I consider a wide range of philosophical and psychological perspectives on knowledge. Then develop a Model of Scientific Knowledge, based in large part on a similar model created by Paul Ernest (Social constructivism as a philosophy of mathematics, SUNY Press, Albany, NY, 1998a; Situated cognition and the learning of mathematics, University of Oxford Department of Educational Studies, Oxford, 1998b). Finally, I consider the work that has been done by those in fields beyond education and the ways in which tacit knowledge can be used as a starting point for knowledge building.

Fitting a Structured Juvenile-Adult Model for Green Tree Frogs to Population Estimates from Capture-Mark-Recapture Field Data

USGS Publications Warehouse

Ackleh, A.S.; Carter, J.; Deng, K.; Huang, Q.; Pal, N.; Yang, X.

2012-01-01

We derive point and interval estimates for an urban population of green tree frogs (Hyla cinerea) from capture-mark-recapture field data obtained during the years 2006-2009. We present an infinite-dimensional least-squares approach which compares a mathematical population model to the statistical population estimates obtained from the field data. The model is composed of nonlinear first-order hyperbolic equations describing the dynamics of the amphibian population where individuals are divided into juveniles (tadpoles) and adults (frogs). To solve the least-squares problem, an explicit finite difference approximation is developed. Convergence results for the computed parameters are presented. Parameter estimates for the vital rates of juveniles and adults are obtained, and standard deviations for these estimates are computed. Numerical results for the model sensitivity with respect to these parameters are given. Finally, the above-mentioned parameter estimates are used to illustrate the long-time behavior of the population under investigation. ?? 2011 Society for Mathematical Biology.

Mathematical model of gas plasma applied to chronic wounds

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

Wang, J. G.; Liu, X. Y.; Liu, D. W.

2013-11-15

Chronic wounds are a major burden for worldwide health care systems, and patients suffer pain and discomfort from this type of wound. Recently gas plasmas have been shown to safely speed chronic wounds healing. In this paper, we develop a deterministic mathematical model formulated by eight-species reaction-diffusion equations, and use it to analyze the plasma treatment process. The model follows spatial and temporal concentration within the wound of oxygen, chemoattractants, capillary sprouts, blood vessels, fibroblasts, extracellular matrix material, nitric oxide (NO), and inflammatory cell. Two effects of plasma, increasing NO concentration and reducing bacteria load, are considered in this model.more » The plasma treatment decreases the complete healing time from 25 days (normal wound healing) to 17 days, and the contributions of increasing NO concentration and reducing bacteria load are about 1/4 and 3/4, respectively. Increasing plasma treatment frequency from twice to three times per day accelerates healing process. Finally, the response of chronic wounds of different etiologies to treatment with gas plasmas is analyzed.« less

Student Assistance General Provisions; Federal Pell Grant Program; Academic Competitiveness Grant Program; and National Science and Mathematics Access to Retain Talent Grant Program. Final Rule. Federal Register, Part IV, Department of Education, 34 CFR Parts 668, 690, and 691

ERIC Educational Resources Information Center

National Archives and Records Administration, 2006

2006-01-01

The Secretary is adopting as final, with changes, interim final regulations in: 34 CFR part 691 for the Academic Competitiveness Grant (ACG) and National Science and Mathematics Access to Retain Talent Grant (National SMART Grant) programs; 34 CFR part 668 (Student Assistance General Provisions); and 34 CFR part 690 (Federal Pell Grant Program).…

High-throughput mathematical analysis identifies Turing networks for patterning with equally diffusing signals.

PubMed

Marcon, Luciano; Diego, Xavier; Sharpe, James; Müller, Patrick

2016-04-08

The Turing reaction-diffusion model explains how identical cells can self-organize to form spatial patterns. It has been suggested that extracellular signaling molecules with different diffusion coefficients underlie this model, but the contribution of cell-autonomous signaling components is largely unknown. We developed an automated mathematical analysis to derive a catalog of realistic Turing networks. This analysis reveals that in the presence of cell-autonomous factors, networks can form a pattern with equally diffusing signals and even for any combination of diffusion coefficients. We provide a software (available at http://www.RDNets.com) to explore these networks and to constrain topologies with qualitative and quantitative experimental data. We use the software to examine the self-organizing networks that control embryonic axis specification and digit patterning. Finally, we demonstrate how existing synthetic circuits can be extended with additional feedbacks to form Turing reaction-diffusion systems. Our study offers a new theoretical framework to understand multicellular pattern formation and enables the wide-spread use of mathematical biology to engineer synthetic patterning systems.

High-throughput mathematical analysis identifies Turing networks for patterning with equally diffusing signals

PubMed Central

Marcon, Luciano; Diego, Xavier; Sharpe, James; Müller, Patrick

2016-01-01

The Turing reaction-diffusion model explains how identical cells can self-organize to form spatial patterns. It has been suggested that extracellular signaling molecules with different diffusion coefficients underlie this model, but the contribution of cell-autonomous signaling components is largely unknown. We developed an automated mathematical analysis to derive a catalog of realistic Turing networks. This analysis reveals that in the presence of cell-autonomous factors, networks can form a pattern with equally diffusing signals and even for any combination of diffusion coefficients. We provide a software (available at http://www.RDNets.com) to explore these networks and to constrain topologies with qualitative and quantitative experimental data. We use the software to examine the self-organizing networks that control embryonic axis specification and digit patterning. Finally, we demonstrate how existing synthetic circuits can be extended with additional feedbacks to form Turing reaction-diffusion systems. Our study offers a new theoretical framework to understand multicellular pattern formation and enables the wide-spread use of mathematical biology to engineer synthetic patterning systems. DOI: http://dx.doi.org/10.7554/eLife.14022.001 PMID:27058171

Retrieving the optical parameters of biological tissues using diffuse reflectance spectroscopy and Fourier series expansions. I. theory and application.

PubMed

Muñoz Morales, Aarón A; Vázquez Y Montiel, Sergio

2012-10-01

The determination of optical parameters of biological tissues is essential for the application of optical techniques in the diagnosis and treatment of diseases. Diffuse Reflection Spectroscopy is a widely used technique to analyze the optical characteristics of biological tissues. In this paper we show that by using diffuse reflectance spectra and a new mathematical model we can retrieve the optical parameters by applying an adjustment of the data with nonlinear least squares. In our model we represent the spectra using a Fourier series expansion finding mathematical relations between the polynomial coefficients and the optical parameters. In this first paper we use spectra generated by the Monte Carlo Multilayered Technique to simulate the propagation of photons in turbid media. Using these spectra we determine the behavior of Fourier series coefficients when varying the optical parameters of the medium under study. With this procedure we find mathematical relations between Fourier series coefficients and optical parameters. Finally, the results show that our method can retrieve the optical parameters of biological tissues with accuracy that is adequate for medical applications.

Computer-Aided Air-Traffic Control In The Terminal Area

NASA Technical Reports Server (NTRS)

Erzberger, Heinz

1995-01-01

Developmental computer-aided system for automated management and control of arrival traffic at large airport includes three integrated subsystems. One subsystem, called Traffic Management Advisor, another subsystem, called Descent Advisor, and third subsystem, called Final Approach Spacing Tool. Data base that includes current wind measurements and mathematical models of performances of types of aircraft contributes to effective operation of system.

CSMP Mathematics for the Intermediate Grades Part IV, Teacher's Guide. General Introduction. Workbooks. Experimental Version.

ERIC Educational Resources Information Center

Armstrong, Richard; And Others

This guide represents the final experimental version of a pilot project which was conducted in the United States between 1973 and 1976. The ideas and the manner of presentation are based on the works of Georges and Frederique Papy. They are recognized for having introduced colored arrow drawings ("papygrams") and models of our numeration…

CSMP Mathematics for the Intermediate Grades Part III, Teacher's Guide [and] Worksheets. General Introduction. Workbooks. Experimental Version.

ERIC Educational Resources Information Center

Harpel, Jim; And Others

This guide represents the final experimental version of a pilot project which was conducted in the United States between 1973 and 1976. The ideas and the manner of presentation are based on the works of Georges and Frederique Papy. They are recognized for having introduced colored arrow drawings ("papygrams") and models of our numeration…

CSMP Mathematics for the Intermediate Grades Part III, Teacher's Guide. The World of Numbers. Experimental Version.

ERIC Educational Resources Information Center

CEMREL, Inc., St. Ann, MO.

This guide represents the final experimental version of a pilot project which was conducted in the United States between 1973 and 1976. The ideas and the manner of presentation are based on the works of Georges and Frederique Papy. They are recognized for having introduced colored arrow drawings ("papygrams") and models of our numeration…

CSMP Mathematics for the Intermediate Grades Part II, Teacher's Guide. General Introduction. Workbooks. Experimental Version.

ERIC Educational Resources Information Center

Harpel, Jim; And Others

This guide represents the final experimental version of a pilot project which was conducted in the United States between 1973 and 1976. The ideas and the manner of presentation are based on the works of Georges and Frederique Papy. They are recognized for having introduced colored arrow drawings ("papygrams") and models of our numeration…

CSMP Mathematics for the Intermediate Grades Part IV, Teacher's Guide. The World of Numbers. Experimental Version.

ERIC Educational Resources Information Center

CEMREL, Inc., St. Ann, MO.

This guide represents the final experimental version of a pilot project which was conducted in the United States between 1973 and 1976. The ideas and the manner of presentation are based on the works of Georges and Frederique Papy. They are recognized for having introduced colored arrow drawings ("papygrams") and models of our numeration…

Title I/PSEN Individualized Reading and Math Services for the Handicapped, 1980-81. Final Evaluation Report.

ERIC Educational Resources Information Center

New York City Board of Education, Brooklyn, NY. Office of Educational Evaluation.

The Title I Umbrella Program provided compensatory instruction in reading, mathematics, and writing to 24,000 mildly or moderately handicapped students in New York City. The program was comprised of seven discrete components for the remediation of reading and writing skills, five after-school models, and two components for the remediation of math…

Optimization design of the angle detecting system used in the fast steering mirror

NASA Astrophysics Data System (ADS)

Ni, Ying-xue; Wu, Jia-bin; San, Xiao-gang; Gao, Shi-jie; Ding, Shao-hang; Wang, Jing; Wang, Tao; Wang, Hui-xian

2018-01-01

In this paper, in order to design a fast steering mirror (FSM) with large deflection angle and high linearity, a deflection angle detecting system (DADS) using quadrant detector (QD) is developed. And the mathematical model describing DADS is established by analyzing the principle of position detecting and error characteristics of QD. Based on this mathematical model, the variation tendencies of deflection angle and linearity of FSM are simulated. Then, by changing the parameters of the DADS, the optimization of deflection angle and linearity of FSM is demonstrated. Finally, a QD-based FSM is designed based on this method, which achieves ±2° deflection angle and 0.72% and 0.68% linearity along x and y axis, respectively. Moreover, this method will be beneficial to the design of large deflection angle and high linearity FSM.

Post-Primary Students' Images of Mathematics: Findings from a Survey of Irish Ordinary Level Mathematics Students

ERIC Educational Resources Information Center

Lane, Ciara; Stynes, Martin; O'Donoghue, John

2016-01-01

A questionnaire survey was carried out as part of a PhD research study to investigate the image of mathematics held by post-primary students in Ireland. The study focused on students in fifth year of post-primary education studying ordinary level mathematics for the Irish Leaving Certificate examination--the final examination for students in…

"Attrition Processes Out of Mathematics for Undergraduate Students." Attrition from Mathematics as a Social Process. Final Report.

ERIC Educational Resources Information Center

Maines, David R.; And Others

Investigated were those long-term processes which contribute to high rates of attrition for women out of mathematics. It is based on the contention that university students drop out of mathematics as a consequence of prior socialization, educational career contingencies, and goal commitment and career aspirations, with the mix of these factors…

Second International Mathematics Study; Longitudinal, Classroom Process Surveys for Population A: Students, Teachers, and Schools, 1981-1982 [machine-readable data file].

ERIC Educational Resources Information Center

Wolfe, Richard G.

The Second International Mathematics Study (SIMS) of the International Association for the Evaluation of Educational Achievement (IEA) was conducted in 20 countries on two sampled populations: Population A of 13-year-olds and Population B of students studying mathematics in their final year of secondary school. Mathematics achievement was measured…

[New trends in the evaluation of mathematics learning disabilities. The role of metacognition].

PubMed

Miranda-Casas, A; Acosta-Escareño, G; Tarraga-Minguez, R; Fernández, M I; Rosel-Remírez, J

2005-01-15

The current trends in the evaluation of mathematics learning disabilities (MLD), based on cognitive and empirical models, are oriented towards combining procedures involving the criteria and the evaluation of cognitive and metacognitive processes, associated to performance in mathematical tasks. The objective of this study is to analyse the metacognitive skills of prediction and evaluation in performing maths tasks and to compare metacognitive performance among pupils with MLD and younger pupils without MLD, who have the same level of mathematical performance. Likewise, we analyse these pupils' desire to learn. Subjects and methods. We compare a total of 44 pupils from the second cycle of primary education (8-10 years old) with and without mathematics learning disabilities. Significant differences are observed between pupils with and without mathematics learning disabilities in their capacity to predict and assess all of the tasks evaluated. As regards their 'desire to learn', no significant differences were found between pupils with and without MLD, which indicated that those with MLD assess their chances of successfully performing maths tasks in the same way as those without MLD. Finally, the findings reveal a similar metacognitive profile in pupils with MLD and the younger pupils with no mathematics learning disabilities. In future studies we consider it important to analyse the influence of the socio-affective belief system in the use of metacognitive skills.

An analytically linearized helicopter model with improved modeling accuracy

NASA Technical Reports Server (NTRS)

Jensen, Patrick T.; Curtiss, H. C., Jr.; Mckillip, Robert M., Jr.

1991-01-01

An analytically linearized model for helicopter flight response including rotor blade dynamics and dynamic inflow, that was recently developed, was studied with the objective of increasing the understanding, the ease of use, and the accuracy of the model. The mathematical model is described along with a description of the UH-60A Black Hawk helicopter and flight test used to validate the model. To aid in utilization of the model for sensitivity analysis, a new, faster, and more efficient implementation of the model was developed. It is shown that several errors in the mathematical modeling of the system caused a reduction in accuracy. These errors in rotor force resolution, trim force and moment calculation, and rotor inertia terms were corrected along with improvements to the programming style and documentation. Use of a trim input file to drive the model is examined. Trim file errors in blade twist, control input phase angle, coning and lag angles, main and tail rotor pitch, and uniform induced velocity, were corrected. Finally, through direct comparison of the original and corrected model responses to flight test data, the effect of the corrections on overall model output is shown.

NARMAX model identification of a palm oil biodiesel engine using multi-objective optimization differential evolution

NASA Astrophysics Data System (ADS)

Mansor, Zakwan; Zakaria, Mohd Zakimi; Nor, Azuwir Mohd; Saad, Mohd Sazli; Ahmad, Robiah; Jamaluddin, Hishamuddin

2017-09-01

This paper presents the black-box modelling of palm oil biodiesel engine (POB) using multi-objective optimization differential evolution (MOODE) algorithm. Two objective functions are considered in the algorithm for optimization; minimizing the number of term of a model structure and minimizing the mean square error between actual and predicted outputs. The mathematical model used in this study to represent the POB system is nonlinear auto-regressive moving average with exogenous input (NARMAX) model. Finally, model validity tests are applied in order to validate the possible models that was obtained from MOODE algorithm and lead to select an optimal model.

Space flight visual simulation.

PubMed

Xu, L

1985-01-01

In this paper, based on the scenes of stars seen by astronauts in their orbital flights, we have studied the mathematical model which must be constructed for CGI system to realize the space flight visual simulation. Considering such factors as the revolution and rotation of the Earth, exact date, time and site of orbital injection of the spacecraft, as well as its orbital flight and attitude motion, etc., we first defined all the instantaneous lines of sight and visual fields of astronauts in space. Then, through a series of coordinate transforms, the pictures of the scenes of stars changing with time-space were photographed one by one mathematically. In the procedure, we have designed a method of three-times "mathematical cutting." Finally, we obtained each instantaneous picture of the scenes of stars observed by astronauts through the window of the cockpit. Also, the dynamic conditions shaded by the Earth in the varying pictures of scenes of stars could be displayed.

Learning to teach upper primary school algebra: changes to teachers' mathematical knowledge for teaching functional thinking

NASA Astrophysics Data System (ADS)

Wilkie, Karina J.

2016-06-01

A key aspect of learning algebra in the middle years of schooling is exploring the functional relationship between two variables: noticing and generalising the relationship, and expressing it mathematically. This article describes research on the professional learning of upper primary school teachers for developing their students' functional thinking through pattern generalisation. This aspect of algebra learning has been explicitly brought to the attention of upper primary teachers in the recently introduced Australian curriculum. Ten practising teachers participated over 1 year in a design-based research project involving a sequence of geometric pattern generalisation lessons with their classes. Initial and final survey responses and teachers' interactions in regular meetings and lessons were analysed from cognitive and situated perspectives on professional learning, using a theoretical model for the different types of knowledge needed for teaching mathematics. The teachers demonstrated an increase in certain aspects of their mathematical knowledge for teaching algebra as well as some residual issues. Implications for the professional learning of practising and pre-service teachers to develop their mathematics knowledge for teaching functional thinking, and challenges with operationalising knowledge categories for field-based research are presented.

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.

The Implementation of an Interdisciplinary Co-planning Team Model Among Mathematics and Science Teachers

NASA Astrophysics Data System (ADS)

Brown, Michelle Cetner

In recent years, Science, Technology, Engineering, and Mathematics (STEM) education has become a significant focus of numerous theoretical and commentary articles as researchers have advocated for active and conceptually integrated learning in classrooms. Drawing connections between previously isolated subjects, especially mathematics and science, has been shown to increase student engagement, performance, and critical thinking skills. However, obstacles exist to the widespread implementation of integrated curricula in schools, such as teacher knowledge and school structure and culture. The Interdisciplinary Co-planning Team (ICT) model, in which teachers of different subjects come together regularly to discuss connections between content and to plan larger interdisciplinary activities and smaller examples and discussion points, offers a method for teachers to create sustainable interdisciplinary experiences for students within the bounds of the current school structure. The ICT model is designed to be an iterative, flexible model, providing teachers with both a regular time to come together as "experts" and "teach" each other important concepts from their separate disciplines, and then to bring their shared knowledge and language back to their own classrooms to implement with their students in ways that fit their individual classes. In this multiple-case study, which aims to describe the nature of the co-planning process, the nature of plans, and changes in teacher beliefs as a result of co-planning, three pairs of secondary mathematics and science teachers participated in a 10-week intervention with the ICT model. Each pair constituted one case. Data included observations, interviews, and artifact collection. All interviews, whole-group sessions, and co-planning sessions were transcribed and coded using both theory-based and data-based codes. Finally, a cross-case comparison was used to present similarities and differences across cases. Findings suggest that the ICT model can be implemented with pairs of mathematics and science teachers to create a sustainable way to share experience and expertise, and to create powerful interdisciplinary experiences for their students. In addition, there is evidence that participation with the ICT model positively influences teacher beliefs about the nature of mathematics and science, about teaching and learning, and about interdisciplinary connections. These findings seem to hold across grades, school type, and personal experience. Future implementation of the ICT model on a larger scale is recommended to continue to observe the effects on teachers and students.

A Self-paced Course in Pharmaceutical Mathematics Using Web-based Databases

PubMed Central

Bourne, David W.A.; Davison, A. Machelle

2006-01-01

Objective To transform a pharmaceutical mathematics course to a self-paced instructional format using Web-accessed databases for student practice and examination preparation. Design The existing pharmaceutical mathematics course was modified from a lecture style with midsemester and final examinations to a self-paced format in which students had multiple opportunities to complete online, nongraded self-assessments as well as in-class module examinations. Assessment Grades and course evaluations were compared between students taking the class in lecture format with midsemester and final examinations and students taking the class in the self-paced instructional format. The number of times it took students to pass examinations was also analyzed. Conclusions Based on instructor assessment and student feedback, the course succeeded in giving students who were proficient in pharmaceutical mathematics a chance to progress quickly and students who were less skillful the opportunity to receive instruction at their own pace and develop mathematical competence. PMID:17149445

A self-paced course in pharmaceutical mathematics using web-based databases.

PubMed

Bourne, David W A; Davison, A Machelle

2006-10-15

To transform a pharmaceutical mathematics course to a self-paced instructional format using Web-accessed databases for student practice and examination preparation. The existing pharmaceutical mathematics course was modified from a lecture style with midsemester and final examinations to a self-paced format in which students had multiple opportunities to complete online, nongraded self-assessments as well as in-class module examinations. Grades and course evaluations were compared between students taking the class in lecture format with midsemester and final examinations and students taking the class in the self-paced instructional format. The number of times it took students to pass examinations was also analyzed. Based on instructor assessment and student feedback, the course succeeded in giving students who were proficient in pharmaceutical mathematics a chance to progress quickly and students who were less skillful the opportunity to receive instruction at their own pace and develop mathematical competence.

Dynamical properties of a minimally parameterized mathematical model for metronomic chemotherapy.

PubMed

Schättler, Heinz; Ledzewicz, Urszula; Amini, Behrooz

2016-04-01

A minimally parameterized mathematical model for low-dose metronomic chemotherapy is formulated that takes into account angiogenic signaling between the tumor and its vasculature and tumor inhibiting effects of tumor-immune system interactions. The dynamical equations combine a model for tumor development under angiogenic signaling formulated by Hahnfeldt et al. with a model for tumor-immune system interactions by Stepanova. The dynamical properties of the model are analyzed. Depending on the parameter values, the system encompasses a variety of medically realistic scenarios that range from cases when (i) low-dose metronomic chemotherapy is able to eradicate the tumor (all trajectories converge to a tumor-free equilibrium point) to situations when (ii) tumor dormancy is induced (a unique, globally asymptotically stable benign equilibrium point exists) to (iii) multi-stable situations that have both persistent benign and malignant behaviors separated by the stable manifold of an unstable equilibrium point and finally to (iv) situations when tumor growth cannot be overcome by low-dose metronomic chemotherapy. The model forms a basis for a more general study of chemotherapy when the main components of a tumor's microenvironment are taken into account.

Manitoba Mathematics Assessment Program, 1981. Final Report.

ERIC Educational Resources Information Center

Manitoba Dept. of Education, Winnipeg.

This document contains conclusions, recommendations, a summary of results, and interpretations of the 1981 Mathematics Assessment Program. The Assessment Program involved the production of achievement tests and teacher questionnaires for the third, sixth, ninth, and twelth-grade students. These were a test related to general mathematics skills,…

Construction Industry Related Mathematics: Seventh Grade.

ERIC Educational Resources Information Center

Mundell, Scott

The field tested construction industry-related mathematics unit is intended to familiarize seventh grade students with various facets of the construction industry, including the various occupations available and the mathematical abilities and other skills and training necessary to pursue an occupation in the industry. The final set of activities…

Extinction and persistence of a stochastic nonlinear SIS epidemic model with jumps

NASA Astrophysics Data System (ADS)

Ge, Qing; Ji, Guilin; Xu, Jiabo; Fan, Xiaolin

2016-11-01

In this paper, Brownian motion and L e ´ vy jumps are introduced to a SIS type epidemic model with nonlinear incidence rate. The dynamical behavior of the considered model is investigated. In order to reveal the extinction and permanence of the disease, two threshold values R˜0 ,R¯0 are showed. We find that if R˜0 < 1, the disease may die out, and when R¯0 > 1, the disease may be persistent. Finally, the numerical simulations are presented to illustrate our mathematical results.

Design and optimization of a fiber optic data link for new generation on-board SAR processing architectures

NASA Astrophysics Data System (ADS)

Ciminelli, Caterina; Dell'Olio, Francesco; Armenise, Mario N.; Iacomacci, Francesco; Pasquali, Franca; Formaro, Roberto

2017-11-01

A fiber optic digital link for on-board data handling is modeled, designed and optimized in this paper. Design requirements and constraints relevant to the link, which is in the frame of novel on-board processing architectures, are discussed. Two possible link configurations are investigated, showing their advantages and disadvantages. An accurate mathematical model of each link component and the entire system is reported and results of link simulation based on those models are presented. Finally, some details on the optimized design are provided.

Economic demand predicts addiction-like behavior and therapeutic efficacy of oxytocin in the rat.

PubMed

Bentzley, Brandon S; Jhou, Thomas C; Aston-Jones, Gary

2014-08-12

Development of new treatments for drug addiction will depend on high-throughput screening in animal models. However, an addiction biomarker fit for rapid testing, and useful in both humans and animals, is not currently available. Economic models are promising candidates. They offer a structured quantitative approach to modeling behavior that is mathematically identical across species, and accruing evidence indicates economic-based descriptors of human behavior may be particularly useful biomarkers of addiction severity. However, economic demand has not yet been established as a biomarker of addiction-like behavior in animals, an essential final step in linking animal and human studies of addiction through economic models. We recently developed a mathematical approach for rapidly modeling economic demand in rats trained to self-administer cocaine. We show here that economic demand, as both a spontaneous trait and induced state, predicts addiction-like behavior, including relapse propensity, drug seeking in abstinence, and compulsive (punished) drug taking. These findings confirm economic demand as a biomarker of addiction-like behavior in rats. They also support the view that excessive motivation plays an important role in addiction while extending the idea that drug dependence represents a shift from initially recreational to compulsive drug use. Finally, we found that economic demand for cocaine predicted the efficacy of a promising pharmacotherapy (oxytocin) in attenuating cocaine-seeking behaviors across individuals, demonstrating that economic measures may be used to rapidly identify the clinical utility of prospective addiction treatments.

Economic demand predicts addiction-like behavior and therapeutic efficacy of oxytocin in the rat

PubMed Central

Bentzley, Brandon S.; Jhou, Thomas C.; Aston-Jones, Gary

2014-01-01

Development of new treatments for drug addiction will depend on high-throughput screening in animal models. However, an addiction biomarker fit for rapid testing, and useful in both humans and animals, is not currently available. Economic models are promising candidates. They offer a structured quantitative approach to modeling behavior that is mathematically identical across species, and accruing evidence indicates economic-based descriptors of human behavior may be particularly useful biomarkers of addiction severity. However, economic demand has not yet been established as a biomarker of addiction-like behavior in animals, an essential final step in linking animal and human studies of addiction through economic models. We recently developed a mathematical approach for rapidly modeling economic demand in rats trained to self-administer cocaine. We show here that economic demand, as both a spontaneous trait and induced state, predicts addiction-like behavior, including relapse propensity, drug seeking in abstinence, and compulsive (punished) drug taking. These findings confirm economic demand as a biomarker of addiction-like behavior in rats. They also support the view that excessive motivation plays an important role in addiction while extending the idea that drug dependence represents a shift from initially recreational to compulsive drug use. Finally, we found that economic demand for cocaine predicted the efficacy of a promising pharmacotherapy (oxytocin) in attenuating cocaine-seeking behaviors across individuals, demonstrating that economic measures may be used to rapidly identify the clinical utility of prospective addiction treatments. PMID:25071176

Mathematical model of silicon smelting process basing on pelletized charge from technogenic raw materials

NASA Astrophysics Data System (ADS)

Nemchinova, N. V.; Tyutrin, A. A.; Salov, V. M.

2018-03-01

The silicon production process in the electric arc reduction furnaces (EAF) is studied using pelletized charge as an additive to the standard on the basis of the generated mathematical model. The results obtained due to the model will contribute to the analysis of the charge components behavior during melting with the achievement of optimum final parameters of the silicon production process. The authors proposed using technogenic waste as a raw material for the silicon production in a pelletized form using liquid glass and aluminum production dust from the electrostatic precipitators as a binder. The method of mathematical modeling with the help of the ‘Selector’ software package was used as a basis for the theoretical study. A model was simulated with the imitation of four furnace temperature zones and a crystalline silicon phase (25 °C). The main advantage of the created model is the ability to analyze the behavior of all burden materials (including pelletized charge) in the carbothermic process. The behavior analysis is based on the thermodynamic probability data of the burden materials interactions in the carbothermic process. The model accounts for 17 elements entering the furnace with raw materials, electrodes and air. The silicon melt, obtained by the modeling, contained 91.73 % wt. of the target product. The simulation results showed that in the use of the proposed combined charge, the recovery of silicon reached 69.248 %, which is in good agreement with practical data. The results of the crystalline silicon chemical composition modeling are compared with the real silicon samples of chemical analysis data, which showed the results of convergence. The efficiency of the mathematical modeling methods in the studying of the carbothermal silicon obtaining process with complex interphase transformations and the formation of numerous intermediate compounds using a pelletized charge as an additive to the traditional one is shown.

The Nature of Quantum Truth: Logic, Set Theory, & Mathematics in the Context of Quantum Theory

NASA Astrophysics Data System (ADS)

Frey, Kimberly

The purpose of this dissertation is to construct a radically new type of mathematics whose underlying logic differs from the ordinary classical logic used in standard mathematics, and which we feel may be more natural for applications in quantum mechanics. Specifically, we begin by constructing a first order quantum logic, the development of which closely parallels that of ordinary (classical) first order logic --- the essential differences are in the nature of the logical axioms, which, in our construction, are motivated by quantum theory. After showing that the axiomatic first order logic we develop is sound and complete (with respect to a particular class of models), this logic is then used as a foundation on which to build (axiomatic) mathematical systems --- and we refer to the resulting new mathematics as "quantum mathematics." As noted above, the hope is that this form of mathematics is more natural than classical mathematics for the description of quantum systems, and will enable us to address some foundational aspects of quantum theory which are still troublesome --- e.g. the measurement problem --- as well as possibly even inform our thinking about quantum gravity. After constructing the underlying logic, we investigate properties of several mathematical systems --- e.g. axiom systems for abstract algebras, group theory, linear algebra, etc. --- in the presence of this quantum logic. In the process, we demonstrate that the resulting quantum mathematical systems have some strange, but very interesting features, which indicates a richness in the structure of mathematics that is classically inaccessible. Moreover, some of these features do indeed suggest possible applications to foundational questions in quantum theory. We continue our investigation of quantum mathematics by constructing an axiomatic quantum set theory, which we show satisfies certain desirable criteria. Ultimately, we hope that such a set theory will lead to a foundation for quantum mathematics in a sense which parallels the foundational role of classical set theory in classical mathematics. One immediate application of the quantum set theory we develop is to provide a foundation on which to construct quantum natural numbers, which are the quantum analog of the classical counting numbers. It turns out that in a special class of models, there exists a 1-1 correspondence between the quantum natural numbers and bounded observables in quantum theory whose eigenvalues are (ordinary) natural numbers. This 1-1 correspondence is remarkably satisfying, and not only gives us great confidence in our quantum set theory, but indicates the naturalness of such models for quantum theory itself. We go on to develop a Peano-like arithmetic for these new "numbers," as well as consider some of its consequences. Finally, we conclude by summarizing our results, and discussing directions for future work.

A physiome standards-based model publication paradigm.

PubMed

Nickerson, David P; Buist, Martin L

2009-05-28

In this era of widespread broadband Internet penetration and powerful Web browsers on most desktops, a shift in the publication paradigm for physiome-style models is envisaged. No longer will model authors simply submit an essentially textural description of the development and behaviour of their model. Rather, they will submit a complete working implementation of the model encoded and annotated according to the various standards adopted by the physiome project, accompanied by a traditional human-readable summary of the key scientific goals and outcomes of the work. While the final published, peer-reviewed article will look little different to the reader, in this new paradigm, both reviewers and readers will be able to interact with, use and extend the models in ways that are not currently possible. Here, we review recent developments that are laying the foundations for this new model publication paradigm. Initial developments have focused on the publication of mathematical models of cellular electrophysiology, using technology based on a CellML- or Systems Biology Markup Language (SBML)-encoded implementation of the mathematical models. Here, we review the current state of the art and what needs to be done before such a model publication becomes commonplace.

Survey mirrors and lenses and their required surface accuracy. Volume 2. Concentrator optical performance software (COPS) user's manual. Final report for September 15, 1978-December 1, 1979

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

Not Available

1980-01-01

The mathematical modeling of 11 different concentrating collectors is documented and instructions are given for use of the computer code. The 11 concentrators modeled are: faceted mirror concentration; fixed mirror, two-axis tracking receiver; parabolic trough collector; linear Fresnel; incremental reflector; inflated cylindrical concentrator; CPC-involute reflector with evacuated receiver; CPC-parabolic/involute reflector; V trough collectors, imaging collapsing concentrator; and parabolic dish collector. (MHR)

A new ODE tumor growth modeling based on tumor population dynamics

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

Oroji, Amin; Omar, Mohd bin; Yarahmadian, Shantia

2015-10-22

In this paper a new mathematical model for the population of tumor growth treated by radiation is proposed. The cells dynamics population in each state and the dynamics of whole tumor population are studied. Furthermore, a new definition of tumor lifespan is presented. Finally, the effects of two main parameters, treatment parameter (q), and repair mechanism parameter (r) on tumor lifespan are probed, and it is showed that the change in treatment parameter (q) highly affects the tumor lifespan.

Community College Technical Mathematics Project. Final Report.

ERIC Educational Resources Information Center

Self, Samuel L.

The purpose of the research project was to develop an applied or technical mathematics curriculum which would meet the needs of vocational-technical students at the community college level. The research project was divided into three distinct phases: Identifying the mathematical concepts requisite for job-entry competencies in each of the…

A National Study of Mathematics Requirements for Scientists and Engineers. Final Report.

ERIC Educational Resources Information Center

Miller, G. H.

The National Study of Mathematics Requirements for Scientists and Engineers is concerned with establishing the mathematics experiences desired for the many specializations in science and engineering, such as microbiology, organic chemistry, electrical engineering, and molecular physics. An instruction and course content sheet and a course…

Mathematical Anxiety among Business Statistics Students.

ERIC Educational Resources Information Center

High, Robert V.

A survey instrument was developed to identify sources of mathematics anxiety among undergraduate business students in a statistics class. A number of statistics classes were selected at two colleges in Long Island, New York. A final sample of n=102 respondents indicated that there was a relationship between the mathematics grade in prior…

Numerical Analysis of a Class of THM Coupled Model for Porous Materials

NASA Astrophysics Data System (ADS)

Liu, Tangwei; Zhou, Jingying; Lu, Hongzhi

2018-01-01

We consider the coupled models of the Thermo-hydro-mechanical (THM) problem for porous materials which arises in many engineering applications. Firstly, mathematical models of the THM coupled problem for porous materials were discussed. Secondly, for different cases, some numerical difference schemes of coupled model were constructed, respectively. Finally, aassuming that the original water vapour effect is neglectable and that the volume fraction of liquid phase and the solid phase are constants, the nonlinear equations can be reduced to linear equations. The discrete equations corresponding to the linear equations were solved by the Arnodli method.

Review of Final Year MSP Evaluations, Performance Period 2007. Analytic and Technical Support for Mathematics and Science Partnerships

ERIC Educational Resources Information Center

Bobronnikov, Ellen; Rhodes, Hilary; Bradley, Cay

2010-01-01

This final report culminates the evaluation and technical assistance provided for the U.S. Department of Education's Mathematics and Science Partnership (MSP) Program and its projects since 2005. As part of this support, Abt Associates looked across the portfolio of projects funded by the MSP program to draw lessons on best practices. This…

Mathematical modeling of climate change and malaria transmission dynamics: a historical review.

PubMed

Eikenberry, Steffen E; Gumel, Abba B

2018-04-24

Malaria, one of the greatest historical killers of mankind, continues to claim around half a million lives annually, with almost all deaths occurring in children under the age of five living in tropical Africa. The range of this disease is limited by climate to the warmer regions of the globe, and so anthropogenic global warming (and climate change more broadly) now threatens to alter the geographic area for potential malaria transmission, as both the Plasmodium malaria parasite and Anopheles mosquito vector have highly temperature-dependent lifecycles, while the aquatic immature Anopheles habitats are also strongly dependent upon rainfall and local hydrodynamics. A wide variety of process-based (or mechanistic) mathematical models have thus been proposed for the complex, highly nonlinear weather-driven Anopheles lifecycle and malaria transmission dynamics, but have reached somewhat disparate conclusions as to optimum temperatures for transmission, and the possible effect of increasing temperatures upon (potential) malaria distribution, with some projecting a large increase in the area at risk for malaria, but others predicting primarily a shift in the disease's geographic range. More generally, both global and local environmental changes drove the initial emergence of P. falciparum as a major human pathogen in tropical Africa some 10,000 years ago, and the disease has a long and deep history through the present. It is the goal of this paper to review major aspects of malaria biology, methods for formalizing these into mathematical forms, uncertainties and controversies in proper modeling methodology, and to provide a timeline of some major modeling efforts from the classical works of Sir Ronald Ross and George Macdonald through recent climate-focused modeling studies. Finally, we attempt to place such mathematical work within a broader historical context for the "million-murdering Death" of malaria.

The Worm Propagation Model with Dual Dynamic Quarantine Strategy

NASA Astrophysics Data System (ADS)

Yao, Yu; Xie, Xiao-Wu; Guo, Hao; Gao, Fu-Xiang; Yu, Ge

Internet worms are becoming more and more harmful with the rapid development of the Internet. Due to the extremely fast spread and great destructive power of network worms, strong dynamic quarantine strategies are necessary. Inspired by the real-world approach to the prevention and treatment of infectious diseases, this paper proposes a quarantine strategy based on dynamic worm propagation model: the SIQRV dual quarantine model. This strategy uses dynamic quarantine method to make the vulnerable host and infected host quarantined, and then release them after a certain period of time, regardless of whether quarantined host security is checked. Through mathematic modeling, it has been found that when the basic reproduction number R0 is less than a critical value, the system will stabilize in the disease-free equilibrium, that is, in theory, the infected hosts will be completely immune. Finally, by comparing the simulation results and numerical analysis, the basic agreement between the two curves supports the validity of the mathematical model. Our future work will be focusing on taking both the delay and double-quarantine strategy into account and further expanding the scale of our simulation work.

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.

Reduced linear noise approximation for biochemical reaction networks with time-scale separation: The stochastic tQSSA+

NASA Astrophysics Data System (ADS)

Herath, Narmada; Del Vecchio, Domitilla

2018-03-01

Biochemical reaction networks often involve reactions that take place on different time scales, giving rise to "slow" and "fast" system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In this paper, we consider stochastic dynamics of biochemical reaction networks modeled using the Linear Noise Approximation (LNA). Under time-scale separation conditions, we obtain a reduced-order LNA that approximates both the slow and fast variables in the system. We mathematically prove that the first and second moments of this reduced-order model converge to those of the full system as the time-scale separation becomes large. These mathematical results, in particular, provide a rigorous justification to the accuracy of LNA models derived using the stochastic total quasi-steady state approximation (tQSSA). Since, in contrast to the stochastic tQSSA, our reduced-order model also provides approximations for the fast variable stochastic properties, we term our method the "stochastic tQSSA+". Finally, we demonstrate the application of our approach on two biochemical network motifs found in gene-regulatory and signal transduction networks.

German undergraduate mathematics enrolment numbers: background and change

NASA Astrophysics Data System (ADS)

Ammann, Claudia; Frauendiener, Jörg; Holton, Derek

2010-06-01

Before we consider the German tertiary system, we review the education system and consider other relevant background details. We then concentrate on the tertiary system and observe that the mathematical enrolments are keeping up with the overall student enrolments. At the same time, the first year mathematics enrolments for women are greater than that for men, although more men are still studying mathematics at university. Finally, we note that the German economy seems to play a role in mathematics enrolments though not necessarily to its comparative detriment.

CSMP Mathematics for the Intermediate Grades Part II, Teacher's Guide [and] Worksheets. The World of Numbers. Experimental Version.

ERIC Educational Resources Information Center

CEMREL, Inc., St. Ann, MO.

This guide represents the final experimental version of a pilot project which was conducted in the United States between 1973 and 1976. The ideas and the manner of presentation are based on the works of Georges and Frederique Papy. They are recognized for having introduced colored arrow drawings ("papygrams") and models of our numeration…

Physico-chemical study of some areas of fundamental significance to biophysics. Final report, 1974--1977

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

McGlynn, S.P.

1977-08-18

The comprehensive report includes a complete list of publications resulting from the work and a review of studies made in the vacuum ultraviolet, photoelectron spectroscopy, excited states and electron structure of inorganic salts, a model for polar molecules, application of abstract mathematics to the genetic code, the orbital approximation in which orbital properties are related to state properties. (JSR)

A Center for Excellence in Mathematical Sciences Final Progress Report

DTIC Science & Technology

1997-02-18

together with a sampling rule of the form of (5): i(t) = G(x(t), t) + B(t) (4) G(., t) = continualized version of g(-, k), t E [ kA , (k + 1)A), k e N (5...Nobuki Takayama * 25 Pages 27 I I 93-97 Databases PF Actovotoes And Modeling Eugen Ardeleanu And Adriana Ardeleanu 6 Pages 93-98 Methodological Issues In

New mathematics for old physics: The case of lattice fluids

NASA Astrophysics Data System (ADS)

Barberousse, Anouk; Imbert, Cyrille

2013-08-01

We analyze the effects of the introduction of new mathematical tools on an old branch of physics by focusing on lattice fluids, which are cellular automata (CA)-based hydrodynamical models. We examine the nature of these discrete models, the type of novelty they bring about within scientific practice and the role they play in the field of fluid dynamics. We critically analyze Rohrlich's, Fox Keller's and Hughes' claims about CA-based models. We distinguish between different senses of the predicates "phenomenological" and "theoretical" for scientific models and argue that it is erroneous to conclude, as they do, that CA-based models are necessarily phenomenological in any sense of the term. We conversely claim that CA-based models of fluids, though at first sight blatantly misrepresenting fluids, are in fact conservative as far as the basic laws of statistical physics are concerned and not less theoretical than more traditional models in the field. Based on our case-study, we propose a general discussion of the prospect of CA for modeling in physics. We finally emphasize that lattice fluids are not just exotic oddities but do bring about new advantages in the investigation of fluids' behavior.

Research on efficiency evaluation model of integrated energy system based on hybrid multi-attribute decision-making.

PubMed

Li, Yan

2017-05-25

The efficiency evaluation model of integrated energy system, involving many influencing factors, and the attribute values are heterogeneous and non-deterministic, usually cannot give specific numerical or accurate probability distribution characteristics, making the final evaluation result deviation. According to the characteristics of the integrated energy system, a hybrid multi-attribute decision-making model is constructed. The evaluation model considers the decision maker's risk preference. In the evaluation of the efficiency of the integrated energy system, the evaluation value of some evaluation indexes is linguistic value, or the evaluation value of the evaluation experts is not consistent. These reasons lead to ambiguity in the decision information, usually in the form of uncertain linguistic values and numerical interval values. In this paper, the risk preference of decision maker is considered when constructing the evaluation model. Interval-valued multiple-attribute decision-making method and fuzzy linguistic multiple-attribute decision-making model are proposed. Finally, the mathematical model of efficiency evaluation of integrated energy system is constructed.

D2 Delta Robot Structural Design and Kinematics Analysis

NASA Astrophysics Data System (ADS)

Yang, Xudong; wang, Song; Dong, Yu; Yang, Hai

2017-12-01

In this paper, a new type of Delta robot with only two degrees of freedom is proposed on the basis of multi - degree - of - freedom delta robot. In order to meet our application requirements, we have carried out structural design and analysis of the robot. Through SolidWorks modeling, combined with 3D printing technology to determine the final robot structure. In order to achieve the precise control of the robot, the kinematics analysis of the robot was carried out. The SimMechanics toolbox of MATLAB is used to establish the mechanism model, and the kinematics mathematical model is used to simulate the robot motion control in Matlab environment. Finally, according to the design mechanism, the working space of the robot is drawn by the graphic method, which lays the foundation for the motion control of the subsequent robot.

Safety Verification of the Small Aircraft Transportation System Concept of Operations

NASA Technical Reports Server (NTRS)

Carreno, Victor; Munoz, Cesar

2005-01-01

A critical factor in the adoption of any new aeronautical technology or concept of operation is safety. Traditionally, safety is accomplished through a rigorous process that involves human factors, low and high fidelity simulations, and flight experiments. As this process is usually performed on final products or functional prototypes, concept modifications resulting from this process are very expensive to implement. This paper describe an approach to system safety that can take place at early stages of a concept design. It is based on a set of mathematical techniques and tools known as formal methods. In contrast to testing and simulation, formal methods provide the capability of exhaustive state exploration analysis. We present the safety analysis and verification performed for the Small Aircraft Transportation System (SATS) Concept of Operations (ConOps). The concept of operations is modeled using discrete and hybrid mathematical models. These models are then analyzed using formal methods. The objective of the analysis is to show, in a mathematical framework, that the concept of operation complies with a set of safety requirements. It is also shown that the ConOps has some desirable characteristic such as liveness and absence of dead-lock. The analysis and verification is performed in the Prototype Verification System (PVS), which is a computer based specification language and a theorem proving assistant.

Quantitative skills as a graduate learning outcome of university science degree programmes: student performance explored through theplanned-enacted-experiencedcurriculum model

NASA Astrophysics Data System (ADS)

Matthews, Kelly E.; Adams, Peter; Goos, Merrilyn

2016-07-01

Application of mathematical and statistical thinking and reasoning, typically referred to as quantitative skills, is essential for university bioscience students. First, this study developed an assessment task intended to gauge graduating students' quantitative skills. The Quantitative Skills Assessment of Science Students (QSASS) was the result, which examined 10 mathematical and statistical sub-topics. Second, the study established an evidential baseline of students' quantitative skills performance and confidence levels by piloting the QSASS with 187 final-year biosciences students at a research-intensive university. The study is framed within the planned-enacted-experienced curriculum model and contributes to science reform efforts focused on enhancing the quantitative skills of university graduates, particularly in the biosciences. The results found, on average, weak performance and low confidence on the QSASS, suggesting divergence between academics' intentions and students' experiences of learning quantitative skills. Implications for curriculum design and future studies are discussed.

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.

Research on the Multiple Factors Influencing Human Identification Based on Pyroelectric Infrared Sensors

PubMed Central

Lou, Ping; Hu, Jianmin

2018-01-01

Analysis of the multiple factors affecting human identification ability based on pyroelectric infrared technology is a complex problem. First, we examine various sensed pyroelectric waveforms of the human body thermal infrared signal and reveal a mechanism for affecting human identification. Then, we find that the mechanism is decided by the distance, human target, pyroelectric infrared (PIR) sensor, the body type, human moving velocity, signal modulation mask, and Fresnel lens. The mapping relationship between the sensed waveform and multiple influencing factors is established, and a group of mathematical models are deduced which fuse the macro factors and micro factors. Finally, the experimental results show the macro-factors indirectly affect the recognition ability of human based on the pyroelectric technology. At the same time, the correctness and effectiveness of the mathematical models is also verified, which make it easier to obtain more pyroelectric infrared information about the human body for discriminating human targets. PMID:29462908

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.

Nonlinear model predictive control for chemical looping process

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

Joshi, Abhinaya; Lei, Hao; Lou, Xinsheng

A control system for optimizing a chemical looping ("CL") plant includes a reduced order mathematical model ("ROM") that is designed by eliminating mathematical terms that have minimal effect on the outcome. A non-linear optimizer provides various inputs to the ROM and monitors the outputs to determine the optimum inputs that are then provided to the CL plant. An estimator estimates the values of various internal state variables of the CL plant. The system has one structure adapted to control a CL plant that only provides pressure measurements in the CL loops A and B, a second structure adapted to amore » CL plant that provides pressure measurements and solid levels in both loops A, and B, and a third structure adapted to control a CL plant that provides full information on internal state variables. A final structure provides a neural network NMPC controller to control operation of loops A and B.« less

Petri Nets - A Mathematical Formalism to Analyze Chemical Reaction Networks.

PubMed

Koch, Ina

2010-12-17

In this review we introduce and discuss Petri nets - a mathematical formalism to describe and analyze chemical reaction networks. Petri nets were developed to describe concurrency in general systems. We find most applications to technical and financial systems, but since about twenty years also in systems biology to model biochemical systems. This review aims to give a short informal introduction to the basic formalism illustrated by a chemical example, and to discuss possible applications to the analysis of chemical reaction networks, including cheminformatics. We give a short overview about qualitative as well as quantitative modeling Petri net techniques useful in systems biology, summarizing the state-of-the-art in that field and providing the main literature references. Finally, we discuss advantages and limitations of Petri nets and give an outlook to further development. Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Teacher Leaders for Mathematics Success (TL=MS). Final Evaluation Report

ERIC Educational Resources Information Center

Fancsali, Cheri

2004-01-01

Teacher Leaders for Mathematics Success (TL=MS) is a five-year project designed to build the capacity of Bronx teachers and schools in supporting continued improvement in mathematics education for all students in a standards-based environment. The project, implemented by the Institute for Literacy Studies at Lehman College and funded by the…

The Challenge to Situate Digital Learning Technologies in Preservice Teacher Mathematics Education

ERIC Educational Resources Information Center

McDonald, Susan

2012-01-01

This paper focuses on how preservice primary teachers can be supported to embrace digital learning technologies (DLTs) in their teaching of mathematics. The nature of the instruction and the assessment in the final mathematics unit of the bachelor of education program were changed. Despite being tagged as "tech-savvy," preservice…

Mathematics and Structural Learning. Final Report.

ERIC Educational Resources Information Center

Scandura, Joseph M.

This report contains four papers describing research based on the view of mathematical knowledge as a hierarchy of "rules." The first paper: "The Role of Rules in Behavior" was abstracted in ED 040 036 (October 1970). The second paper: "A Theory of Mathematical Knowledge" defends the thesis that rules are the basic building blocks of mathematical…

Primary Mathematics Teacher Education Encountering Difficult Terrain: A Personal Perspective

ERIC Educational Resources Information Center

Norton, Stephen

2016-01-01

This paper is a case study in preparing prospective primary teachers to teach mathematics at one Australian university. The paper describes the content knowledge of prospective teachers, pre and post a final mathematics curriculum subject. The teaching approach which attempts to account for both content and pedagogical content knowledge is…

1970-71 Basic Mathematics Improvement Component. Final Report.

ERIC Educational Resources Information Center

Rodosky, Robert

The Basic Mathematics Improvement Component, funded under Title I of the 1965 Elementary Secondary Education Act, served nearly 800 pupils in grades four through nine in 20 high priority inner-city schools. The philosophy behind the program was that high achievement in mathematics correlates highly with the high achievement in other areas, and a…

STUDY OF VARIABLES ASSOCIATED WITH FINAL GRADES IN MATHEMATICS COURSES.

ERIC Educational Resources Information Center

DAVIS, ELTON C.; RISSER, JOHN J.

THIS STUDY WAS CONDUCTED IN ORDER TO DETERMINE THE RELATIVE VALUE OF PREVIOUS GRADES IN MATHEMATICS COURSES, THE OVERALL HIGH SCHOOL GRADE POINT AVERAGE, AND THE PLACEMENT TEST IN MATHEMATICS DEVELOPED AT THE COLLEGE AS PREDICTORS OF ACHIEVEMENT IN INTRODUCTORY AND INTERMEDIATE ALGEBRA, IN COLLEGE ALGEBRA, IN TRIGONOMETRY, AND IN ANALYTIC GEOMETRY…

Inventing (in) Early Geometry, or How Creativity Inheres in the Doing of Mathematics

ERIC Educational Resources Information Center

Maheux, Jean-François; Roth, Wolf-Michael

2015-01-01

Inventing is fundamental to mathematical activity, should one be a professional mathematician or a primary school student. Research on mathematical creativity generally is organized along three axes according to its focus on the final product, the overall process, or the individual person. Through these conceptualizations, however, research rarely…

A Revision of Technical Mathematics Based on the NCTM Standards. Final Report.

ERIC Educational Resources Information Center

Near, Barbara

Between 1993 and 1996, Henry Ford Community College (Michigan) worked with business, industry, and technical instructors to revise their Technical Mathematics program in accordance with the National Council of Teachers of Mathematics (NCTM) Standards. The purpose of the project was to restructure the technical math curriculum and create a context…

Mathematics Instruction in Tokyo's and Hawaii's Junior High Schools. Final Report.

ERIC Educational Resources Information Center

Hawaii Univ., Honolulu. Coll. of Education.

Mathematics instruction in junior high schools in Tokyo and Hawaii was compared in order to gain knowledge of how mathematics teachers' effectiveness in the classroom may be improved. Because they were likely to influence teachers' behavior, these factors were considered: teachers' background and teaching load, allocation of time, views on…

Seasonally forced disease dynamics explored as switching between attractors

NASA Astrophysics Data System (ADS)

Keeling, Matt J.; Rohani, Pejman; Grenfell, Bryan T.

2001-01-01

Biological phenomena offer a rich diversity of problems that can be understood using mathematical techniques. Three key features common to many biological systems are temporal forcing, stochasticity and nonlinearity. Here, using simple disease models compared to data, we examine how these three factors interact to produce a range of complicated dynamics. The study of disease dynamics has been amongst the most theoretically developed areas of mathematical biology; simple models have been highly successful in explaining the dynamics of a wide variety of diseases. Models of childhood diseases incorporate seasonal variation in contact rates due to the increased mixing during school terms compared to school holidays. This ‘binary’ nature of the seasonal forcing results in dynamics that can be explained as switching between two nonlinear spiral sinks. Finally, we consider the stability of the attractors to understand the interaction between the deterministic dynamics and demographic and environmental stochasticity. Throughout attention is focused on the behaviour of measles, whooping cough and rubella.

QR-STEM: Energy and Environment as a Context for Improving QR and STEM Understandings of 6-12 Grade Teachers II. The Quantitative Reasoning

NASA Astrophysics Data System (ADS)

Mayes, R.; Lyford, M. E.; Myers, J. D.

2009-12-01

The Quantitative Reasoning in STEM (QR STEM) project is a state level Mathematics and Science Partnership Project (MSP) with a focus on the mathematics and statistics that underlies the understanding of complex global scientific issues. This session is a companion session to the QR STEM: The Science presentation. The focus of this session is the quantitative reasoning aspects of the project. As students move from understandings that range from local to global in perspective on issues of energy and environment, there is a significant increase in the need for mathematical and statistical conceptual understanding. These understandings must be accessible to the students within the scientific context, requiring the special understandings that are endemic within quantitative reasoning. The QR STEM project brings together interdisciplinary teams of higher education faculty and middle/high school teachers to explore complex problems in energy and environment. The disciplines include life sciences, physics, chemistry, earth science, statistics, and mathematics. These interdisciplinary teams develop open ended performance tasks to implement in the classroom, based on scientific concepts that underpin energy and environment. Quantitative reasoning is broken down into three components: Quantitative Literacy, Quantitative Interpretation, and Quantitative Modeling. Quantitative Literacy is composed of arithmetic concepts such as proportional reasoning, numeracy, and descriptive statistics. Quantitative Interpretation includes algebraic and geometric concepts that underlie the ability to interpret a model of natural phenomena which is provided for the student. This model may be a table, graph, or equation from which the student is to make predictions or identify trends, or from which they would use statistics to explore correlations or patterns in data. Quantitative modeling is the ability to develop the model from data, including the ability to test hypothesis using statistical procedures. We use the term model very broadly, so it includes visual models such as box models, as well as best fit equation models and hypothesis testing. One of the powerful outcomes of the project is the conversation which takes place between science teachers and mathematics teachers. First they realize that though they are teaching concepts that cross their disciplines, the barrier of scientific language within their subjects restricts students from applying the concepts across subjects. Second the mathematics teachers discover the context of science as a means of providing real world situations that engage students in the utility of mathematics as a tool for solving problems. Third the science teachers discover the barrier to understanding science that is presented by poor quantitative reasoning ability. Finally the students are engaged in exploring energy and environment in a manner which exposes the importance of seeing a problem from multiple interdisciplinary perspectives. The outcome is a democratic citizen capable of making informed decisions, and perhaps a future scientist.

Accommodating Thickness in Origami-Based Deployable Arrays

NASA Technical Reports Server (NTRS)

Zirbel, Shannon A.; Magleby, Spencer P.; Howell, Larry L.; Lang, Robert J.; Thomson, Mark W.; Sigel, Deborah A.; Walkemeyer, Phillip E.; Trease, Brian P.

2013-01-01

The purpose of this work is to create deployment systems with a large ratio of stowed-to-deployed diameter. Deployment from a compact form to a final flat state can be achieved through origami-inspired folding of panels. There are many models capable of this motion when folded in a material with negligible thickness; however, when the application requires the folding of thick, rigid panels, attention must be paid to the effect of material thickness not only on the final folded state, but also during the folding motion (i.e., the panels must not be required to flex to attain the final folded form). The objective is to develop new methods for deployment from a compact folded form to a large circular array (or other final form). This paper describes a mathematical model for modifying the pattern to accommodate material thickness in the context of the design, modeling, and testing of a deployable system inspired by an origami six-sided flasher model. The model is demonstrated in hardware as a 1/20th scale prototype of a deployable solar array for space applications. The resulting prototype has a ratio of stowed-to-deployed diameter of 9.2 (or 1.25 m deployed outer diameter to 0.136 m stowed outer diameter).

Mathematical analysis of compressive/tensile molecular and nuclear structures

NASA Astrophysics Data System (ADS)

Wang, Dayu

Mathematical analysis in chemistry is a fascinating and critical tool to explain experimental observations. In this dissertation, mathematical methods to present chemical bonding and other structures for many-particle systems are discussed at different levels (molecular, atomic, and nuclear). First, the tetrahedral geometry of single, double, or triple carbon-carbon bonds gives an unsatisfying demonstration of bond lengths, compared to experimental trends. To correct this, Platonic solids and Archimedean solids were evaluated as atoms in covalent carbon or nitrogen bond systems in order to find the best solids for geometric fitting. Pentagonal solids, e.g. the dodecahedron and icosidodecahedron, give the best fit with experimental bond lengths; an ideal pyramidal solid which models covalent bonds was also generated. Second, the macroscopic compression/tension architectural approach was applied to forces at the molecular level, considering atomic interactions as compressive (repulsive) and tensile (attractive) forces. Two particle interactions were considered, followed by a model of the dihydrogen molecule (H2; two protons and two electrons). Dihydrogen was evaluated as two different types of compression/tension structures: a coaxial spring model and a ring model. Using similar methods, covalent diatomic molecules (made up of C, N, O, or F) were evaluated. Finally, the compression/tension model was extended to the nuclear level, based on the observation that nuclei with certain numbers of protons/neutrons (magic numbers) have extra stability compared to other nucleon ratios. A hollow spherical model was developed that combines elements of the classic nuclear shell model and liquid drop model. Nuclear structure and the trend of the "island of stability" for the current and extended periodic table were studied.

Adolescent-perceived parent and teacher overestimation of mathematics ability: Developmental implications for students' mathematics task values.

PubMed

Gniewosz, Burkhard; Watt, Helen M G

2017-07-01

This study examines whether and how student-perceived parents' and teachers' overestimation of students' own perceived mathematical ability can explain trajectories for adolescents' mathematical task values (intrinsic and utility) controlling for measured achievement, following expectancy-value and self-determination theories. Longitudinal data come from a 3-cohort (mean ages 13.25, 12.36, and 14.41 years; Grades 7-10), 4-wave data set of 1,271 Australian secondary school students. Longitudinal structural equation models revealed positive effects of student-perceived overestimation of math ability by parents and teachers on students' intrinsic and utility math task values development. Perceived parental overestimations predicted intrinsic task value changes between all measurement occasions, whereas utility task value changes only were predicted between Grades 9 and 10. Parental influences were stronger for intrinsic than utility task values. Teacher influences were similar for both forms of task values and commenced after the curricular school transition in Grade 8. Results support the assumptions that the perceived encouragement conveyed by student-perceived mathematical ability beliefs of parents and teachers, promote positive mathematics task values development. Moreover, results point to different mechanisms underlying parents' and teachers' support. Finally, the longitudinal changes indicate transition-related increases in the effects of student-perceived overestimations and stronger effects for intrinsic than utility values. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Controlling acrylamide in French fry and potato chip models and a mathematical model of acrylamide formation: acrylamide: acidulants, phytate and calcium.

PubMed

Park, Yeonhwa; Yang, Heewon; Storkson, Jayne M; Albright, Karen J; Liu, Wei; Lindsay, Robert C; Pariza, Michael W

2005-01-01

We previously reported that in potato chip and French fry models, the formation of acrylamide can be reduced by controlling pH during processing steps, either by organic (acidulants) or inorganic acids. Use of phytate, a naturally occurring chelator, with or without Ca++ (or divalent ions), can reduce acrylamide formation in both models. However, since phytate itself is acidic, the question remains as to whether the effect of phytate is due to pH alone or to additional effects. In the French fry model, the effects on acrylamide formation of pH, phytate, and/or Ca++ in various combinations were tested in either blanching or soaking (after blanching) steps. All treatments significantly reduced acrylamide levels compared to control. Among variables tested, pH may be the single most important factor for reducing acrylamide levels, while there were independent effects of phytate and/or Ca++ in this French fry model. We also developed a mathematical formula to estimate the final concentration of acrylamide in a potato chip model, using variables that can affect acrylamide formation: glucose and asparagine concentrations, cut potato surface area and shape, cooking temperature and time, and other processing conditions.

Identifiability of PBPK Models with Applications to ...

EPA Pesticide Factsheets

Any statistical model should be identifiable in order for estimates and tests using it to be meaningful. We consider statistical analysis of physiologically-based pharmacokinetic (PBPK) models in which parameters cannot be estimated precisely from available data, and discuss different types of identifiability that occur in PBPK models and give reasons why they occur. We particularly focus on how the mathematical structure of a PBPK model and lack of appropriate data can lead to statistical models in which it is impossible to estimate at least some parameters precisely. Methods are reviewed which can determine whether a purely linear PBPK model is globally identifiable. We propose a theorem which determines when identifiability at a set of finite and specific values of the mathematical PBPK model (global discrete identifiability) implies identifiability of the statistical model. However, we are unable to establish conditions that imply global discrete identifiability, and conclude that the only safe approach to analysis of PBPK models involves Bayesian analysis with truncated priors. Finally, computational issues regarding posterior simulations of PBPK models are discussed. The methodology is very general and can be applied to numerous PBPK models which can be expressed as linear time-invariant systems. A real data set of a PBPK model for exposure to dimethyl arsinic acid (DMA(V)) is presented to illustrate the proposed methodology. We consider statistical analy

Mathematical Modeling of Extinction of Inhomogeneous Populations

PubMed Central

Karev, G.P.; Kareva, I.

2016-01-01

Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction. Unlike the more traditional exponential models, the life duration of sub-exponential models is finite. In the first model, the population is assumed to be composed clones that are independent from each other. In the second model, we assume that the size of the population as a whole decreases according to the sub-exponential equation. We then investigate the “unobserved heterogeneity”, i.e. the underlying inhomogeneous population model, and calculate the distribution of frequencies of clones for both models. We show that the dynamics of frequencies in the first model is governed by the principle of minimum of Tsallis information loss. In the second model, the notion of “internal population time” is proposed; with respect to the internal time, the dynamics of frequencies is governed by the principle of minimum of Shannon information loss. The results of this analysis show that the principle of minimum of information loss is the underlying law for the evolution of a broad class of models of population extinction. Finally, we propose a possible application of this modeling framework to mechanisms underlying time perception. PMID:27090117

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…

Mathematics Teachers' Views about Teaching as a Profession: Final Results of a Four-Year Longitudinal Study. A Report from the Urban Mathematics Collaborative Documentation Project. Program Report 91-4.

ERIC Educational Resources Information Center

Middleton, James A.; And Others

This paper reports the results of a 4-year longitudinal study of approximately 600 urban mathematics teachers who were surveyed to ascertain their attitudes regarding certain attributes of the profession of mathematics teaching, specifically: the use of the professional organization as a major referent, the belief in service to the public, the…

A Mathematical Theory of System Information Flow

DTIC Science & Technology

2016-06-27

AFRL-AFOSR-VA-TR-2016-0232 A Mathematical Theory of System Information Flow Michael Mislove ADMINISTRATORS OF THE TULANE EDUCATIONAL FUND THE 6823...MM-YYYY) 17-06-2016 2. REPORT TYPE Final 3. DATES COVERED (From - To) 27MAR2013 - 31MAR2016 4. TITLE AND SUBTITLE A Mathematical Theory of System...systems using techniques from information theory , domain theory and other areas of mathematics and computer science. Over time, the focus shifted

Tools for Accurate and Efficient Analysis of Complex Evolutionary Mechanisms in Microbial Genomes. Final Report

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

Nakhleh, Luay

I proposed to develop computationally efficient tools for accurate detection and reconstruction of microbes' complex evolutionary mechanisms, thus enabling rapid and accurate annotation, analysis and understanding of their genomes. To achieve this goal, I proposed to address three aspects. (1) Mathematical modeling. A major challenge facing the accurate detection of HGT is that of distinguishing between these two events on the one hand and other events that have similar "effects." I proposed to develop a novel mathematical approach for distinguishing among these events. Further, I proposed to develop a set of novel optimization criteria for the evolutionary analysis of microbialmore » genomes in the presence of these complex evolutionary events. (2) Algorithm design. In this aspect of the project, I proposed to develop an array of e cient and accurate algorithms for analyzing microbial genomes based on the formulated optimization criteria. Further, I proposed to test the viability of the criteria and the accuracy of the algorithms in an experimental setting using both synthetic as well as biological data. (3) Software development. I proposed the nal outcome to be a suite of software tools which implements the mathematical models as well as the algorithms developed.« less

On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics

NASA Astrophysics Data System (ADS)

Motsepa, Tanki; Masood Khalique, Chaudry

2018-05-01

In this paper, we study a (2+1) dimensional KdV-mKdV equation, which models many physical phenomena of mathematical physics. This equation has two integral terms in it. By an appropriate substitution, we convert this equation into two partial differential equations, which do not have integral terms and are equivalent to the original equation. We then work with the system of two equations and obtain its exact travelling wave solutions in form of Jacobi elliptic functions. Furthermore, we employ the multiplier method to construct conservation laws for the system. Finally, we revert the results obtained into the original variables of the (2+1) dimensional KdV-mKdV equation.

Temporal model of an optically pumped co-doped solid state laser

NASA Technical Reports Server (NTRS)

Wangler, T. G.; Swetits, J. J.; Buoncristiani, A. M.

1993-01-01

Currently, research is being conducted on the optical properties of materials associated with the development of solid state lasers in the two micron region. In support of this effort, a mathematical model describing the energy transfer in a holmium laser sensitized with thulium is developed. In this paper, we establish some qualitative properties of the solution of the model, such as non-negativity, boundedness, and integrability. A local stability analysis is then performed from which conditions for asymptotic stability are attained. Finally, we report on our numerical analysis of the system and how it compares with experimental results.

A Plan for Improving Mathematics Instruction in California Elementary Schools. Final Report of the Mathematics Education Task Force.

ERIC Educational Resources Information Center

Hoffman, Joseph R.; Tardif, Robert F.

In a project designed to improve elementary school instruction in mathematics, the California Department of Education collected achievement and profile data from 67 elementary schools. Schools were classified according to size, socioeconomic status, minority representation and mobility of students, city size, and type of community. Profile data…

Getting to the Point: Storying the United States Military Academy’s and Its Preparatory School’s English Program.

DTIC Science & Technology

1998-01-01

34modules" identified as key to the needed changes at the Prep School (Final 11). Three modules— composition/grammar, precalculus mathematics, and...composition/grammar and performance enhancement, and precalculus mathematics) set out to determine how to define mathematics "gateways," to examine

Mathematical Induction and Recursive Definition in Teaching Training

ERIC Educational Resources Information Center

Vármonostory, Endre

2009-01-01

The method of proof by mathematical induction follows from Peano axiom 5. We give three properties which are often used in the proofs by mathematical induction. We show that these are equivalent. Supposing the well-ordering property we prove the validity of this method without using Peano axiom 5. Finally, we introduce the simplest form of…

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…

Mathematical modeling and design of a novel 2-DOF micro attraction actuator for a micro optical switch

NASA Astrophysics Data System (ADS)

Kamiya, Daiki; Bagheri, Saeed; Horie, Mikio

2004-08-01

Many studies on optical switches have been performed in an attempt to develop optical information networks to speed information technology. In reality, however, mirror manipulators cannot be applied to multiple input and output systems due to both insufficient output displacements by the mirror parts inside the manipulator, and the difficulty of designing structures and mechanisms suitable for multi-dimensional manipulation. The principal reasons for insufficient displacement are the high rigidity of the elastic parts compared to the available driving forces and the pull-in effect. Therefore, in order to develop optical switches capable of multiple input and output switching, we suggest a novel 2-DOF(degree of freedom) electrostatic microactuator. The actuator is composed of one mirror with four beams laid about it in a corkscrew pattern, with four corkscrew electrodes on the substrate below and one mirror support pyramid situated under the mirror. Using electrostatic force, one or more of the beams are attracted from their outer ends toward the substrate. The mirror is then tilted by an angle proportional to the attracted length along the beam. The inclination and direction of the mirror are determined by the combined attracted length of the four beams. In this work we derive the mathematical model for the corkscrew beam microactuator for optical switches and show that this mathematical model accurately simulates the device by comparison with finite element analysis results. We use this mathematical model for design of the microactuator. Further we show that the designed optical switch microactuator is capable of rotating the mirror from +32 to -32 degrees about two axes with a maximum operating voltage of 163 volts. Finally, stress analysis of the actuator shows that the generated stress in the structure is at most 369 MPa.

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…

CSMP Mathematics for the Intermediate Grades Part IV, Teacher's Guide. The Languages of Strings and Arrows. Geometry and Measurement. Probability and Statistics.

ERIC Educational Resources Information Center

CEMREL, Inc., St. Ann, MO.

This guide represents the final experimental version of a pilot project which was conducted in the United States between 1973 and 1976. The ideas and the manner of presentation are based on the works of Georges and Frederique Papy. They are recognized for having introduced colored arrow drawings ("papygrams") and models of our numeration…

CSMP Mathematics for the Intermediate Grades Part II, Teacher's Guide. The Languages of Strings and Arrows. Geometry and Measurement. Probability and Statistics. Experimental Version.

ERIC Educational Resources Information Center

CEMREL, Inc., St. Ann, MO.

This guide represents the final experimental version of a pilot project which was conducted in the United States between 1973 and 1976. The ideas and the manner of presentation are based on the works of Georges and Frederique Papy. They are recognized for having introduced colored arrow drawings ("papygrams") and models of our numeration…

CSMP Mathematics for the Intermediate Grades Part III, Teacher's Guide. The Languages of Strings and Arrows. Geometry and Measurement. Probability and Statistics. Experimental Version.

ERIC Educational Resources Information Center

CEMREL, Inc., St. Ann, MO.

This guide represents the final experimental version of a pilot project which was conducted in the United States between 1973 and 1976. The ideas and the manner of presentation are based on the works of Georges and Frederique Papy. They are recognized for having introduced colored arrow drawings ("papygrams") and models of our numeration…

Arc program documentation

NASA Technical Reports Server (NTRS)

Mcmillan, J. D.

1976-01-01

A description of the input and output files and the data control cards for the altimeter residual computation (ARC) computer program is given. The program acts as the final altimeter preprocessor before the data is reformatted for external users. It calculates all parameters necessary for the computation of the altimeter observation residuals and the sea surface height. Mathematical models used for calculating tropospheric refraction, geoid height, tide height, ephemeris, and orbit geometry are described.

One-dimensional cold cap model for melters with bubblers

DOE PAGES

Pokorny, Richard; Hilliard, Zachary J.; Dixon, Derek R.; ...

2015-07-28

The rate of glass production during vitrification in an all-electrical melter greatly impacts the cost and schedule of nuclear waste treatment and immobilization. The feed is charged to the melter on the top of the molten glass, where it forms a layer of reacting and melting material, called the cold cap. During the final stages of the batch-to-glass conversion process, gases evolved from reactions produce primary foam, the growth and collapse of which controls the glass production rate. The mathematical model of the cold cap was revised to include functional representation of primary foam behavior and to account for themore » dry cold cap surface. The melting rate is computed as a response to the dependence of the primary foam collapse temperature on the heating rate and melter operating conditions, including the effect of bubbling on the cold cap bottom and top surface temperatures. The simulation results are in good agreement with experimental data from laboratory-scale and pilot-scale melter studies. Lastly, the cold cap model will become part of the full three-dimensional mathematical model of the waste glass melter.« less

Flow Induced by Ex-Vivo Nasal Cilia: Developing an Index of Dyskinesis

NASA Astrophysics Data System (ADS)

Grotberg, James; Bottier, Mathieu; Pena-Fernandez, Marta; Blanchon, Sylvain; Pelle, Gabriel; Bequignon, Emilie; Isabey, Daniel; Coste, Andre; Escudier, Estelle; Papon, Jean-Francois; Filoche, Marcel; Louis, Bruno

2017-11-01

Mucociliary clearance is one of the major lines of defense of the respiratory system. The mucus layer coating the pulmonary airways is moved along and out of the lung by the activity of motile cilia, thus expelling the particles trapped in it. Here we compare ex vivomeasurements of a Newtonian flow induced by cilia beating (using micro-beads as tracers) and a mathematical model of this fluid flow. Samples of nasal epithelial cells placed in water are recorded by high-speed video-microscopy and ciliary beat pattern is inferred. Automatic tracking of micro-beads, used as markers of the flow generated by cilia motion, enables us also to assess the steady velocity profile as a function of the distance above the cilia. This profile is shown to be essentially parabolic. This compares well to a 2D mathematical model for ciliary fluid propulsion using an envelope model. From the model and the experimental measurements, the shear stress exerted by the cilia is deduced. Finally, this shear stress is proposed as a new index for characterizing the efficiency of ciliary beating and diagnosing dyskinesis.

A 3D mathematical model for the horizontal anode baking furnace

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

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

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

Biosorption of alpacide blue from aqueous solution by lignocellulosic biomass: Luffa cylindrica fibers.

PubMed

Kesraoui, Aida; Moussa, Asma; Ali, Ghada Ben; Seffen, Mongi

2016-08-01

The aim of the present work is to develop an effective and inexpensive pollutant-removal technology using lignocellulosic fibers: Luffa cylindrica, for the biosorption of an anionic dye: alpacide blue. The influence of some experimental parameters such as pH, temperature, initial concentration of the polluted solution, and mass of the sorbent L. cylindrica on the biosorption of alpacide blue by L. cylindrica fibers has been investigated. Optimal parameters for maximum quantity of biosorption dye were achieved after 2 h of treatment in a batch system using an initial dye concentration of 20 mg/L, a mass of 1 g of L. cylindrica fibers, and pH 2. In these conditions, the quantity of dye retained is 2 mg/g and the retention rate is 78 %. Finally, a mathematical modeling of kinetics and isotherms has been used for mathematical modeling; the model of pseudo-second order is more appropriate to describe this phenomenon of biosorption. Concerning biosorption isotherms, the Freundlich model is the most appropriate for a biosorption of alpacide blue dye by L. cylindrica fibers.

Modeling for intra-body communication with bone effect.

PubMed

Pun, S H; Gao, Y M; Mak, P U; Du, M; Vai, M I

2009-01-01

Intra-body communication (IBC) is a new, different "wireless" communication technique based on the human tissue. This short range "wireless" communication technology provides an alternative solution to wearable sensors, home health system, telemedicine and implanted devices. The development of the IBC enables the possibilities of providing less complexity and convenient communication methodologies for these devices. By regarding human tissue as communication channel, IBC making use of the conductivities properties of human tissue to send electrical signal from transmitter to receiver. In this paper, the authors proposed a new mathematical model for galvanic coupling type IBC based on a human limb. Starting from the electromagnetic theory, the authors treat human tissue as volume conductor, which is in analogous with the bioelectric phenomena analysis. In order to explain the mechanism of galvanic coupling type technique of IBC, applying the quasi-static approximation, the governing equation can be reduced to Laplace Equation. Finally, the analytical model is evaluated with on-body measurement for testing its performance. The comparison result shows that the developed mathematical model can provide good approximation for galvanic coupling type IBC on human limb under low operating frequencies.

On Mathematical Modeling Of Quantum Systems

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

Achuthan, P.; Dept. of Mathematics, Indian Institute of Technology, Madras, 600 036; Narayanankutty, Karuppath

2009-07-02

The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM,more » though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.« less

Modeling Flow in Porous Media with Double Porosity/Permeability.

NASA Astrophysics Data System (ADS)

Seyed Joodat, S. H.; Nakshatrala, K. B.; Ballarini, R.

2016-12-01

Although several continuum models are available to study the flow of fluids in porous media with two pore-networks [1], they lack a firm theoretical basis. In this poster presentation, we will present a mathematical model with firm thermodynamic basis and a robust computational framework for studying flow in porous media that exhibit double porosity/permeability. The mathematical model will be derived by appealing to the maximization of rate of dissipation hypothesis, which ensures that the model is in accord with the second law of thermodynamics. We will also present important properties that the solutions under the model satisfy, along with an analytical solution procedure based on the Green's function method. On the computational front, a stabilized mixed finite element formulation will be derived based on the variational multi-scale formalism. The equal-order interpolation, which is computationally the most convenient, is stable under this formulation. The performance of this formulation will be demonstrated using patch tests, numerical convergence study, and representative problems. It will be shown that the pressure and velocity profiles under the double porosity/permeability model are qualitatively and quantitatively different from the corresponding ones under the classical Darcy equations. Finally, it will be illustrated that the surface pore-structure is not sufficient in characterizing the flow through a complex porous medium, which pitches a case for using advanced characterization tools like micro-CT. References [1] G. I. Barenblatt, I. P. Zheltov, and I. N. Kochina, "Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata]," Journal of Applied Mathematics and Mechanics, vol. 24, pp. 1286-1303, 1960.

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 modeling and computational prediction of cancer drug resistance.

PubMed

Sun, Xiaoqiang; Hu, Bin

2017-06-23

Diverse forms of resistance to anticancer drugs can lead to the failure of chemotherapy. Drug resistance is one of the most intractable issues for successfully treating cancer in current clinical practice. Effective clinical approaches that could counter drug resistance by restoring the sensitivity of tumors to the targeted agents are urgently needed. As numerous experimental results on resistance mechanisms have been obtained and a mass of high-throughput data has been accumulated, mathematical modeling and computational predictions using systematic and quantitative approaches have become increasingly important, as they can potentially provide deeper insights into resistance mechanisms, generate novel hypotheses or suggest promising treatment strategies for future testing. In this review, we first briefly summarize the current progress of experimentally revealed resistance mechanisms of targeted therapy, including genetic mechanisms, epigenetic mechanisms, posttranslational mechanisms, cellular mechanisms, microenvironmental mechanisms and pharmacokinetic mechanisms. Subsequently, we list several currently available databases and Web-based tools related to drug sensitivity and resistance. Then, we focus primarily on introducing some state-of-the-art computational methods used in drug resistance studies, including mechanism-based mathematical modeling approaches (e.g. molecular dynamics simulation, kinetic model of molecular networks, ordinary differential equation model of cellular dynamics, stochastic model, partial differential equation model, agent-based model, pharmacokinetic-pharmacodynamic model, etc.) and data-driven prediction methods (e.g. omics data-based conventional screening approach for node biomarkers, static network approach for edge biomarkers and module biomarkers, dynamic network approach for dynamic network biomarkers and dynamic module network biomarkers, etc.). Finally, we discuss several further questions and future directions for the use of computational methods for studying drug resistance, including inferring drug-induced signaling networks, multiscale modeling, drug combinations and precision medicine. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

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.

A comparison of rural high school students in Germany with rural Tennessee high school students' mathematics and science achievement

NASA Astrophysics Data System (ADS)

Harding, R. Fredrick

This descriptive study compared the science and mathematics aptitudes and achievement test scores for the final school year students in rural White County and Van Buren County, Tennessee with rural county students in Germany. In accordance with the previous research literature (Stevenson, 2002), German students outperformed U.S. students on The International Trends in Math and Science test (TIMSS). As reform in the U.S. education system has been underway, this study intended to compare German county student final school year performance with White County and Van Buren County (Grade 12) performance in science and mathematics. The entire populations of 176 White and Van Buren Counties senior high final school year students were compared with 120 school final year students from two rural German county high schools. The student responses to identical test and questionnaire items were compared using the t-test statistical analysis. In conclusion after t-test analyses, there was no significant difference (p>.05 level) in student attitudes on the 27 problem achievement and the 35 TIMSS questionnaire items between the sampled population of 120 German students compared with the population of 176 White and Van Buren students. Also, there was no statistically significant difference (p>.05 level) between the German, White, and Van Buren County rural science and math achievement in the TIMSS problem section of the final year test. Based on the research, recommendations to improve U.S. student scores to number one in the world include making changes in teaching methodology in mathematics and science; incorporating pamphlet lessons rather than heavily reliance on textbooks; focusing on problem solving; establishing an online clearinghouse for effective lessons; creating national standards in mathematics and science; matching students' course choices to job aspirations; tracking misbehaving students rather than mainstreaming them into the regular classroom; and designing individual educational plans for every student. Further study and future investigations are recommended from this study to compare White County and Van Buren County Students with other rural county schools in Tennessee, as well as other states. In addition, the Tennessee students' state mandated science and mathematics could be correlated to the TIMMS to identify trends and relationships. Future comparisons of White County and Van Buren County with higher scoring rural Asian students could be done in search of more effective methods of teaching science and mathematics.

Mathematical modeling of zika virus disease with nonlinear incidence and optimal control

NASA Astrophysics Data System (ADS)

Goswami, Naba Kumar; Srivastav, Akhil Kumar; Ghosh, Mini; Shanmukha, B.

2018-04-01

The Zika virus was first discovered in a rhesus monkey in the Zika Forest of Uganda in 1947, and it was isolated from humans in Nigeria in 1952. Zika virus disease is primarily a mosquito-borne disease, which is transmitted to human primarily through the bite of an infected Aedes species mosquito. However, there is documented evidence of sexual transmission of this disease too. In this paper, a nonlinear mathematical model for Zika virus by considering nonlinear incidence is formulated and analyzed. The equilibria and the basic reproduction number (R0) of the model are found. The stability of the different equilibria of the model is discussed in detail. When the basic reproduction number R0 < 1, the disease-free equilibrium is locally and globally stable i.e. in this case disease dies out. For R0 > 1, we have endemic equilibrium which is locally stable under some restriction on parameters. Further this model is extended to optimal control model and is analyzed by using Pontryagin’s Maximum Principle. It has been observed that optimal control plays a significant role in reducing the number of zika infectives. Finally, numerical simulation is performed to illustrate the analytical findings.

Assessment of Galileo modal test results for mathematical model verification

NASA Technical Reports Server (NTRS)

Trubert, M.

1984-01-01

The modal test program for the Galileo Spacecraft was completed at the Jet Propulsion Laboratory in the summer of 1983. The multiple sine dwell method was used for the baseline test. The Galileo Spacecraft is a rather complex 2433 kg structure made of a central core on which seven major appendages representing 30 percent of the total mass are attached, resulting in a high modal density structure. The test revealed a strong nonlinearity in several major modes. This nonlinearity discovered in the course of the test necessitated running additional tests at the unusually high response levels of up to about 21 g. The high levels of response were required to obtain a model verification valid at the level of loads for which the spacecraft was designed. Because of the high modal density and the nonlinearity, correlation between the dynamic mathematical model and the test results becomes a difficult task. Significant changes in the pre-test analytical model are necessary to establish confidence in the upgraded analytical model used for the final load verification. This verification, using a test verified model, is required by NASA to fly the Galileo Spacecraft on the Shuttle/Centaur launch vehicle in 1986.

Finite element and analytical models for twisted and coiled actuator

NASA Astrophysics Data System (ADS)

Tang, Xintian; Liu, Yingxiang; Li, Kai; Chen, Weishan; Zhao, Jianguo

2018-01-01

Twisted and coiled actuator (TCA) is a class of recently discovered artificial muscle, which is usually made by twisting and coiling polymer fibers into spring-like structures. It has been widely studied since discovery due to its impressive output characteristics and bright prospects. However, its mathematical models describing the actuation in response to the temperature are still not fully developed. It is known that the large tensile stroke is resulted from the untwisting of the twisted fiber when heated. Thus, the recovered torque during untwisting is a key parameter in the mathematical model. This paper presents a simplified model for the recovered torque of TCA. Finite element method is used for evaluating the thermal stress of the twisted fiber. Based on the results of the finite element analyses, the constitutive equations of twisted fibers are simplified to develop an analytic model of the recovered torque. Finally, the model of the recovered torque is used to predict the deformation of TCA under varying temperatures and validated against experimental results. This work will enhance our understanding of the deformation mechanism of TCAs, which will pave the way for the closed-loop position control.

Analysis of the Articulated Total Body (ATB) and Mathematical Dynamics Model (MADYMO) Software Suites for Modeling Anthropomorphic Test Devices (ATDs) in Blast Environments

DTIC Science & Technology

2013-05-01

REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188 Public reporting burden for this collection of information is estimated to average 1 ...valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1 . REPORT DATE (DD-MM-YYYY) May 2013 2. REPORT TYPE Final 3. DATES...area code) (410) 278-7386 Standard Form 298 (Rev. 8/98) Prescribed by ANSI Std. Z39.18 iii Contents List of Figures v List of Tables v 1

Dynamic design and control of a high-speed pneumatic jet actuator

NASA Astrophysics Data System (ADS)

Misyurin, S. Yu; Ivlev, V. I.; Kreinin, G. V.

2017-12-01

Mathematical model of an actuator, consisting of a pneumatic (gas) high-speed jet engine, transfer mechanism, and a control device used for switching the ball valve is worked out. The specific attention was paid to the transition (normalization) of the dynamic model into the dimensionless form. Its dynamic simulation criteria are determined, and dynamics study of an actuator was carried out. The simple control algorithm of relay action with a velocity feedback enabling the valve plug to be turned with a smooth nonstop and continuous approach to the final position is demonstrated

Research on air and missile defense task allocation based on extended contract net protocol

NASA Astrophysics Data System (ADS)

Zhang, Yunzhi; Wang, Gang

2017-10-01

Based on the background of air and missile defense distributed element corporative engagement, the interception task allocation problem of multiple weapon units with multiple targets under network condition is analyzed. Firstly, a mathematical model of task allocation is established by combat task decomposition. Secondly, the initialization assignment based on auction contract and the adjustment allocation scheme based on swap contract were introduced to the task allocation. Finally, through the simulation calculation of typical situation, the model can be used to solve the task allocation problem in complex combat environment.

Numerical simulation of freckle formation in directional solidification of binary alloys

NASA Technical Reports Server (NTRS)

Felicelli, Sergio D.; Heinrich, Juan C.; Poirier, David R.

1992-01-01

A mathematical model of solidification is presented which simulates the formation of segregation models known as 'freckles' during directional solidification of binary alloys. The growth of the two-phase or dendritic zone is calculated by solving the coupled equations of momentum, energy, and solute transport, as well as maintaining the thermodynamic constraints dictated by the phase diagram of the alloy. Calculations for lead-tin alloys show that the thermosolutal convection in the dendritic zone during solidification can produce heavily localized inhomogeneities in the composition of the final alloy.

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…

Middle School Mathematics Professional Development Impact Study: Findings after the Second Year of Implementation. NCEE 2011-4024

ERIC Educational Resources Information Center

Garet, Michael S.; Wayne, Andrew J.; Stancavage, Fran; Taylor, James; Eaton, Marian; Walters, Kirk; Song, Mengli; Brown, Seth; Hurlburt, Steven; Zhu, Pei; Sepanik, Susan; Doolittle, Fred

2011-01-01

This is the second and final report of the Middle School Mathematics Professional Development Impact Study, which examines the impact of providing a professional development (PD) program in rational number topics to seventh-grade mathematics teachers. An interim report (Garet et al. 2010) described the findings after one year of PD. The current…

New Outcomes: Learning Improvement in Mathematics Integrating Technology - NO LIMIT! An Enhancing Education through Technology Project. Final Report: Years Five and Six (2005-2007)

ERIC Educational Resources Information Center

Popejoy, Kate

2009-01-01

NO LIMIT! (New Outcomes: Learning Improvement in Mathematics Integrating Technology) in Washington state was a six-year initiative originally designed to enhance mathematics teaching and learning in the middle grades through integration of technology, alignment of pedagogical practice with NCTM standards, and strong mentorship of teachers. The…

Mathematical Preparedness for Tertiary Mathematics--A Need for Focused Intervention in the First Year?

ERIC Educational Resources Information Center

Du Preez, Jeanetta; Steyn, Tobia; Owen, Rina

2008-01-01

Ongoing action research at the University of Pretoria investigates first-year students' preparedness for a study in calculus. In 2005 first-year engineering students completed a mathematics diagnostic survey at the beginning and end of the year. In this article the results of the 2005 survey are compared with the students' final school marks in…

Space--The First and Final Frontier. Conference Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (15th, Richmond, New South Wales, Australia, July 4-8, 1992).

ERIC Educational Resources Information Center

Southwell, Beth, Ed.; And Others

A conference proceedings on mathematics education research contained the following keynote addresses: "Doing and Constructing Mathematics in Screen-Space" (Mason); "Students' Understanding of Geometry: Theoretical Perspectives" (Pegg); "The Australian Research Council and its Role in Supporting Education Research"…

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…

Simulation of dental collisions and occlusal dynamics in the virtual environment.

PubMed

Stavness, I K; Hannam, A G; Tobias, D L; Zhang, X

2016-04-01

Semi-adjustable articulators have often been used to simulate occlusal dynamics, but advances in intra-oral scanning and computer software now enable dynamics to be modelled mathematically. Computer simulation of occlusal dynamics requires accurate virtual casts, records to register them and methods to handle mesh collisions during movement. Here, physical casts in a semi-adjustable articulator were scanned with a conventional clinical intra-oral scanner. A coordinate measuring machine was used to index their positions in intercuspation, protrusion, right and left laterotrusion, and to model features of the articulator. Penetrations between the indexed meshes were identified and resolved using restitution forces, and the final registrations were verified by distance measurements between dental landmarks at multiple sites. These sites were confirmed as closely approximating via measurements made from homologous transilluminated vinylpolysiloxane interocclusal impressions in the mounted casts. Movements between the indexed positions were simulated with two models in a custom biomechanical software platform. In model DENTAL, 6 degree-of-freedom movements were made to minimise deviation from a straight line path and also shaped by dynamic mesh collisions detected and resolved mathematically. In model ARTIC, the paths were further constrained by surfaces matching the control settings of the articulator. Despite these differences, the lower mid-incisor point paths were very similar in both models. The study suggests that mathematical simulation utilising interocclusal 'bite' registrations can closely replicate the primary movements of casts mounted in a semi-adjustable articulator. Additional indexing positions and appropriate software could, in some situations, replace the need for mechanical semi-adjustable articulation and/or its virtual representation. © 2015 John Wiley & Sons Ltd.

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…

The limitations of mathematical modeling in high school physics education

NASA Astrophysics Data System (ADS)

Forjan, Matej

The theme of the doctoral dissertation falls within the scope of didactics of physics. Theoretical analysis of the key constraints that occur in the transmission of mathematical modeling of dynamical systems into field of physics education in secondary schools is presented. In an effort to explore the extent to which current physics education promotes understanding of models and modeling, we analyze the curriculum and the three most commonly used textbooks for high school physics. We focus primarily on the representation of the various stages of modeling in the solved tasks in textbooks and on the presentation of certain simplifications and idealizations, which are in high school physics frequently used. We show that one of the textbooks in most cases fairly and reasonably presents the simplifications, while the other two half of the analyzed simplifications do not explain. It also turns out that the vast majority of solved tasks in all the textbooks do not explicitly represent model assumptions based on what we can conclude that in high school physics the students do not develop sufficiently a sense of simplification and idealizations, which is a key part of the conceptual phase of modeling. For the introduction of modeling of dynamical systems the knowledge of students is also important, therefore we performed an empirical study on the extent to which high school students are able to understand the time evolution of some dynamical systems in the field of physics. The research results show the students have a very weak understanding of the dynamics of systems in which the feedbacks are present. This is independent of the year or final grade in physics and mathematics. When modeling dynamical systems in high school physics we also encounter the limitations which result from the lack of mathematical knowledge of students, because they don't know how analytically solve the differential equations. We show that when dealing with one-dimensional dynamical systems geometrical approach to solving differential equations is appropriate, while in dynamical systems of higher dimensions mathematical constraints are avoided by using a graphical oriented programs for modeling. Because in dealing with dynamical systems with four or more dimensions we may encounter problems in numerical solving, we also show how to overcome them. In the case of electrostatic pendulum we show the process of modeling the real dynamical system and we put a particular emphasize on the different phases of modeling and on the way of overcoming constraints on which we encounter in the development of the model.

Dispersive shock waves and modulation theory

NASA Astrophysics Data System (ADS)

El, G. A.; Hoefer, M. A.

2016-10-01

There is growing physical and mathematical interest in the hydrodynamics of dissipationless/dispersive media. Since G.B. Whitham's seminal publication fifty years ago that ushered in the mathematical study of dispersive hydrodynamics, there has been a significant body of work in this area. However, there has been no comprehensive survey of the field of dispersive hydrodynamics. Utilizing Whitham's averaging theory as the primary mathematical tool, we review the rich mathematical developments over the past fifty years with an emphasis on physical applications. The fundamental, large scale, coherent excitation in dispersive hydrodynamic systems is an expanding, oscillatory dispersive shock wave or DSW. Both the macroscopic and microscopic properties of DSWs are analyzed in detail within the context of the universal, integrable, and foundational models for uni-directional (Korteweg-de Vries equation) and bi-directional (Nonlinear Schrödinger equation) dispersive hydrodynamics. A DSW fitting procedure that does not rely upon integrable structure yet reveals important macroscopic DSW properties is described. DSW theory is then applied to a number of physical applications: superfluids, nonlinear optics, geophysics, and fluid dynamics. Finally, we survey some of the more recent developments including non-classical DSWs, DSW interactions, DSWs in perturbed and inhomogeneous environments, and two-dimensional, oblique DSWs.

An exploration of gender differences in tertiary mathematics

NASA Astrophysics Data System (ADS)

Watson, Jane M.

1989-02-01

Data from 400 students in a tertiary mathematics course were analysed to explore gender differences on a number of variables associated with learning mathematics. It was concluded that while differences did occur on variables associated with confidence, self-concept, test anxiety and quantitative ability indicating a detrimental effect for women, compensating behaviour by women, including increased assignment work and tutorial attendance, resulted in comparable final course performance for women and men. These findings are discussed in light of participation rates of women in mathematics.

Mathematics Anxiety: What Have We Learned in 60 Years?

PubMed

Dowker, Ann; Sarkar, Amar; Looi, Chung Yen

2016-01-01

The construct of mathematics anxiety has been an important topic of study at least since the concept of "number anxiety" was introduced by Dreger and Aiken (1957), and has received increasing attention in recent years. This paper focuses on what research has revealed about mathematics anxiety in the last 60 years, and what still remains to be learned. We discuss what mathematics anxiety is; how distinct it is from other forms of anxiety; and how it relates to attitudes to mathematics. We discuss the relationships between mathematics anxiety and mathematics performance. We describe ways in which mathematics anxiety is measured, both by questionnaires, and by physiological measures. We discuss some possible factors in mathematics anxiety, including genetics, gender, age, and culture. Finally, we describe some research on treatment. We conclude with a brief discussion of what still needs to be learned.

Modeling and Control of the Redundant Parallel Adjustment Mechanism on a Deployable Antenna Panel

PubMed Central

Tian, Lili; Bao, Hong; Wang, Meng; Duan, Xuechao

2016-01-01

With the aim of developing multiple input and multiple output (MIMO) coupling systems with a redundant parallel adjustment mechanism on the deployable antenna panel, a structural control integrated design methodology is proposed in this paper. Firstly, the modal information from the finite element model of the structure of the antenna panel is extracted, and then the mathematical model is established with the Hamilton principle; Secondly, the discrete Linear Quadratic Regulator (LQR) controller is added to the model in order to control the actuators and adjust the shape of the panel. Finally, the engineering practicality of the modeling and control method based on finite element analysis simulation is verified. PMID:27706076

Ambiguities in model-independent partial-wave analysis

NASA Astrophysics Data System (ADS)

Krinner, F.; Greenwald, D.; Ryabchikov, D.; Grube, B.; Paul, S.

2018-06-01

Partial-wave analysis is an important tool for analyzing large data sets in hadronic decays of light and heavy mesons. It commonly relies on the isobar model, which assumes multihadron final states originate from successive two-body decays of well-known undisturbed intermediate states. Recently, analyses of heavy-meson decays and diffractively produced states have attempted to overcome the strong model dependences of the isobar model. These analyses have overlooked that model-independent, or freed-isobar, partial-wave analysis can introduce mathematical ambiguities in results. We show how these ambiguities arise and present general techniques for identifying their presence and for correcting for them. We demonstrate these techniques with specific examples in both heavy-meson decay and pion-proton scattering.

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

NASA Astrophysics Data System (ADS)

Khusna, H.; Heryaningsih, N. Y.

2018-01-01

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

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…

Chances of success in and engagement with mathematics for students who enter university with a weak mathematics background

NASA Astrophysics Data System (ADS)

Varsavsky, Cristina

2010-12-01

An increasing number of Australian students elect not to undertake studies in mathematical methods in the final years of their secondary schooling. Some higher education providers now offer pathways for these students to pursue mathematics studies up to a major specialization within the bachelor of science programme. This article analyses the performance in and engagement with mathematics of the students who elect to take up this option. Findings indicate that these are not very different when compared to students who enter university with an intermediate mathematics preparation. The biggest contrast in performance and engagement is with those students who have studied mathematics in senior secondary school to an advanced level.

A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion.

PubMed

Anderson, Alexander R A

2005-06-01

In this paper we present a hybrid mathematical model of the invasion of healthy tissue by a solid tumour. In particular we consider early vascular growth, just after angiogenesis has occurred. We examine how the geometry of the growing tumour is affected by tumour cell heterogeneity caused by genetic mutations. As the tumour grows, mutations occur leading to a heterogeneous tumour cell population with some cells having a greater ability to migrate, proliferate or degrade the surrounding tissue. All of these cell properties are closely controlled by cell-cell and cell-matrix interactions and as such the physical geometry of the whole tumour will be dependent on these individual cell interactions. The hybrid model we develop focuses on four key variables implicated in the invasion process: tumour cells, host tissue (extracellular matrix), matrix-degradative enzymes and oxygen. The model is considered to be hybrid since the latter three variables are continuous (i.e. concentrations) and the tumour cells are discrete (i.e. individuals). With this hybrid model we examine how individual-based cell interactions (with one another and the matrix) can affect the tumour shape and discuss which of these interactions is perhaps most crucial in influencing the tumour's final structure.

The dispersion releaser technology is an effective method for testing drug release from nanosized drug carriers.

PubMed

Janas, Christine; Mast, Marc-Phillip; Kirsamer, Li; Angioni, Carlo; Gao, Fiona; Mäntele, Werner; Dressman, Jennifer; Wacker, Matthias G

2017-06-01

The dispersion releaser (DR) is a dialysis-based setup for the analysis of the drug release from nanosized drug carriers. It is mounted into dissolution apparatus2 of the United States Pharmacopoeia. The present study evaluated the DR technique investigating the drug release of the model compound flurbiprofen from drug solution and from nanoformulations composed of the drug and the polymer materials poly (lactic acid), poly (lactic-co-glycolic acid) or Eudragit®RSPO. The drug loaded nanocarriers ranged in size between 185.9 and 273.6nm and were characterized by a monomodal size distribution (PDI<0.1). The membrane permeability constants of flurbiprofen were calculated and mathematical modeling was applied to obtain the normalized drug release profiles. For comparing the sensitivities of the DR and the dialysis bag technique, the differences in the membrane permeation rates were calculated. Finally, different formulation designs of flurbiprofen were sensitively discriminated using the DR technology. The mechanism of drug release from the nanosized carriers was analyzed by applying two mathematical models described previously, the reciprocal powered time model and the three parameter model. Copyright © 2017 Elsevier B.V. All rights reserved.

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…

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…

Characterization, scaling, and partial representation of diffuse and discrete input junctions to CA3 hippocampus.

PubMed

Ascarrunz, F G; Kisley, M A; Flach, K A; Hamilton, R W; MacGregor, R J

1995-07-01

This paper applies a general mathematical system for characterizing and scaling functional connectivity and information flow across the diffuse (EC) and discrete (DG) input junctions to the CA3 hippocampus. Both gross connectivity and coordinated multiunit informational firing patterns are quantitatively characterized in terms of 32 defining parameters interrelated by 17 equations, and then scaled down according to rules for uniformly proportional scaling and for partial representation. The diffuse EC-CA3 junction is shown to be uniformly scalable with realistic representation of both essential spatiotemporal cooperativity and coordinated firing patterns down to populations of a few hundred neurons. Scaling of the discrete DG-CA3 junction can be effected with a two-step process, which necessarily deviates from uniform proportionality but nonetheless produces a valuable and readily interpretable reduced model, also utilizing a few hundred neurons in the receiving population. Partial representation produces a reduced model of only a portion of the full network where each model neuron corresponds directly to a biological neuron. The mathematical analysis illustrated here shows that although omissions and distortions are inescapable in such an application, satisfactorily complete and accurate models the size of pattern modules are possible. Finally, the mathematical characterization of these junctions generates a theory which sees the DG as a definer of the fine structure of embedded traces in the hippocampus and entire coordinated patterns of sequences of 14-cell links in CA3 as triggered by the firing of sequences of individual neurons in DG.

Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (31st, Seoul, Korea, July 8-13, 2007). Volume 4

ERIC Educational Resources Information Center

Woo, Jeong-Ho, Ed.; Lew, Hee-Chan, Ed.; Park, Kyo-Sik, Ed.; Seo, Dong-Yeop, Ed.

2007-01-01

This fourth and final volume of the 31st annual proceedings of the International Group for the Psychology of Mathematics Education conference presents research reports for author surnames beginning Na- through Zod-. Reports include: (1) Mathematically Gifted Students' Problem Solving Approaches on Conditional Probability (GwiSoo Na, DaeHee Han,…

Middle School Mathematics Professional Development Impact Study: Findings after the Second Year of Implementation. Executive Summary. NCEE 2011-4025

ERIC Educational Resources Information Center

Garet, Michael S.; Wayne, Andrew J.; Stancavage, Fran; Taylor, James; Eaton, Marian; Walters, Kirk; Song, Mengli; Brown, Seth; Hurlburt, Steven; Zhu, Pei; Sepanik, Susan; Doolittle, Fred

2011-01-01

This is the second and final report of the Middle School Mathematics Professional Development Impact Study, which examines the impact of providing a professional development (PD) program in rational number topics to seventh-grade mathematics teachers. An interim report (Garet et al. 2010) described the findings after one year of PD. The current…

Regularization and Approximation of a Class of Evolution Problems in Applied Mathematics

DTIC Science & Technology

1991-01-01

8217 DT)IG AD-A242 223 FINAL REPORT Nov61991:ti -ll IN IImI 1OV1 Ml99 1 REGULARIZATION AND APPROXIMATION OF A-CLASS OF EVOLUTION -PROBLEMS IN APPLIED...The University of Texas at Austin Austin, TX 78712 91 10 30 050 FINAL REPORT "Regularization and Approximation of a Class of Evolution Problems in...micro-structured parabolic system. A mathematical analysis of the regularized equations-has been developed to support our approach. Supporting

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…

Engineering physics and mathematics division

NASA Astrophysics Data System (ADS)

Sincovec, R. F.

1995-07-01

This report provides a record of the research activities of the Engineering Physics and Mathematics Division for the period 1 Jan. 1993 - 31 Dec. 1994. This report is the final archival record of the EPM Division. On 1 Oct. 1994, ORELA was transferred to Physics Division and on 1 Jan. 1995, the Engineering Physics and Mathematics Division and the Computer Applications Division reorganized to form the Computer Science and Mathematics Division and the Computational Physics and Engineering Division. Earlier reports in this series are identified on the previous pages, along with the progress reports describing ORNL's research in the mathematical sciences prior to 1984 when those activities moved into the Engineering Physics and Mathematics Division.

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…

Using a Summer REU to Help Develop the Next Generation of Mathematical Ecologists.

PubMed

Bennie, Barbara; Eager, Eric Alan; Peirce, James P; Sandland, Gregory J

2018-04-01

Understanding the complexities of environmental issues requires individuals to bring together ideas and data from different disciplines, including ecology and mathematics. With funding from the national science foundation (NSF), scientists from the University of Wisconsin-La Crosse and the US geological survey held a research experience for undergraduates (REU) program in the summer of 2016. The goals of the program were to expose students to open problems in the area of mathematical ecology, motivate students to pursue STEM-related positions, and to prepare students for research within interdisciplinary, collaborative settings. Based on backgrounds and interests, eight students were selected to participate in one of two research projects: wind energy and wildlife conservation or the establishment and spread of waterfowl diseases. Each research program was overseen by a mathematician and a biologist. Regardless of the research focus, the program first began with formal lectures to provide students with foundational knowledge followed by student-driven research projects. Throughout this period, student teams worked in close association with their mentors to create, parameterize and evaluate ecological models to better understand their systems of interest. Students then disseminated their results at local, regional, and international meetings and through publications (one in press and one in progress). Direct and indirect measures of student development revealed that our REU program fostered a deep appreciation for and understanding of mathematical ecology. Finally, the program allowed students to gain experiences working with individuals with different backgrounds and perspectives. Taken together, this REU program allowed us to successfully excite, motivate and prepare students for future positions in the area of mathematical biology, and because of this it can be used as a model for interdisciplinary programs at other institutions.

Epidemic spreading and global stability of an SIS model with an infective vector on complex networks

NASA Astrophysics Data System (ADS)

Kang, Huiyan; Fu, Xinchu

2015-10-01

In this paper, we present a new SIS model with delay on scale-free networks. The model is suitable to describe some epidemics which are not only transmitted by a vector but also spread between individuals by direct contacts. In view of the biological relevance and real spreading process, we introduce a delay to denote average incubation period of disease in a vector. By mathematical analysis, we obtain the epidemic threshold and prove the global stability of equilibria. The simulation shows the delay will effect the epidemic spreading. Finally, we investigate and compare two major immunization strategies, uniform immunization and targeted immunization.

Modelling and simulation of a pervaporation process using tubular module for production of anhydrous ethanol

NASA Astrophysics Data System (ADS)

Hieu, Nguyen Huu

2017-09-01

Pervaporation is a potential process for the final step of ethanol biofuel production. In this study, a mathematical model was developed based on the resistance-in-series model and a simulation was carried out using the specialized simulation software COMSOL Multiphysics to describe a tubular type pervaporation module with membranes for the dehydration of ethanol solution. The permeance of membranes, operating conditions, and feed conditions in the simulation were referred from experimental data reported previously in literature. Accordingly, the simulated temperature and density profiles of pure water and ethanol-water mixture were validated based on existing published data.

Dynamical behavior of susceptible-infected-recovered-susceptible epidemic model on weighted networks

NASA Astrophysics Data System (ADS)

Wu, Qingchu; Zhang, Fei

2018-02-01

We study susceptible-infected-recovered-susceptible epidemic model in weighted, regular, and random complex networks. We institute a pairwise-type mathematical model with a general transmission rate to evaluate the influence of the link-weight distribution on the spreading process. Furthermore, we develop a dimensionality reduction approach to derive the condition for the contagion outbreak. Finally, we analyze the influence of the heterogeneity of weight distribution on the outbreak condition for the scenario with a linear transmission rate. Our theoretical analysis is in agreement with stochastic simulations, showing that the heterogeneity of link-weight distribution can have a significant effect on the epidemic dynamics.

Analysis of a novel stochastic SIRS epidemic model with two different saturated incidence rates

NASA Astrophysics Data System (ADS)

Chang, Zhengbo; Meng, Xinzhu; Lu, Xiao

2017-04-01

This paper presents a stochastic SIRS epidemic model with two different nonlinear incidence rates and double epidemic asymmetrical hypothesis, and we devote to develop a mathematical method to obtain the threshold of the stochastic epidemic model. We firstly investigate the boundness and extinction of the stochastic system. Furthermore, we use Ito's formula, the comparison theorem and some new inequalities techniques of stochastic differential systems to discuss persistence in mean of two diseases on three cases. The results indicate that stochastic fluctuations can suppress the disease outbreak. Finally, numerical simulations about different noise disturbance coefficients are carried out to illustrate the obtained theoretical results.

A preference aggregation model and application in AHP-group decision making

NASA Astrophysics Data System (ADS)

Yang, Taiyi; Yang, De; Chao, Xiangrui

2018-04-01

Group decision making process integrate individual preferences to obtain the group preference by applying aggregation rules and preference relations. The two most useful approaches, the aggregation of individual judgements and the aggregation of individual priorities, traditionally are employed in the Analytic Hierarchy Process to deal with group decision making problems. In both cases, it is assumed that the group preference is approximate weighted mathematical expectation of individual judgements and individual priorities. We propose new preference aggregation methods using optimization models in order to obtain group preference which is close to all individual priorities. Some illustrative examples are finally examined to demonstrate proposed models for application.

A mathematical model of phosphorylation AKT in Acute Myeloid Leukemia

NASA Astrophysics Data System (ADS)

Adi, Y. A.; Kusumo, F. A.; Aryati, L.; Hardianti, M. S.

2016-04-01

In this paper we consider a mathematical model of PI3K/AKT signaling pathways in phosphorylation AKT. PI3K/AKT pathway is an important mediator of cytokine signaling implicated in regulation of hematopoiesis. Constitutive activation of PI3K/AKT signaling pathway has been observed in Acute Meyloid Leukemia (AML) it caused by the mutation of Fms-like Tyrosine Kinase 3 in internal tandem duplication (FLT3-ITD), the most common molecular abnormality associated with AML. Depending upon its phosphorylation status, protein interaction, substrate availability, and localization, AKT can phosphorylate or inhibite numerous substrates in its downstream pathways that promote protein synthesis, survival, proliferation, and metabolism. Firstly, we present a mass action ordinary differential equation model describing AKT double phosphorylation (AKTpp) in a system with 11 equations. Finally, under the asumtion enzyme catalyst constant and steady state equilibrium, we reduce the system in 4 equation included Michaelis Menten constant. Simulation result suggested that a high concentration of PI3K and/or a low concentration of phospatase increased AKTpp activation. This result also indicates that PI3K is a potential target theraphy in AML.

Optimization of CO2 laser cutting parameters on Austenitic type Stainless steel sheet

NASA Astrophysics Data System (ADS)

Parthiban, A.; Sathish, S.; Chandrasekaran, M.; Ravikumar, R.

2017-03-01

Thin AISI 316L stainless steel sheet widely used in sheet metal processing industries for specific applications. CO2 laser cutting is one of the most popular sheet metal cutting processes for cutting of sheets in different profile. In present work various cutting parameters such as laser power (2000 watts-4000 watts), cutting speed (3500mm/min - 5500 mm/min) and assist gas pressure (0.7 Mpa-0.9Mpa) for cutting of AISI 316L 2mm thickness stainless sheet. This experimentation was conducted based on Box-Behenken design. The aim of this work is to develop a mathematical model kerf width for straight and curved profile through response surface methodology. The developed mathematical models for straight and curved profile have been compared. The Quadratic models have the best agreement with experimental data, and also the shape of the profile a substantial role in achieving to minimize the kerf width. Finally the numerical optimization technique has been used to find out best optimum laser cutting parameter for both straight and curved profile cut.

Analysis on Experimental Investigation and Mathematical Modeling of Incompressible Flow Through Ceramic Foam Filters

NASA Astrophysics Data System (ADS)

Akbarnejad, Shahin; Jonsson, Lage Tord Ingemar; Kennedy, Mark William; Aune, Ragnhild Elizabeth; Jönsson, Pӓr Göran

2016-08-01

This paper presents experimental results of pressure drop measurements on 30, 50, and 80 pores per inch (PPI) commercial alumina ceramic foam filters (CFF) and compares the obtained pressure drop profiles to numerically modeled values. In addition, it is aimed at investigating the adequacy of the mathematical correlations used in the analytical and the computational fluid dynamics (CFD) simulations. It is shown that the widely used correlations for predicting pressure drop in porous media continuously under-predict the experimentally obtained pressure drop profiles. For analytical predictions, the negative deviations from the experimentally obtained pressure drop using the unmodified Ergun and Dietrich equations could be as high as 95 and 74 pct, respectively. For the CFD predictions, the deviation to experimental results is in the range of 84.3 to 88.5 pct depending on filter PPI. Better results can be achieved by applying the Forchheimer second-order drag term instead of the Brinkman-Forchheimer drag term. Thus, the final deviation of the CFD model estimates lie in the range of 0.3 to 5.5 pct compared to the measured values.

Mathematics Anxiety: What Have We Learned in 60 Years?

PubMed Central

Dowker, Ann; Sarkar, Amar; Looi, Chung Yen

2016-01-01

The construct of mathematics anxiety has been an important topic of study at least since the concept of “number anxiety” was introduced by Dreger and Aiken (1957), and has received increasing attention in recent years. This paper focuses on what research has revealed about mathematics anxiety in the last 60 years, and what still remains to be learned. We discuss what mathematics anxiety is; how distinct it is from other forms of anxiety; and how it relates to attitudes to mathematics. We discuss the relationships between mathematics anxiety and mathematics performance. We describe ways in which mathematics anxiety is measured, both by questionnaires, and by physiological measures. We discuss some possible factors in mathematics anxiety, including genetics, gender, age, and culture. Finally, we describe some research on treatment. We conclude with a brief discussion of what still needs to be learned. PMID:27199789

Towards a category theory approach to analogy: Analyzing re-representation and acquisition of numerical knowledge.

PubMed

Navarrete, Jairo A; Dartnell, Pablo

2017-08-01

Category Theory, a branch of mathematics, has shown promise as a modeling framework for higher-level cognition. We introduce an algebraic model for analogy that uses the language of category theory to explore analogy-related cognitive phenomena. To illustrate the potential of this approach, we use this model to explore three objects of study in cognitive literature. First, (a) we use commutative diagrams to analyze an effect of playing particular educational board games on the learning of numbers. Second, (b) we employ a notion called coequalizer as a formal model of re-representation that explains a property of computational models of analogy called "flexibility" whereby non-similar representational elements are considered matches and placed in structural correspondence. Finally, (c) we build a formal learning model which shows that re-representation, language processing and analogy making can explain the acquisition of knowledge of rational numbers. These objects of study provide a picture of acquisition of numerical knowledge that is compatible with empirical evidence and offers insights on possible connections between notions such as relational knowledge, analogy, learning, conceptual knowledge, re-representation and procedural knowledge. This suggests that the approach presented here facilitates mathematical modeling of cognition and provides novel ways to think about analogy-related cognitive phenomena.

A Mathematical Framework for the Complex System Approach to Group Dynamics: The Case of Recovery House Social Integration.

PubMed

Light, John M; Jason, Leonard A; Stevens, Edward B; Callahan, Sarah; Stone, Ariel

2016-03-01

The complex system conception of group social dynamics often involves not only changing individual characteristics, but also changing within-group relationships. Recent advances in stochastic dynamic network modeling allow these interdependencies to be modeled from data. This methodology is discussed within a context of other mathematical and statistical approaches that have been or could be applied to study the temporal evolution of relationships and behaviors within small- to medium-sized groups. An example model is presented, based on a pilot study of five Oxford House recovery homes, sober living environments for individuals following release from acute substance abuse treatment. This model demonstrates how dynamic network modeling can be applied to such systems, examines and discusses several options for pooling, and shows how results are interpreted in line with complex system concepts. Results suggest that this approach (a) is a credible modeling framework for studying group dynamics even with limited data, (b) improves upon the most common alternatives, and (c) is especially well-suited to complex system conceptions. Continuing improvements in stochastic models and associated software may finally lead to mainstream use of these techniques for the study of group dynamics, a shift already occurring in related fields of behavioral science.

Intelligent classifier for dynamic fault patterns based on hidden Markov model

NASA Astrophysics Data System (ADS)

Xu, Bo; Feng, Yuguang; Yu, Jinsong

2006-11-01

It's difficult to build precise mathematical models for complex engineering systems because of the complexity of the structure and dynamics characteristics. Intelligent fault diagnosis introduces artificial intelligence and works in a different way without building the analytical mathematical model of a diagnostic object, so it's a practical approach to solve diagnostic problems of complex systems. This paper presents an intelligent fault diagnosis method, an integrated fault-pattern classifier based on Hidden Markov Model (HMM). This classifier consists of dynamic time warping (DTW) algorithm, self-organizing feature mapping (SOFM) network and Hidden Markov Model. First, after dynamic observation vector in measuring space is processed by DTW, the error vector including the fault feature of being tested system is obtained. Then a SOFM network is used as a feature extractor and vector quantization processor. Finally, fault diagnosis is realized by fault patterns classifying with the Hidden Markov Model classifier. The importing of dynamic time warping solves the problem of feature extracting from dynamic process vectors of complex system such as aeroengine, and makes it come true to diagnose complex system by utilizing dynamic process information. Simulating experiments show that the diagnosis model is easy to extend, and the fault pattern classifier is efficient and is convenient to the detecting and diagnosing of new faults.

Towards a category theory approach to analogy: Analyzing re-representation and acquisition of numerical knowledge

PubMed Central

2017-01-01

Category Theory, a branch of mathematics, has shown promise as a modeling framework for higher-level cognition. We introduce an algebraic model for analogy that uses the language of category theory to explore analogy-related cognitive phenomena. To illustrate the potential of this approach, we use this model to explore three objects of study in cognitive literature. First, (a) we use commutative diagrams to analyze an effect of playing particular educational board games on the learning of numbers. Second, (b) we employ a notion called coequalizer as a formal model of re-representation that explains a property of computational models of analogy called “flexibility” whereby non-similar representational elements are considered matches and placed in structural correspondence. Finally, (c) we build a formal learning model which shows that re-representation, language processing and analogy making can explain the acquisition of knowledge of rational numbers. These objects of study provide a picture of acquisition of numerical knowledge that is compatible with empirical evidence and offers insights on possible connections between notions such as relational knowledge, analogy, learning, conceptual knowledge, re-representation and procedural knowledge. This suggests that the approach presented here facilitates mathematical modeling of cognition and provides novel ways to think about analogy-related cognitive phenomena. PMID:28841643

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…

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)…

Full-scale flammability test data for validation of aircraft fire mathematical models

NASA Technical Reports Server (NTRS)

Kuminecz, J. F.; Bricker, R. W.

1982-01-01

Twenty-five large scale aircraft flammability tests were conducted in a Boeing 737 fuselage at the NASA Johnson Space Center (JSC). The objective of this test program was to provide a data base on the propagation of large scale aircraft fires to support the validation of aircraft fire mathematical models. Variables in the test program included cabin volume, amount of fuel, fuel pan area, fire location, airflow rate, and cabin materials. A number of tests were conducted with jet A-1 fuel only, while others were conducted with various Boeing 747 type cabin materials. These included urethane foam seats, passenger service units, stowage bins, and wall and ceiling panels. Two tests were also included using special urethane foam and polyimide foam seats. Tests were conducted with each cabin material individually, with various combinations of these materials, and finally, with all materials in the cabin. The data include information obtained from approximately 160 locations inside the fuselage.

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…

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.

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.

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.…

Research and application of multi-agent genetic algorithm in tower defense game

NASA Astrophysics Data System (ADS)

Jin, Shaohua

2018-04-01

In this paper, a new multi-agent genetic algorithm based on orthogonal experiment is proposed, which is based on multi-agent system, genetic algorithm and orthogonal experimental design. The design of neighborhood competition operator, orthogonal crossover operator, Son and self-learning operator. The new algorithm is applied to mobile tower defense game, according to the characteristics of the game, the establishment of mathematical models, and finally increases the value of the game's monster.

Status of Complex Langevin

NASA Astrophysics Data System (ADS)

Seiler, Erhard

2018-03-01

I review the status of the Complex Langevin method, which was invented to make simulations of models with complex action feasible. I discuss the mathematical justification of the procedure, as well as its limitations and open questions. Various pragmatic measures for dealing with the existing problems are described. Finally I report on the progress in the application of the method to QCD, with the goal of determining the phase diagram of QCD as a function of temperature and baryonic chemical potential.

High-accuracy process based on the corrective calibration of removal function in the magnetorheological finishing

NASA Astrophysics Data System (ADS)

Zhong, Xianyun; Fan, Bin; Wu, Fan

2017-08-01

The corrective calibration of the removal function plays an important role in the magnetorheological finishing (MRF) high-accuracy process. This paper mainly investigates the asymmetrical characteristic of the MRF removal function shape and further analyzes its influence on the surface residual error by means of an iteration algorithm and simulations. By comparing the ripple errors and convergence ratios based on the ideal MRF tool function and the deflected tool function, the mathematical models for calibrating the deviation of horizontal and flowing directions are presented. Meanwhile, revised mathematical models for the coordinate transformation of an MRF machine is also established. Furthermore, a Ø140-mm fused silica plane and a Ø196 mm, f/1∶1, fused silica concave sphere samples are taken as the experiments. After two runs, the plane mirror final surface error reaches PV 17.7 nm, RMS 1.75 nm, and the polishing time is 16 min in total; after three runs, the sphere mirror final surfer error reaches RMS 2.7 nm and the polishing time is 70 min in total. The convergence ratios are 96.2% and 93.5%, respectively. The spherical simulation error and the polishing result are almost consistent, which fully validate the efficiency and feasibility of the calibration method of MRF removal function error using for the high-accuracy subaperture optical manufacturing.

Mathematical modeling in realistic mathematics education

NASA Astrophysics Data System (ADS)

Riyanto, B.; Zulkardi; Putri, R. I. I.; Darmawijoyo

2017-12-01

The purpose of this paper is to produce Mathematical modelling in Realistics Mathematics Education of Junior High School. This study used development research consisting of 3 stages, namely analysis, design and evaluation. The success criteria of this study were obtained in the form of local instruction theory for school mathematical modelling learning which was valid and practical for students. The data were analyzed using descriptive analysis method as follows: (1) walk through, analysis based on the expert comments in the expert review to get Hypothetical Learning Trajectory for valid mathematical modelling learning; (2) analyzing the results of the review in one to one and small group to gain practicality. Based on the expert validation and students’ opinion and answers, the obtained mathematical modeling problem in Realistics Mathematics Education was valid and practical.

Modelling of Molecular Structures and Properties. Proceedings of the International Meeting of Physical Chemistry on Modeling of Molecular Structures and Properties in Physical Chemistry and Biophysics Organized by the Division de Chimie Physique of the Societe Francaise de Chimie Held in Nancy, France on 11-15 September 1989

DTIC Science & Technology

1990-01-01

expert systems, "intelligent" computer-aided instruction , symbolic learning . These aspects will be discussed, focusing on the specific problems the...VLSI chips) according to preliminary specifications. Finally ES are also used in computer-aided instruction (CAI) due to their ability of... instructions to process controllers), academic teaching (for mathematics , physics, foreign language, etc.). Domains of application The different

Preliminary description of the area navigation software for a microcomputer-based Loran-C receiver

NASA Technical Reports Server (NTRS)

Oguri, F.

1983-01-01

The development of new software implementation of this software on a microcomputer (MOS 6502) to provide high quality navigation information is described. This software development provides Area/Route Navigation (RNAV) information from Time Differences (TDs) in raw form using an elliptical Earth model and a spherical model. The software is prepared for the microcomputer based Loran-C receiver. To compute navigation infomation, a (MOS 6502) microcomputer and a mathematical chip (AM 9511A) were combined with the Loran-C receiver. Final data reveals that this software does indeed provide accurate information with reasonable execution times.

A system-level mathematical model of Basal Ganglia motor-circuit for kinematic planning of arm movements.

PubMed

Salimi-Badr, Armin; Ebadzadeh, Mohammad Mehdi; Darlot, Christian

2018-01-01

In this paper, a novel system-level mathematical model of the Basal Ganglia (BG) for kinematic planning, is proposed. An arm composed of several segments presents a geometric redundancy. Thus, selecting one trajectory among an infinite number of possible ones requires overcoming redundancy, according to some kinds of optimization. Solving this optimization is assumed to be the function of BG in planning. In the proposed model, first, a mathematical solution of kinematic planning is proposed for movements of a redundant arm in a plane, based on minimizing energy consumption. Next, the function of each part in the model is interpreted as a possible role of a nucleus of BG. Since the kinematic variables are considered as vectors, the proposed model is presented based on the vector calculus. This vector model predicts different neuronal populations in BG which is in accordance with some recent experimental studies. According to the proposed model, the function of the direct pathway is to calculate the necessary rotation of each joint, and the function of the indirect pathway is to control each joint rotation considering the movement of the other joints. In the proposed model, the local feedback loop between Subthalamic Nucleus and Globus Pallidus externus is interpreted as a local memory to store the previous amounts of movements of the other joints, which are utilized by the indirect pathway. In this model, activities of dopaminergic neurons would encode, at short-term, the error between the desired and actual positions of the end-effector. The short-term modulating effect of dopamine on Striatum is also modeled as cross product. The model is simulated to generate the commands of a redundant manipulator. The performance of the model is studied for different reaching movements between 8 points in a plane. Finally, some symptoms of Parkinson's disease such as bradykinesia and akinesia are simulated by modifying the model parameters, inspired by the dopamine depletion. Copyright © 2017 Elsevier Ltd. All rights reserved.

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.

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;…

A simulation model of the oxygen alveolo-capillary exchange in normal and pathological conditions.

PubMed

Brighenti, Chiara; Gnudi, Gianni; Avanzolini, Guido

2003-05-01

This paper presents a mathematical model of the oxygen alveolo-capillary exchange to provide the capillary oxygen partial pressure profile in normal and pathological conditions. In fact, a thickening of the blood-gas barrier, heavy exercise or a low oxygen partial pressure (PO2) in the alveolar space can reduce the O2 alveolo-capillary exchange. Since the reversible binding between haemoglobin and oxygen makes it impossible to determine the closed form for the mathematical description of the PO2 profile along the pulmonary capillaries, an approximate analytical solution of the capillary PO2 profile is proposed. Simulation results are compared with the capillary PO2 profile obtained by numerical integration and by a piecewise linear interpolation of the oxyhaemoglobin dissociation curve. Finally, the proposed model is evaluated in a large range of physiopathological diffusive conditions. The good fit to numerical solutions in all experimental conditions seems to represent a substantial improvement with respect to the approach based on a linear approximation of the oxyhaemoglobin dissociation curve, and makes this model a candidate to be incorporated into the integrated descriptions of the entire respiratory system, where the datum of primary interest is the value of end capillary PO2.

Estimation of energetic efficiency of heat supply in front of the aircraft at supersonic accelerated flight. Part 1. Mathematical models

NASA Astrophysics Data System (ADS)

Latypov, A. F.

2008-12-01

Fuel economy at boost trajectory of the aerospace plane was estimated during energy supply to the free stream. Initial and final flight velocities were specified. The model of a gliding flight above cold air in an infinite isobaric thermal wake was used. The fuel consumption rates were compared at optimal trajectory. The calculations were carried out using a combined power plant consisting of ramjet and liquid-propellant engine. An exergy model was built in the first part of the paper to estimate the ramjet thrust and specific impulse. A quadratic dependence on aerodynamic lift was used to estimate the aerodynamic drag of aircraft. The energy for flow heating was obtained at the expense of an equivalent reduction of the exergy of combustion products. The dependencies were obtained for increasing the range coefficient of cruise flight for different Mach numbers. The second part of the paper presents a mathematical model for the boost interval of the aircraft flight trajectory and the computational results for the reduction of fuel consumption at the boost trajectory for a given value of the energy supplied in front of the aircraft.

Estimation of energetic efficiency of heat supply in front of the aircraft at supersonic accelerated flight. Part II. Mathematical model of the trajectory boost part and computational results

NASA Astrophysics Data System (ADS)

Latypov, A. F.

2009-03-01

The fuel economy was estimated at boost trajectory of aerospace plane during energy supply to the free stream. Initial and final velocities of the flight were given. A model of planning flight above cold air in infinite isobaric thermal wake was used. The comparison of fuel consumption was done at optimal trajectories. The calculations were done using a combined power plant consisting of ramjet and liquid-propellant engine. An exergy model was constructed in the first part of the paper for estimating the ramjet thrust and specific impulse. To estimate the aerodynamic drag of aircraft a quadratic dependence on aerodynamic lift is used. The energy for flow heating is obtained at the sacrifice of an equivalent decrease of exergy of combustion products. The dependencies are obtained for increasing the range coefficient of cruise flight at different Mach numbers. In the second part of the paper, a mathematical model is presented for the boost part of the flight trajectory of the flying vehicle and computational results for reducing the fuel expenses at the boost trajectory at a given value of the energy supplied in front of the aircraft.

Mathematical Models for Controlled Drug Release Through pH-Responsive Polymeric Hydrogels.

PubMed

Manga, Ramya D; Jha, Prateek K

2017-02-01

Hydrogels consisting of weakly charged acidic/basic groups are ideal candidates for carriers in oral delivery, as they swell in response to pH changes in the gastrointestinal tract, resulting in drug entrapment at low pH conditions of the stomach and drug release at high pH conditions of the intestine. We have developed 1-dimensional mathematical models to study the drug release behavior through pH-responsive hydrogels. Models are developed for 3 different cases that vary in the level of rigor, which together can be applied to predict both in vitro (drug release from carrier) and in vivo (drug concentration in the plasma) behavior of hydrogel-drug formulations. A detailed study of the effect of hydrogel and drug characteristics and physiological conditions is performed to gain a fundamental insight into the drug release behavior, which may be useful in the design of pH-responsive drug carriers. Finally, we describe a successful application of these models to predict both in vitro and in vivo behavior of docetaxel-loaded micelle in a pH-responsive hydrogel, as reported in a recent experimental study. Copyright © 2017 American Pharmacists Association®. Published by Elsevier Inc. All rights reserved.

[The enigma of the biological interpretation of the linear-quadratic model finally resolved? A summary for non-mathematicians].

PubMed

Bodgi, L; Canet, A; Granzotto, A; Britel, M; Puisieux, A; Bourguignon, M; Foray, N

2016-06-01

The linear-quadratic (LQ) model is the only mathematical formula linking cellular survival and radiation dose that is sufficiently consensual to help radiation oncologists and radiobiologists in describing the radiation-induced events. However, this formula proposed in the 1970s and α and β parameters on which it is based remained without relevant biological meaning. From a collection of cutaneous fibroblasts with different radiosensitivity, built over 12 years by more than 50 French radiation oncologists, we recently pointed out that the ATM protein, major actor of the radiation response, diffuses from the cytoplasm to the nucleus after irradiation. The evidence of this nuclear shuttling of ATM allowed us to provide a biological interpretation of the LQ model in its mathematical features, validated by a hundred of radiosensitive cases. A mechanistic explanation of the radiosensitivity of syndromes caused by the mutation of cytoplasmic proteins and of the hypersensitivity to low-dose phenomenon has been proposed, as well. In this review, we present our resolution of the LQ model in the most didactic way. Copyright © 2016 Société française de radiothérapie oncologique (SFRO). Published by Elsevier SAS. All rights reserved.

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.

Mathematical and Statistical Software Index. Final Report.

ERIC Educational Resources Information Center

Black, Doris E., Comp.

Brief descriptions are provided of general-purpose mathematical and statistical software, including 27 "stand-alone" programs, three subroutine systems, and two nationally recognized statistical packages, which are available in the Air Force Human Resources Laboratory (AFHRL) software library. This index was created to enable researchers…

A novel approach for inventory problem in the pharmaceutical supply chain.

PubMed

Candan, Gökçe; Yazgan, Harun Reşit

2016-02-24

In pharmaceutical enterprises, keeping up with global market conditions is possible with properly selected supply chain management policies. Generally; demand-driven classical supply chain model is used in the pharmaceutical industry. In this study, a new mathematical model is developed to solve an inventory problem in the pharmaceutical supply chain. Unlike the studies in literature, the "shelf life and product transition times" constraints are considered, simultaneously, first time in the pharmaceutical production inventory problem. The problem is formulated as a mixed-integer linear programming (MILP) model with a hybrid time representation. The objective is to maximize total net profit. Effectiveness of the proposed model is illustrated considering a classical and a vendor managed inventory (VMI) supply chain on an experimental study. To show the effectiveness of the model, an experimental study is performed; which contains 2 different supply chain policy (Classical and VMI), 24 and 30 months planning horizon, 10 and 15 different cephalosporin products. Finally the mathematical model is compared to another model in literature and the results show that proposed model is superior. This study suggest a novel approach for solving pharmaceutical inventory problem. The developed model is maximizing total net profit while determining optimal production plan under shelf life and product transition constraints in the pharmaceutical industry. And we believe that the proposed model is much more closed to real life unlike the other studies in literature.

Autonomous control of production networks using a pheromone approach

NASA Astrophysics Data System (ADS)

Armbruster, D.; de Beer, C.; Freitag, M.; Jagalski, T.; Ringhofer, C.

2006-04-01

The flow of parts through a production network is usually pre-planned by a central control system. Such central control fails in presence of highly fluctuating demand and/or unforeseen disturbances. To manage such dynamic networks according to low work-in-progress and short throughput times, an autonomous control approach is proposed. Autonomous control means a decentralized routing of the autonomous parts themselves. The parts’ decisions base on backward propagated information about the throughput times of finished parts for different routes. So, routes with shorter throughput times attract parts to use this route again. This process can be compared to ants leaving pheromones on their way to communicate with following ants. The paper focuses on a mathematical description of such autonomously controlled production networks. A fluid model with limited service rates in a general network topology is derived and compared to a discrete-event simulation model. Whereas the discrete-event simulation of production networks is straightforward, the formulation of the addressed scenario in terms of a fluid model is challenging. Here it is shown, how several problems in a fluid model formulation (e.g. discontinuities) can be handled mathematically. Finally, some simulation results for the pheromone-based control with both the discrete-event simulation model and the fluid model are presented for a time-dependent influx.

A clinical data validated mathematical model of prostate cancer growth under intermittent androgen suppression therapy

NASA Astrophysics Data System (ADS)

Portz, Travis; Kuang, Yang; Nagy, John D.

2012-03-01

Prostate cancer is commonly treated by a form of hormone therapy called androgen suppression. This form of treatment, while successful at reducing the cancer cell population, adversely affects quality of life and typically leads to a recurrence of the cancer in an androgen-independent form. Intermittent androgen suppression aims to alleviate some of these adverse affects by cycling the patient on and off treatment. Clinical studies have suggested that intermittent therapy is capable of maintaining androgen dependence over multiple treatment cycles while increasing quality of life during off-treatment periods. This paper presents a mathematical model of prostate cancer to study the dynamics of androgen suppression therapy and the production of prostate-specific antigen (PSA), a clinical marker for prostate cancer. Preliminary models were based on the assumption of an androgen-independent (AI) cell population with constant net growth rate. These models gave poor accuracy when fitting clinical data during simulation. The final model presented hypothesizes an AI population with increased sensitivity to low levels of androgen. It also hypothesizes that PSA production is heavily dependent on androgen. The high level of accuracy in fitting clinical data with this model appears to confirm these hypotheses, which are also consistent with biological evidence.

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…

Using a Mathematical Model to Analyze the Role of Probiotics and Inflammation in Necrotizing Enterocolitis

PubMed Central

Arciero, Julia C.; Ermentrout, G. Bard; Upperman, Jeffrey S.; Vodovotz, Yoram; Rubin, Jonathan E.

2010-01-01

Background Necrotizing enterocolitis (NEC) is a severe disease of the gastrointestinal tract of pre-term babies and is thought to be related to the physiological immaturity of the intestine and altered levels of normal flora in the gut. Understanding the factors that contribute to the pathology of NEC may lead to the development of treatment strategies aimed at re-establishing the integrity of the epithelial wall and preventing the propagation of inflammation in NEC. Several studies have shown a reduced incidence and severity of NEC in neonates treated with probiotics (beneficial bacteria species). Methodology/Principal Findings The objective of this study is to use a mathematical model to predict the conditions under which probiotics may be successful in promoting the health of infants suffering from NEC. An ordinary differential equation model is developed that tracks the populations of pathogenic and probiotic bacteria in the intestinal lumen and in the blood/tissue region. The permeability of the intestinal epithelial layer is treated as a variable, and the role of the inflammatory response is included. The model predicts that in the presence of probiotics health is restored in many cases that would have been otherwise pathogenic. The timing of probiotic administration is also shown to determine whether or not health is restored. Finally, the model predicts that probiotics may be harmful to the NEC patient under very specific conditions, perhaps explaining the detrimental effects of probiotics observed in some clinical studies. Conclusions/Significance The reduced, experimentally motivated mathematical model that we have developed suggests how a certain general set of characteristics of probiotics can lead to beneficial or detrimental outcomes for infants suffering from NEC, depending on the influences of probiotics on defined features of the inflammatory response. PMID:20419099

Be-CoDiS: A Mathematical Model to Predict the Risk of Human Diseases Spread Between Countries--Validation and Application to the 2014-2015 Ebola Virus Disease Epidemic.

PubMed

Ivorra, Benjamin; Ngom, Diène; Ramos, Ángel M

2015-09-01

Ebola virus disease is a lethal human and primate disease that currently requires a particular attention from the international health authorities due to important outbreaks in some Western African countries and isolated cases in the UK, the USA and Spain. Regarding the emergency of this situation, there is a need for the development of decision tools, such as mathematical models, to assist the authorities to focus their efforts in important factors to eradicate Ebola. In this work, we propose a novel deterministic spatial-temporal model, called Between-Countries Disease Spread (Be-CoDiS), to study the evolution of human diseases within and between countries. The main interesting characteristics of Be-CoDiS are the consideration of the movement of people between countries, the control measure effects and the use of time-dependent coefficients adapted to each country. First, we focus on the mathematical formulation of each component of the model and explain how its parameters and inputs are obtained. Then, in order to validate our approach, we consider two numerical experiments regarding the 2014-2015 Ebola epidemic. The first one studies the ability of the model in predicting the EVD evolution between countries starting from the index cases in Guinea in December 2013. The second one consists of forecasting the evolution of the epidemic by using some recent data. The results obtained with Be-CoDiS are compared to real data and other model outputs found in the literature. Finally, a brief parameter sensitivity analysis is done. A free MATLAB version of Be-CoDiS is available at: http://www.mat.ucm.es/momat/software.htm.

Mathematical modeling of tumor-induced immunosuppression by myeloid-derived suppressor cells: Implications for therapeutic targeting strategies.

PubMed

Shariatpanahi, Seyed Peyman; Shariatpanahi, Seyed Pooya; Madjidzadeh, Keivan; Hassan, Moustapha; Abedi-Valugerdi, Manuchehr

2018-04-07

Myeloid-derived suppressor cells (MDSCs) belong to immature myeloid cells that are generated and accumulated during the tumor development. MDSCs strongly suppress the anti-tumor immunity and provide conditions for tumor progression and metastasis. In this study, we present a mathematical model based on ordinary differential equations (ODE) to describe tumor-induced immunosuppression caused by MDSCs. The model consists of four equations and incorporates tumor cells, cytotoxic T cells (CTLs), natural killer (NK) cells and MDSCs. We also provide simulation models that evaluate or predict the effects of anti-MDSC drugs (e.g., l-arginine and 5-Fluorouracil (5-FU)) on the tumor growth and the restoration of anti-tumor immunity. The simulated results obtained using our model were in good agreement with the corresponding experimental findings on the expansion of splenic MDSCs, immunosuppressive effects of these cells at the tumor site and effectiveness of l-arginine and 5-FU on the re-establishment of antitumor immunity. Regarding this latter issue, our predictive simulation results demonstrated that intermittent therapy with low-dose 5-FU alone could eradicate the tumors irrespective of their origins and types. Furthermore, at the time of tumor eradication, the number of CTLs prevailed over that of cancer cells and the number of splenic MDSCs returned to the normal levels. Finally, our predictive simulation results also showed that the addition of l-arginine supplementation to the intermittent 5-FU therapy reduced the time of the tumor eradication and the number of iterations for 5-FU treatment. Thus, the present mathematical model provides important implications for designing new therapeutic strategies that aim to restore antitumor immunity by targeting MDSCs. Copyright © 2018 Elsevier Ltd. All rights reserved.

Influence of dynamic coupled hydro-bio-mechanical processes on response of municipal solid waste and liner system in bioreactor landfills.

PubMed

Reddy, Krishna R; Kumar, Girish; Giri, Rajiv K

2017-05-01

A two-dimensional (2-D) mathematical model is presented to predict the response of municipal solid waste (MSW) of conventional as well as bioreactor landfills undergoing coupled hydro-bio-mechanical processes. The newly developed and validated 2-D coupled mathematical modeling framework combines and simultaneously solves a two-phase flow model based on the unsaturated Richard's equation, a plain-strain formulation of Mohr-Coulomb mechanical model and first-order decay kinetics biodegradation model. The performance of both conventional and bioreactor landfill was investigated holistically, by evaluating the mechanical settlement, extent of waste degradation with subsequent changes in geotechnical properties, landfill slope stability, and in-plane shear behavior (shear stress-displacement) of composite liner system and final cover system. It is concluded that for the given specific conditions considered, bioreactor landfill attained an overall stabilization after a continuous leachate injection of 16years, whereas the stabilization was observed after around 50years of post-closure in conventional landfills, with a total vertical strain of 36% and 37% for bioreactor and conventional landfills, respectively. The significant changes in landfill settlement, the extent of MSW degradation, MSW geotechnical properties, along with their influence on the in-plane shear response of composite liner and final cover system, between the conventional and bioreactor landfills, observed using the mathematical model proposed in this study, corroborates the importance of considering coupled hydro-bio-mechanical processes while designing and predicting the performance of engineered bioreactor landfills. The study underscores the importance of considering the effect of coupled processes while examining the stability and integrity of the liner and cover systems, which form the integral components of a landfill. Moreover, the spatial and temporal variations in the landfill settlement, the stability of landfill slope under pressurized leachate injection conditions and the rapid changes in the MSW properties with degradation emphasizes the complexity of the bioreactor landfill system and the need for understanding the interrelated processes to design and operate stable and effective bioreactor landfills. A detailed discussion on the results obtained from the numerical simulations along with limitations and key challenges in this study are also presented. Copyright © 2016 Elsevier Ltd. All rights reserved.

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)

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.

Robust check loss-based variable selection of high-dimensional single-index varying-coefficient model

NASA Astrophysics Data System (ADS)

Song, Yunquan; Lin, Lu; Jian, Ling

2016-07-01

Single-index varying-coefficient model is an important mathematical modeling method to model nonlinear phenomena in science and engineering. In this paper, we develop a variable selection method for high-dimensional single-index varying-coefficient models using a shrinkage idea. The proposed procedure can simultaneously select significant nonparametric components and parametric components. Under defined regularity conditions, with appropriate selection of tuning parameters, the consistency of the variable selection procedure and the oracle property of the estimators are established. Moreover, due to the robustness of the check loss function to outliers in the finite samples, our proposed variable selection method is more robust than the ones based on the least squares criterion. Finally, the method is illustrated with numerical simulations.

Characterization and modeling of an advanced flexible thermal protection material for space applications

NASA Technical Reports Server (NTRS)

Clayton, Joseph P.; Tinker, Michael L.

1991-01-01

This paper describes experimental and analytical characterization of a new flexible thermal protection material known as Tailorable Advanced Blanket Insulation (TABI). This material utilizes a three-dimensional ceramic fabric core structure and an insulation filler. TABI is the leading candidate for use in deployable aeroassisted vehicle designs. Such designs require extensive structural modeling, and the most significant in-plane material properties necessary for model development are measured and analytically verified in this study. Unique test methods are developed for damping measurements. Mathematical models are developed for verification of the experimental modulus and damping data, and finally, transverse properties are described in terms of the inplane properties through use of a 12-dof finite difference model of a simple TABI configuration.

Computational models of neuromodulation.

PubMed

Fellous, J M; Linster, C

1998-05-15

Computational modeling of neural substrates provides an excellent theoretical framework for the understanding of the computational roles of neuromodulation. In this review, we illustrate, with a large number of modeling studies, the specific computations performed by neuromodulation in the context of various neural models of invertebrate and vertebrate preparations. We base our characterization of neuromodulations on their computational and functional roles rather than on anatomical or chemical criteria. We review the main framework in which neuromodulation has been studied theoretically (central pattern generation and oscillations, sensory processing, memory and information integration). Finally, we present a detailed mathematical overview of how neuromodulation has been implemented at the single cell and network levels in modeling studies. Overall, neuromodulation is found to increase and control computational complexity.

Two-dimensional CFD modeling of the heat and mass transfer process during sewage sludge drying in a solar dryer

NASA Astrophysics Data System (ADS)

Krawczyk, Piotr; Badyda, Krzysztof

2011-12-01

The paper presents key assumptions of the mathematical model which describes heat and mass transfer phenomena in a solar sewage drying process, as well as techniques used for solving this model with the Fluent computational fluid dynamics (CFD) software. Special attention was paid to implementation of boundary conditions on the sludge surface, which is a physical boundary between the gaseous phase - air, and solid phase - dried matter. Those conditions allow to model heat and mass transfer between the media during first and second drying stages. Selection of the computational geometry is also discussed - it is a fragment of the entire drying facility. Selected modelling results are presented in the final part of the paper.

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…

Modeling of light-induced degradation due to Cu precipitation in p-type silicon. II. Comparison of simulations and experiments

NASA Astrophysics Data System (ADS)

Vahlman, H.; Haarahiltunen, A.; Kwapil, W.; Schön, J.; Inglese, A.; Savin, H.

2017-05-01

The presence of copper impurities is known to deteriorate the bulk minority carrier lifetime of silicon. In p-type silicon, the degradation occurs only under carrier injection (e.g., illumination), but the reason for this phenomenon called copper-related light-induced degradation (Cu-LID) has long remained uncertain. To clarify the physics of this problem, a mathematical model of Cu-LID was introduced in Paper I of this article. Within the model, kinetic precipitation simulations are interlinked with a Schottky junction model for electric behavior of metallic precipitates. As this approach enables simulating precipitation directly at the minority carrier lifetime level, the model is verified in this second part with a direct comparison to the corresponding degradation experiments and literature data. Convincing agreement is found with different doping and Cu concentrations as well as at increased temperature, and in the dark, both simulated degradation and measured degradation are very slow. In addition, modeled final lifetimes after illumination are very close to experimental final lifetimes, and a correlation with the final precipitate size is found. However, the model underestimates experimentally observed differences in the degradation rate at different illumination intensities. Nevertheless, the results of this work support the theory of Cu-LID as a precipitate formation process. Part of the results also imply that heterogeneous nucleation sites play a role during precipitate nucleation. The model reveals fundamental aspects of the physics of Cu-LID including how doping and heterogeneous nucleation site concentrations can considerably influence the final recombination activity.

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

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…

Past and future perspectives on mathematical models of tick-borne pathogens.

PubMed

Norman, R A; Worton, A J; Gilbert, L

2016-06-01

Ticks are vectors of pathogens which are important both with respect to human health and economically. They have a complex life cycle requiring several blood meals throughout their life. These blood meals take place on different individual hosts and potentially on different host species. Their life cycle is also dependent on environmental conditions such as the temperature and habitat type. Mathematical models have been used for the more than 30 years to help us understand how tick dynamics are dependent on these environmental factors and host availability. In this paper, we review models of tick dynamics and summarize the main results. This summary is split into two parts, one which looks at tick dynamics and one which looks at tick-borne pathogens. In general, the models of tick dynamics are used to determine when the peak in tick densities is likely to occur in the year and how that changes with environmental conditions. The models of tick-borne pathogens focus more on the conditions under which the pathogen can persist and how host population densities might be manipulated to control these pathogens. In the final section of the paper, we identify gaps in the current knowledge and future modelling approaches. These include spatial models linked to environmental information and Geographic Information System maps, and development of new modelling techniques which model tick densities per host more explicitly.

The Ability of Students’ Mathematical Proof in Determining the Validity of Argument Reviewed from Gender Differences

NASA Astrophysics Data System (ADS)

Feriyanto

2018-01-01

This research aims to describe the ability of students’ mathematical proof in determining the validity of argument reviewed from gender differences. The subjects of this research were one male and one female student of the fifth semester of Mathematic Education study program. The subjects were selected based on the highest mathematics ability which was assesed from their previous assignments and tests. In addition, the communication ability of the subjects was also considered in order to facilitate the researcher in conducting interviews. Based on the result of the test with direct and indirect proof, it could be concluded that the subjects were able to: 1) mention all facts/premises and write about what should be shown (conclusion) in direct proof and write additional premise in indirect proof; 2) connect facts/premises to concepts which must be mastered; 3) use equivalent concept to manipulate and organize the proof; 4) use the concept of syllogism and tollens mode to obtain the desired conclusion; 5) construct mathematical evidence systematically, and logically; 6) complement the reason for each step appropriately. The difference was that the male subject wrote the final conclusion, while the female subject did not write the final conclusion on the proof.

Views from the Field on Needs in Precollege Science, Mathematics, and Social Studies Education.

ERIC Educational Resources Information Center

Buccino, Alphonse; Evans, Paul L.

1981-01-01

Summarizes the findings reported in the final volume of an eight-volume series sponsored by the National Science Foundation that deal with the key elements responsible for influencing and shaping science, mathematics, and social studies education at the precollege level. (CS)

Proof Mapping

ERIC Educational Resources Information Center

Linares, Leanne A.; Smith, Phil R.

2009-01-01

A geometry textbook or mathematics journal that prints all the work that mathematicians use as they generate proofs of mathematical results would be rare indeed. The false starts, the tentative conjectures, and the arguments that led nowhere--these are conveniently omitted; only the final successful product is presented to the world. To students…

Research on Mathematical Techniques in Psychology. Final Report.

ERIC Educational Resources Information Center

Gulliksen, Harold

Mathematical techniques are developed for studying psychological problems in three fields: (1) psychological scaling, (2) learning and concept formation, and (3) mental measurement. Psychological scaling procedures are demonstrated to be useful in many areas, ranging from sensory discrimination of physical stimuli, such as colors, sounds, etc.,…

An Improved Cochlea Model with a General User Interface

NASA Astrophysics Data System (ADS)

Duifhuis, H.; Kruseman, J. M.; van Hengel, P. W. J.

2003-02-01

We have developed a flexible 1D cochlea model to test hypotheses and data against physical and mathematical constraints. The model is flexible in the sense that several linear and nonlinear model characteristics can be selected, and different boundary conditions can be tested. The software model runs at a reasonable speed at a modern PC. As an example, we will show the results of the model in comparison with the systematic study of the phase behavior (group delay) of distortion product otoacoustic emissions (DPOAEs) in the guinea pig (S. Schneider, V. Prijs and R. Schoonhoven, [9]). We also will demonstrate the effects of some common non-physical boundary conditions. Finally, we briefly indicate that this model of the auditory periphery provides a superior front end for an ASR (automatic speech recognition)-system.

ICT media design for higher grade of elementary school mathematics learning using CS6 program

NASA Astrophysics Data System (ADS)

Zainil, M.; Prahmana, R. C. I.; Helsa, Y.; Hendri, S.

2017-12-01

Technological innovation contributes to the emerging of new possibilities to change the learning process. The development of technology could bring the higher quality of education through the integration of technology in the learning. The purpose of this research is to create an interactive multimedia using CS6 program for mathematics learning in higher grade of elementary school. It was a development research using ADDIE model which consists of analysis, design, and evaluation stages. It has successfully developed interactive multimedia in a form of learning CD used in the material of plane figures and solid figures. The prototype has been validated and then tested for the 4th grade of elementary schools. Two schools were involved and the students taught by utilizing the prototype, and then, in the end of learning, they are examined to determine the learning result. There were 72% of the students passed the examination as they classified at good and excellent categories. Finally, the use of CS6 program is promising to help the students learning plane and solid figure in mathematics learning.

Fuzzy Performance between Surface Fitting and Energy Distribution in Turbulence Runner

PubMed Central

Liang, Zhongwei; Liu, Xiaochu; Ye, Bangyan; Brauwer, Richard Kars

2012-01-01

Because the application of surface fitting algorithms exerts a considerable fuzzy influence on the mathematical features of kinetic energy distribution, their relation mechanism in different external conditional parameters must be quantitatively analyzed. Through determining the kinetic energy value of each selected representative position coordinate point by calculating kinetic energy parameters, several typical algorithms of complicated surface fitting are applied for constructing microkinetic energy distribution surface models in the objective turbulence runner with those obtained kinetic energy values. On the base of calculating the newly proposed mathematical features, we construct fuzzy evaluation data sequence and present a new three-dimensional fuzzy quantitative evaluation method; then the value change tendencies of kinetic energy distribution surface features can be clearly quantified, and the fuzzy performance mechanism discipline between the performance results of surface fitting algorithms, the spatial features of turbulence kinetic energy distribution surface, and their respective environmental parameter conditions can be quantitatively analyzed in detail, which results in the acquirement of final conclusions concerning the inherent turbulence kinetic energy distribution performance mechanism and its mathematical relation. A further turbulence energy quantitative study can be ensured. PMID:23213287

Mathematical investigation of tsunami-like long waves interaction with submerge dike of different thickness

NASA Astrophysics Data System (ADS)

Zhiltsov, Konstantin; Kostyushin, Kirill; Kagenov, Anuar; Tyryshkin, Ilya

2017-11-01

This paper presents a mathematical investigation of the interaction of a long tsunami-type wave with a submerge dike. The calculations were performed by using the freeware package OpenFOAM. Unsteady two-dimensional Navier-Stokes equations were used for mathematical modeling of incompressible two-phase medium. The Volume of Fluid (VOF) method is used to capture the free surface of a liquid. The effects caused by long wave of defined amplitude motion through a submerged dike of varying thickness were discussed in detail. Numerical results show that after wave passing through the barrier, multiple vortex structures were formed behind. Intensity of vortex depended on the size of the barrier. The effectiveness of the submerge barrier was estimated by evaluating the wave reflection and transmission coefficients using the energy integral method. Then, the curves of the dependences of the reflection and transmission coefficients were obtained for the interaction of waves with the dike. Finally, it was confirmed that the energy of the wave could be reduced by more than 50% when it passed through the barrier.

Parameters of Models of Structural Transformations in Alloy Steel Under Welding Thermal Cycle

NASA Astrophysics Data System (ADS)

Kurkin, A. S.; Makarov, E. L.; Kurkin, A. B.; Rubtsov, D. E.; Rubtsov, M. E.

2017-05-01

A mathematical model of structural transformations in an alloy steel under the thermal cycle of multipass welding is suggested for computer implementation. The minimum necessary set of parameters for describing the transformations under heating and cooling is determined. Ferritic-pearlitic, bainitic and martensitic transformations under cooling of a steel are considered. A method for deriving the necessary temperature and time parameters of the model from the chemical composition of the steel is described. Published data are used to derive regression models of the temperature ranges and parameters of transformation kinetics in alloy steels. It is shown that the disadvantages of the active visual methods of analysis of the final phase composition of steels are responsible for inaccuracy and mismatch of published data. The hardness of a specimen, which correlates with some other mechanical properties of the material, is chosen as the most objective and reproducible criterion of the final phase composition. The models developed are checked by a comparative analysis of computational results and experimental data on the hardness of 140 alloy steels after cooling at various rates.

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.

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 Modeling in Mathematics Education

ERIC Educational Resources Information Center

Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant

2016-01-01

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

Vaccine approaches to malaria control and elimination: Insights from mathematical models.

PubMed

White, Michael T; Verity, Robert; Churcher, Thomas S; Ghani, Azra C

2015-12-22

A licensed malaria vaccine would provide a valuable new tool for malaria control and elimination efforts. Several candidate vaccines targeting different stages of the malaria parasite's lifecycle are currently under development, with one candidate, RTS,S/AS01 for the prevention of Plasmodium falciparum infection, having recently completed Phase III trials. Predicting the public health impact of a candidate malaria vaccine requires using clinical trial data to estimate the vaccine's efficacy profile--the initial efficacy following vaccination and the pattern of waning of efficacy over time. With an estimated vaccine efficacy profile, the effects of vaccination on malaria transmission can be simulated with the aid of mathematical models. Here, we provide an overview of methods for estimating the vaccine efficacy profiles of pre-erythrocytic vaccines and transmission-blocking vaccines from clinical trial data. In the case of RTS,S/AS01, model estimates from Phase II clinical trial data indicate a bi-phasic exponential profile of efficacy against infection, with efficacy waning rapidly in the first 6 months after vaccination followed by a slower rate of waning over the next 4 years. Transmission-blocking vaccines have yet to be tested in large-scale Phase II or Phase III clinical trials so we review ongoing work investigating how a clinical trial might be designed to ensure that vaccine efficacy can be estimated with sufficient statistical power. Finally, we demonstrate how parameters estimated from clinical trials can be used to predict the impact of vaccination campaigns on malaria using a mathematical model of malaria transmission. Copyright © 2015 Elsevier Ltd. All rights reserved.

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.

Coaching in Early Mathematics.

PubMed

Germeroth, Carrie; Sarama, Julie

2017-01-01

Falling scores in math have prompted a renewed interest in math instruction at early ages. By their own admission, early childhood educators are generally underprepared and not always comfortable teaching math. Professional development (PD) in early mathematics is widely considered a main way to increase teachers' skills and efficacy (e.g., Guskey, 2000; Hyson & Woods, 2014; Munby, Russell, & Martin, 2001; Piasta, Logan, Pelatti, Capps, & Petrill, 2015; Richardson & Placier, 2001; Sarama, Clements, Wolfe, & Spitler, 2016; Sarama & DiBiase, 2004; Zaslow, 2014). However, it has been documented that stand-alone PD is not as effective in changing practice (e.g., Biancarosa & Bryk, 2011; Garet et al., 2008; Guskey, 2000; Hyson & Woods, 2014; Institute of Medicine and National Research Council, 2015; Joyce & Showers, 2002; Zaslow, 2014). Site-embedded ongoing support in the form of coaching or mentoring has been shown to be critical for successful implementation (Neuman & Cunningham, 2009; Powell, Diamond, Burchinal, & Koehler, 2010). In this chapter, we describe coaching models and abstract characteristics of effective coaching from the research. With this background, we provide an in-depth view of the coaching aspect of two large empirical studies in early mathematics. We introduce the theoretical framework from which the coaching models for these projects were developed and describe the research on which they were based. We then summarize how the planned models were instantiated and challenges to their implementation within each project. In the final section, we summarize what we have learned and described implications and challenges for the field. © 2017 Elsevier Inc. All rights reserved.

Numerical approximation abilities correlate with and predict informal but not formal mathematics abilities.

PubMed

Libertus, Melissa E; Feigenson, Lisa; Halberda, Justin

2013-12-01

Previous research has found a relationship between individual differences in children's precision when nonverbally approximating quantities and their school mathematics performance. School mathematics performance emerges from both informal (e.g., counting) and formal (e.g., knowledge of mathematics facts) abilities. It remains unknown whether approximation precision relates to both of these types of mathematics abilities. In the current study, we assessed the precision of numerical approximation in 85 3- to 7-year-old children four times over a span of 2years. In addition, at the final time point, we tested children's informal and formal mathematics abilities using the Test of Early Mathematics Ability (TEMA-3). We found that children's numerical approximation precision correlated with and predicted their informal, but not formal, mathematics abilities when controlling for age and IQ. These results add to our growing understanding of the relationship between an unlearned nonsymbolic system of quantity representation and the system of mathematics reasoning that children come to master through instruction. Copyright © 2013 Elsevier Inc. All rights reserved.

Outsourcing and scheduling for a two-machine flow shop with release times

NASA Astrophysics Data System (ADS)

Ahmadizar, Fardin; Amiri, Zeinab

2018-03-01

This article addresses a two-machine flow shop scheduling problem where jobs are released intermittently and outsourcing is allowed. The first operations of outsourced jobs are processed by the first subcontractor, they are transported in batches to the second subcontractor for processing their second operations, and finally they are transported back to the manufacturer. The objective is to select a subset of jobs to be outsourced, to schedule both the in-house and the outsourced jobs, and to determine a transportation plan for the outsourced jobs so as to minimize the sum of the makespan and the outsourcing and transportation costs. Two mathematical models of the problem and several necessary optimality conditions are presented. A solution approach is then proposed by incorporating the dominance properties with an ant colony algorithm. Finally, computational experiments are conducted to evaluate the performance of the models and solution approach.

A 3-D Mathematical Model to Identify Organ-Specific Risks in Rats During Thermal Stress

DTIC Science & Technology

2013-01-01

1800. This response is anticipatory of the active period when feeding, grooming, and other behaviors are manifested during the normal circadian cycle... Sports Exerc 37: 1338–1344, 2005. 11. Casa DJ, Armstrong LE, Ganio MS, Yeargin SW. Exertional heat stroke in competitive athletes. Curr Sports Med Rep 4...an integra- tive view of the final common pathway. Scand J Med Sci Sports 21: 742–748, 2011. 25. Even PC, Rolland V, Roseau S, Bouthegourd JC, Tome D

The study on the Layout of the Charging Station in Chengdu

NASA Astrophysics Data System (ADS)

Cai, yun; Zhang, wanquan; You, wei; Mao, pan

2018-03-01

In this paper, the comprehensive analysis of the factors affecting the layout of the electric car, considering the principle of layout of the charging station. Using queuing theory in operational research to establish mathematical model and basing on the principle of saving resource and convenient owner to optimize site number. Combining the theory of center to determine the service radius, Using the Gravity method to determine the initial location, Finally using the method of center of gravity to locate the charging station’s location.

Color Addition and Subtraction Apps

NASA Astrophysics Data System (ADS)

Ruiz, Frances; Ruiz, Michael J.

2015-10-01

Color addition and subtraction apps in HTML5 have been developed for students as an online hands-on experience so that they can more easily master principles introduced through traditional classroom demonstrations. The evolution of the additive RGB color model is traced through the early IBM color adapters so that students can proceed step by step in understanding mathematical representations of RGB color. Finally, color addition and subtraction are presented for the X11 colors from web design to illustrate yet another real-life application of color mixing.

Development of a GA-Fuzzy-Immune PID Controller with Incomplete Derivation for Robot Dexterous Hand

PubMed Central

Liu, Xin-hua; Chen, Xiao-hu; Zheng, Xian-hua; Li, Sheng-peng; Wang, Zhong-bin

2014-01-01

In order to improve the performance of robot dexterous hand, a controller based on GA-fuzzy-immune PID was designed. The control system of a robot dexterous hand and mathematical model of an index finger were presented. Moreover, immune mechanism was applied to the controller design and an improved approach through integration of GA and fuzzy inference was proposed to realize parameters' optimization. Finally, a simulation example was provided and the designed controller was proved ideal. PMID:25097881

Collaborative Research: Atmospheric Pressure Microplasma Chemistry-Photon Synergies Final Report

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

Graves, David

Combining the effects of low temperature, atmospheric pressure microplasmas and microplasma photon sources shows greatly expanded range of applications of each of them. The plasma sources create active chemical species and these can be activated further by addition of photons and associated photochemistry. There are many ways to combine the effects of plasma chemistry and photochemistry, especially if there are multiple phases present. The project combines construction of appropriate test experimental systems, various spectroscopic diagnostics and mathematical modeling.

Flight dynamics research for highly agile aircraft

NASA Technical Reports Server (NTRS)

Nguyen, Luat T.

1989-01-01

This paper highlights recent results of research conducted at the NASA Langley Research Center as part of a broad flight dynamics program aimed at developing technology that will enable future combat aircraft to achieve greatly enhanced agility capability at subsonic combat conditions. Studies of advanced control concepts encompassing both propulsive and aerodynamic approaches are reviewed. Dynamic stall phenomena and their potential impact on maneuvering performance and stability are summarized. Finally, issues of mathematical modeling of complex aerodynamics occurring during rapid, large amplitude maneuvers are discussed.

Elementary School Mathematics Priorities

ERIC Educational Resources Information Center

Wilson, W. Stephen

2009-01-01

This article first describes some of the basic skills and knowledge that a solid elementary school mathematics foundation requires. It then elaborates on several points germane to these practices. These are then followed with a discussion and conclude with final comments and suggestions for future research. The article sets out the five…

The Lottery Is a Mathematics Powerball

ERIC Educational Resources Information Center

Lim, Vivian; Rubel, Laurie; Shookhoff, Lauren; Sullivan, Mathew; Williams, Sarah

2016-01-01

The lottery has rich potential for mathematical explorations. It serves as a real-world context to explore concepts of permutations, combinations, sample space, and probability in terms of making sense of the lottery games. The lottery offers additional possibilities in terms of scaling, data analysis, and spatial analysis. Finally, by readily…

The Ideology of Certainty in Mathematics Education.

ERIC Educational Resources Information Center

Borba, Marcelo C.; Skovsmose, Ole

1997-01-01

Presents one aspect that makes mathematics the final word in many discussions, the ideology of certainty. Argues that one way of challenging the ideology of certainty is to change classroom practice by introducing a landscape of discussion on chaotic nature where relativity, provisional starting points, different points of view, and uncertainty…

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

The influence of naphthaleneacetic acid (NAA) and coumarin on flavonoid production by fungus Phellinus sp.: modeling of production kinetic profiles.

PubMed

Ma, Xiao-Kui; Li, Le; Peterson, Eric Charles; Ruan, Tingting; Duan, Xiaoyi

2015-11-01

For the purpose of improving the fungal production of flavonoids, the influence of naphthaleneacetic acid (NAA) and coumarin on flavonoid production by fungus Phellinus sp. P0988 was investigated by developing the corresponding kinetics of flavonoid production in a 7-L bioreactor. Phellinus sp. was confirmed to form flavonoids in pellets and broth when cultivated in basic medium, and the optimum concentration of NAA and coumarin in medium for flavonoid production were determined to be 0.03 and 0.02 g/L, respectively. The developed unstructured mathematical models were in good agreement with the experimental results with respect to flavonoid production kinetic profiles with NAA and coumarin supplementation at optimum levels and revealed significant accuracy in terms of statistical consistency and robustness. Analysis of these kinetic processes indicated that NAA and coumarin supplementations imposed a stronger positive influence on flavonoid production and substrate consumption compared to their effects on cell growth. The separate addition of NAA and coumarin resulted in enhancements in final product accumulation and productivity, achieving final flavonoid concentrations of 3.60 and 2.75 g/L, respectively, and glucose consumption showed a significant decrease compared to the non-supplemented control as well. Also, the separate presence of NAA and coumarin respectively decreased maintenance coefficients (M s) from 2.48 in the control to 1.39 and 0.22, representing decreases of 43.9 and 91.1 %, respectively. The current study is the first known application of mathematical kinetic models to explore the influence of medium components adding on flavonoid production by fungi.

Mathematical model reveals role of nucleotide signaling in airway surface liquid homeostasis and its dysregulation in cystic fibrosis

PubMed Central

Sandefur, Conner I.; Boucher, Richard C.; Elston, Timothy C.

2017-01-01

Mucociliary clearance is composed of three components (i.e., mucin secretion, airway surface hydration, and ciliary-activity) which function coordinately to clear inhaled microbes and other foreign particles from airway surfaces. Airway surface hydration is maintained by water fluxes driven predominantly by active chloride and sodium ion transport. The ion channels that mediate electrogenic ion transport are regulated by extracellular purinergic signals that signal through G protein-coupled receptors. These purinoreceptors and the signaling pathways they activate have been identified as possible therapeutic targets for treating lung disease. A systems-level description of airway surface liquid (ASL) homeostasis could accelerate development of such therapies. Accordingly, we developed a mathematical model to describe the dynamic coupling of ion and water transport to extracellular purinergic signaling. We trained our model from steady-state and time-dependent experimental measurements made using normal and cystic fibrosis (CF) cultured human airway epithelium. To reproduce CF conditions, reduced chloride secretion, increased potassium secretion, and increased sodium absorption were required. The model accurately predicted ASL height under basal normal and CF conditions and the collapse of surface hydration due to the accelerated nucleotide metabolism associated with CF exacerbations. Finally, the model predicted a therapeutic strategy to deliver nucleotide receptor agonists to effectively rehydrate the ASL of CF airways. PMID:28808008

The evolutionary dynamics of receptor binding avidity in influenza A: a mathematical model for a new antigenic drift hypothesis

PubMed Central

Yuan, Hsiang-Yu; Koelle, Katia

2013-01-01

The most salient feature of influenza evolution in humans is its antigenic drift. This process is characterized by structural changes in the virus's B-cell epitopes and ultimately results in the ability of the virus to evade immune recognition and thereby reinfect previously infected hosts. Until recently, amino acid substitutions in epitope regions of the viral haemagglutinin were thought to be positively selected for their ability to reduce antibody binding and therefore were thought to be responsible for driving antigenic drift. However, a recent hypothesis put forward by Hensley and co-workers posits that cellular receptor binding avidity is the dominant phenotype under selection, with antigenic drift being a side effect of these binding avidity changes. Here, we present a mathematical formulation of this new antigenic drift model and use it to show how rates of antigenic drift depend on epidemiological parameters. We further use the model to evaluate how two different vaccination strategies can impact antigenic drift rates and ultimately disease incidence levels. Finally, we discuss the assumptions present in the model formulation, predictions of the model, and future work that needs to be done to determine the consistency of this hypothesis with known patterns of influenza's genetic and antigenic evolution. PMID:23382426

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.

Threshold for extinction and survival in stochastic tumor immune system

NASA Astrophysics Data System (ADS)

Li, Dongxi; Cheng, Fangjuan

2017-10-01

This paper mainly investigates the stochastic character of tumor growth and extinction in the presence of immune response of a host organism. Firstly, the mathematical model describing the interaction and competition between the tumor cells and immune system is established based on the Michaelis-Menten enzyme kinetics. Then, the threshold conditions for extinction, weak persistence and stochastic persistence of tumor cells are derived by the rigorous theoretical proofs. Finally, stochastic simulation are taken to substantiate and illustrate the conclusion we have derived. The modeling results will be beneficial to understand to concept of immunoediting, and develop the cancer immunotherapy. Besides, our simple theoretical model can help to obtain new insight into the complexity of tumor growth.

Some further developments in the dynamic modelling and control of the large angle magnetic suspension test fixture

NASA Technical Reports Server (NTRS)

Britcher, Colin P.; Foster, Lucas E.

1994-01-01

A small-scale laboratory magnetic suspension system, the Large Angle Magnetic Suspension Test Fixture (LAMSTF) has been constructed at NASA Langley Research Center. This paper first presents some recent developments in the mathematical modelling of the system, particularly in the area of eddy current effects. It is shown that these effects are significant, but may be amenable to modelling and measurement. Next, a theoretical framework is presented, together with a comparison of computed and experimental data. Finally, some control aspects are discussed, together with illustration that the major design objective of LAMSTF - a controlled 360 deg rotation about the vertical axis, has been accomplished.

Complex optimization for big computational and experimental neutron datasets

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

Bao, Feng; Oak Ridge National Lab.; Archibald, Richard

Here, we present a framework to use high performance computing to determine accurate solutions to the inverse optimization problem of big experimental data against computational models. We demonstrate how image processing, mathematical regularization, and hierarchical modeling can be used to solve complex optimization problems on big data. We also demonstrate how both model and data information can be used to further increase solution accuracy of optimization by providing confidence regions for the processing and regularization algorithms. Finally, we use the framework in conjunction with the software package SIMPHONIES to analyze results from neutron scattering experiments on silicon single crystals, andmore » refine first principles calculations to better describe the experimental data.« less

Complex optimization for big computational and experimental neutron datasets

DOE PAGES

Bao, Feng; Oak Ridge National Lab.; Archibald, Richard; ...

2016-11-07

Here, we present a framework to use high performance computing to determine accurate solutions to the inverse optimization problem of big experimental data against computational models. We demonstrate how image processing, mathematical regularization, and hierarchical modeling can be used to solve complex optimization problems on big data. We also demonstrate how both model and data information can be used to further increase solution accuracy of optimization by providing confidence regions for the processing and regularization algorithms. Finally, we use the framework in conjunction with the software package SIMPHONIES to analyze results from neutron scattering experiments on silicon single crystals, andmore » refine first principles calculations to better describe the experimental data.« less

Transmission Dinamics Model Of Dengue Fever

NASA Astrophysics Data System (ADS)

Debora; Rendy; Rahmi

2018-01-01

Dengue fever is an endemic disease that is transmitted through the Aedes aegypti mosquito vector. The disease is present in more than 100 countries in America, Africa, and Asia, especially tropical countries. Differential equations can be used to represent the spread of dengue virus occurring in time intervals and model in the form of mathematical models. The mathematical model in this study tries to represent the spread of dengue fever based on the data obtained and the assumptions used. The mathematical model used is a mathematical model consisting of Susceptible (S), Infected (I), Viruses (V) subpopulations. The SIV mathematical model is then analyzed to see the solution behaviour of the system.

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,…

Mathematical modeling of acid-base physiology

PubMed Central

Occhipinti, Rossana; Boron, Walter F.

2015-01-01

pH is one of the most important parameters in life, influencing virtually every biological process at the cellular, tissue, and whole-body level. Thus, for cells, it is critical to regulate intracellular pH (pHi) and, for multicellular organisms, to regulate extracellular pH (pHo). pHi regulation depends on the opposing actions of plasma-membrane transporters that tend to increase pHi, and others that tend to decrease pHi. In addition, passive fluxes of uncharged species (e.g., CO2, NH3) and charged species (e.g., HCO3− , NH4+) perturb pHi. These movements not only influence one another, but also perturb the equilibria of a multitude of intracellular and extracellular buffers. Thus, even at the level of a single cell, perturbations in acid-base reactions, diffusion, and transport are so complex that it is impossible to understand them without a quantitative model. Here we summarize some mathematical models developed to shed light onto the complex interconnected events triggered by acids-base movements. We then describe a mathematical model of a spherical cell–which to our knowledge is the first one capable of handling a multitude of buffer reaction–that our team has recently developed to simulate changes in pHi and pHo caused by movements of acid-base equivalents across the plasma membrane of a Xenopus oocyte. Finally, we extend our work to a consideration of the effects of simultaneous CO2 and HCO3− influx into a cell, and envision how future models might extend to other cell types (e.g., erythrocytes) or tissues (e.g., renal proximal-tubule epithelium) important for whole-body pH homeostasis. PMID:25617697

Collaborative Emission Reduction Model Based on Multi-Objective Optimization for Greenhouse Gases and Air Pollutants.

PubMed

Meng, Qing-chun; Rong, Xiao-xia; Zhang, Yi-min; Wan, Xiao-le; Liu, Yuan-yuan; Wang, Yu-zhi

2016-01-01

CO2 emission influences not only global climate change but also international economic and political situations. Thus, reducing the emission of CO2, a major greenhouse gas, has become a major issue in China and around the world as regards preserving the environmental ecology. Energy consumption from coal, oil, and natural gas is primarily responsible for the production of greenhouse gases and air pollutants such as SO2 and NOX, which are the main air pollutants in China. In this study, a mathematical multi-objective optimization method was adopted to analyze the collaborative emission reduction of three kinds of gases on the basis of their common restraints in different ways of energy consumption to develop an economic, clean, and efficient scheme for energy distribution. The first part introduces the background research, the collaborative emission reduction for three kinds of gases, the multi-objective optimization, the main mathematical modeling, and the optimization method. The second part discusses the four mathematical tools utilized in this study, which include the Granger causality test to analyze the causality between air quality and pollutant emission, a function analysis to determine the quantitative relation between energy consumption and pollutant emission, a multi-objective optimization to set up the collaborative optimization model that considers energy consumption, and an optimality condition analysis for the multi-objective optimization model to design the optimal-pole algorithm and obtain an efficient collaborative reduction scheme. In the empirical analysis, the data of pollutant emission and final consumption of energies of Tianjin in 1996-2012 was employed to verify the effectiveness of the model and analyze the efficient solution and the corresponding dominant set. In the last part, several suggestions for collaborative reduction are recommended and the drawn conclusions are stated.

Collaborative Emission Reduction Model Based on Multi-Objective Optimization for Greenhouse Gases and Air Pollutants

PubMed Central

Zhang, Yi-min; Wan, Xiao-le; Liu, Yuan-yuan; Wang, Yu-zhi

2016-01-01

CO2 emission influences not only global climate change but also international economic and political situations. Thus, reducing the emission of CO2, a major greenhouse gas, has become a major issue in China and around the world as regards preserving the environmental ecology. Energy consumption from coal, oil, and natural gas is primarily responsible for the production of greenhouse gases and air pollutants such as SO2 and NOX, which are the main air pollutants in China. In this study, a mathematical multi-objective optimization method was adopted to analyze the collaborative emission reduction of three kinds of gases on the basis of their common restraints in different ways of energy consumption to develop an economic, clean, and efficient scheme for energy distribution. The first part introduces the background research, the collaborative emission reduction for three kinds of gases, the multi-objective optimization, the main mathematical modeling, and the optimization method. The second part discusses the four mathematical tools utilized in this study, which include the Granger causality test to analyze the causality between air quality and pollutant emission, a function analysis to determine the quantitative relation between energy consumption and pollutant emission, a multi-objective optimization to set up the collaborative optimization model that considers energy consumption, and an optimality condition analysis for the multi-objective optimization model to design the optimal-pole algorithm and obtain an efficient collaborative reduction scheme. In the empirical analysis, the data of pollutant emission and final consumption of energies of Tianjin in 1996–2012 was employed to verify the effectiveness of the model and analyze the efficient solution and the corresponding dominant set. In the last part, several suggestions for collaborative reduction are recommended and the drawn conclusions are stated. PMID:27010658

The Modeling and Simulation of the Galvanic Coupling Intra-Body Communication via Handshake Channel.

PubMed

Li, Maoyuan; Song, Yong; Li, Wansong; Wang, Guangfa; Bu, Tianpeng; Zhao, Yufei; Hao, Qun

2017-04-14

Intra-body communication (IBC) is a technology using the conductive properties of the body to transmit signal, and information interaction by handshake is regarded as one of the important applications of IBC. In this paper, a method for modeling the galvanic coupling intra-body communication via handshake channel is proposed, while the corresponding parameters are discussed. Meanwhile, the mathematical model of this kind of IBC is developed. Finally, the validity of the developed model has been verified by measurements. Moreover, its characteristics are discussed and compared with that of the IBC via single body channel. Our results indicate that the proposed method will lay a foundation for the theoretical analysis and application of the IBC via handshake channel.

The Modeling and Simulation of the Galvanic Coupling Intra-Body Communication via Handshake Channel

PubMed Central

Li, Maoyuan; Song, Yong; Li, Wansong; Wang, Guangfa; Bu, Tianpeng; Zhao, Yufei; Hao, Qun

2017-01-01

Intra-body communication (IBC) is a technology using the conductive properties of the body to transmit signal, and information interaction by handshake is regarded as one of the important applications of IBC. In this paper, a method for modeling the galvanic coupling intra-body communication via handshake channel is proposed, while the corresponding parameters are discussed. Meanwhile, the mathematical model of this kind of IBC is developed. Finally, the validity of the developed model has been verified by measurements. Moreover, its characteristics are discussed and compared with that of the IBC via single body channel. Our results indicate that the proposed method will lay a foundation for the theoretical analysis and application of the IBC via handshake channel. PMID:28420119

A Markovian model for assessment of personnel hiring plans

NASA Technical Reports Server (NTRS)

Katz, L. G.

1974-01-01

As a result of the current economic environment, many organizations are having to operate with fewer resources. In the manpower area, these constraints have forced organizations to operate within well-defined hiring plans. Exceeding personnel ceilings is in most cases an intolerable situation. A mathematical model, based on the theory of Markov processes, is presented which can be used to assess the chances of success of personnel hiring plans. The model considers a plan to be successful if the final population size, at the end of the planning period, lies within a range specified by management. Although this model was developed to assess personnel hiring plans at the Goddard Space Flight Center, it is directly applicable wherever personnel hiring plans are used.

On the dynamics of HIV-AIDS and cryptosporidiosis

NASA Astrophysics Data System (ADS)

Okosun, K. O.; Khan, M. A.; Bonyah, E.; Ogunlade, S. T.

2017-08-01

This paper seeks to examine a mathematical model for cryptosporidiosis-HIV co-infection, in order to explore their synergistic relationship in the presence of prevention and treatment. Firstly, we investigate the sub-models and their steady states properties. They are found to be locally and globally stable. Thereafter, the steady states of the co-infected model waswere studied and itthey proved to exhibit backward bifurcation phenomena. Furthermore, we incorporate time-dependent controls in the model and apply Pontryagin's maximum principle, so that we can determine the best optimal strategy to control the co-infected diseases. Finally, we present the numerical results, which show that the best strategy to control co-infection is to combine all the five controls at the same time.

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 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.

A discrete mathematical model applied to genetic regulation and metabolic networks.

PubMed

Asenjo, A J; Ramirez, P; Rapaport, I; Aracena, J; Goles, E; Andrews, B A

2007-03-01

This paper describes the use of a discrete mathematical model to represent the basic mechanisms of regulation of the bacteria E. coli in batch fermentation. The specific phenomena studied were the changes in metabolism and genetic regulation when the bacteria use three different carbon substrates (glucose, glycerol, and acetate). The model correctly predicts the behavior of E. coli vis-à-vis substrate mixtures. In a mixture of glucose, glycerol, and acetate, it prefers glucose, then glycerol, and finally acetate. The model included 67 nodes; 28 were genes, 20 enzymes, and 19 regulators/biochemical compounds. The model represents both the genetic regulation and metabolic networks in an inrtegrated form, which is how they function biologically. This is one of the first attempts to include both of these networks in one model. Previously, discrete mathematical models were used only to describe genetic regulation networks. The study of the network dynamics generated 8 (2(3)) fixed points, one for each nutrient configuration (substrate mixture) in the medium. The fixed points of the discrete model reflect the phenotypes described. Gene expression and the patterns of the metabolic fluxes generated are described accurately. The activation of the gene regulation network depends basically on the presence of glucose and glycerol. The model predicts the behavior when mixed carbon sources are utilized as well as when there is no carbon source present. Fictitious jokers (Joker1, Joker2, and Repressor SdhC) had to be created to control 12 genes whose regulation mechanism is unknown, since glycerol and glucose do not act directly on the genes. The approach presented in this paper is particularly useful to investigate potential unknown gene regulation mechanisms; such a novel approach can also be used to describe other gene regulation situations such as the comparison between non-recombinant and recombinant yeast strain, producing recombinant proteins, presently under investigation in our group.

Multi-scale model of the ionosphere from the combination of modern space-geodetic satellite techniques - project status and first results

NASA Astrophysics Data System (ADS)

Schmidt, M.; Hugentobler, U.; Jakowski, N.; Dettmering, D.; Liang, W.; Limberger, M.; Wilken, V.; Gerzen, T.; Hoque, M.; Berdermann, J.

2012-04-01

Near real-time high resolution and high precision ionosphere models are needed for a large number of applications, e.g. in navigation, positioning, telecommunications or astronautics. Today these ionosphere models are mostly empirical, i.e., based purely on mathematical approaches. In the DFG project 'Multi-scale model of the ionosphere from the combination of modern space-geodetic satellite techniques (MuSIK)' the complex phenomena within the ionosphere are described vertically by combining the Chapman electron density profile with a plasmasphere layer. In order to consider the horizontal and temporal behaviour the fundamental target parameters of this physics-motivated approach are modelled by series expansions in terms of tensor products of localizing B-spline functions depending on longitude, latitude and time. For testing the procedure the model will be applied to an appropriate region in South America, which covers relevant ionospheric processes and phenomena such as the Equatorial Anomaly. The project connects the expertise of the three project partners, namely Deutsches Geodätisches Forschungsinstitut (DGFI) Munich, the Institute of Astronomical and Physical Geodesy (IAPG) of the Technical University Munich (TUM) and the German Aerospace Center (DLR), Neustrelitz. In this presentation we focus on the current status of the project. In the first year of the project we studied the behaviour of the ionosphere in the test region, we setup appropriate test periods covering high and low solar activity as well as winter and summer and started the data collection, analysis, pre-processing and archiving. We developed partly the mathematical-physical modelling approach and performed first computations based on simulated input data. Here we present information on the data coverage for the area and the time periods of our investigations and we outline challenges of the multi-dimensional mathematical-physical modelling approach. We show first results, discuss problems in modelling and possible solution strategies and finally, we address open questions.

Evaluating four mathematical models for nitrous oxide production by autotrophic ammonia-oxidizing bacteria.

PubMed

Ni, Bing-Jie; Yuan, Zhiguo; Chandran, Kartik; Vanrolleghem, Peter A; Murthy, Sudhir

2013-01-01

There is increasing evidence showing that ammonia-oxidizing bacteria (AOB) are major contributors to N(2)O emissions from wastewater treatment plants (WWTPs). Although the fundamental metabolic pathways for N(2)O production by AOB are now coming to light, the mechanisms responsible for N(2)O production by AOB in WWTP are not fully understood. Mathematical modeling provides a means for testing hypotheses related to mechanisms and triggers for N(2)O emissions in WWTP, and can then also become a tool to support the development of mitigation strategies. This study examined the ability of four mathematical model structures to describe two distinct mechanisms of N(2)O production by AOB. The production mechanisms evaluated are (1) N(2)O as the final product of nitrifier denitrification with NO(2)- as the terminal electron acceptor and (2) N(2)O as a byproduct of incomplete oxidation of hydroxylamine (NH(2)OH) to NO(2)-. The four models were compared based on their ability to predict N(2)O dynamics observed in three mixed culture studies. Short-term batch experimental data were employed to examine model assumptions related to the effects of (1) NH4+ concentration variations, (2) dissolved oxygen (DO) variations, (3) NO(2)- accumulations and (4) NH(2OH as an externally provided substrate. The modeling results demonstrate that all these models can generally describe the NH4+, NO(2)-, and NO(3)- data. However, none of these models were able to reproduce all measured N(2)O data. The results suggest that both the denitrification and NH(2)OH pathways may be involved in N(2)O production and could be kinetically linked by a competition for intracellular reducing equivalents. A unified model capturing both mechanisms and their potential interactions needs to be developed with consideration of physiological complexity. Copyright © 2012 Wiley Periodicals, Inc.

Mathematical model to analyze the dissolution behavior of metastable crystals or amorphous drug accompanied with a solid-liquid interface reaction.

PubMed

Hirai, Daiki; Iwao, Yasunori; Kimura, Shin-Ichiro; Noguchi, Shuji; Itai, Shigeru

2017-04-30

Metastable crystals and the amorphous state of poorly water-soluble drugs in solid dispersions (SDs), are subject to a solid-liquid interface reaction upon exposure to a solvent. The dissolution behavior during the solid-liquid interface reaction often shows that the concentration of drugs is supersaturated, with a high initial drug concentration compared with the solubility of stable crystals but finally approaching the latter solubility with time. However, a method for measuring the precipitation rate of stable crystals and/or the potential solubility of metastable crystals or amorphous drugs has not been established. In this study, a novel mathematical model that can represent the dissolution behavior of the solid-liquid interface reaction for metastable crystals or amorphous drug was developed and its validity was evaluated. The theory for this model was based on the Noyes-Whitney equation and assumes that the precipitation of stable crystals at the solid-liquid interface occurs through a first-order reaction. Moreover, two models were developed, one assuming that the surface area of the drug remains constant because of the presence of excess drug in the bulk and the other that the surface area changes in time-dependency because of agglomeration of the drug. SDs of Ibuprofen (IB)/polyvinylpyrrolidone (PVP) were prepared and their dissolution behaviors under non-sink conditions were fitted by the models to evaluate improvements in solubility. The model assuming time-dependent surface area showed good agreement with experimental values. Furthermore, by applying the model to the dissolution profile, parameters such as the precipitation rate and the potential solubility of the amorphous drug were successfully calculated. In addition, it was shown that the improvement in solubility with supersaturation was able to be evaluated quantitatively using this model. Therefore, this mathematical model would be a useful tool to quantitatively determine the supersaturation concentration of a metastable drug from solid dispersions. Copyright © 2017 Elsevier B.V. All rights reserved.

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…

Incentivizing advanced mathematics study at upper secondary level: the case of bonus points in Ireland

NASA Astrophysics Data System (ADS)

Treacy, Páraic Thomas

2018-04-01

Secondary level mathematics education in Ireland has recently experienced a period of significant change with the introduction of new curricula and the addition of an incentive to study upper secondary mathematics at the most advanced level (Higher Level). This incentive, typically referred to as 'bonus points', appears to have aided a significant increase in the number of students studying upper secondary mathematics at Higher Level. However, thematic analysis of interviews with experienced upper secondary mathematics examiners and exploration of mathematics diagnostic test data outlined in this paper suggest that the difficulty of the Higher Level upper secondary mathematics final examination in Ireland has reduced since the introduction of the bonus points initiative. The sharp increase in students attempting this examination coupled with a policy of maintaining a consistent proportion of students achieving passing grades was identified as a key reason for this possible reduction in standards.

Mathematical Modeling of Fluid Flow in a Water Physical Model of an Aluminum Degassing Ladle Equipped with an Impeller-Injector

NASA Astrophysics Data System (ADS)

Gómez, Eudoxio Ramos; Zenit, Roberto; Rivera, Carlos González; Trápaga, Gerardo; Ramírez-Argáez, Marco A.

2013-04-01

In this work, a 3D numerical simulation using a Euler-Euler-based model implemented into a commercial CFD code was used to simulate fluid flow and turbulence structure in a water physical model of an aluminum ladle equipped with an impeller for degassing treatment. The effect of critical process parameters such as rotor speed, gas flow rate, and the point of gas injection (conventional injection through the shaft vs a novel injection through the bottom of the ladle) on the fluid flow and vortex formation was analyzed with this model. The commercial CFD code PHOENICS 3.4 was used to solve all conservation equations governing the process for this two-phase fluid flow system. The mathematical model was reasonably well validated against experimentally measured liquid velocity and vortex sizes in a water physical model built specifically for this investigation. From the results, it was concluded that the angular speed of the impeller is the most important parameter in promoting better stirred baths and creating smaller and better distributed bubbles in the liquid. The pumping effect of the impeller is increased as the impeller rotation speed increases. Gas flow rate is detrimental to bath stirring and diminishes the pumping effect of the impeller. Finally, although the injection point was the least significant variable, it was found that the "novel" injection improves stirring in the ladle.

Meta-modelling, visualization and emulation of multi-dimensional data for virtual production intelligence

NASA Astrophysics Data System (ADS)

Schulz, Wolfgang; Hermanns, Torsten; Al Khawli, Toufik

2017-07-01

Decision making for competitive production in high-wage countries is a daily challenge where rational and irrational methods are used. The design of decision making processes is an intriguing, discipline spanning science. However, there are gaps in understanding the impact of the known mathematical and procedural methods on the usage of rational choice theory. Following Benjamin Franklin's rule for decision making formulated in London 1772, he called "Prudential Algebra" with the meaning of prudential reasons, one of the major ingredients of Meta-Modelling can be identified finally leading to one algebraic value labelling the results (criteria settings) of alternative decisions (parameter settings). This work describes the advances in Meta-Modelling techniques applied to multi-dimensional and multi-criterial optimization by identifying the persistence level of the corresponding Morse-Smale Complex. Implementations for laser cutting and laser drilling are presented, including the generation of fast and frugal Meta-Models with controlled error based on mathematical model reduction Reduced Models are derived to avoid any unnecessary complexity. Both, model reduction and analysis of multi-dimensional parameter space are used to enable interactive communication between Discovery Finders and Invention Makers. Emulators and visualizations of a metamodel are introduced as components of Virtual Production Intelligence making applicable the methods of Scientific Design Thinking and getting the developer as well as the operator more skilled.

Windfield and trajectory models for tornado-propelled objects. Final report

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

Redmann, G.H.; Radbill, J.R.; Marte, J.E.

1983-03-01

This is the final report of a three-phased research project to develop a six-degree-of-freedom mathematical model to predict the trajectories of tornado-propelled objects. The model is based on the meteorological, aerodynamic, and dynamic processes that govern the trajectories of missiles in a tornadic windfield. The aerodynamic coefficients for the postulated missiles were obtained from full-scale wind tunnel tests on a 12-inch pipe and car and from drop tests. Rocket sled tests were run whereby the 12-inch pipe and car were injected into a worst-case tornado windfield in order to verify the trajectory model. To simplify and facilitate the use ofmore » the trajectory model for design applications without having to run the computer program, this report gives the trajectory data for NRC-postulated missiles in tables based on given variables of initial conditions of injection and tornado windfield. Complete descriptions of the tornado windfield and trajectory models are presented. The trajectory model computer program is also included for those desiring to perform trajectory or sensitivity analyses beyond those included in the report or for those wishing to examine other missiles and use other variables.« 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…

Post-primary students' images of mathematics: findings from a survey of Irish ordinary level mathematics students

NASA Astrophysics Data System (ADS)

Lane, Ciara; Stynes, Martin; O'Donoghue, John

2016-10-01

A questionnaire survey was carried out as part of a PhD research study to investigate the image of mathematics held by post-primary students in Ireland. The study focused on students in fifth year of post-primary education studying ordinary level mathematics for the Irish Leaving Certificate examination - the final examination for students in second-level or post-primary education. At the time this study was conducted, ordinary level mathematics students constituted approximately 72% of Leaving Certificate students. Students were aged between 15 and 18 years. A definition for 'image of mathematics' was adapted from Lim and Wilson, with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. A questionnaire was composed incorporating 84 fixed-response items chosen from eight pre-established scales by Aiken, Fennema and Sherman, Gourgey and Schoenfeld. This paper focuses on the findings from the questionnaire survey. Students' images of mathematics are compared with regard to gender, type of post-primary school attended and prior mathematical achievement.

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.

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

NASA Astrophysics Data System (ADS)

Afrizal, Irfan Mufti; Dachlan, Jarnawi Afghani

2017-05-01

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

Mathematical modelling in 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.

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.

[Research on optimization of mathematical model of flow injection-hydride generation-atomic fluorescence spectrometry].

PubMed

Cui, Jian; Zhao, Xue-Hong; Wang, Yan; Xiao, Ya-Bing; Jiang, Xue-Hui; Dai, Li

2014-01-01

Flow injection-hydride generation-atomic fluorescence spectrometry was a widely used method in the industries of health, environmental, geological and metallurgical fields for the merit of high sensitivity, wide measurement range and fast analytical speed. However, optimization of this method was too difficult as there exist so many parameters affecting the sensitivity and broadening. Generally, the optimal conditions were sought through several experiments. The present paper proposed a mathematical model between the parameters and sensitivity/broadening coefficients using the law of conservation of mass according to the characteristics of hydride chemical reaction and the composition of the system, which was proved to be accurate as comparing the theoretical simulation and experimental results through the test of arsanilic acid standard solution. Finally, this paper has put a relation map between the parameters and sensitivity/broadening coefficients, and summarized that GLS volume, carrier solution flow rate and sample loop volume were the most factors affecting sensitivity and broadening coefficients. Optimizing these three factors with this relation map, the relative sensitivity was advanced by 2.9 times and relative broadening was reduced by 0.76 times. This model can provide a theoretical guidance for the optimization of the experimental conditions.

Novel 1,3,4-thiadiazoles inhibit colorectal cancer via blockade of IL-6/COX-2 mediated JAK2/STAT3 signals as evidenced through data-based mathematical modeling.

PubMed

Raj, Vinit; Bhadauria, Archana S; Singh, Ashok K; Kumar, Umesh; Rai, Amit; Keshari, Amit K; Kumar, Pranesh; Kumar, Dinesh; Maity, Biswanath; Nath, Sneha; Prakash, Anand; Ansari, Kausar M; Jat, Jawahar L; Saha, Sudipta

2018-03-23

We attempted a preclinical study using DMH-induced CRC rat model to evaluate the antitumor potential of our recently synthesized 1,3,4-thiadiazoles. The molecular insights were confirmed through ELISA, qRT-PCR and western blot analyses. The CRC condition was produced in response to COX-2 and IL-6 induced activation of JAK2/STAT3 which, in turn, was due to the enhanced phosphorylation of JAK2 and STAT3. The treatment with 1,3,4-thiadiazole derivatives (VR24 and VR27) caused the significant blockade of this signaling pathway. The behavior of STAT3 populations in response to IL-6 and COX-2 stimulations was further confirmed through data-based mathematical modeling using the quantitative western blot data. Finally, VR24 and VR27 restored the perturbed metabolites associated to DMH-induced CRC as evidenced through 1 H NMR based serum metabolomics. The tumor protecting ability of VR24 and VR27 was found comparable or to some degree better than the marketed chemotherapeutics, 5-flurouracil. Copyright © 2018 Elsevier Ltd. All rights reserved.

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.

Solution of non-steady-state substrate concentration in the action of biosensor response at mixed enzyme kinetics

NASA Astrophysics Data System (ADS)

Senthamarai, R.; Jana Ranjani, R.

2018-04-01

In this paper, a mathematical model of an amperometric biosensor at mixed enzyme kinetics and diffusion limitation in the case of substrate inhibition has been developed. The model is based on time dependent reaction diffusion equation containing a non -linear term related to non -Michaelis - Menten kinetics of the enzymatic reaction. Solution for the concentration of the substrate has been derived for all values of parameters using the homotopy perturbation method. All the approximate analytic expressions of substrate concentration are compared with simulation results using Scilab/Matlab program. Finally, we have given a satisfactory agreement between them.

Active controls: A look at analytical methods and associated tools

NASA Technical Reports Server (NTRS)

Newsom, J. R.; Adams, W. M., Jr.; Mukhopadhyay, V.; Tiffany, S. H.; Abel, I.

1984-01-01

A review of analytical methods and associated tools for active controls analysis and design problems is presented. Approaches employed to develop mathematical models suitable for control system analysis and/or design are discussed. Significant efforts have been expended to develop tools to generate the models from the standpoint of control system designers' needs and develop the tools necessary to analyze and design active control systems. Representative examples of these tools are discussed. Examples where results from the methods and tools have been compared with experimental data are also presented. Finally, a perspective on future trends in analysis and design methods is presented.

Final Commentary to the Cross-Disciplinary Thematic Special Series: Special Education and Mathematics Education

ERIC Educational Resources Information Center

Woodward, John; Tzur, Ron

2017-01-01

Four studies into characteristics and instructional needs of students with learning disabilities are summarized in this article. These studies are also reviewed in the wider context of mathematics intervention research in special education. These studies generally rely on qualitative methodology, and they are best understood in light of a…

Why Go Modular? A Review of Modular A-Level Mathematics.

ERIC Educational Resources Information Center

Taverner, Sally; Wright, Martin

1997-01-01

Attitudes, academic intentions, and attainment of students gaining a grade in A-level (Advanced level) mathematics were compared for those who followed a modular course and those assessed at the end of two years of study. Overall, the final grades of those assessed modularly were half a grade higher. (JOW)

Polyhedra in Poland

ERIC Educational Resources Information Center

Pawlikowski, Piotr

2007-01-01

Polish students learn about Platonic solids in the final year of secondary grammar school, but in such a way that few perceive the beauty of this branch of mathematics. An average student associates polyhedra with calculating lengths and angles in a cube, cuboid or pyramid. But for the author, 3-D geometry is the branch of mathematics that shows…

Impact Evaluation of Further Mathematics Curriculum in Nigeria

ERIC Educational Resources Information Center

Odili, Godwin Alo; Asuru, Vincent A.

2011-01-01

This research was a perceptual survey study carried out to determine whether the goals of Further Mathematics Curriculum (FMC) are being achieved at the Senior Secondary School level. The sample for the study consisted of 240 FM final year students, 45 FM teachers and 180 undergraduates who were selected by a multistage stratified random sampling…

Connecting Research to Teaching: Lenses for Examining Students' Mathematical Thinking

ERIC Educational Resources Information Center

Linsenmeier, Katherine A.; Sherin, Miriam; Walkoe, Janet; Mulligan, Martha

2014-01-01

The authors present three strategies for making sense of students' mathematical thinking. These lenses make the abstract idea of "making sense of student thinking" more manageable and concrete. We start by taking an initial look at a student's idea, going deeper, and finally looking across several ideas.

Picture Book Power: Connecting Children's Literature and Mathematics

ERIC Educational Resources Information Center

Shatzer, Joyce

2008-01-01

The author's experiences in using children's literature to engage her students in mathematics are described in this article. Using the book "The Wolf's Chicken Stew", the author's class participated in an interactive read-aloud, graphed favorite foods from the story, and finally followed a recipe to bake chocolate chip cookies. Reasons for making…

A Research on Future Mathematics Teachers' Instructional Explanations: The case of Algebra

ERIC Educational Resources Information Center

Guler, Mustafa; Celik, Derya

2016-01-01

In this study, explanations of future mathematics teachers about algebra were analysed according to the levels of understanding used by Kinach (2002). The participants for the study were 101 teacher candidates attending the final semester of a teacher training program. For data collection, a form containing four scenario-type items were…

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

ERIC Educational Resources Information Center

Gould, Heather; Wasserman, Nicholas H.

2014-01-01

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

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

ERIC Educational Resources Information Center

Jacobs, Gerrie J.; Durandt, Rina

2017-01-01

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

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.

Measuring Technological and Content Knowledge of Undergraduate Primary Teachers in Mathematics

NASA Astrophysics Data System (ADS)

Doukakis, Spyros; Chionidou-Moskofoglou, Maria; Mangina-Phelan, Eleni; Roussos, Petros

Twenty-five final-year undergraduate students of primary education who were attending a course on mathematics education participated in a research project during the 2009 spring semester. A repeated measures experimental design was used. Quantitative data on students' computer attitudes, self-efficacy in ICT, attitudes toward educational software, and self-efficacy in maths were collected. Data analysis showed a statistically non-significant improvement on participants' computer attitudes and self-efficacy in ICT and ES, but a significant improvement of self-efficacy in mathematics.

RADSOURCE. Volume 1, Part 1, A scaling factor prediction computer program technical manual and code validation: Final report

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

Vance, J.N.; Holderness, J.H.; James, D.W.

1992-12-01

Waste stream scaling factors based on sampling programs are vulnerable to one or more of the following factors: sample representativeness, analytic accuracy, and measurement sensitivity. As an alternative to sample analyses or as a verification of the sampling results, this project proposes the use of the RADSOURCE code, which accounts for the release of fuel-source radionuclides. Once the release rates of these nuclides from fuel are known, the code develops scaling factors for waste streams based on easily measured Cobalt-60 (Co-60) and Cesium-137 (Cs-137). The project team developed mathematical models to account for the appearance rate of 10CFR61 radionuclides inmore » reactor coolant. They based these models on the chemistry and nuclear physics of the radionuclides involved. Next, they incorporated the models into a computer code that calculates plant waste stream scaling factors based on reactor coolant gamma- isotopic data. Finally, the team performed special sampling at 17 reactors to validate the models in the RADSOURCE code.« less

How to build a course in mathematical-biological modeling: content and processes for knowledge and skill.

PubMed

Hoskinson, Anne-Marie

2010-01-01

Biological problems in the twenty-first century are complex and require mathematical insight, often resulting in mathematical models of biological systems. Building mathematical-biological models requires cooperation among biologists and mathematicians, and mastery of building models. A new course in mathematical modeling presented the opportunity to build both content and process learning of mathematical models, the modeling process, and the cooperative process. There was little guidance from the literature on how to build such a course. Here, I describe the iterative process of developing such a course, beginning with objectives and choosing content and process competencies to fulfill the objectives. I include some inductive heuristics for instructors seeking guidance in planning and developing their own courses, and I illustrate with a description of one instructional model cycle. Students completing this class reported gains in learning of modeling content, the modeling process, and cooperative skills. Student content and process mastery increased, as assessed on several objective-driven metrics in many types of assessments.

Comparison between sparsely distributed memory and Hopfield-type neural network models

NASA Technical Reports Server (NTRS)

Keeler, James D.

1986-01-01

The Sparsely Distributed Memory (SDM) model (Kanerva, 1984) is compared to Hopfield-type neural-network models. A mathematical framework for comparing the two is developed, and the capacity of each model is investigated. The capacity of the SDM can be increased independently of the dimension of the stored vectors, whereas the Hopfield capacity is limited to a fraction of this dimension. However, the total number of stored bits per matrix element is the same in the two models, as well as for extended models with higher order interactions. The models are also compared in their ability to store sequences of patterns. The SDM is extended to include time delays so that contextual information can be used to cover sequences. Finally, it is shown how a generalization of the SDM allows storage of correlated input pattern vectors.

A Comparison of Simplified Two-dimensional Flow Models Exemplified by Water Flow in a Cavern

NASA Astrophysics Data System (ADS)

Prybytak, Dzmitry; Zima, Piotr

2017-12-01

The paper shows the results of a comparison of simplified models describing a two-dimensional water flow in the example of a water flow through a straight channel sector with a cavern. The following models were tested: the two-dimensional potential flow model, the Stokes model and the Navier-Stokes model. In order to solve the first two, the boundary element method was employed, whereas to solve the Navier-Stokes equations, the open-source code library OpenFOAM was applied. The results of numerical solutions were compared with the results of measurements carried out on a test stand in a hydraulic laboratory. The measurements were taken with an ADV probe (Acoustic Doppler Velocimeter). Finally, differences between the results obtained from the mathematical models and the results of laboratory measurements were analysed.