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

PubMed

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

2016-01-01

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

A mathematical model for predicting photo-induced voltage and photostriction of PLZT with coupled multi-physics fields and its application

NASA Astrophysics Data System (ADS)

Huang, J. H.; Wang, X. J.; Wang, J.

2016-02-01

The primary purpose of this paper is to propose a mathematical model of PLZT ceramic with coupled multi-physics fields, e.g. thermal, electric, mechanical and light field. To this end, the coupling relationships of multi-physics fields and the mechanism of some effects resulting in the photostrictive effect are analyzed theoretically, based on which a mathematical model considering coupled multi-physics fields is established. According to the analysis and experimental results, the mathematical model can explain the hysteresis phenomenon and the variation trend of the photo-induced voltage very well and is in agreement with the experimental curves. In addition, the PLZT bimorph is applied as an energy transducer for a photovoltaic-electrostatic hybrid actuated micromirror, and the relation of the rotation angle and the photo-induced voltage is discussed based on the novel photostrictive mathematical model.

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

PubMed

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

2008-06-01

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

Performance analysis on free-piston Stirling cryocooler based on an idealized mathematical model

NASA Astrophysics Data System (ADS)

Guo, Y. X.; Chao, Y. J.; Gan, Z. H.; Li, S. Z.; Wang, B.

2017-12-01

Free-piston Stirling cryocoolers have extensive applications for its simplicity in structure and decrease in mass. However, the elimination of the motor and the crankshaft has made its thermodynamic characteristic different from that of Stirling cryocoolers with displacer driving mechanism. Therefore, an idealized mathematical model has been established, and with this model, an attempt has been made to analyse the thermodynamic characteristic and the performance of free-piston Stirling cryocooler. To certify this mathematical model, a comparison has been made between the model and a numerical model. This study reveals that due to the displacer damping force necessary for the production of cooling capacity, the free-piston Stirling cryocooler is inherently less efficient than Stirling cryocooler with displacer driving mechanism. Viscous flow resistance and incomplete heat transfer in the regenerator are the two major causes of the discrepancy between the results of the idealized mathematical model and the numerical model.

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

NASA Technical Reports Server (NTRS)

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

1974-01-01

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

A mathematical model for municipal solid waste management - A case study in Hong Kong.

PubMed

Lee, C K M; Yeung, C L; Xiong, Z R; Chung, S H

2016-12-01

With the booming economy and increasing population, the accumulation of waste has become an increasingly arduous issue and has aroused the attention from all sectors of society. Hong Kong which has a relative high daily per capita domestic waste generation rate in Asia has not yet established a comprehensive waste management system. This paper conducts a review of waste management approaches and models. Researchers highlight that mathematical models provide useful information for decision-makers to select appropriate choices and save cost. It is suggested to consider municipal solid waste management in a holistic view and improve the utilization of waste management infrastructures. A mathematical model which adopts integer linear programming and mixed integer programming has been developed for Hong Kong municipal solid waste management. A sensitivity analysis was carried out to simulate different scenarios which provide decision-makers important information for establishing Hong Kong waste management system. Copyright © 2016 Elsevier Ltd. All rights reserved.

A spatially explicit model for an Allee effect: why wolves recolonize so slowly in Greater Yellowstone.

PubMed

Hurford, Amy; Hebblewhite, Mark; Lewis, Mark A

2006-11-01

A reduced probability of finding mates at low densities is a frequently hypothesized mechanism for a component Allee effect. At low densities dispersers are less likely to find mates and establish new breeding units. However, many mathematical models for an Allee effect do not make a distinction between breeding group establishment and subsequent population growth. Our objective is to derive a spatially explicit mathematical model, where dispersers have a reduced probability of finding mates at low densities, and parameterize the model for wolf recolonization in the Greater Yellowstone Ecosystem (GYE). In this model, only the probability of establishing new breeding units is influenced by the reduced probability of finding mates at low densities. We analytically and numerically solve the model to determine the effect of a decreased probability in finding mates at low densities on population spread rate and density. Our results suggest that a reduced probability of finding mates at low densities may slow recolonization rate.

Mathematical model of biological order state or syndrome in traditional Chinese medicine: based on electromagnetic radiation within the human body.

PubMed

Han, Jinxiang; Huang, Jinzhao

2012-03-01

In this study, based on the resonator model and exciplex model of electromagnetic radiation within the human body, mathematical model of biological order state, also referred to as syndrome in traditional Chinese medicine, was established and expressed as: "Sy = v/ 1n(6I + 1)". This model provides the theoretical foundation for experimental research addressing the order state of living system, especially the quantitative research syndrome in traditional Chinese medicine.

Study of the Factors Affecting the Mathematics Achievement of Turkish Students According to Data from the Programme for International Student Assessment (PISA) 2012

ERIC Educational Resources Information Center

Güzeller, Cem Oktay; Eser, Mehmet Taha; Aksu, Gökhan

2016-01-01

This study attempts to determine the factors affecting the mathematics achievement of students in Turkey based on data from the Programme for International Student Assessment 2012 and the correct classification ratio of the established model. The study used mathematics achievement as a dependent variable while sex, having a study room, preparation…

A report on the zombie outbreak of 2009: how mathematics can save us (no, really)

PubMed Central

Smith?, Robert

2009-01-01

An outbreak of zombification wreaked havoc recently in Canada and the rest of the world. Mathematical models were created to establish the speed of zombie infection and evaluate potential scenarios for intervention, mainly because mathematicians don’t have anything better to do with their time. We review the development of these models and their effect on the undead. PMID:19969573

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

NASA Astrophysics Data System (ADS)

Easters, D. J.

2014-03-01

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

Connecting Biology and Mathematics: First Prepare the Teachers

PubMed Central

2010-01-01

Developing the connection between biology and mathematics is one of the most important ways to shift the paradigms of both established science disciplines. However, adding some mathematic content to biology or biology content to mathematics is not enough but must be accompanied by development of suitable pedagogical models. I propose a model of pedagogical mathematical biological content knowledge as a feasible starting point for connecting biology and mathematics in schools and universities. The process of connecting these disciplines should start as early as possible in the educational process, in order to produce prepared minds that will be able to combine both disciplines at graduate and postgraduate levels of study. Because teachers are a crucial factor in introducing innovations in education, the first step toward such a goal should be the education of prospective and practicing elementary and secondary school teachers. PMID:20810951

[Mathematic modeling and experimental validation of macrostate quality expression for multicomponent in Chinese materia medica].

PubMed

He, Fuyuan; Deng, Kaiwen; Shi, Jilian; Liu, Wenlong; Pi, Fengjuan

2011-11-01

To establish the unitive multicomponent quality system bridged macrostate mathematic model parameters of material quality and microstate component concentration for Chinese materia medica (CMM). According to law of biologic laws of thermodynamics, the state functions of macrostate qulity of the CMM were established. The validation test was carried out as modeling drug as alcohol extract of Radix Rhozome (AERR), their enthalpy of combustion was determined, and entropy and the capability of information by chromatographic fingerprint were assayed, and then the biologic apparent macrostate parameters were calculated. The biologic macrostate mathematic models, for the CMM quality controll, were established as parameters as the apparent equilibrium constant, biologic enthalpy, Gibbs free energy and biologic entropy etc. The total molarity for the 10 batchs of AERR were 0.153 4 mmol x g(-1) with 28.26% of RSD, with the average of apparent equilibrium constants, biologic enthalpy, Gibbs free energy and biologic entropy were 0.039 65, 8 005 J x mol(-1), -2.408 x 10(7) J x mol(-1) and - 8.078 x 10(4) J x K(-1) with RSD as 6.020%, 1.860%, 42.32% and 42.31%, respectively. The macrostate quality models for CMM can represent their intrinsic quality for multicomponent dynamic system such as the CMM, to manifest out as if the forest away from or tree near from to see it.

Will big data yield new mathematics? An evolving synergy with neuroscience

PubMed Central

Feng, S.; Holmes, P.

2016-01-01

New mathematics has often been inspired by new insights into the natural world. Here we describe some ongoing and possible future interactions among the massive data sets being collected in neuroscience, methods for their analysis and mathematical models of the underlying, still largely uncharted neural substrates that generate these data. We start by recalling events that occurred in turbulence modelling when substantial space-time velocity field measurements and numerical simulations allowed a new perspective on the governing equations of fluid mechanics. While no analogous global mathematical model of neural processes exists, we argue that big data may enable validation or at least rejection of models at cellular to brain area scales and may illuminate connections among models. We give examples of such models and survey some relatively new experimental technologies, including optogenetics and functional imaging, that can report neural activity in live animals performing complex tasks. The search for analytical techniques for these data is already yielding new mathematics, and we believe their multi-scale nature may help relate well-established models, such as the Hodgkin–Huxley equations for single neurons, to more abstract models of neural circuits, brain areas and larger networks within the brain. In brief, we envisage a closer liaison, if not a marriage, between neuroscience and mathematics. PMID:27516705

Will big data yield new mathematics? An evolving synergy with neuroscience.

PubMed

Feng, S; Holmes, P

2016-06-01

New mathematics has often been inspired by new insights into the natural world. Here we describe some ongoing and possible future interactions among the massive data sets being collected in neuroscience, methods for their analysis and mathematical models of the underlying, still largely uncharted neural substrates that generate these data. We start by recalling events that occurred in turbulence modelling when substantial space-time velocity field measurements and numerical simulations allowed a new perspective on the governing equations of fluid mechanics. While no analogous global mathematical model of neural processes exists, we argue that big data may enable validation or at least rejection of models at cellular to brain area scales and may illuminate connections among models. We give examples of such models and survey some relatively new experimental technologies, including optogenetics and functional imaging, that can report neural activity in live animals performing complex tasks. The search for analytical techniques for these data is already yielding new mathematics, and we believe their multi-scale nature may help relate well-established models, such as the Hodgkin-Huxley equations for single neurons, to more abstract models of neural circuits, brain areas and larger networks within the brain. In brief, we envisage a closer liaison, if not a marriage, between neuroscience and mathematics.

Thermal Network Modelling Handbook

NASA Technical Reports Server (NTRS)

1972-01-01

Thermal mathematical modelling is discussed in detail. A three-fold purpose was established: (1) to acquaint the new user with the terminology and concepts used in thermal mathematical modelling, (2) to present the more experienced and occasional user with quick formulas and methods for solving everyday problems, coupled with study cases which lend insight into the relationships that exist among the various solution techniques and parameters, and (3) to begin to catalog in an orderly fashion the common formulas which may be applied to automated conversational language techniques.

Mathematical model for steady state, simple ampholyte isoelectric focusing: Development, computer simulation and implementation

NASA Technical Reports Server (NTRS)

Palusinski, O. A.; Allgyer, T. T.

1979-01-01

The elimination of Ampholine from the system by establishing the pH gradient with simple ampholytes is proposed. A mathematical model was exercised at the level of the two-component system by using values for mobilities, diffusion coefficients, and dissociation constants representative of glutamic acid and histidine. The constants assumed in the calculations are reported. The predictions of the model and computer simulation of isoelectric focusing experiments are in direct importance to obtain Ampholine-free, stable pH gradients.

Numerical simulation of injection process of warm carbon dioxide into layer saturated with methane and its hydrate

NASA Astrophysics Data System (ADS)

Khasanov, M. K.; Stolpovsky, M. V.; Gimaltdinov, I. K.

2018-05-01

In this article, in a flat-one-dimensional approximation, a mathematical model is presented for injecting warm carbon dioxide into a methane hydrate formation of finite length. It is established that the model of formation of hydrate of carbon dioxide in the absence of an area saturated with methane and water, under certain parameters, leads to thermodynamic contradiction. The mathematical model of carbon dioxide injection with formation of the region saturated with methane and water is constructed.

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

NASA Technical Reports Server (NTRS)

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

2005-01-01

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

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

NASA Technical Reports Server (NTRS)

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

2003-01-01

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

A Mathematical Model for Continuous Fiber Reinforced Thermoplastic Composite in Melt Impregnation

NASA Astrophysics Data System (ADS)

Ren, Feng; Yu, Yang; Yang, Jianjun; Xin, Chunling; He, Yadong

2017-06-01

Through the combination of Reynolds equation and Darcy's law, a mathematical model was established to calculate the pressure distribution in wedge area, which contributed to the forecast effect of processing parameters on impregnation degree of the fiber bundle. The experiments were conducted to verify the capacity of the proposed model with satisfactory results, which means that the model is effective in predicting the influence of processing parameters on impregnation. From the mathematical model, it was known that the impregnation degree of the fiber bundle would be improved by increasing the processing temperature, number and radius of pins, or decreasing the pulling speed and the center distance of pins, which provided a possible solution to the difficulty of melt with high viscosity in melt impregnation and optimization of impregnation processing.

Study on the Influence of Building Materials on Indoor Pollutants and Pollution Sources

NASA Astrophysics Data System (ADS)

Wang, Yao

2018-01-01

The paper summarizes the achievements and problems of indoor air quality research at home and abroad. The pollutants and pollution sources in the room are analyzed systematically. The types of building materials and pollutants are also discussed. The physical and chemical properties and health effects of main pollutants were analyzed and studied. According to the principle of mass balance, the basic mathematical model of indoor air quality is established. Considering the release rate of pollutants and indoor ventilation, a mathematical model for predicting the concentration of indoor air pollutants is derived. The model can be used to analyze and describe the variation of pollutant concentration in indoor air, and to predict and calculate the concentration of pollutants in indoor air at a certain time. The results show that the mathematical model established in this study can be used to analyze and predict the variation law of pollutant concentration in indoor air. The evaluation model can be used to evaluate the impact of indoor air quality and evaluation of current situation. Especially in the process of building and interior decoration, through pre-evaluation, it can provide reliable design parameters for selecting building materials and determining ventilation volume.

Estimating Setup of Driven Piles into Louisiana Clayey Soils

DOT National Transportation Integrated Search

2009-11-15

Two types of mathematical models for pile setup prediction, the Skov-Denver model and the newly developed rate-based model, have been established from all the dynamic and static testing data, including restrikes of the production piles, restrikes, st...

Estimating setup of driven piles into Louisiana clayey soils.

DOT National Transportation Integrated Search

2010-11-15

Two types of mathematical models for pile setup prediction, the Skov-Denver model and the newly developed rate-based model, have been established from all the dynamic and static testing data, including restrikes of the production piles, restrikes, st...

Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.

PubMed

Said, Nadia; Engelhart, Michael; Kirches, Christian; Körkel, Stefan; Holt, Daniel V

2016-01-01

Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods.

[Relationship between HPLC fingerprint chromatogram and inhibitory effect on respiratory burst of rat PMN of leaves of crataegus].

PubMed

Liu, Rong-hua; Yu, Bo-yang; Chen, Lan-ying; Liu, Ji-hua; Shao, Feng; Ma, Zhi-lin; Yang, Ming

2008-08-01

To study the relationship between HPLC fingerprint chromatogram and inhibitory effect on respiratory burst of rat PMN of leaves of crataegus L. HPLC fingerprint peaks of different species of hawthorn leaves were isolated and used for the effective experiment on the respiratory burst of rat PMN. The mathematic models of the relationship between the area and the effect of fingerprint peaks were established. According to the mathematic models, the HPLC fingerprint were change into bioactive fingerprint (include effective fingerprint and potency fingerprint) with the helps of mathematics, chemometrics, computer program simulation and etc. The chromatogram-effect relationship of leaves of crataegus. on respiratory burst of rat PMN was established. According to this relationship, the activities of fourteen samples of leaves of crataegus. were forecasted. It was positive correlation between the expected value and the practical value. And the correlation coefficients was 0.968 (P < 0.01). An all-around evaluative system, which includes not only chemical identification but also effective evaluation for traditional Chinese medicine was established. It will provide a new idea for study on fingerprint chromatogram of traditional Chinese medicine.

The biology and mathematical modelling of glioma invasion: a review

PubMed Central

Talkenberger, K.; Seifert, M.; Klink, B.; Hawkins-Daarud, A.; Swanson, K. R.; Hatzikirou, H.

2017-01-01

Adult gliomas are aggressive brain tumours associated with low patient survival rates and limited life expectancy. The most important hallmark of this type of tumour is its invasive behaviour, characterized by a markedly phenotypic plasticity, infiltrative tumour morphologies and the ability of malignant progression from low- to high-grade tumour types. Indeed, the widespread infiltration of healthy brain tissue by glioma cells is largely responsible for poor prognosis and the difficulty of finding curative therapies. Meanwhile, mathematical models have been established to analyse potential mechanisms of glioma invasion. In this review, we start with a brief introduction to current biological knowledge about glioma invasion, and then critically review and highlight future challenges for mathematical models of glioma invasion. PMID:29118112

Quantitative assessment model for gastric cancer screening

PubMed Central

Chen, Kun; Yu, Wei-Ping; Song, Liang; Zhu, Yi-Min

2005-01-01

AIM: To set up a mathematic model for gastric cancer screening and to evaluate its function in mass screening for gastric cancer. METHODS: A case control study was carried on in 66 patients and 198 normal people, then the risk and protective factors of gastric cancer were determined, including heavy manual work, foods such as small yellow-fin tuna, dried small shrimps, squills, crabs, mothers suffering from gastric diseases, spouse alive, use of refrigerators and hot food, etc. According to some principles and methods of probability and fuzzy mathematics, a quantitative assessment model was established as follows: first, we selected some factors significant in statistics, and calculated weight coefficient for each one by two different methods; second, population space was divided into gastric cancer fuzzy subset and non gastric cancer fuzzy subset, then a mathematic model for each subset was established, we got a mathematic expression of attribute degree (AD). RESULTS: Based on the data of 63 patients and 693 normal people, AD of each subject was calculated. Considering the sensitivity and specificity, the thresholds of AD values calculated were configured with 0.20 and 0.17, respectively. According to these thresholds, the sensitivity and specificity of the quantitative model were about 69% and 63%. Moreover, statistical test showed that the identification outcomes of these two different calculation methods were identical (P>0.05). CONCLUSION: The validity of this method is satisfactory. It is convenient, feasible, economic and can be used to determine individual and population risks of gastric cancer. PMID:15655813

A mathematical model of nutrient influence on fungal competition.

PubMed

Jabed A Choudhury, M; M J Trevelyan, Philip; P Boswell, Graeme

2018-02-07

Fungi have a well-established role in nutrient cycling and are widely used as agents in biological control and in the remediation of polluted landscapes. Competition for resources between different fungal communities is common in these contexts and its outcome impacts on the success of such biotechnological applications. In this investigation a mathematical model is constructed to represent competition between two fungal colonies that have access to different resources. It is shown that the model equations display a multitude of travelling wave solutions and that the outcome of competition between two fungal biomasses can be controlled through the simple manipulation of the nutrient resources available to each. The model equations are also numerically integrated to illustrate the range of outcomes arising from fungal competition and these results are placed in context of established experimental observations. Copyright © 2017 Elsevier Ltd. All rights reserved.

Mathematical model for HIV spreads control program with ART treatment

NASA Astrophysics Data System (ADS)

Maimunah; Aldila, Dipo

2018-03-01

In this article, using a deterministic approach in a seven-dimensional nonlinear ordinary differential equation, we establish a mathematical model for the spread of HIV with an ART treatment intervention. In a simplified model, when no ART treatment is implemented, disease-free and the endemic equilibrium points were established analytically along with the basic reproduction number. The local stability criteria of disease-free equilibrium and the existing criteria of endemic equilibrium were analyzed. We find that endemic equilibrium exists when the basic reproduction number is larger than one. From the sensitivity analysis of the basic reproduction number of the complete model (with ART treatment), we find that the increased number of infected humans who follow the ART treatment program will reduce the basic reproduction number. We simulate this result also in the numerical experiment of the autonomous system to show how treatment intervention impacts the reduction of the infected population during the intervention time period.

Off-Road Mobility Research

DTIC Science & Technology

1967-09-01

Lewandowski, Thomas R. Magorian, H. T. McAdams, James N. Naylor, Walter F. Wood -ii- VJ-2330-G-2 Section 6 Stephen C. Cowin, Vito De Palma, Patrick M. Miller...providing detailed inputs to a)). 2. The establishing of the general framework for the Phenomenological Model. 3. A prelim.na ry methodology study using the...of current practice in mathematical modeling of vehicle-terrain systems. 2) The establishing of the framework for a vehicle-terrain dynamics model as

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

PubMed

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

2011-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

Comparing functional responses in predator-infected eco-epidemics models.

PubMed

Haque, Mainul; Rahman, Md Sabiar; Venturino, Ezio

2013-11-01

The current paper deals with the mathematical models of predator-prey system where a transmissible disease spreads among the predator species only. Four mathematical models are proposed and analysed with several popular predator functional responses in order to show the influence of functional response on eco-epidemic models. The existence, boundedness, uniqueness of solutions of all the models are established. Mathematical analysis including stability and bifurcation are observed. Comparison among the results of these models allows the general conclusion that relevant behaviour of the eco-epidemic predator-prey system, including switching of stability, extinction, persistence and oscillations for any species depends on four important parameters viz. the rate of infection, predator interspecies competition and the attack rate on susceptible predator. The paper ends with a discussion of the biological implications of the analytical and numerical results. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

The system-resonance approach in modeling genetic structures.

PubMed

Petoukhov, Sergey V

2016-01-01

The founder of the theory of resonance in structural chemistry Linus Pauling established the importance of resonance patterns in organization of living systems. Any living organism is a great chorus of coordinated oscillatory processes. From the formal point of view, biological organism is an oscillatory system with a great number of degrees of freedom. Such systems are studied in the theory of oscillations using matrix mathematics of their resonance characteristics. This study is devoted to a new approach for modeling genetically inherited structures and processes in living organisms using mathematical tools of the theory of resonances. This approach reveals hidden relationships in a number of genetic phenomena and gives rise to a new class of bio-mathematical models, which contribute to a convergence of biology with physics and informatics. In addition some relationships of molecular-genetic ensembles with mathematics of noise-immunity coding of information in modern communications technology are shown. Perspectives of applications of the phenomena of vibrational mechanics for modeling in biology are discussed. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

State and trait effects on individual differences in children's mathematical development.

PubMed

Bailey, Drew H; Watts, Tyler W; Littlefield, Andrew K; Geary, David C

2014-11-01

Substantial longitudinal relations between children's early mathematics achievement and their much later mathematics achievement are firmly established. These findings are seemingly at odds with studies showing that early educational interventions have diminishing effects on children's mathematics achievement across time. We hypothesized that individual differences in children's later mathematical knowledge are more an indicator of stable, underlying characteristics related to mathematics learning throughout development than of direct effects of early mathematical competency on later mathematical competency. We tested this hypothesis in two longitudinal data sets, by simultaneously modeling effects of latent traits (stable characteristics that influence learning across time) and states (e.g., prior knowledge) on children's mathematics achievement over time. Latent trait effects on children's mathematical development were substantially larger than state effects. Approximately 60% of the variance in trait mathematics achievement was accounted for by commonly used control variables, such as working memory, but residual trait effects remained larger than state effects. Implications for research and practice are discussed. © The Author(s) 2014.

State and Trait Effects on Individual Differences in Children's Mathematical Development

PubMed Central

Bailey, Drew H.; Watts, Tyler W.; Littlefield, Andrew K.; Geary, David C.

2015-01-01

Substantial longitudinal relations between children's early mathematics achievement and their much later mathematics achievement are firmly established. These findings are seemingly at odds with studies showing that early educational interventions have diminishing effects on children's mathematics achievement across time. We hypothesized that individual differences in children's later mathematical knowledge are more an indicator of stable, underlying characteristics related to mathematics learning throughout development than of direct effects of early mathematical competency on later mathematical competency. We tested this hypothesis in two longitudinal data sets, by simultaneously modeling effects of latent traits (stable characteristics that influence learning across time) and states (e.g., prior knowledge) on children's mathematics achievement over time. Latent trait effects on children's mathematical development were substantially larger than state effects. Approximately 60% of the variance in trait mathematics achievement was accounted for by commonly used control variables, such as working memory, but residual trait effects remained larger than state effects. Implications for research and practice are discussed. PMID:25231900

Structural equation modeling assessing relationship between mathematics beliefs, teachers' attitudes and teaching practices among novice teachers in Malaysia

NASA Astrophysics Data System (ADS)

Borhan, Noziati; Zakaria, Effandi

2017-05-01

This quantitative study was conducted to investigate the perception level of novice teachers about mathematics belief, teachers' attitude towards mathematics and teaching practices of mathematics in the classroom. In addition, it also aims to identify whether there is a correspondence model with the data obtained and to identify the relationship between the variables of beliefs, attitudes and practices among novice teachers in Malaysia. A total of 263 primary novice teachers throughout the country were involved in this study were selected randomly. Respondents are required to provide a response to the questionnaire of 66 items related to mathematics beliefs, attitudes and practices of the teaching mathematics. There are ten sub-factors which have been established in this instrument for three major constructs using a Likert scale rating of five points. The items of the constructs undergo the exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) procedure involve of unidimensionality test, convergent validity, construct validity and discriminant validity. Descriptive statistics were used to describe the frequency, percentage, the mean and standard deviation for completing some research questions that have been expressed. As for inferential statistical analysis, the researchers used structural equation modeling (SEM) to answer the question of correspondents model and the relationship between these three variables. The results of the study were found that there exist a correspondence measurement and structural model with the data obtained. While the relationship between variable found that mathematics beliefs have a significant influence on teachers' attitudes towards mathematics as well as the relationship between the attitudes with teaching practices. Meanwhile, mathematics belief had no significant relationship with mathematics teaching practices among novice teachers in Malaysia.

A survey on the measure of combat readiness

NASA Astrophysics Data System (ADS)

Wen, Kwong Fook; Nor, Norazman Mohamad; Soon, Lee Lai

2014-09-01

Measuring the combat readiness in military forces involves the measures of tangible and intangible elements of combat power. Though these measures are applicable, the mathematical models and formulae used focus mainly on either the tangible or the intangible elements. In this paper, a review is done to highlight the research gap in the formulation of a mathematical model that incorporates tangible elements with intangible elements to measure the combat readiness of a military force. It highlights the missing link between the tangible and intangible elements of combat power. To bridge the gap and missing link, a mathematical model could be formulated that measures both the tangible and intangible aspects of combat readiness by establishing the relationship between the causal (tangible and intangible) elements and its effects on the measure of combat readiness. The model uses multiple regression analysis as well as mathematical modeling and simulation which digest the capability component reflecting its assets and resources, the morale component reflecting human needs, and the quality of life component reflecting soldiers' state of satisfaction in life. The results of the review provide a mean to bridge the research gap through the formulation of a mathematical model that shows the total measure of a military force's combat readiness. The results also significantly identify parameters for each of the variables and factors in the model.

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

[Research advances in mathematical model of coniferous trees cold hardiness].

PubMed

Zhang, Gang; Wang, Ai-Fang

2007-07-01

Plant cold hardiness has complicated attributes. This paper introduced the research advances in establishing the dynamic models of coniferous trees cold hardiness, with the advantages and disadvantages of the models presented and the further studies suggested. In the models established initially, temperature was concerned as the only environmental factor affecting the cold hardiness, and the concept of stationary level of cold hardiness was introduced. Due to the obvious prediction errors of these models, the stationary level of cold hardiness was modeled later by assuming the existence of an additive effect of temperature and photoperiod on the increase of cold hardiness. Furthermore, the responses of the annual development phases for cold hardiness to environment were considered. The model researchers have paid more attention to the additive effect models, and run some experiments to test the additivity principle. However, the research results on Scots pine (Pinus sylvestris) indicated that its organs did not support the presumption of an additive response of cold hardiness by temperature and photoperiod, and the interaction between environmental factors should be taken into account. The mathematical models of cold hardiness need to be developed and improved.

A discrete mathematical model for the aggregation of β-Amyloid.

PubMed

Dayeh, Maher A; Livadiotis, George; Elaydi, Saber

2018-01-01

Dementia associated with the Alzheimer's disease is thought to be correlated with the conversion of the β - Amyloid (Aβ) peptides from soluble monomers to aggregated oligomers and insoluble fibrils. We present a discrete-time mathematical model for the aggregation of Aβ monomers into oligomers using concepts from chemical kinetics and population dynamics. Conditions for the stability and instability of the equilibria of the model are established. A formula for the number of monomers that is required for producing oligomers is also given. This may provide compound designers a mechanism to inhibit the Aβ aggregation.

Mathematical Analysis of an SIQR Influenza Model with Imperfect Quarantine.

PubMed

Erdem, Mustafa; Safan, Muntaser; Castillo-Chavez, Carlos

2017-07-01

The identification of mechanisms responsible for recurrent epidemic outbreaks, such as age structure, cross-immunity and variable delays in the infective classes, has challenged and fascinated epidemiologists and mathematicians alike. This paper addresses, motivated by mathematical work on influenza models, the impact of imperfect quarantine on the dynamics of SIR-type models. A susceptible-infectious-quarantine-recovered (SIQR) model is formulated with quarantined individuals altering the transmission dynamics process through their possibly reduced ability to generate secondary cases of infection. Mathematical and numerical analyses of the model of the equilibria and their stability have been carried out. Uniform persistence of the model has been established. Numerical simulations show that the model supports Hopf bifurcation as a function of the values of the quarantine effectiveness and other parameters. The upshot of this work is somewhat surprising since it is shown that SIQR model oscillatory behavior, as shown by multiple researchers, is in fact not robust to perturbations in the quarantine regime.

Evaluation of the lambda model for human postural control during ankle strategy.

PubMed

Micheau, Philippe; Kron, Aymeric; Bourassa, Paul

2003-09-01

An accurate modeling of human stance might be helpful in assessing postural deficit. The objective of this article is to validate a mathematical postural control model for quiet standing posture. The postural dynamics is modeled in the sagittal plane as an inverted pendulum with torque applied at the ankle joint. The torque control system is represented by the physiological lambda model. Two neurophysiological command variables of the central nervous system, designated lambda and micro, establish the dynamic threshold muscle at which motoneuron recruitment begins. Kinematic data and electromyographic signals were collected on four young males in order to measure small voluntary sway and quiet standing posture. Validation of the mathematical model was achieved through comparison of the experimental and simulated results. The mathematical model allows computation of the unmeasurable neurophysiological commands lambda and micro that control the equilibrium position and stability. Furthermore, with the model it is possible to conclude that low-amplitude body sway during quiet stance is commanded by the central nervous system.

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.

Inverse Modelling Problems in Linear Algebra Undergraduate Courses

ERIC Educational Resources Information Center

Martinez-Luaces, Victor E.

2013-01-01

This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

Establishing Mathematics for Teaching within Classroom Interactions in Teacher Education

ERIC Educational Resources Information Center

Ryve, Andreas; Nilsson, Per; Mason, John

2012-01-01

Teacher educators' processes of establishing "mathematics for teaching" in teacher education programs have been recognized as an important area for further research. In this study, we examine how two teacher educators establish and make explicit features of mathematics for teaching within classroom interactions. The study shows how the…

Enhancing Established Counting Routines to Promote Place-Value Understanding: An Empirical Study in Early Elementary Classrooms

ERIC Educational Resources Information Center

Fraivillig, Judith L.

2018-01-01

Understanding place value is a critical and foundational competency for elementary mathematics. Classroom teachers who endeavor to promote place-value development adopt a variety of established practices to varying degrees of effectiveness. In parallel, researchers have validated models of how young children acquire place-value understanding.…

Thermodynamic investigation of the interaction between cyclodextrins and preservatives - Application and verification in a mathematical model to determine the needed preservative surplus in aqueous cyclodextrin formulations.

PubMed

Holm, René; Olesen, Niels Erik; Alexandersen, Signe Dalgaard; Dahlgaard, Birgitte N; Westh, Peter; Mu, Huiling

2016-05-25

Preservatives are inactivated when added to conserve aqueous cyclodextrin (CD) formulations due to complex formation between CDs and the preservative. To maintain the desired conservation effect the preservative needs to be added in apparent surplus to account for this inactivation. The purpose of the present work was to establish a mathematical model, which defines this surplus based upon knowledge of stability constants and the minimal concentration of preservation to inhibit bacterial growth. The stability constants of benzoic acid, methyl- and propyl-paraben with different frequently used βCDs were determined by isothermal titration calorimetry. Based upon this knowledge mathematical models were constructed to account for the equilibrium systems and to calculate the required concentration of the preservations, which was evaluated experimentally based upon the USP/Ph. Eur./JP monograph. The mathematical calculations were able to predict the needed concentration of preservation in the presence of CDs; it clearly demonstrated the usefulness of including all underlying chemical equilibria in a mathematical model, such that the formulation design can be based on quantitative arguments. Copyright © 2015 Elsevier B.V. All rights reserved.

The `M' in SMEC: a short history of the mathematics education presence

NASA Astrophysics Data System (ADS)

Malone, John A.

2011-09-01

In this paper I examine the history of the integration of mathematics education into the Science Education Centre, which had been established by physicist, John de Laeter, within the School of Science and Engineering at Curtin University in Perth, Australia. De Laeter's vision for science education was that teachers should have access to professional education that allowed them to extend their discipline and pedagogical knowledge using strategies that brought together theory and practice in ways that were meaningful for teachers. This model was expanded when mathematics education was also included, paving the way also for technology education. I present the history of this integration laying out the themes that are important for the continued educational effectiveness of the Science and Mathematics Education Centre (SMEC) and the role that mathematics education has played in this process. As the title suggests, this article focuses on the activities of the group of mathematics educators who have worked within the Science and Mathematics Education Centre of Curtin University since it was established 30 or so years ago and who have contributed to its reputation. The two streams operated then and now more-or-less independently in matters of student thesis topic choice but offered students opportunities for interaction that might not have been available if the "M" had not been incorporated into the Science Education Centre (SEC). This article's focus is on the mathematics educators who contributed to the Centre's success and reputation, highlighting the synergistic relationship between mathematics and science that helped to make SMEC a leading center for mathematics and science education.

Applying Mathematical Tools to Accelerate Vaccine Development: Modeling Shigella Immune Dynamics

PubMed Central

Davis, Courtney L.; Wahid, Rezwanul; Toapanta, Franklin R.; Simon, Jakub K.

2013-01-01

We establish a mathematical framework for studying immune interactions with Shigella, a bacteria that kills over one million people worldwide every year. The long-term goal of this novel approach is to inform Shigella vaccine design by elucidating which immune components and bacterial targets are crucial for establishing Shigella immunity. Our delay differential equation model focuses on antibody and B cell responses directed against antigens like lipopolysaccharide in Shigella’s outer membrane. We find that antibody-based vaccines targeting only surface antigens cannot elicit sufficient immunity for protection. Additional boosting prior to infection would require a four-orders-of-magnitude increase in antibodies to sufficiently prevent epithelial invasion. However, boosting anti-LPS B memory can confer protection, which suggests these cells may correlate with immunity. We see that IgA antibodies are slightly more effective per molecule than IgG, but more total IgA is required due to spatial functionality. An extension of the model reveals that targeting both LPS and epithelial entry proteins is a promising avenue to advance vaccine development. This paper underscores the importance of multifaceted immune targeting in creating an effective Shigella vaccine. It introduces mathematical models to the Shigella vaccine development effort and lays a foundation for joint theoretical/experimental/clinical approaches to Shigella vaccine design. PMID:23589755

Applying mathematical tools to accelerate vaccine development: modeling Shigella immune dynamics.

PubMed

Davis, Courtney L; Wahid, Rezwanul; Toapanta, Franklin R; Simon, Jakub K; Sztein, Marcelo B; Levy, Doron

2013-01-01

We establish a mathematical framework for studying immune interactions with Shigella, a bacteria that kills over one million people worldwide every year. The long-term goal of this novel approach is to inform Shigella vaccine design by elucidating which immune components and bacterial targets are crucial for establishing Shigella immunity. Our delay differential equation model focuses on antibody and B cell responses directed against antigens like lipopolysaccharide in Shigella's outer membrane. We find that antibody-based vaccines targeting only surface antigens cannot elicit sufficient immunity for protection. Additional boosting prior to infection would require a four-orders-of-magnitude increase in antibodies to sufficiently prevent epithelial invasion. However, boosting anti-LPS B memory can confer protection, which suggests these cells may correlate with immunity. We see that IgA antibodies are slightly more effective per molecule than IgG, but more total IgA is required due to spatial functionality. An extension of the model reveals that targeting both LPS and epithelial entry proteins is a promising avenue to advance vaccine development. This paper underscores the importance of multifaceted immune targeting in creating an effective Shigella vaccine. It introduces mathematical models to the Shigella vaccine development effort and lays a foundation for joint theoretical/experimental/clinical approaches to Shigella vaccine design.

Modal analysis of human body vibration model for Indian subjects under sitting posture.

PubMed

Singh, Ishbir; Nigam, S P; Saran, V H

2015-01-01

Need and importance of modelling in human body vibration research studies are well established. The study of biodynamic responses of human beings can be classified into experimental and analytical methods. In the past few decades, plenty of mathematical models have been developed based on the diverse field measurements to describe the biodynamic responses of human beings. In this paper, a complete study on lumped parameter model derived from 50th percentile anthropometric data for a seated 54- kg Indian male subject without backrest support under free un-damped conditions has been carried out considering human body segments to be of ellipsoidal shape. Conventional lumped parameter modelling considers the human body as several rigid masses interconnected by springs and dampers. In this study, concept of mass of interconnecting springs has been incorporated and eigenvalues thus obtained are found to be closer to the values reported in the literature. Results obtained clearly establish decoupling of vertical and fore-and-aft oscillations. The mathematical modelling of human body vibration studies help in validating the experimental investigations for ride comfort of a sitting subject. This study clearly establishes the decoupling of vertical and fore-and-aft vibrations and helps in better understanding of possible human response to single and multi-axial excitations.

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.

Mathematical model of whole-process calculation for bottom-blowing copper smelting

NASA Astrophysics Data System (ADS)

Li, Ming-zhou; Zhou, Jie-min; Tong, Chang-ren; Zhang, Wen-hai; Li, He-song

2017-11-01

The distribution law of materials in smelting products is key to cost accounting and contaminant control. Regardless, the distribution law is difficult to determine quickly and accurately by mere sampling and analysis. Mathematical models for material and heat balance in bottom-blowing smelting, converting, anode furnace refining, and electrolytic refining were established based on the principles of material (element) conservation, energy conservation, and control index constraint in copper bottom-blowing smelting. Simulation of the entire process of bottom-blowing copper smelting was established using a self-developed MetCal software platform. A whole-process simulation for an enterprise in China was then conducted. Results indicated that the quantity and composition information of unknown materials, as well as heat balance information, can be quickly calculated using the model. Comparison of production data revealed that the model can basically reflect the distribution law of the materials in bottom-blowing copper smelting. This finding provides theoretical guidance for mastering the performance of the entire process.

Detecting isotopic ratio outliers

NASA Astrophysics Data System (ADS)

Bayne, C. K.; Smith, D. H.

An alternative method is proposed for improving isotopic ratio estimates. This method mathematically models pulse-count data and uses iterative reweighted Poisson regression to estimate model parameters to calculate the isotopic ratios. This computer-oriented approach provides theoretically better methods than conventional techniques to establish error limits and to identify outliers.

Mathematic model analysis of Gaussian beam propagation through an arbitrary thickness random phase screen.

PubMed

Tian, Yuzhen; Guo, Jin; Wang, Rui; Wang, Tingfeng

2011-09-12

In order to research the statistical properties of Gaussian beam propagation through an arbitrary thickness random phase screen for adaptive optics and laser communication application in the laboratory, we establish mathematic models of statistical quantities, which are based on the Rytov method and the thin phase screen model, involved in the propagation process. And the analytic results are developed for an arbitrary thickness phase screen based on the Kolmogorov power spectrum. The comparison between the arbitrary thickness phase screen and the thin phase screen shows that it is more suitable for our results to describe the generalized case, especially the scintillation index.

Studies in Mathematical Models of Human Decisionmaking in Gaming Situations

DTIC Science & Technology

1986-04-06

option evaluation, and action selection. Empirical research on human declslonmaking [41,[51, has established that all of the above assumptions are...into account the possibility of "irrational" actions . The work of Aumann and Maschler [9’], Ho [10], and others [111 studies games where the assumption...8217 expected actions of the other decisionmakers by subjective probabilities. The purposeof our research effort was to further develop the mathemat- ical

A magneto-rheological fluid mount featuring squeeze mode: analysis and testing

NASA Astrophysics Data System (ADS)

Chen, Peng; Bai, Xian-Xu; Qian, Li-Jun; Choi, Seung-Bok

2016-05-01

This paper presents a mathematical model for a new semi-active vehicle engine mount utilizing magneto-rheological (MR) fluids in squeeze mode (MR mount in short) and validates the model by comparing analysis results with experimental tests. The proposed MR mount is mainly comprised of a frame for installation, a main rubber, a squeeze plate and a bobbin for coil winding. When the magnetic fields on, MR effect occurs in the upper gap between the squeeze plate and the bobbin, and the dynamic stiffness can be controlled by tuning the applied currents. Employing Bingham model and flow properties between parallel plates of MR fluids, a mathematical model for the squeeze type of MR mount is formulated with consideration of the fluid inertia, MR effect and hysteresis property. The field-dependent dynamic stiffness of the MR mount is then analyzed using the established mathematical model. Subsequently, in order to validate the mathematical model, an appropriate size of MR mount is fabricated and tested. The field-dependent force and dynamic stiffness of the proposed MR mount are evaluated and compared between the model and experimental tests in both time and frequency domains to verify the model efficiency. In addition, it is shown that both the damping property and the stiffness property of the proposed MR mount can be simultaneously controlled.

Some thoughts on estimating the cost of common equity for a regulated business

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

Malko, J. Robert; Swensen, Philip R.; Monteleone, Joseph A.

2007-06-15

While mathematical models are useful in establishing a zone of reasonableness for a determination of allowed return on equity, it is important to consider the results of several models. Also key is to consider whether the analysis appropriately reflects longer-term market conditions. (author)

An Innovative Near-Peer Mentoring Model for Undergraduate and Secondary Students: STEM Focus

ERIC Educational Resources Information Center

Tenenbaum, Laura S.; Anderson, Margery K.; Jett, Marti; Yourick, Debra L.

2014-01-01

This study examined a novel mentoring model, "near-peer mentorship," that supports the development of mentee and mentor, incorporates established principles of mentoring, and offers unique opportunities to integrate research and teaching in a science, technology, engineering, and mathematics (STEM) internship. Using qualitative methods,…

Wind shear modeling for aircraft hazard definition

NASA Technical Reports Server (NTRS)

Frost, W.; Camp, D. W.; Wang, S. T.

1978-01-01

Mathematical models of wind profiles were developed for use in fast time and manned flight simulation studies aimed at defining and eliminating these wind shear hazards. A set of wind profiles and associated wind shear characteristics for stable and neutral boundary layers, thunderstorms, and frontal winds potentially encounterable by aircraft in the terminal area are given. Engineering models of wind shear for direct hazard analysis are presented in mathematical formulae, graphs, tables, and computer lookup routines. The wind profile data utilized to establish the models are described as to location, how obtained, time of observation and number of data points up to 500 m. Recommendations, engineering interpretations and guidelines for use of the data are given and the range of applicability of the wind shear models is described.

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

Modeling HCV cure after an ultra-short duration of therapy with direct acting agents

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

Goyal, Ashish; Lurie, Yoav; Meissner, Eric G.

In cases of sustained-virological response (SVR or cure) after an ultra-short duration (≤ 27 days) of direct-acting antiviral (DAA)-based therapy, despite HCV being detected at end of treatment (EOT), have been reported. Established HCV mathematical models that predict the treatment duration required to achieve cure do not take into account the possibility that the infectivity of virus produced during treatment might be reduced. The aim of this study was to develop a new mathematical model that considers the fundamental and critical concept that HCV RNA in serum represents both infectious virus (V i) and non-infectious virus (V ni) in ordermore » to explain the observation of cure with ultrashort DAA therapy. Established HCV models were compared to the new mathematical model to retrospectively explain cure in 2 patients who achieved cure after 24 or 27 days of paritaprevir, ombitasvir, dasabuvir, ritonavir and ribavirin or sofosbuvir plus ribavirin, respectively. Fitting established models with measured longitudinal HCV viral loads indicated that in both cases, cure would not have been expected without an additional 3–6 weeks of therapy after the actual EOT. In contrast, the new model fits the observed outcome by considering that in addition to blocking V i and V ni production (ε~0.998), these DAA + ribavirin treatments further enhanced the ratio of V ni to V i, thus increasing the log (V ni/V i) from 1 at pretreatment to 6 by EOT, which led to <1 infectious-virus particle in the extracellular body fluid (i.e., cure) prior to EOT. This new model can explain cure after short duration of DAA + ribavirin therapy by suggesting that a minimum 6-fold increase of log (V ni/V i) results from drug-induced enhancement of the V ni/V i.« less

Modeling HCV cure after an ultra-short duration of therapy with direct acting agents

DOE PAGES

Goyal, Ashish; Lurie, Yoav; Meissner, Eric G.; ...

2017-06-30

In cases of sustained-virological response (SVR or cure) after an ultra-short duration (≤ 27 days) of direct-acting antiviral (DAA)-based therapy, despite HCV being detected at end of treatment (EOT), have been reported. Established HCV mathematical models that predict the treatment duration required to achieve cure do not take into account the possibility that the infectivity of virus produced during treatment might be reduced. The aim of this study was to develop a new mathematical model that considers the fundamental and critical concept that HCV RNA in serum represents both infectious virus (V i) and non-infectious virus (V ni) in ordermore » to explain the observation of cure with ultrashort DAA therapy. Established HCV models were compared to the new mathematical model to retrospectively explain cure in 2 patients who achieved cure after 24 or 27 days of paritaprevir, ombitasvir, dasabuvir, ritonavir and ribavirin or sofosbuvir plus ribavirin, respectively. Fitting established models with measured longitudinal HCV viral loads indicated that in both cases, cure would not have been expected without an additional 3–6 weeks of therapy after the actual EOT. In contrast, the new model fits the observed outcome by considering that in addition to blocking V i and V ni production (ε~0.998), these DAA + ribavirin treatments further enhanced the ratio of V ni to V i, thus increasing the log (V ni/V i) from 1 at pretreatment to 6 by EOT, which led to <1 infectious-virus particle in the extracellular body fluid (i.e., cure) prior to EOT. This new model can explain cure after short duration of DAA + ribavirin therapy by suggesting that a minimum 6-fold increase of log (V ni/V i) results from drug-induced enhancement of the V ni/V i.« less

Making dynamic modeling effective in economics

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2005-09-01

Mathematics has been extremely effective in physics, but not in economics beyond finance. To establish economics as science we should follow the Galilean method and try to deduce mathematical models of markets from empirical data, as has been done for financial markets. Financial markets are nonstationary. This means that ‘value’ is subjective. Nonstationarity also means that the form of the noise in a market cannot be postulated a priori, but must be deduced from the empirical data. I discuss the essence of complexity in a market as unexpected events, and end with a biologically motivated speculation about market growth.

Dynamics of a stochastic tuberculosis model with constant recruitment and varying total population size

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed

2017-03-01

In this paper, we develop a mathematical model for a tuberculosis model with constant recruitment and varying total population size by incorporating stochastic perturbations. By constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of an ergodic stationary distribution as well as extinction of the disease to the stochastic system.

Silver release from nanocomposite Ag/alginate hydrogels in the presence of chloride ions: experimental results and mathematical modeling

NASA Astrophysics Data System (ADS)

Kostic, Danijela; Vidovic, Srđan; Obradovic, Bojana

2016-03-01

A stepwise experimental and mathematical modeling approach was used to assess silver release from nanocomposite Ag/alginate microbeads in wet and dried forms into water and into normal saline solution chosen as a simplified model for certain biological fluids (e.g., blood plasma, wound exudates, sweat, etc). Three phenomena were connected and mathematically described: diffusion of silver nanoparticles (AgNPs) within the alginate hydrogel, AgNP oxidation/dissolution and reaction with chloride ions, and diffusion of the resultant silver-chloride species. Mathematical modeling results agreed well with the experimental data with the AgNP diffusion coefficient estimated as 1.3 × 10-18 m2 s-1, while the first-order kinetic rate constant of AgNP oxidation/dissolution and diffusivity of silver-chloride species were shown to be inversely related. In specific, rapid rehydration and swelling of dry Ag/alginate microbeads induced fast AgNP oxidation/dissolution reaction with Cl- and AgCl precipitation within the microbeads with the lowest diffusivity of silver-chloride species compared to wet microbeads in normal saline. The proposed mathematical model provided an insight into the phenomena related to silver release from nanocomposite Ca-alginate hydrogels relevant for use of antimicrobial devices and established, at the same time, a basis for further in-depth studies of AgNP interactions in hydrogels in the presence of chloride ions.

Mathematical Description of Dendrimer Structure

NASA Technical Reports Server (NTRS)

Majoros, Istvan J.; Mehta, Chandan B.; Baker, James R., Jr.

2004-01-01

Characteristics of starburst dendrimers can be easily attributed to the multiplicity of the monomers used to synthesize them. The molecular weight, degree of polymerization, number of terminal groups and branch points for each generation of a dendrimer can be calculated using mathematical formulas incorporating these variables. Mathematical models for the calculation of degree of polymerization, molecular weight, and number of terminal groups and branching groups previously published were revised and elaborated on for poly(amidoamine) (PAMAM) dendrimers, and introduced for poly(propyleneimine) (POPAM) dendrimers and the novel POPAM-PAMAM hybrid, which we call the POMAM dendrimer. Experimental verification of the relationship between theoretical and actual structure for the PAMAM dendrimer was also established.

Mathematical modeling of infectious disease dynamics

PubMed Central

Siettos, Constantinos I.; Russo, Lucia

2013-01-01

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

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

PubMed

Peper, Abraham

2004-08-21

A mathematical model of drug tolerance and its underlying theory is presented. The model extends a first approach, published previously. The model is essentially more complex than the generally used model of homeostasis, which is demonstrated to fail in describing tolerance development to repeated drug administrations. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a regulated adaptive process. The oral detection and analysis of exogenous substances is proposed to be the primary stimulus for the mechanism of drug tolerance. Anticipation and environmental cues are in the model considered secondary stimuli, becoming primary only in dependence and addiction or when the drug administration bypasses the natural-oral-route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomous tolerance processes. Simulations with the mathematical model demonstrate the model's behavior to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. The mathematical model verifies the proposed theory and provides a basis for the implementation of mathematical models of specific physiological processes. In addition, it establishes a relation between the drug dose at any moment, and the resulting drug effect and relates the magnitude of the reactions following withdrawal to the rate of tolerance and other parameters involved in the tolerance process. The present paper analyses the concept behind the model. The next paper discusses the mathematical model.

ESTABLISHING CHANGES IN METABOLISM OF CARBON TETRACHLORIDE IN THE PRESENCE OF TRICHLOROETHYLENE IN THE RAT THROUGH THE USE OF PHYSIOLOGICALLY BASED PHARMACOKINETIC (PBPK) MODELING

EPA Science Inventory

Toxicological interactions of chemicals can affect metabolism, often decreasing overall associated metabolic rates; and changes in metabolism can be evaluated through the use of mathematical models. Trichloroethylene (TCE) and carbon tetrachloride (CCl₄) are common co...

Personalizing oncology treatments by predicting drug efficacy, side-effects, and improved therapy: mathematics, statistics, and their integration.

PubMed

Agur, Zvia; Elishmereni, Moran; Kheifetz, Yuri

2014-01-01

Despite its great promise, personalized oncology still faces many hurdles, and it is increasingly clear that targeted drugs and molecular biomarkers alone yield only modest clinical benefit. One reason is the complex relationships between biomarkers and the patient's response to drugs, obscuring the true weight of the biomarkers in the overall patient's response. This complexity can be disentangled by computational models that integrate the effects of personal biomarkers into a simulator of drug-patient dynamic interactions, for predicting the clinical outcomes. Several computational tools have been developed for personalized oncology, notably evidence-based tools for simulating pharmacokinetics, Bayesian-estimated tools for predicting survival, etc. We describe representative statistical and mathematical tools, and discuss their merits, shortcomings and preliminary clinical validation attesting to their potential. Yet, the individualization power of mathematical models alone, or statistical models alone, is limited. More accurate and versatile personalization tools can be constructed by a new application of the statistical/mathematical nonlinear mixed effects modeling (NLMEM) approach, which until recently has been used only in drug development. Using these advanced tools, clinical data from patient populations can be integrated with mechanistic models of disease and physiology, for generating personal mathematical models. Upon a more substantial validation in the clinic, this approach will hopefully be applied in personalized clinical trials, P-trials, hence aiding the establishment of personalized medicine within the main stream of clinical oncology. © 2014 Wiley Periodicals, Inc.

Characterising the perceived value of mathematics educational apps in preservice teachers

NASA Astrophysics Data System (ADS)

Handal, Boris; Campbell, Chris; Cavanagh, Michael; Petocz, Peter

2016-03-01

This study validated the semantic items of three related scales aimed at characterising the perceived worth of mathematics-education-related mobile applications (apps). The technological pedagogical content knowledge (TPACK) model was used as the conceptual framework for the analysis. Three hundred and seventy-three preservice students studying primary school education from two public and one private Australian universities participated in the study. The respondents examined three different apps using a purposively designed instrument in regard to either their explorative, productive or instructive instructional role. While construct validity could not be established due to a broad range of variability in responses implying a high degree of subjectivity in respondents' judgments, the qualitative analysis was effective in establishing content validity.

Mathematical Description Development of Reactions of Metallic Gallium Using Kinetic Block Diagram

NASA Astrophysics Data System (ADS)

Yakovleva, A. A.; Soboleva, V. G.; Filatova, E. G.

2018-05-01

A kinetic block diagram based on a logical sequence of actions in the mathematical processing of a kinetic data is used. A type of reactions of metallic gallium in hydrochloric acid solutions is determined. It has been established that the reactions of the formation of gallium oxide and its salts proceed independently and in the absence of the diffusion resistance. Kinetic models connecting the constants of the reaction rate with the activation energy and describing the evolution of the process are obtained.

Extended mathematical model for "in vivo" quantification of the interaction betweeen atazanavir and bilirubin.

PubMed

Lozano, Roberto; Domeque, Nieves; Apesteguia, Alberto-Fermín

2014-02-01

The objective of the present work was to conduct an "in vivo" analysis of the atazanavir-bilirubin interaction. We developed a new mathematical approach to PK/PDPK models for competitive interaction based on the Michaelis-Menten equation, which was applied to patients with polymorphisms in the gene for UDP-glucuronosyltransferase 1A1 (UGT1A1). Atazanavir is known to induce concentration-dependent increases in bilirubin plasma levels. Thus, we employed our mathematical model to analyse rises in steady state atazanavir and bilirubin concentrations, ultimately plotting a nomogram for detection of suboptimal atazanavir exposure. Application of our model revealed that an absolute value or a steady state increase in bilirubin falling below 3.8Φ µmol/L (where Φ is a correction factor, =1 for UGT1A1 wild type and ≠1 for UGT1A1 variants) could be used to predict suboptimal atazanavir exposure and treatment failure. Thus, we have successfully established a new mathematical approach for pharmacodynamic-pharmacokinetic modelling of the interaction between atazanavir and bilirubin, as it relates to genetic variants of UGT1A1. Taken together, our findings indicate that bilirubin plasma levels represent a valuable marker of atazanavir exposure. © 2013, The American College of Clinical Pharmacology.

Development of the electromagnetic technology for broken rail detection from a mobil platform

NASA Astrophysics Data System (ADS)

Plotnikov, Yuri; Raghunathan, Arun; Kumar, Ajith; Noffsinger, Joseph; Fries, Jeffrey; Ehret, Steven; Frangieh, Tannous; Palanganda, Samhitha

2016-02-01

Timely detection of breaks in running rails remains a topic of significant importance for the railroad industry. GE has been investigating new ideas of the Rail Integrity Monitoring or RIM technology that can be implemented on a wide range of the rolling stock platforms including locomotives, passenger and freight cars. The focus of the project is to establish a simple, non-contact, and inexpensive means of nondestructive inspection by fusion of known solutions with new technology development that can result in detection with high reliability. A scaled down model of a typical locomotive-track system has been developed at GE Global research for detailed study of the detection process. In addition, a finite element model has been established and used to understand distribution of the magnetic field and currents in such a system. Both models have been using the rails and wheel-axles geometry to establish a realistic model that would provide the electric current and magnetic field distribution close to the real world phenomenon. Initial magnetic field maps were obtained by scanning a 1:15 model constructed of steel bars using a 3D scanner and an inductive coil. Sensitivity to a broken rail located between two locomotive axles simulated by an opening in this metallic frame was demonstrated. Further investigation and optimization was conducted on a larger, 1:3 scale, physical model and by running mathematical simulations. Special attention was paid to consistency between the finite element and physical model results. The obtained results allowed establishment of a working frequency range, inductive current injection into the rail-wheel-axle loop and measuring the electromagnetic response to a broken rail. The verification and full scale system prototype tests are following the laboratory experiments and mathematical simulations.

Hydrogen production by the hyperthermophilic bacterium Thermotoga maritima Part II: modeling and experimental approaches for hydrogen production.

PubMed

Auria, Richard; Boileau, Céline; Davidson, Sylvain; Casalot, Laurence; Christen, Pierre; Liebgott, Pierre Pol; Combet-Blanc, Yannick

2016-01-01

Thermotoga maritima is a hyperthermophilic bacterium known to produce hydrogen from a large variety of substrates. The aim of the present study is to propose a mathematical model incorporating kinetics of growth, consumption of substrates, product formations, and inhibition by hydrogen in order to predict hydrogen production depending on defined culture conditions. Our mathematical model, incorporating data concerning growth, substrates, and products, was developed to predict hydrogen production from batch fermentations of the hyperthermophilic bacterium, T. maritima . It includes the inhibition by hydrogen and the liquid-to-gas mass transfer of H 2 , CO 2 , and H 2 S. Most kinetic parameters of the model were obtained from batch experiments without any fitting. The mathematical model is adequate for glucose, yeast extract, and thiosulfate concentrations ranging from 2.5 to 20 mmol/L, 0.2-0.5 g/L, or 0.01-0.06 mmol/L, respectively, corresponding to one of these compounds being the growth-limiting factor of T. maritima . When glucose, yeast extract, and thiosulfate concentrations are all higher than these ranges, the model overestimates all the variables. In the window of the model validity, predictions of the model show that the combination of both variables (increase in limiting factor concentration and in inlet gas stream) leads up to a twofold increase of the maximum H 2 -specific productivity with the lowest inhibition. A mathematical model predicting H 2 production in T. maritima was successfully designed and confirmed in this study. However, it shows the limit of validity of such mathematical models. Their limit of applicability must take into account the range of validity in which the parameters were established.

A mathematical model of a lithium/thionyl chloride primary cell

NASA Technical Reports Server (NTRS)

Evans, T. I.; Nguyen, T. V.; White, R. E.

1987-01-01

A 1-D mathematical model for the lithium/thionyl chloride primary cell was developed to investigate methods of improving its performance and safety. The model includes many of the components of a typical lithium/thionyl chloride cell such as the porous lithium chloride film which forms on the lithium anode surface. The governing equations are formulated from fundamental conservation laws using porous electrode theory and concentrated solution theory. The model is used to predict 1-D, time dependent profiles of concentration, porosity, current, and potential as well as cell temperature and voltage. When a certain discharge rate is required, the model can be used to determine the design criteria and operating variables which yield high cell capacities. Model predictions can be used to establish operational and design limits within which the thermal runaway problem, inherent in these cells, can be avoided.

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

PubMed

Koch, Ina; Nöthen, Joachim; Schleiff, Enrico

2017-01-01

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

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

PubMed Central

Koch, Ina; Nöthen, Joachim; Schleiff, Enrico

2017-01-01

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

Well test mathematical model for fractures network in tight oil reservoirs

NASA Astrophysics Data System (ADS)

Diwu, Pengxiang; Liu, Tongjing; Jiang, Baoyi; Wang, Rui; Yang, Peidie; Yang, Jiping; Wang, Zhaoming

2018-02-01

Well test, especially build-up test, has been applied widely in the development of tight oil reservoirs, since it is the only available low cost way to directly quantify flow ability and formation heterogeneity parameters. However, because of the fractures network near wellbore, generated from artificial fracturing linking up natural factures, traditional infinite and finite conductivity fracture models usually result in significantly deviation in field application. In this work, considering the random distribution of natural fractures, physical model of fractures network is proposed, and it shows a composite model feature in the large scale. Consequently, a nonhomogeneous composite mathematical model is established with threshold pressure gradient. To solve this model semi-analytically, we proposed a solution approach including Laplace transform and virtual argument Bessel function, and this method is verified by comparing with existing analytical solution. The matching data of typical type curves generated from semi-analytical solution indicates that the proposed physical and mathematical model can describe the type curves characteristic in typical tight oil reservoirs, which have up warping in late-term rather than parallel lines with slope 1/2 or 1/4. It means the composite model could be used into pressure interpretation of artificial fracturing wells in tight oil reservoir.

[Risk factor analysis of the patients with solitary pulmonary nodules and establishment of a prediction model for the probability of malignancy].

PubMed

Wang, X; Xu, Y H; Du, Z Y; Qian, Y J; Xu, Z H; Chen, R; Shi, M H

2018-02-23

Objective: This study aims to analyze the relationship among the clinical features, radiologic characteristics and pathological diagnosis in patients with solitary pulmonary nodules, and establish a prediction model for the probability of malignancy. Methods: Clinical data of 372 patients with solitary pulmonary nodules who underwent surgical resection with definite postoperative pathological diagnosis were retrospectively analyzed. In these cases, we collected clinical and radiologic features including gender, age, smoking history, history of tumor, family history of cancer, the location of lesion, ground-glass opacity, maximum diameter, calcification, vessel convergence sign, vacuole sign, pleural indentation, speculation and lobulation. The cases were divided to modeling group (268 cases) and validation group (104 cases). A new prediction model was established by logistic regression analying the data from modeling group. Then the data of validation group was planned to validate the efficiency of the new model, and was compared with three classical models(Mayo model, VA model and LiYun model). With the calculated probability values for each model from validation group, SPSS 22.0 was used to draw the receiver operating characteristic curve, to assess the predictive value of this new model. Results: 112 benign SPNs and 156 malignant SPNs were included in modeling group. Multivariable logistic regression analysis showed that gender, age, history of tumor, ground -glass opacity, maximum diameter, and speculation were independent predictors of malignancy in patients with SPN( P <0.05). We calculated a prediction model for the probability of malignancy as follow: p =e(x)/(1+ e(x)), x=-4.8029-0.743×gender+ 0.057×age+ 1.306×history of tumor+ 1.305×ground-glass opacity+ 0.051×maximum diameter+ 1.043×speculation. When the data of validation group was added to the four-mathematical prediction model, The area under the curve of our mathematical prediction model was 0.742, which is greater than other models (Mayo 0.696, VA 0.634, LiYun 0.681), while the differences between any two of the four models were not significant ( P >0.05). Conclusions: Age of patient, gender, history of tumor, ground-glass opacity, maximum diameter and speculation are independent predictors of malignancy in patients with solitary pulmonary nodule. This logistic regression prediction mathematic model is not inferior to those classical models in estimating the prognosis of SPNs.

Optimal control of HIV/AIDS dynamic: Education and treatment

NASA Astrophysics Data System (ADS)

Sule, Amiru; Abdullah, Farah Aini

2014-07-01

A mathematical model which describes the transmission dynamics of HIV/AIDS is developed. The optimal control representing education and treatment for this model is explored. The existence of optimal Control is established analytically by the use of optimal control theory. Numerical simulations suggest that education and treatment for the infected has a positive impact on HIV/AIDS control.

Algebra for Enterprise Ontology: towards analysis and synthesis of enterprise models

NASA Astrophysics Data System (ADS)

Suga, Tetsuya; Iijima, Junichi

2018-03-01

Enterprise modeling methodologies have made enterprises more likely to be the object of systems engineering rather than craftsmanship. However, the current state of research in enterprise modeling methodologies lacks investigations of the mathematical background embedded in these methodologies. Abstract algebra, a broad subfield of mathematics, and the study of algebraic structures may provide interesting implications in both theory and practice. Therefore, this research gives an empirical challenge to establish an algebraic structure for one aspect model proposed in Design & Engineering Methodology for Organizations (DEMO), which is a major enterprise modeling methodology in the spotlight as a modeling principle to capture the skeleton of enterprises for developing enterprise information systems. The results show that the aspect model behaves well in the sense of algebraic operations and indeed constructs a Boolean algebra. This article also discusses comparisons with other modeling languages and suggests future work.

Impact of coverage on the reliability of a fault tolerant computer

NASA Technical Reports Server (NTRS)

Bavuso, S. J.

1975-01-01

A mathematical reliability model is established for a reconfigurable fault tolerant avionic computer system utilizing state-of-the-art computers. System reliability is studied in light of the coverage probabilities associated with the first and second independent hardware failures. Coverage models are presented as a function of detection, isolation, and recovery probabilities. Upper and lower bonds are established for the coverage probabilities and the method for computing values for the coverage probabilities is investigated. Further, an architectural variation is proposed which is shown to enhance coverage.

Computational Control of Flexible Aerospace Systems

NASA Technical Reports Server (NTRS)

Sharpe, Lonnie, Jr.; Shen, Ji Yao

1994-01-01

The main objective of this project is to establish a distributed parameter modeling technique for structural analysis, parameter estimation, vibration suppression and control synthesis of large flexible aerospace structures. This report concentrates on the research outputs produced in the last two years of the project. The main accomplishments can be summarized as follows. A new version of the PDEMOD Code had been completed. A theoretical investigation of the NASA MSFC two-dimensional ground-based manipulator facility by using distributed parameter modelling technique has been conducted. A new mathematical treatment for dynamic analysis and control of large flexible manipulator systems has been conceived, which may provide a embryonic form of a more sophisticated mathematical model for future modified versions of the PDEMOD Codes.

Jonathan J. Stickel | NREL

Science.gov Websites

research interests in fluid mechanics, rheology, separation science, reaction engineering, mathematical -established Newtonian fluid mechanics and solution reaction kinetics do not apply to these biomass slurries , and reaction kinetics of the biomass slurries in order to develop predictive modeling capabilities

Mathematics and Physics: The Idea of a Pre-Established Harmony

ERIC Educational Resources Information Center

Kragh, Helge

2015-01-01

For more than a century the notion of a pre-established harmony between the mathematical and physical sciences has played an important role not only in the rhetoric of mathematicians and theoretical physicists, but also as a doctrine guiding much of their research. Strongly mathematized branches of physics, such as the vortex theory of atoms…

Establishing a Professional Development Network around Dynamic Mathematics Software in England

ERIC Educational Resources Information Center

Lavicza, Zsolt; Hohenwarter, Markus; Jones, Keith; Lu, Allison; Dawes, Mark

2010-01-01

In this paper, we will outline some results of an NCETM (National Centre for Excellence in the Teaching of Mathematics) funded project that aimed to establish a professional development network with an open-source mathematical software--GeoGebra--in England. During the past few years a large international user and developer community has formed…

New mathematic model for predicting chiral separation using molecular docking: mechanism of chiral recognition of triadimenol analogues.

PubMed

Zhang, Guoqing; Sun, Qingyan; Hou, Ying; Hong, Zhanying; Zhang, Jun; Zhao, Liang; Zhang, Hai; Chai, Yifeng

2009-07-01

The purpose of this paper was to study the enantioseparation mechanism of triadimenol compounds by carboxymethylated (CM)-beta-CD mediated CE. All the enantiomers were separated under the same experimental conditions to study the chiral recognition mechanism using a 30 mM sodium dihydrogen phosphate buffer at pH 2.2 adjusted by phosphoric acid. The inclusion courses between CM-beta-CD and enantiomers were investigated by the means of molecular docking technique. It was found that there were at least three points (one hydrophobic bond and two hydrogen bonds) involved in the interaction of each enantiomer with the chiral selectors. A new mathematic model has been built up based on the results of molecular mechanics calculations, which could analyze the relationship between the resolution of enantioseparation and the interaction energy in the docking area. Comparing the results of the separation by CE, the established mathematic model demonstrated good capability to predict chiral separation of triadimenol enantiomers using CM-beta-CD mediated CE.

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

PubMed Central

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

2013-01-01

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

Modeling and experimental examination of water level effects on radon exhalation from fragmented uranium ore.

PubMed

Ye, Yong-Jun; Dai, Xin-Tao; Ding, De-Xin; Zhao, Ya-Li

2016-12-01

In this study, a one-dimensional steady-state mathematical model of radon transport in fragmented uranium ore was established according to Fick's law and radon transfer theory in an air-water interface. The model was utilized to obtain an analytical solution for radon concentration in the air-water, two-phase system under steady state conditions, as well as a corresponding radon exhalation rate calculation formula. We also designed a one-dimensional experimental apparatus for simulating radon diffusion migration in the uranium ore with various water levels to verify the mathematical model. The predicted results were in close agreement with the measured results, suggesting that the proposed model can be readily used to determine radon concentrations and exhalation rates in fragmented uranium ore with varying water levels. Copyright © 2016. Published by Elsevier Ltd.

Mathematical optimization of high dose-rate brachytherapy—derivation of a linear penalty model from a dose-volume model

NASA Astrophysics Data System (ADS)

Morén, B.; Larsson, T.; Carlsson Tedgren, Å.

2018-03-01

High dose-rate brachytherapy is a method for cancer treatment where the radiation source is placed within the body, inside or close to a tumour. For dose planning, mathematical optimization techniques are being used in practice and the most common approach is to use a linear model which penalizes deviations from specified dose limits for the tumour and for nearby organs. This linear penalty model is easy to solve, but its weakness lies in the poor correlation of its objective value and the dose-volume objectives that are used clinically to evaluate dose distributions. Furthermore, the model contains parameters that have no clear clinical interpretation. Another approach for dose planning is to solve mixed-integer optimization models with explicit dose-volume constraints which include parameters that directly correspond to dose-volume objectives, and which are therefore tangible. The two mentioned models take the overall goals for dose planning into account in fundamentally different ways. We show that there is, however, a mathematical relationship between them by deriving a linear penalty model from a dose-volume model. This relationship has not been established before and improves the understanding of the linear penalty model. In particular, the parameters of the linear penalty model can be interpreted as dual variables in the dose-volume model.

A Highly Similar Mathematical Model for Cerebral Blood Flow Velocity in Geriatric Patients with Suspected Cerebrovascular Disease

NASA Astrophysics Data System (ADS)

Liu, Bo; Li, Qi; Wang, Jisheng; Xiang, Hu; Ge, Hong; Wang, Hui; Xie, Peng

2015-10-01

Cerebral blood flow velocity(CBFV) is an important parameter for study of cerebral hemodynamics. However, a simple and highly similar mathematical model has not yet been established for analyzing CBFV. To alleviate this issue, through TCD examination in 100 geriatric patients with suspected cerebrovascular disease (46 males and 54 females), we established a representative eighth-order Fourier function Vx(t) that simulates the CBFV. The measured TCD waveforms were compared to those derived from Vx(t), an illustrative Kolmogorov-Smirnov test was employed to determine the validity. The results showed that the TCD waves could been reconstructed for patients with different CBFVs by implementing their variable heart rates and the formulated maximum/minimum of Vx(t). Comparisons between derived and measured TCD waveforms suggest that the two waveforms are very similar. The results confirm that CBFV can be well-modeled through an eighth-order Fourier function. This function Vx(t) can be used extensively for a prospective study of cerebral hemodynamics in geriatric patients with suspected cerebrovascular disease.

Establishing a Professional Learning Community among Middle School Mathematics Teachers

ERIC Educational Resources Information Center

Koellner-Clark, Karen; Borko, Hilda

2004-01-01

The paper examines how community was established in a professional development institute that focused on algebra content knowledge for middle school mathematics teachers. This qualitative study was framed within a situative perspective. We analyzed multiple data sources to identify the ways in which community was established. Results indicate…

Mathematical and Computational Aspects Related to Soil Modeling and Simulation

DTIC Science & Technology

2017-09-26

and simulation challenges at the interface of applied math (homogenization, handling of discontinuous behavior, discrete vs. continuum representations...applied math tools need to be established and used to figure out how to impose compatible boundary conditions, how to better approximate the gradient

Application of Hamilton's Law of Varying Action

NASA Technical Reports Server (NTRS)

Bailey, C. D.

1973-01-01

The application of Hamilton's Law to the direct solution of nonstationary as well as stationary problems in mechanics of solids is discussed. Solutions are demonstrated for conservative and monconservative, stationary and/or nonstationary particle motion. Mathematical models are developed to establish the relationships of the parameters.

[The relationship between eyeball structure and visual acuity in high myopia].

PubMed

Liu, Yi-Chang; Xia, Wen-Tao; Zhu, Guang-You; Zhou, Xing-Tao; Fan, Li-Hua; Liu, Rui-Jue; Chen, Jie-Min

2010-06-01

To explore the relationship between eyeball structure and visual acuity in high myopia. Totally, 152 people (283 eyeballs) with different levels of myopia were tested for visual acuity, axial length, and fundus. All cases were classified according to diopter, axial length, and fundus. The relationships between diopter, axial length, fundus and visual acuity were studied. The mathematical models were established for visual acuity and eyeball structure markers. The visual acuity showed a moderate correlation with fundus class, comus, axial length and diopter ([r] > 0.4, P < 0.000 1). The visual acuity in people with the axial length longer than 30.00 mm, diopter above -20.00 D and fundus in 4th class were mostly below 0.5. The mathematical models were established by visual acuity and eyeball structure markers. The visual acuity should decline with axial length extension, diopter deepening and pathological deterioration of fundus. To detect the structure changes by combining different kinds of objective methods can help to assess and to judge the vision in high myopia.

Age estimation based on pulp chamber volume of first molars from cone-beam computed tomography images.

PubMed

Ge, Zhi-pu; Ma, Ruo-han; Li, Gang; Zhang, Ji-zong; Ma, Xu-chen

2015-08-01

To establish a method that can be used for human age estimation on the basis of pulp chamber volume of first molars and to identify whether the method is good enough for age estimation in real human cases. CBCT images of 373 maxillary first molars and 372 mandibular first molars were collected to establish the mathematical model from 190 female and 213 male patients whose age between 12 and 69 years old. The inclusion criteria of the first molars were: no caries, no excessive tooth wear, no dental restorations, no artifacts due to metal restorative materials present in adjacent teeth, and no pulpal calcification. All the CBCT images were acquired with a CBCT unit NewTom VG (Quantitative Radiology, Verona, Italy) and reconstructed with a voxel-size of 0.15mm. The images were subsequently exported as DICOM data sets and imported into an open source 3D image semi-automatic segmenting and voxel-counting software ITK-SNAP 2.4 for the calculation of pulp chamber volumes. A logarithmic regression analysis was conducted with age as dependent variable and pulp chamber volume as independent variables to establish a mathematical model for the human age estimation. To identify the precision and accuracy of the model for human age estimation, another 104 maxillary first molars and 103 mandibular first molars from 55 female and 57 male patients whose age between 12 and 67 years old were collected, too. Mean absolute error and root mean square error between the actual age and estimated age were used to determine the precision and accuracy of the mathematical model. The study was approved by the Institutional Review Board of Peking University School and Hospital of Stomatology. A mathematical model was suggested for: AGE=117.691-26.442×ln (pulp chamber volume). The regression was statistically significant (p=0.000<0.01). The coefficient of determination (R(2)) was 0.564. There is a mean absolute error of 8.122 and root mean square error of 5.603 between the actual age and estimated age for all the tested teeth. The pulp chamber volume of first molar is a useful index for the estimation of human age with reasonable precision and accuracy. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Theory, Modeling, Software and Hardware Development for Analytical and Computational Materials Science

NASA Technical Reports Server (NTRS)

Young, Gerald W.; Clemons, Curtis B.

2004-01-01

The focus of this Cooperative Agreement between the Computational Materials Laboratory (CML) of the Processing Science and Technology Branch of the NASA Glenn Research Center (GRC) and the Department of Theoretical and Applied Mathematics at The University of Akron was in the areas of system development of the CML workstation environment, modeling of microgravity and earth-based material processing systems, and joint activities in laboratory projects. These efforts complement each other as the majority of the modeling work involves numerical computations to support laboratory investigations. Coordination and interaction between the modelers, system analysts, and laboratory personnel are essential toward providing the most effective simulations and communication of the simulation results. Toward these means, The University of Akron personnel involved in the agreement worked at the Applied Mathematics Research Laboratory (AMRL) in the Department of Theoretical and Applied Mathematics while maintaining a close relationship with the personnel of the Computational Materials Laboratory at GRC. Network communication between both sites has been established. A summary of the projects we undertook during the time period 9/1/03 - 6/30/04 is included.

A novel medical information management and decision model for uncertain demand optimization.

PubMed

Bi, Ya

2015-01-01

Accurately planning the procurement volume is an effective measure for controlling the medicine inventory cost. Due to uncertain demand it is difficult to make accurate decision on procurement volume. As to the biomedicine sensitive to time and season demand, the uncertain demand fitted by the fuzzy mathematics method is obviously better than general random distribution functions. To establish a novel medical information management and decision model for uncertain demand optimization. A novel optimal management and decision model under uncertain demand has been presented based on fuzzy mathematics and a new comprehensive improved particle swarm algorithm. The optimal management and decision model can effectively reduce the medicine inventory cost. The proposed improved particle swarm optimization is a simple and effective algorithm to improve the Fuzzy interference and hence effectively reduce the calculation complexity of the optimal management and decision model. Therefore the new model can be used for accurate decision on procurement volume under uncertain demand.

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.

Model correlation and damage location for large space truss structures: Secant method development and evaluation

NASA Technical Reports Server (NTRS)

Smith, Suzanne Weaver; Beattie, Christopher A.

1991-01-01

On-orbit testing of a large space structure will be required to complete the certification of any mathematical model for the structure dynamic response. The process of establishing a mathematical model that matches measured structure response is referred to as model correlation. Most model correlation approaches have an identification technique to determine structural characteristics from the measurements of the structure response. This problem is approached with one particular class of identification techniques - matrix adjustment methods - which use measured data to produce an optimal update of the structure property matrix, often the stiffness matrix. New methods were developed for identification to handle problems of the size and complexity expected for large space structures. Further development and refinement of these secant-method identification algorithms were undertaken. Also, evaluation of these techniques is an approach for model correlation and damage location was initiated.

A systematic review of mathematical models of mosquito-borne pathogen transmission: 1970–2010

PubMed Central

Reiner, Robert C.; Perkins, T. Alex; Barker, Christopher M.; Niu, Tianchan; Chaves, Luis Fernando; Ellis, Alicia M.; George, Dylan B.; Le Menach, Arnaud; Pulliam, Juliet R. C.; Bisanzio, Donal; Buckee, Caroline; Chiyaka, Christinah; Cummings, Derek A. T.; Garcia, Andres J.; Gatton, Michelle L.; Gething, Peter W.; Hartley, David M.; Johnston, Geoffrey; Klein, Eili Y.; Michael, Edwin; Lindsay, Steven W.; Lloyd, Alun L.; Pigott, David M.; Reisen, William K.; Ruktanonchai, Nick; Singh, Brajendra K.; Tatem, Andrew J.; Kitron, Uriel; Hay, Simon I.; Scott, Thomas W.; Smith, David L.

2013-01-01

Mathematical models of mosquito-borne pathogen transmission originated in the early twentieth century to provide insights into how to most effectively combat malaria. The foundations of the Ross–Macdonald theory were established by 1970. Since then, there has been a growing interest in reducing the public health burden of mosquito-borne pathogens and an expanding use of models to guide their control. To assess how theory has changed to confront evolving public health challenges, we compiled a bibliography of 325 publications from 1970 through 2010 that included at least one mathematical model of mosquito-borne pathogen transmission and then used a 79-part questionnaire to classify each of 388 associated models according to its biological assumptions. As a composite measure to interpret the multidimensional results of our survey, we assigned a numerical value to each model that measured its similarity to 15 core assumptions of the Ross–Macdonald model. Although the analysis illustrated a growing acknowledgement of geographical, ecological and epidemiological complexities in modelling transmission, most models during the past 40 years closely resemble the Ross–Macdonald model. Modern theory would benefit from an expansion around the concepts of heterogeneous mosquito biting, poorly mixed mosquito-host encounters, spatial heterogeneity and temporal variation in the transmission process. PMID:23407571

What Is behind the Priority Heuristic? A Mathematical Analysis and Comment on Brandstatter, Gigerenzer, and Hertwig (2006)

ERIC Educational Resources Information Center

Rieger, Marc Oliver; Wang, Mei

2008-01-01

Comments on the article by E. Brandstatter, G. Gigerenzer, and R. Hertwig (2006). 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…

Mathematical Modeling in Support of Military Operational Medicine

DTIC Science & Technology

2006-07-01

of PBPK models in toxicol- ogy research and chemical risk assessment today is pri- marily related to their ability to make more quantitative ...derived earlier. The biomechanical basis of SFC is established by its correlation with strain. (a) Pretest Scan (b) Posttest Fracture...Three-Dimensional Reconstruction of Pretest and Posttest CT Scans Cited References Vander Vorst, M., Stuhmiller, J., et al., (2003). Biomechanically

Exploring the benefits of antibody immune response in HIV-1 infection using a discrete model.

PubMed

Showa, S P; Nyabadza, F; Hove-Musekwa, S D; Magombedze, G

2016-06-01

The role of antibodies in HIV-1 infection is investigated using a discrete-time mathematical model that considers cell-free and cell-associated transmission of the virus. Model analysis shows that the effect of each type of antibody is dependent on the stage of the infection. Neutralizing antibodies are efficient in controlling the viral levels in the early days after seroconversion and antibodies that coat HIV-1-infected cells and recruit effector cells to either kill the HIV-1-infected cells or inhibit viral replication are efficient when the infection becomes established. Model simulations show that antibodies that inhibit viral replication are more effective in controlling the infection than those that recruit Natural Killer T cells after infection establishment. The model was fitted to subjects of the Tsedimoso study conducted in Botswana and conclusions similar to elasticity analysis results were obtained. Model fitting results predicted that neutralizing antibodies are more efficient in controlling the viral levels than antibodies that coat HIV-1-infected cells and recruit effector cells to either kill the HIV-1-infected cells or inhibit viral replication in the early days after seroconversion. © The Authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

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

PubMed

Bürger, Raimund; Diehl, Stefan; Nopens, Ingmar

2011-03-01

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

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

PubMed

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

2017-02-01

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

Nonlinear analysis of a model of vascular tumour growth and treatment

NASA Astrophysics Data System (ADS)

Tao, Youshan; Yoshida, Norio; Guo, Qian

2004-05-01

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

The Impact of Problem-Based Learning on Non-Science Undergraduate Students' Attitudes towards Mathematics in an Egyptian Classroom

NASA Astrophysics Data System (ADS)

Rizkallah, Mohammed W.

While Problem-based Learning (PBL) has been established in the literature in different contexts, there remains few studies on how PBL has an impact on students' attitude towards mathematics and their conceptual understanding of it in Egyptian classrooms. This study was conducted in an international university in Egypt, and the participants were non-science undergraduate students who took a course called "Fun with Problem-Solving" as a requirement core class. The study shows that students' attitude towards mathematics developed throughout the course, and this was tested using the Fennema-Sherman Mathematics Attitude Scale, where students had a pretest and posttest. While the sample size was small, there was statistical significance in the change of the means of how students perceived mathematics as a male domain, and how teachers perceived students' achievements. This notion was coupled with students' development of conceptual understanding, which was tracked throughout the semester by mapping students' work with the Lesh Translation Model.

The Chinese number naming system and its impact on the arithmetic performance of pre-schoolers in Hong Kong

NASA Astrophysics Data System (ADS)

Ng, Sharon Sui Ngan

2012-06-01

Asian children, including Chinese children, perform better than their English-speaking peers in cross-national mathematics studies. This superior Asian performance is attributed to several factors including cultural beliefs, educational systems and practices, and the Chinese number naming system. Given the limited empirical evidence on pre-school mathematics learning in Chinese societies, the outcomes of Western studies are often borrowed and adopted in curriculum planning in Asian schools. The study reported in this paper investigated the performance of Hong Kong Chinese pre-school children based on Western studies involving English-speaking children, and examined the relationship between the Chinese number naming system and children's performance in number and operation concepts. Data were collected from 299 pre-school children aged between 3 and 5 years. The learning sequence of the children in mastering number and operation concepts was established using the Rasch Model. This study provides empirical evidence for the feasibility of borrowing lists of mathematics concepts from studies of English-speaking children to serve as a reference for school-based curriculum planning in a Chinese-speaking context. However, it is not enough to establish the relationship between children's performance and the Chinese number naming system. Classroom instruction and cultural beliefs in mathematics learning are also important in explaining children's performance.

Cadastral data model established and perfected with 4S technology

NASA Astrophysics Data System (ADS)

He, Beijing; He, Jiang; He, Jianpeng

1998-08-01

Considering China's social essential system and the actual case of the formation of cadastral information in urban and rural area, and based on the 4S technology and the theory and method of canton's GPS geodetic data bench developed by the authors, we thoroughly research on some correlative technical problems about establishing and perfecting all-level's microcosmic cadastral data model (called model in the following) once again. Such problems as the following are included: cadastral, feature and topographic information and its modality and expressing method, classifying and grading the model, coordinate system to be selected, data basis for the model, the collecting method and digitalization of information, database's structural model, mathematical model and the establishing technology of 3 or more dimensional model, dynamic monitoring of and the development and application of the model. Then, the domestic and overseas application prospect is revealed. It also has the tendency to intrude markets cooperated with 'data bench' technology or RS image maps' all-analysis digital surveying and mapping technology.

Modelling and simulating reaction-diffusion systems using coloured Petri nets.

PubMed

Liu, Fei; Blätke, Mary-Ann; Heiner, Monika; Yang, Ming

2014-10-01

Reaction-diffusion systems often play an important role in systems biology when developmental processes are involved. Traditional methods of modelling and simulating such systems require substantial prior knowledge of mathematics and/or simulation algorithms. Such skills may impose a challenge for biologists, when they are not equally well-trained in mathematics and computer science. Coloured Petri nets as a high-level and graphical language offer an attractive alternative, which is easily approachable. In this paper, we investigate a coloured Petri net framework integrating deterministic, stochastic and hybrid modelling formalisms and corresponding simulation algorithms for the modelling and simulation of reaction-diffusion processes that may be closely coupled with signalling pathways, metabolic reactions and/or gene expression. Such systems often manifest multiscaleness in time, space and/or concentration. We introduce our approach by means of some basic diffusion scenarios, and test it against an established case study, the Brusselator model. Copyright © 2014 Elsevier Ltd. All rights reserved.

Mathematical modeling of spinning elastic bodies for modal analysis.

NASA Technical Reports Server (NTRS)

Likins, P. W.; Barbera, F. J.; Baddeley, V.

1973-01-01

The problem of modal analysis of an elastic appendage on a rotating base is examined to establish the relative advantages of various mathematical models of elastic structures and to extract general inferences concerning the magnitude and character of the influence of spin on the natural frequencies and mode shapes of rotating structures. In realization of the first objective, it is concluded that except for a small class of very special cases the elastic continuum model is devoid of useful results, while for constant nominal spin rate the distributed-mass finite-element model is quite generally tractable, since in the latter case the governing equations are always linear, constant-coefficient, ordinary differential equations. Although with both of these alternatives the details of the formulation generally obscure the essence of the problem and permit very little engineering insight to be gained without extensive computation, this difficulty is not encountered when dealing with simple concentrated mass models.

Analysis of geologic terrain models for determination of optimum SAR sensor configuration and optimum information extraction for exploration of global non-renewable resources. Pilot study: Arkansas Remote Sensing Laboratory, part 1, part 2, and part 3

NASA Technical Reports Server (NTRS)

Kaupp, V. H.; Macdonald, H. C.; Waite, W. P.; Stiles, J. A.; Frost, F. S.; Shanmugam, K. S.; Smith, S. A.; Narayanan, V.; Holtzman, J. C. (Principal Investigator)

1982-01-01

Computer-generated radar simulations and mathematical geologic terrain models were used to establish the optimum radar sensor operating parameters for geologic research. An initial set of mathematical geologic terrain models was created for three basic landforms and families of simulated radar images were prepared from these models for numerous interacting sensor, platform, and terrain variables. The tradeoffs between the various sensor parameters and the quantity and quality of the extractable geologic data were investigated as well as the development of automated techniques of digital SAR image analysis. Initial work on a texture analysis of SEASAT SAR imagery is reported. Computer-generated radar simulations are shown for combinations of two geologic models and three SAR angles of incidence.

Mathematical Models of Continuous Flow Electrophoresis

NASA Technical Reports Server (NTRS)

Saville, D. A.; Snyder, R. S.

1985-01-01

Development of high resolution continuous flow electrophoresis devices ultimately requires comprehensive understanding of the ways various phenomena and processes facilitate or hinder separation. A comprehensive model of the actual three dimensional flow, temperature and electric fields was developed to provide guidance in the design of electrophoresis chambers for specific tasks and means of interpreting test data on a given chamber. Part of the process of model development includes experimental and theoretical studies of hydrodynamic stability. This is necessary to understand the origin of mixing flows observed with wide gap gravitational effects. To insure that the model accurately reflects the flow field and particle motion requires extensive experimental work. Another part of the investigation is concerned with the behavior of concentrated sample suspensions with regard to sample stream stability particle-particle interactions which might affect separation in an electric field, especially at high field strengths. Mathematical models will be developed and tested to establish the roles of the various interactions.

How Well Does A-Level Mathematics Prepare Students for the Mathematical Demands of Chemistry Degrees?

ERIC Educational Resources Information Center

Darlington, Ellie; Bowyer, Jessica

2016-01-01

332 undergraduate chemistry students were surveyed in order to establish whether they had found A-level Mathematics and/or Further Mathematics to be good preparation for their degree. Perceptions of both subjects were found to be positive, with more than 80% of participants describing Mathematics or Further Mathematics as good preparation. In…

A Constructive Response to "Where Mathematics Comes From."

ERIC Educational Resources Information Center

Schiralli, Martin; Sinclair, Nathalie

2003-01-01

Reviews the Lakoff and Nunez's book, "Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being (2000)," which provided many mathematics education researchers with a novel and startling perspective on mathematical thinking. Suggests that several of the book's flaws can be addressed through a more rigorous establishment of…

Cultural Horizons for Mathematics

ERIC Educational Resources Information Center

Owens, Kay; Paraides, Patricia; Nutti, Ylva Jannok; Johansson, Gunilla; Bennet, Maria; Doolan, Pat; Peckham, Ray; Hill, John; Doolan, Frank; O'Sullivan, Dominic; Murray, Libbey; Logan, Patricia; McNair, Melissa; Sunnari, Vappu; Murray, Beatrice; Miller, Alissa; Nolan, John; Simpson, Alca; Ohrin, Christine; Doolan, Terry; Doolan, Michelle; Taylor, Paul

2011-01-01

As a result of a number of government reports, there have been numerous systemic changes in Indigenous education in Australia revolving around the importance of partnerships with the community. A forum with our local Dubbo community established the importance of working together and developed a model which placed the child in an ecological…

Dissemination, resuspension, and filtration of carbon fibers. [aircraft fires

NASA Technical Reports Server (NTRS)

Elber, W.

1980-01-01

Carbon fiber transport was studied using mathematical models established for other pollution problems. It was demonstrated that resuspension is not a major factor contributing to the risk. Filtration and fragmentation tests revealed that fiber fragmentation shifts the fiber spectrum to shorter mean lengths in high velocity air handling systems.

THE CLIMATIC AND HYDROLOGIC FACTORS AFFECTING THE REDISTRIBUTION OF SR-90

DTIC Science & Technology

leaching solution present and the chemical and cation exchange properties of the soil solution ; a mathematical model of movement was established...manual for using high speed computers to compute the factors of the daily water balance was prepared; the influence of the soil solution in

Peer-Assisted Learning in Mathematics: An Observational Study of Student Success

ERIC Educational Resources Information Center

Cheng, Dorothy; Walters, Matthew

2009-01-01

The Peer-Assisted Learning (PAL) program at the University of Minnesota has drawn from the best practices of Supplemental Instruction, Peer-Led Team Learning, Structured Learning Assistance, the Emerging Scholars Program, and other successful postsecondary peer cooperative learning models to establish guiding principles for structuring learning…

The Engineering Design Process as a Model for STEM Curriculum Design

ERIC Educational Resources Information Center

Corbett, Krystal Sno

2012-01-01

Engaging pedagogics have been proven to be effective in the promotion of deep learning for science, technology, engineering, and mathematics (STEM) students. In many cases, academic institutions have shown a desire to improve education by implementing more engaging techniques in the classroom. The research framework established in this…

Design of a Field Test for Probability of Hit by Antiaircraft Guns

DTIC Science & Technology

1973-02-01

not available. • The cost of conducting the numerous field test trials that would be needed to establish the loss rates of aircraft to antiaircraft...mathematical models provide a readily available and relatively inexpensive way to obtain estimates of aircraft losses to antiaircraft guns. Because these...aircraft losses to antiaircraft guns, the use of the models can contribute greatly to better decisions. But if the models produce invalid estimates

Study of Vis/NIR spectroscopy measurement on acidity of yogurt

NASA Astrophysics Data System (ADS)

He, Yong; Feng, Shuijuan; Wu, Di; Li, Xiaoli

2006-09-01

A fast measurement of pH of yogurt using Vis/NIR-spectroscopy techniques was established in order to measuring the acidity of yogurt rapidly. 27 samples selected separately from five different brands of yogurt were measured by Vis/NIR-spectroscopy. The pH of yogurt on positions scanned by spectrum was measured by a pH meter. The mathematical model between pH and Vis/NIR spectral measurements was established and developed based on partial least squares (PLS) by using Unscramble V9.2. Then 25 unknown samples from 5 different brands were predicted based on the mathematical model. The result shows that The correlation coefficient of pH based on PLS model is more than 0.890, and standard error of calibration (SEC) is 0.037, standard error of prediction (SEP) is 0.043. Through predicting the pH of 25 samples of yogurt from 5 different brands, the correlation coefficient between predictive value and measured value of those samples is more than 0918. The results show the good to excellent prediction performances. The Vis/NIR spectroscopy technique had a significant greater accuracy for determining the value of pH. It was concluded that the VisINIRS measurement technique can be used to measure pH of yogurt fast and accurately, and a new method for the measurement of pH of yogurt was established.

[A dynamic model of the extravehicular (correction of extravehicuar) activity space suit].

PubMed

Yang, Feng; Yuan, Xiu-gan

2002-12-01

Objective. To establish a dynamic model of the space suit base on the particular configuration of the space suit. Method. The mass of the space suit components, moment of inertia, mobility of the joints of space suit, as well as the suit-generated torques, were considered in this model. The expressions to calculate the moment of inertia were developed by simplifying the geometry of the space suit. A modified Preisach model was used to mathematically describe the hysteretic torque characteristics of joints in a pressurized space suit, and it was implemented numerically basing on the observed suit parameters. Result. A dynamic model considering mass, moment of inertia and suit-generated torques was established. Conclusion. This dynamic model provides some elements for the dynamic simulation of the astronaut extravehicular activity.

Early Number Skills Gains and Mathematics Achievement: Intervening to Establish Successful Early Mathematics Trajectories

ERIC Educational Resources Information Center

Shanley, Lina; Clarke, Ben; Doabler, Christian T.; Kurtz-Nelson, Evangeline; Fien, Hank

2017-01-01

Early number skills, comprised of both informal and formal skills, are associated with later mathematics achievement. Thus, the development of foundational early number skills is an important aspect of early mathematics instruction. This study explored relations between early number skills gains and mathematics achievement for students at risk for…

Modelling and analysis of gene regulatory network using feedback control theory

NASA Astrophysics Data System (ADS)

El-Samad, H.; Khammash, M.

2010-01-01

Molecular pathways are a part of a remarkable hierarchy of regulatory networks that operate at all levels of organisation. These regulatory networks are responsible for much of the biological complexity within the cell. The dynamic character of these pathways and the prevalence of feedback regulation strategies in their operation make them amenable to systematic mathematical analysis using the same tools that have been used with success in analysing and designing engineering control systems. In this article, we aim at establishing this strong connection through various examples where the behaviour exhibited by gene networks is explained in terms of their underlying control strategies. We complement our analysis by a survey of mathematical techniques commonly used to model gene regulatory networks and analyse their dynamic behaviour.

Mathematical analysis of a nutrient-plankton system with delay.

PubMed

Rehim, Mehbuba; Zhang, Zhenzhen; Muhammadhaji, Ahmadjan

2016-01-01

A mathematical model describing the interaction of nutrient-plankton is investigated in this paper. In order to account for the time needed by the phytoplankton to mature after which they can release toxins, a discrete time delay is incorporated into the system. Moreover, it is also taken into account discrete time delays which indicates the partially recycled nutrient decomposed by bacteria after the death of biomass. In the first part of our analysis the sufficient conditions ensuring local and global asymptotic stability of the model are obtained. Next, the existence of the Hopf bifurcation as time delay crosses a threshold value is established and, meanwhile, the phenomenon of stability switches is found under certain conditions. Numerical simulations are presented to illustrate the analytical results.

[Impacts of multicomponent environment on solubility of puerarin in biopharmaceutics classification system of Chinese materia medica].

PubMed

Hou, Cheng-Bo; Wang, Guo-Peng; Zhang, Qiang; Yang, Wen-Ning; Lv, Bei-Ran; Wei, Li; Dong, Ling

2014-12-01

To illustrate the solubility involved in biopharmaceutics classification system of Chinese materia medica (CMMBCS) , the influences of artificial multicomponent environment on solubility were investigated in this study. Mathematical model was built to describe the variation trend of their influence on the solubility of puerarin. Carried out with progressive levels, single component environment: baicalin, berberine and glycyrrhizic acid; double-component environment: baicalin and glycyrrhizic acid, baicalin and berberine and glycyrrhizic acid and berberine; and treble-component environment: baicalin, berberin, glycyrrhizic acid were used to describe the variation tendency of their influences on the solubility of puerarin, respectively. And then, the mathematical regression equation model was established to characterize the solubility of puerarin under multicomponent environment.

Microgravity Investigation of Capillary Driven Imbibition

NASA Astrophysics Data System (ADS)

Dushin, V. R.; Nikitin, V. F.; Smirnov, N. N.; Skryleva, E. I.; Tyurenkova, V. V.

2018-05-01

The goal of the present paper is to investigate the capillary driven filtration in porous media under microgravity conditions. New mathematical model that allows taking into account the blurring of the front due to the instability of the displacement that is developing at the front is proposed. The constants in the mathematical model were selected on the basis of the experimental data on imbibition into unsaturated porous media under microgravity conditions. The flow under the action of a combination of capillary forces and a constant pressure drop or a constant flux is considered. The effect of capillary forces and the type of wettability of the medium on the displacement process is studied. A criterion in which case the capillary effects are insignificant and can be neglected is established.

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.

Mathematical modelling and quantitative methods.

PubMed

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

2002-01-01

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

Thermodynamic Modeling and Optimization of the Copper Flash Converting Process Using the Equilibrium Constant Method

NASA Astrophysics Data System (ADS)

Li, Ming-zhou; Zhou, Jie-min; Tong, Chang-ren; Zhang, Wen-hai; Chen, Zhuo; Wang, Jin-liang

2018-05-01

Based on the principle of multiphase equilibrium, a mathematical model of the copper flash converting process was established by the equilibrium constant method, and a computational system was developed with the use of MetCal software platform. The mathematical model was validated by comparing simulated outputs, industrial data, and published data. To obtain high-quality blister copper, a low copper content in slag, and increased impurity removal rate, the model was then applied to investigate the effects of the operational parameters [oxygen/feed ratio (R OF), flux rate (R F), and converting temperature (T)] on the product weights, compositions, and the distribution behaviors of impurity elements. The optimized results showed that R OF, R F, and T should be controlled at approximately 156 Nm3/t, within 3.0 pct, and at approximately 1523 K (1250 °C), respectively.

Battery charging and discharging research based on the interactive technology of smart grid and electric vehicle

NASA Astrophysics Data System (ADS)

Zhang, Mingyang

2018-06-01

To further study the bidirectional flow problem of V2G (Vehicle to Grid) charge and discharge motor, the mathematical model of AC/DC converter and bi-directional DC/DC converter was established. Then, lithium battery was chosen as the battery of electric vehicle and its mathematical model was established. In order to improve the service life of lithium battery, bidirectional DC/DC converter adopted constant current and constant voltage control strategy. In the initial stage of charging, constant current charging was adopted with current single closed loop control. After reaching a certain value, voltage was switched to constant voltage charging controlled by voltage and current. Subsequently, the V2G system simulation model was built in MATLAB/Simulink. The simulation results verified the correctness of the control strategy and showed that when charging, constant current and constant voltage charging was achieved, the grid side voltage and current were in the same phase, and the power factor was about 1. When discharging, the constant current discharge was applied, and the grid voltage and current phase difference was r. To sum up, the simulation results are correct and helpful.

A hybrid model for traffic flow and crowd dynamics with random individual properties.

PubMed

Schleper, Veronika

2015-04-01

Based on an established mathematical model for the behavior of large crowds, a new model is derived that is able to take into account the statistical variation of individual maximum walking speeds. The same model is shown to be valid also in traffic flow situations, where for instance the statistical variation of preferred maximum speeds can be considered. The model involves explicit bounds on the state variables, such that a special Riemann solver is derived that is proved to respect the state constraints. Some care is devoted to a valid construction of random initial data, necessary for the use of the new model. The article also includes a numerical method that is shown to respect the bounds on the state variables and illustrative numerical examples, explaining the properties of the new model in comparison with established models.

Novel mathematic models for quantitative transitivity of quality-markers in extraction process of the Buyanghuanwu decoction.

PubMed

Zhang, Yu-Tian; Xiao, Mei-Feng; Deng, Kai-Wen; Yang, Yan-Tao; Zhou, Yi-Qun; Zhou, Jin; He, Fu-Yuan; Liu, Wen-Long

2018-06-01

Nowadays, to research and formulate an efficiency extraction system for Chinese herbal medicine, scientists have always been facing a great challenge for quality management, so that the transitivity of Q-markers in quantitative analysis of TCM was proposed by Prof. Liu recently. In order to improve the quality of extraction from raw medicinal materials for clinical preparations, a series of integrated mathematic models for transitivity of Q-markers in quantitative analysis of TCM were established. Buyanghuanwu decoction (BYHWD) was a commonly TCMs prescription, which was used to prevent and treat the ischemic heart and brain diseases. In this paper, we selected BYHWD as an extraction experimental subject to study the quantitative transitivity of TCM. Based on theory of Fick's Rule and Noyes-Whitney equation, novel kinetic models were established for extraction of active components. Meanwhile, fitting out kinetic equations of extracted models and then calculating the inherent parameters in material piece and Q-marker quantitative transfer coefficients, which were considered as indexes to evaluate transitivity of Q-markers in quantitative analysis of the extraction process of BYHWD. HPLC was applied to screen and analyze the potential Q-markers in the extraction process. Fick's Rule and Noyes-Whitney equation were adopted for mathematically modeling extraction process. Kinetic parameters were fitted and calculated by the Statistical Program for Social Sciences 20.0 software. The transferable efficiency was described and evaluated by potential Q-markers transfer trajectory via transitivity availability AUC, extraction ratio P, and decomposition ratio D respectively. The Q-marker was identified with AUC, P, D. Astragaloside IV, laetrile, paeoniflorin, and ferulic acid were studied as potential Q-markers from BYHWD. The relative technologic parameters were presented by mathematic models, which could adequately illustrate the inherent properties of raw materials preparation and affection of Q-markers transitivity in equilibrium processing. AUC, P, D for potential Q-markers of AST-IV, laetrile, paeoniflorin, and FA were obtained, with the results of 289.9 mAu s, 46.24%, 22.35%; 1730 mAu s, 84.48%, 1.963%; 5600 mAu s, 70.22%, 0.4752%; 7810 mAu s, 24.29%, 4.235%, respectively. The results showed that the suitable Q-markers were laetrile and paeoniflorin in our study, which exhibited acceptable traceability and transitivity in the extraction process of TCMs. Therefore, these novel mathematic models might be developed as a new standard to control TCMs quality process from raw medicinal materials to product manufacturing. Copyright © 2018 Elsevier GmbH. All rights reserved.

Mathematical Conversations to Transform Algebra Class

ERIC Educational Resources Information Center

Szydlik, Jennifer Earles

2015-01-01

Classroom culture is established through both conversations and practices. Traditionally in mathematics class, the focus is primarily on the latter; that is, students are shown what "doing mathematics" looks like, and then asked that they try it themselves. This article discusses three mathematical conversations that help bring…

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.

Objective estimation of tropical cyclone innercore surface wind structure using infrared satellite images

NASA Astrophysics Data System (ADS)

Zhang, Changjiang; Dai, Lijie; Ma, Leiming; Qian, Jinfang; Yang, Bo

2017-10-01

An objective technique is presented for estimating tropical cyclone (TC) innercore two-dimensional (2-D) surface wind field structure using infrared satellite imagery and machine learning. For a TC with eye, the eye contour is first segmented by a geodesic active contour model, based on which the eye circumference is obtained as the TC eye size. A mathematical model is then established between the eye size and the radius of maximum wind obtained from the past official TC report to derive the 2-D surface wind field within the TC eye. Meanwhile, the composite information about the latitude of TC center, surface maximum wind speed, TC age, and critical wind radii of 34- and 50-kt winds can be combined to build another mathematical model for deriving the innercore wind structure. After that, least squares support vector machine (LSSVM), radial basis function neural network (RBFNN), and linear regression are introduced, respectively, in the two mathematical models, which are then tested with sensitivity experiments on real TC cases. Verification shows that the innercore 2-D surface wind field structure estimated by LSSVM is better than that of RBFNN and linear regression.

The Multiphoton Interaction of Lambda Model Atom and Two-Mode Fields

NASA Technical Reports Server (NTRS)

Liu, Tang-Kun

1996-01-01

The system of two-mode fields interacting with atom by means of multiphotons is addressed, and the non-classical statistic quality of two-mode fields with interaction is discussed. Through mathematical calculation, some new rules of non-classical effects of two-mode fields which evolue with time, are established.

Intelligent Tutoring Systems: Formalization as Automata and Interface Design Using Neural Networks

ERIC Educational Resources Information Center

Curilem, S. Gloria; Barbosa, Andrea R.; de Azevedo, Fernando M.

2007-01-01

This article proposes a mathematical model of Intelligent Tutoring Systems (ITS), based on observations of the behaviour of these systems. One of the most important problems of pedagogical software is to establish a common language between the knowledge areas involved in their development, basically pedagogical, computing and domain areas. A…

The Upward Progress of Unusually Good Ideas in a Four-Tier Hierarchy.

ERIC Educational Resources Information Center

Dunning, Robert Scott; Sincoff, Michael Z.

In long established research organizations, it is necessary to safeguard good research ideas originating at lower organizational levels. The upward progress of unusually good ideas in an organizational hierarchy may be compared with that of ordinary ideas by means of a mathematical model, with the assumption that ideas follow a Poisson…

A Mathematical Model of Anthrax Transmission in Animal Populations.

PubMed

Saad-Roy, C M; van den Driessche, P; Yakubu, Abdul-Aziz

2017-02-01

A general mathematical model of anthrax (caused by Bacillus anthracis) transmission is formulated that includes live animals, infected carcasses and spores in the environment. The basic reproduction number [Formula: see text] is calculated, and existence of a unique endemic equilibrium is established for [Formula: see text] above the threshold value 1. Using data from the literature, elasticity indices for [Formula: see text] and type reproduction numbers are computed to quantify anthrax control measures. Including only herbivorous animals, anthrax is eradicated if [Formula: see text]. For these animals, oscillatory solutions arising from Hopf bifurcations are numerically shown to exist for certain parameter values with [Formula: see text] and to have periodicity as observed from anthrax data. Including carnivores and assuming no disease-related death, anthrax again goes extinct below the threshold. Local stability of the endemic equilibrium is established above the threshold; thus, periodic solutions are not possible for these populations. It is shown numerically that oscillations in spore growth may drive oscillations in animal populations; however, the total number of infected animals remains about the same as with constant spore growth.

Business Mathematics Curriculum Guide. Bulletin 1612. Revised.

ERIC Educational Resources Information Center

Louisiana State Dept. of Education, Baton Rouge. Div. of Academic Programs.

This curriculum guide for business mathematics was developed to establish statewide curriculum standards for the Louisiana Competency-based Education Program. Following an overview of the secondary school mathematics curriculum, eight goals for the business mathematics course are listed. A pacing chart with suggested time periods for each major…

Mathematics anxiety and mathematics achievement

NASA Astrophysics Data System (ADS)

Sherman, Brian F.; Wither (Post.), David P.

2003-09-01

This paper is a distillation of the major result from the 1998 Ph.D. thesis of the late David Wither. It details a longitudinal study over five years of the relationship between mathematics anxiety and mathematics achievement. It starts from the already well documented negative correlation between the two, and seeks to establish one of the three hypotheses—that mathematics anxiety causes an impairment of mathematics achievement; that lack of mathematics achievement causes mathematics anxiety; or that there is a third underlying cause of the two.

Evaluation and clinical significance of the stomach age model for evaluating aging of the stomach-a multicenter study in China

PubMed Central

2014-01-01

Background A higher prevalence of chronic atrophic gastritis (CAG) occurs in younger adults in Asia. We used Stomach Age to examine the different mechanisms of CAG between younger adults and elderly individuals, and established a simple model of cancer risk that can be applied to CAG surveillance. Methods Stomach Age was determined by FISH examination of telomere length in stomach biopsies. Δψm was also determined by flow cytometry. Sixty volunteers were used to confirm the linear relationship between telomere length and age while 120 subjects were used to build a mathematical model by a multivariate analysis. Overall, 146 subjects were used to evaluate the validity of the model, and 1,007 subjects were used to evaluate the relationship between prognosis and Δage (calculated from the mathematical model). ROC curves were used to evaluate the relationship between prognosis and Δage and to determine the cut-off point for Δage. Results We established that a tight linear relationship between the telomere length and the age. The telomere length was obvious different between patients with and without CAG even in the same age. Δψm decreased in individuals whose Stomach Age was greater than real age, especially in younger adults. A mathematical model of Stomach Age (real age + Δage) was successfully constructed which was easy to apply in clinical work. A higher Δage was correlated with a worse outcome. The criterion of Δage >3.11 should be considered as the cut-off to select the subgroup of patients who require endoscopic surveillance. Conclusion Variation in Stomach Age between individuals of the same biological age was confirmed. Attention should be paid to those with a greater Stomach Age, especially in younger adults. The Δage in the Simple Model can be used as a criterion to select CAG patients for gastric cancer surveillance. PMID:25057261

Expanding Mathematics Preparation of Elementary and Middle School Teachers

ERIC Educational Resources Information Center

Buck, Robert E.

2004-01-01

One of the major problems facing education today is the inadequate mathematics' preparation of pre-college students and their teachers. Most colleges and universities have well established programs for students planning to teach mathematics at the secondary schools; however, in many institutions pre-secondary mathematics has been addressed only…

Establishing Validity of the Thai Mathematics Teaching Efficacy Beliefs Instrument

ERIC Educational Resources Information Center

Matney, Gabriel; Jackson, Jack L., II.; Panarach, Yupadee

2016-01-01

This article presents our work in translating the Mathematics Teaching Efficacy Beliefs Instrument (MTEBI) from English to Thai and our resulting investigation of validity with Thai preservice teachers. The translation process occurred over several meetings between two U.S. mathematics educators and one Thai mathematics educator. To check for…

NCTM Principles and Standards for Mathematically Talented Students

ERIC Educational Resources Information Center

Deal, Linda J.; Wismer, Michael G.

2010-01-01

The "Principles and Standards for School Mathematics" published in 2000 by the National Council of Teachers of Mathematics (NCTM) created a vision of mathematical concepts and processes to establish core educational guidelines for instruction from grades K to 12. The overall plan does emphasize higher level thinking, problem solving, and…

The Emergence of Mathematical Structures

ERIC Educational Resources Information Center

Hegedus, Stephen John; Moreno-Armella, Luis

2011-01-01

We present epistemological ruptures that have occurred in mathematical history and in the transformation of using technology in mathematics education in the twenty-first century. We describe how such changes establish a new form of digital semiotics that challenges learning paradigms and mathematical inquiry for learners today. We focus on drawing…

Caries assessment: establishing mathematical link of clinical and benchtop method

NASA Astrophysics Data System (ADS)

Amaechi, Bennett T.

2009-02-01

It is well established that the development of new technologies for early detection and quantitative monitoring of dental caries at its early stage could provide health and economic benefits ranging from timely preventive interventions to reduction of the time required for clinical trials of anti-caries agents. However, the new technologies currently used in clinical setting cannot assess and monitor caries using the actual mineral concentration within the lesion, while a laboratory-based microcomputed tomography (MCT) has been shown to possess this capability. Thus we envision the establishment of mathematical equations relating the measurements of each of the clinical technologies to that of MCT will enable the mineral concentration of lesions detected and assessed in clinical practice to be extrapolated from the equation, and this will facilitate preventitive care in dentistry to lower treatment cost. We utilize MCT and the two prominent clinical caries assessment devices (Quantitative Light-induced Fluorescence [QLF] and Diagnodent) to longitudinally monitor the development of caries in a continuous flow mixed-organisms biofilm model (artificial mouth), and then used the collected data to establish mathematical equation relating the measurements of each of the clinical technologies to that of MCT. A linear correlation was observed between the measurements of MicroCT and that of QLF and Diagnodent. Thus mineral density in a carious lesion detected and measured using QLF or Diagnodent can be extrapolated using the developed equation. This highlights the usefulness of MCT for monitoring the progress of an early caries being treated with therapeutic agents in clinical practice or trials.

Building a Career Mathematics File: Challenging Students to Find the Importance of Mathematics in a Variety of Occupations

ERIC Educational Resources Information Center

Keleher, Lori A.

2006-01-01

The Career Mathematics file is an occupational problem-solving system, which includes a wide range of mathematical problems and solutions, collected from various resources and helps students establish connections between mathematics and their environment. The study shows that the problems given can be used as realistic examples to study and…

Stochastic Models of Human Errors

NASA Technical Reports Server (NTRS)

Elshamy, Maged; Elliott, Dawn M. (Technical Monitor)

2002-01-01

Humans play an important role in the overall reliability of engineering systems. More often accidents and systems failure are traced to human errors. Therefore, in order to have meaningful system risk analysis, the reliability of the human element must be taken into consideration. Describing the human error process by mathematical models is a key to analyzing contributing factors. Therefore, the objective of this research effort is to establish stochastic models substantiated by sound theoretic foundation to address the occurrence of human errors in the processing of the space shuttle.

Establishment of a center of excellence for applied mathematical and statistical research

NASA Technical Reports Server (NTRS)

Woodward, W. A.; Gray, H. L.

1983-01-01

The state of the art was assessed with regards to efforts in support of the crop production estimation problem and alternative generic proportion estimation techniques were investigated. Topics covered include modeling the greeness profile (Badhwarmos model), parameter estimation using mixture models such as CLASSY, and minimum distance estimation as an alternative to maximum likelihood estimation. Approaches to the problem of obtaining proportion estimates when the underlying distributions are asymmetric are examined including the properties of Weibull distribution.

Modeling and stability of electro-hydraulic servo of hydraulic excavator

NASA Astrophysics Data System (ADS)

Jia, Wenhua; Yin, Chenbo; Li, Guo; Sun, Menghui

2017-11-01

The condition of the hydraulic excavator is complicated and the working environment is bad. The safety and stability of the control system is influenced by the external factors. This paper selects hydraulic excavator electro-hydraulic servo system as the research object. A mathematical model and simulation model using AMESIM of servo system is established. Then the pressure and flow characteristics are analyzed. The design and optimization of electro-hydraulic servo system and its application in engineering machinery is provided.

Estimation of the dynamics and rate of transmission of classical swine fever (hog cholera) in wild pigs.

PubMed Central

Hone, J.; Pech, R.; Yip, P.

1992-01-01

Infectious diseases establish in a population of wildlife hosts when the number of secondary infections is greater than or equal to one. To estimate whether establishment will occur requires extensive experience or a mathematical model of disease dynamics and estimates of the parameters of the disease model. The latter approach is explored here. Methods for estimating key model parameters, the transmission coefficient (beta) and the basic reproductive rate (RDRS), are described using classical swine fever (hog cholera) in wild pigs as an example. The tentative results indicate that an acute infection of classical swine fever will establish in a small population of wild pigs. Data required for estimation of disease transmission rates are reviewed and sources of bias and alternative methods discussed. A comprehensive evaluation of the biases and efficiencies of the methods is needed. PMID:1582476

Engineering Bacteria to Search for Specific Concentrations of Molecules by a Systematic Synthetic Biology Design Method

PubMed Central

Chen, Bor-Sen

2016-01-01

Bacteria navigate environments full of various chemicals to seek favorable places for survival by controlling the flagella’s rotation using a complicated signal transduction pathway. By influencing the pathway, bacteria can be engineered to search for specific molecules, which has great potential for application to biomedicine and bioremediation. In this study, genetic circuits were constructed to make bacteria search for a specific molecule at particular concentrations in their environment through a synthetic biology method. In addition, by replacing the “brake component” in the synthetic circuit with some specific sensitivities, the bacteria can be engineered to locate areas containing specific concentrations of the molecule. Measured by the swarm assay qualitatively and microfluidic techniques quantitatively, the characteristics of each “brake component” were identified and represented by a mathematical model. Furthermore, we established another mathematical model to anticipate the characteristics of the “brake component”. Based on this model, an abundant component library can be established to provide adequate component selection for different searching conditions without identifying all components individually. Finally, a systematic design procedure was proposed. Following this systematic procedure, one can design a genetic circuit for bacteria to rapidly search for and locate different concentrations of particular molecules by selecting the most adequate “brake component” in the library. Moreover, following simple procedures, one can also establish an exclusive component library suitable for other cultivated environments, promoter systems, or bacterial strains. PMID:27096615

Dreaming of mathematical neuroscience for half a century.

PubMed

Amari, Shun-ichi

2013-01-01

Theoreticians have been enchanted by the secrets of the brain for many years: how and why does it work so well? There has been a long history of searching for its mechanisms. Theoretical or even mathematical scientists have proposed various models of neural networks which has led to the birth of a new field of research. We can think of the 'pre-historic' period of Rashevski and Wiener, and then the period of perceptrons which is the beginning of learning machines, neurodynamics approaches, and further connectionist approaches. Now is currently the period of computational neuroscience. I have been working in this field for nearly half a century, and have experienced its repeated rise and fall. Now having reached very old age, I would like to state my own endeavors on establishing mathematical neuroscience for half a century, from a personal, even biased, point of view. It would be my pleasure if my experiences could encourage young researchers to participate in mathematical neuroscience. Copyright © 2012 Elsevier Ltd. All rights reserved.

A model of neuro-musculo-skeletal system for human locomotion under position constraint condition.

PubMed

Ni, Jiangsheng; Hiramatsu, Seiji; Kato, Atsuo

2003-08-01

The human locomotion was studied on the basis of the interaction of the musculo-skeletal system, the neural system and the environment. A mathematical model of human locomotion under position constraint condition was established. Besides the neural rhythm generator, the posture controller and the sensory system, the environment feedback controller and the stability controller were taken into account in the model. The environment feedback controller was proposed for two purposes, obstacle avoidance and target position control of the swing foot. The stability controller was proposed to imitate the self-balancing ability of a human body and improve the stability of the model. In the stability controller, the ankle torque was used to control the velocity of the body gravity center. A prediction control algorithm was applied to calculate the torque magnitude of the stability controller. As an example, human stairs climbing movement was simulated and the results were given. The simulation result proved that the mathematical modeling of the task was successful.

Storage and growth of denitrifiers in aerobic granules: part I. model development.

PubMed

Ni, Bing-Jie; Yu, Han-Qing

2008-02-01

A mathematical model, based on the Activated Sludge Model No.3 (ASM3), is developed to describe the storage and growth activities of denitrifiers in aerobic granules under anoxic conditions. In this model, mass transfer, hydrolysis, simultaneous anoxic storage and growth, anoxic maintenance, and endogenous decay are all taken into account. The model established is implemented in the well-established AQUASIM simulation software. A combination of completely mixed reactor and biofilm reactor compartments provided by AQUASIM is used to simulate the mass transport and conversion processes occurring in both bulk liquid and granules. The modeling results explicitly show that the external substrate is immediately utilized for storage and growth at feast phase. More external substrates are diverted to storage process than the primary biomass production process. The model simulation indicates that the nitrate utilization rate (NUR) of granules-based denitrification process includes four linear phases of nitrate reduction. Furthermore, the methodology for determining the most important parameter in this model, that is, anoxic reduction factor, is established. (c) 2007 Wiley Periodicals, Inc.

The need for data science in epidemic modelling. Comment on: "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al.

NASA Astrophysics Data System (ADS)

Danon, Leon; Brooks-Pollock, Ellen

2016-09-01

In their review, Chowell et al. consider the ability of mathematical models to predict early epidemic growth [1]. In particular, they question the central prediction of classical differential equation models that the number of cases grows exponentially during the early stages of an epidemic. Using examples including HIV and Ebola, they argue that classical models fail to capture key qualitative features of early growth and describe a selection of models that do capture non-exponential epidemic growth. An implication of this failure is that predictions may be inaccurate and unusable, highlighting the need for care when embarking upon modelling using classical methodology. There remains a lack of understanding of the mechanisms driving many observed epidemic patterns; we argue that data science should form a fundamental component of epidemic modelling, providing a rigorous methodology for data-driven approaches, rather than trying to enforce established frameworks. The need for refinement of classical models provides a strong argument for the use of data science, to identify qualitative characteristics and pinpoint the mechanisms responsible for the observed epidemic patterns.

Equation Discovery for Model Identification in Respiratory Mechanics of the Mechanically Ventilated Human Lung

NASA Astrophysics Data System (ADS)

Ganzert, Steven; Guttmann, Josef; Steinmann, Daniel; Kramer, Stefan

Lung protective ventilation strategies reduce the risk of ventilator associated lung injury. To develop such strategies, knowledge about mechanical properties of the mechanically ventilated human lung is essential. This study was designed to develop an equation discovery system to identify mathematical models of the respiratory system in time-series data obtained from mechanically ventilated patients. Two techniques were combined: (i) the usage of declarative bias to reduce search space complexity and inherently providing the processing of background knowledge. (ii) A newly developed heuristic for traversing the hypothesis space with a greedy, randomized strategy analogical to the GSAT algorithm. In 96.8% of all runs the applied equation discovery system was capable to detect the well-established equation of motion model of the respiratory system in the provided data. We see the potential of this semi-automatic approach to detect more complex mathematical descriptions of the respiratory system from respiratory data.

How Do Mathematicians Learn Math?: Resources and Acts for Constructing and Understanding Mathematics

ERIC Educational Resources Information Center

Wilkerson-Jerde, Michelle H.; Wilensky, Uri J.

2011-01-01

In this paper, we present an analytic framework for investigating expert mathematical learning as the process of building a "network of mathematical resources" by establishing relationships between different components and properties of mathematical ideas. We then use this framework to analyze the reasoning of ten mathematicians and mathematics…

Establishing and Sustaining an Effective Pre-Kindergarten Math Intervention at Scale

ERIC Educational Resources Information Center

Klein, Alice; Starkey, Prentice; DeFlorio, Lydia; Brown, E. Todd

2012-01-01

Educators are increasingly concerned about the low level of mathematics performance of U.S. students on the TIMSS and other international assessments of mathematics (National Mathematics Advisory Panel, 2008) as well as their insufficient preparation for mathematics standards, such as the Common Core State Standards. Students from low-income and…

Establishment of the mathematical model for diagnosing the engine valve faults by genetic programming

NASA Astrophysics Data System (ADS)

Yang, Wen-Xian

2006-05-01

Available machine fault diagnostic methods show unsatisfactory performances on both on-line and intelligent analyses because their operations involve intensive calculations and are labour intensive. Aiming at improving this situation, this paper describes the development of an intelligent approach by using the Genetic Programming (abbreviated as GP) method. Attributed to the simple calculation of the mathematical model being constructed, different kinds of machine faults may be diagnosed correctly and quickly. Moreover, human input is significantly reduced in the process of fault diagnosis. The effectiveness of the proposed strategy is validated by an illustrative example, in which three kinds of valve states inherent in a six-cylinders/four-stroke cycle diesel engine, i.e. normal condition, valve-tappet clearance and gas leakage faults, are identified. In the example, 22 mathematical functions have been specially designed and 8 easily obtained signal features are used to construct the diagnostic model. Different from existing GPs, the diagnostic tree used in the algorithm is constructed in an intelligent way by applying a power-weight coefficient to each feature. The power-weight coefficients vary adaptively between 0 and 1 during the evolutionary process. Moreover, different evolutionary strategies are employed, respectively for selecting the diagnostic features and functions, so that the mathematical functions are sufficiently utilized and in the meantime, the repeated use of signal features may be fully avoided. The experimental results are illustrated diagrammatically in the following sections.

Complex dynamics of an SEIR epidemic model with saturated incidence rate and treatment

NASA Astrophysics Data System (ADS)

Khan, Muhammad Altaf; Khan, Yasir; Islam, Saeed

2018-03-01

In this paper, we describe the dynamics of an SEIR epidemic model with saturated incidence, treatment function, and optimal control. Rigorous mathematical results have been established for the model. The stability analysis of the model is investigated and found that the model is locally asymptotically stable when R0 < 1. The model is locally as well as globally asymptotically stable at endemic equilibrium when R0 > 1. The proposed model may possess a backward bifurcation. The optimal control problem is designed and obtained their necessary results. Numerical results have been presented for justification of theoretical results.

Critical Masses for Academic Research Groups and Consequences for Higher Education Research Policy and Management

ERIC Educational Resources Information Center

Kenna, Ralph; Berche, Bertrand

2012-01-01

Smaller universities may produce research which is on a par with larger, elite establishments. This is confirmed by a recently developed mathematical model, supported by data from British and French higher education research-evaluation exercises. The detailed nature of the UK system, in particular, allows quantification of the notion of critical…

Teachers' Understanding of and Concerns about Mathematical Modeling in the Common Core Standards

ERIC Educational Resources Information Center

Wolf, Nancy Butler

2013-01-01

Educational reform is most likely to be successful when teachers are knowledgeable about the intended reform, and when their concerns about the reform are understood and addressed. The Common Core State Standards (CCSS) is an effort to establish a set of nationwide expectations for students and teachers. This study examined teacher understanding…

Mathematical modelling of radiotherapy strategies for early breast cancer.

PubMed

Enderling, Heiko; Anderson, Alexander R A; Chaplain, Mark A J; Munro, Alastair J; Vaidya, Jayant S

2006-07-07

Targeted intraoperative radiotherapy (Targit) is a new concept of partial breast irradiation where single fraction radiotherapy is delivered directly to the tumour bed. Apart from logistic advantages, this strategy minimizes the risk of missing the tumour bed and avoids delay between surgery and radiotherapy. It is presently being compared with the standard fractionated external beam radiotherapy (EBRT) in randomized trials. In this paper we present a mathematical model for the growth and invasion of a solid tumour into a domain of tissue (in this case breast tissue), and then a model for surgery and radiation treatment of this tumour. We use the established linear-quadratic (LQ) model to compute the survival probabilities for both tumour cells and irradiated breast tissue and then simulate the effects of conventional EBRT and Targit. True local recurrence of the tumour could arise either from stray tumour cells, or the tumour bed that harbours morphologically normal cells having a predisposition to genetic changes, such as a loss of heterozygosity (LOH) in genes that are crucial for tumourigenesis, e.g. tumour suppressor genes (TSGs). Our mathematical model predicts that the single high dose of radiotherapy delivered by Targit would result in eliminating all these sources of recurrence, whereas the fractionated EBRT would eliminate stray tumour cells, but allow (by virtue of its very schedule) the cells with LOH in TSGs or cell-cycle checkpoint genes to pass on low-dose radiation-induced DNA damage and consequently mutations that may favour the development of a new tumour. The mathematical model presented here is an initial attempt to model a biologically complex phenomenon that has until now received little attention in the literature and provides a 'proof of principle' that it is possible to produce clinically testable hypotheses on the effects of different approaches of radiotherapy for breast cancer.

Sensitivity of the model error parameter specification in weak-constraint four-dimensional variational data assimilation

NASA Astrophysics Data System (ADS)

Shaw, Jeremy A.; Daescu, Dacian N.

2017-08-01

This article presents the mathematical framework to evaluate the sensitivity of a forecast error aspect to the input parameters of a weak-constraint four-dimensional variational data assimilation system (w4D-Var DAS), extending the established theory from strong-constraint 4D-Var. Emphasis is placed on the derivation of the equations for evaluating the forecast sensitivity to parameters in the DAS representation of the model error statistics, including bias, standard deviation, and correlation structure. A novel adjoint-based procedure for adaptive tuning of the specified model error covariance matrix is introduced. Results from numerical convergence tests establish the validity of the model error sensitivity equations. Preliminary experiments providing a proof-of-concept are performed using the Lorenz multi-scale model to illustrate the theoretical concepts and potential benefits for practical applications.

Crash Certification by Analysis - Are We There Yet?

NASA Technical Reports Server (NTRS)

Jackson, Karen E.; Fasanella, Edwin L.; Lyle, Karen H.

2006-01-01

This paper addresses the issue of crash certification by analysis. This broad topic encompasses many ancillary issues including model validation procedures, uncertainty in test data and analysis models, probabilistic techniques for test-analysis correlation, verification of the mathematical formulation, and establishment of appropriate qualification requirements. This paper will focus on certification requirements for crashworthiness of military helicopters; capabilities of the current analysis codes used for crash modeling and simulation, including some examples of simulations from the literature to illustrate the current approach to model validation; and future directions needed to achieve "crash certification by analysis."

Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth

PubMed Central

Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M. L.; Hlatky, Lynn; Hahnfeldt, Philip

2014-01-01

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic. PMID:25167199

Classical mathematical models for description and prediction of experimental tumor growth.

PubMed

Benzekry, Sébastien; Lamont, Clare; Beheshti, Afshin; Tracz, Amanda; Ebos, John M L; Hlatky, Lynn; Hahnfeldt, Philip

2014-08-01

Despite internal complexity, tumor growth kinetics follow relatively simple laws that can be expressed as mathematical models. To explore this further, quantitative analysis of the most classical of these were performed. The models were assessed against data from two in vivo experimental systems: an ectopic syngeneic tumor (Lewis lung carcinoma) and an orthotopically xenografted human breast carcinoma. The goals were threefold: 1) to determine a statistical model for description of the measurement error, 2) to establish the descriptive power of each model, using several goodness-of-fit metrics and a study of parametric identifiability, and 3) to assess the models' ability to forecast future tumor growth. The models included in the study comprised the exponential, exponential-linear, power law, Gompertz, logistic, generalized logistic, von Bertalanffy and a model with dynamic carrying capacity. For the breast data, the dynamics were best captured by the Gompertz and exponential-linear models. The latter also exhibited the highest predictive power, with excellent prediction scores (≥80%) extending out as far as 12 days in the future. For the lung data, the Gompertz and power law models provided the most parsimonious and parametrically identifiable description. However, not one of the models was able to achieve a substantial prediction rate (≥70%) beyond the next day data point. In this context, adjunction of a priori information on the parameter distribution led to considerable improvement. For instance, forecast success rates went from 14.9% to 62.7% when using the power law model to predict the full future tumor growth curves, using just three data points. These results not only have important implications for biological theories of tumor growth and the use of mathematical modeling in preclinical anti-cancer drug investigations, but also may assist in defining how mathematical models could serve as potential prognostic tools in the clinic.

An Evolutionary Approach to Mathematics Education: Enhancing Learning through Contextual Modification

ERIC Educational Resources Information Center

Abate, Charles J.; Cantone, Kathleen A.

2005-01-01

Contemporary mathematics education is at a crossroads. It has become exposed to forces, both static and dynamic, that pose a challenge to its traditional place in academia. Mathematics has a long-established status as perhaps the most critical foundation for analytical knowledge. But the manner in which mathematics instructors choose to respond to…

Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (PME) (15th, Assisi, Italy, June 29-July 4, 1991), Volume 3.

ERIC Educational Resources Information Center

Furinghetti, Fulvia, Ed.

Research reports from the annual conference of the International Group for the Psychology of Mathematics Education include: "La construcion algorithmique: niveaux ou stades?" (Mesquita); "For Establishing the Generality of Conjectures" (Miyazaki); "Teachers' Attitudes Towards Mathematics and Mathematics Teaching:…

Study on mathematical model to predict aerated power consumption in a gas-liquid stirred tank

NASA Astrophysics Data System (ADS)

Luan, Deyu; Zhang, Shengfeng; Wei, Xing; Chen, Yiming

The aerated power consumption characteristics in a transparent tank with diameter of 0.3 m and flat bottom stirred by a Rushton impeller were investigated by means of experimental measurement. The test fluid used was tap water as liquid and air as gas. Based on Weibull model, the complete correlation of aerated power with aerated flow number was established through non-linear fit analysis. The effects of aerated rate and impeller speed on aerated power consumption were made an exploration. Results show that the changeable trend of the aerated power consumption is found to be similar under different impeller speeds and impeller diameters, i.e. the aerated power is close to dropping linear at the beginning of gas input, and then the drop tendency decreases as the aerated rate increases, at the end, the aerated power is a constant on the whole as the aerated rate reaches up the loading state. The non-linear fit curve is done using the software Origin based on the experimental data. The fairly high precision of data fit is obtained, which indicates that the mathematical model established can be used to accurately predict the aerated power consumption, comparatively. The proposed research provides a valuable instruction and reference for the design and enlargement of stirred vessel.

Correlation between age and the parameters of medial epiphysis and metaphysis of the clavicle using CT volume rendering images.

PubMed

Hua, Wei; Guang-you, Zhu; Lei, Wan; Chong-liang, Ying; Ya-hui, Wang

2014-11-01

The aim of this study was to evaluate the correlation between age and the parameters of medial epiphysis of clavicle based on CT volume rendering (VR) images. The CT images of the medial clavicle from 795 teenagers (387 male and 408 female) between 15 and 25 years were collected in East and South China. VR images were recombined from 0.60 mm thickness slice CT images. The ratio of epiphyseal diameter/metaphyseal diameter and the ratio of epiphyseal area/metaphyseal area of two sides of medial clavicle were measured and calculated by three different examiners, the quantitative data consistency was checked by intraclass correlation coefficients (ICC). The diameter ratio of left and right side are depicted as X1 and X3, and the area ratio of left and right side as X2 and X4. Descriptive statistic analysis of the data was performed and several mathematical models were established using least square. CT images from additional 60 teenagers (30 male and 30 female) were used to verify the accuracy of the established mathematical models. ICC indicated that the measurement of epiphyseal diameter, metaphyseal diameter, the ratio of epiphyseal diameter/metaphyseal diameter, epiphyseal area, metaphyseal area and the ratio of epiphyseal area/metaphyseal area of medial clavicle in the left and right side of the three examiners was approaching 1. The 95% reference range for the mean of every examination of both genders gradually increased with age. Females' data indicated by medial epiphysis of the clavicle development were earlier than male's, especially from 15 to 21 years. The difference of medial epiphysis of the clavicle development in gender becomes smaller after 21 years. The highest accuracy of the mathematical models made clear that male's accuracy was 73.5% (±1.0 year) and 85.3% (±1.5 year), and female's was 68.6% (±1.0 year) and 82.2% (±1.5 year) respectively. The methods of data collection and analysis were reliable and feasible. Combined the high accuracy of these established mathematical models, it is applicable to use the ratio of epiphyseal diameter/metaphyseal diameter and the ratio of epiphyseal area/metaphyseal area of left and right side of medial clavicle to estimate the teenager's age. Bearing this in mind, further studies are needed to evaluate slice thickness as the most critical parameter. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Lipid Raft Size and Lipid Mobility in Non-raft Domains Increase during Aging and Are Exacerbated in APP/PS1 Mice Model of Alzheimer's Disease. Predictions from an Agent-Based Mathematical Model

PubMed Central

Santos, Guido; Díaz, Mario; Torres, Néstor V.

2016-01-01

A connection between lipid rafts and Alzheimer's disease has been studied during the last decades. Mathematical modeling approaches have recently been used to correlate the effects of lipid composition changes in the physicochemical properties of raft-like membranes. Here we propose an agent based model to assess the effect of lipid changes in lipid rafts on the evolution and progression of Alzheimer's disease using lipid profile data obtained in an established model of familial Alzheimer's disease. We have observed that lipid raft size and lipid mobility in non-raft domains are two main factors that increase during age and are accelerated in the transgenic Alzheimer's disease mouse model. The consequences of these changes are discussed in the context of neurotoxic amyloid β production. Our agent based model predicts that increasing sterols (mainly cholesterol) and long-chain polyunsaturated fatty acids (LCPUFA) (mainly DHA, docosahexaenoic acid) proportions in the membrane composition might delay the onset and progression of the disease. PMID:27014089

Leadership through Professional Collaborations

ERIC Educational Resources Information Center

Pfeil, Jessica; Hirsch, Jenna

2013-01-01

Leaders in mathematics are responsible for implementing positive change within their school districts and motivating teachers of mathematics to improve their practices. One way mathematics leaders can achieve this goal is by establishing professional collaborations. We analyzed the research and summarized the common attributes found in successful…

Detection of digital FSK using a phase-locked loop

NASA Technical Reports Server (NTRS)

Lindsey, W. C.; Simon, M. K.

1975-01-01

A theory is presented for the design of a digital FSK receiver which employs a phase-locked loop to set up the desired matched filter as the arriving signal frequency switches. The developed mathematical model makes it possible to establish the error probability performance of systems which employ a class of digital FM modulations. The noise mechanism which accounts for decision errors is modeled on the basis of the Meyr distribution and renewal Markov process theory.

Evaluation of an S-system root-finding method for estimating parameters in a metabolic reaction model.

PubMed

Iwata, Michio; Miyawaki-Kuwakado, Atsuko; Yoshida, Erika; Komori, Soichiro; Shiraishi, Fumihide

2018-02-02

In a mathematical model, estimation of parameters from time-series data of metabolic concentrations in cells is a challenging task. However, it seems that a promising approach for such estimation has not yet been established. Biochemical Systems Theory (BST) is a powerful methodology to construct a power-law type model for a given metabolic reaction system and to then characterize it efficiently. In this paper, we discuss the use of an S-system root-finding method (S-system method) to estimate parameters from time-series data of metabolite concentrations. We demonstrate that the S-system method is superior to the Newton-Raphson method in terms of the convergence region and iteration number. We also investigate the usefulness of a translocation technique and a complex-step differentiation method toward the practical application of the S-system method. The results indicate that the S-system method is useful to construct mathematical models for a variety of metabolic reaction networks. Copyright © 2018 Elsevier Inc. All rights reserved.

Mathematical modeling of a single stage ultrasonically assisted distillation process.

PubMed

Mahdi, Taha; Ahmad, Arshad; Ripin, Adnan; Abdullah, Tuan Amran Tuan; Nasef, Mohamed M; Ali, Mohamad W

2015-05-01

The ability of sonication phenomena in facilitating separation of azeotropic mixtures presents a promising approach for the development of more intensified and efficient distillation systems than conventional ones. To expedite the much-needed development, a mathematical model of the system based on conservation principles, vapor-liquid equilibrium and sonochemistry was developed in this study. The model that was founded on a single stage vapor-liquid equilibrium system and enhanced with ultrasonic waves was coded using MATLAB simulator and validated with experimental data for ethanol-ethyl acetate mixture. The effects of both ultrasonic frequency and intensity on the relative volatility and azeotropic point were examined, and the optimal conditions were obtained using genetic algorithm. The experimental data validated the model with a reasonable accuracy. The results of this study revealed that the azeotropic point of the mixture can be totally eliminated with the right combination of sonication parameters and this can be utilized in facilitating design efforts towards establishing a workable ultrasonically intensified distillation system. Copyright © 2014 Elsevier B.V. All rights reserved.

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

PubMed

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

2017-03-21

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

Does one size fit all? A study of beginning science and mathematics teacher induction

NASA Astrophysics Data System (ADS)

Kralik, Jeffrey M.

Over the past few years, many induction programs have been implemented across the country, primarily designed to limit the amount beginning teacher attrition. Few of these programs have focused on improving teacher quality or identifying the specific needs of individual teachers. Research suggests that beginning science and mathematics teachers have specific needs that are not being met by current induction models, possibly resulting in higher rates of attrition. Harry and Janet Knowles created the Knowles Science Teaching Foundation (KSTF) to identify and support young scientists and mathematicians as they dedicate their lives to teaching young people. Through financial, curricular, and emotional support, KSTF encourages new teachers to remain in teaching and become leaders in their schools and districts. This dissertation is a sequential explanatory study, which first establishes national estimates for beginning teacher attrition rates and the reasons for the migration based on subject area taught, with an emphasis on mathematics and science teachers. This study then evaluates the KSTF model through multiple methods---analysis of KSTF survey data and interviews with KSTF participants and stakeholders.

Modeling mammary organogenesis from biological first principles: Cells and their physical constraints.

PubMed

Montévil, Maël; Speroni, Lucia; Sonnenschein, Carlos; Soto, Ana M

2016-10-01

In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing non-identical cells, which organize in tri-dimensional patterns. These association patterns and cells types change as tissues and organs are formed. This contextuality and circularity makes it difficult to establish detailed cause and effect relationships. Here we propose an approach to overcome these intrinsic difficulties by combining the use of two models; 1) an experimental one that employs 3D culture technology to obtain the structures of the mammary gland, namely, ducts and acini, and 2) a mathematical model based on biological principles. The typical approach for mathematical modeling in biology is to apply mathematical tools and concepts developed originally in physics or computer sciences. Instead, we propose to construct a mathematical model based on proper biological principles. Specifically, we use principles identified as fundamental for the elaboration of a theory of organisms, namely i) the default state of cell proliferation with variation and motility and ii) the principle of organization by closure of constraints. This model has a biological component, the cells, and a physical component, a matrix which contains collagen fibers. Cells display agency and move and proliferate unless constrained; they exert mechanical forces that i) act on collagen fibers and ii) on other cells. As fibers organize, they constrain the cells on their ability to move and to proliferate. The model exhibits a circularity that can be interpreted in terms of closure of constraints. Implementing the mathematical model shows that constraints to the default state are sufficient to explain ductal and acinar formation, and points to a target of future research, namely, to inhibitors of cell proliferation and motility generated by the epithelial cells. The success of this model suggests a step-wise approach whereby additional constraints imposed by the tissue and the organism could be examined in silico and rigorously tested by in vitro and in vivo experiments, in accordance with the organicist perspective we embrace. Copyright © 2016. Published by Elsevier Ltd.

Modeling mammary organogenesis from biological first principles: Cells and their physical constraints

PubMed Central

Montévil, Maël; Speroni, Lucia; Sonnenschein, Carlos; Soto, Ana M.

2017-01-01

In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing non-identical cells, which organize in tri-dimensional patterns. These association patterns and cells types change as tissues and organs are formed. This contextuality and circularity makes it difficult to establish detailed cause and effect relationships. Here we propose an approach to overcome these intrinsic difficulties by combining the use of two models; 1) an experimental one that employs 3D culture technology to obtain the structures of the mammary gland, namely, ducts and acini, and 2) a mathematical model based on biological principles. The typical approach for mathematical modeling in biology is to apply mathematical tools and concepts developed originally in physics or computer sciences. Instead, we propose to construct a mathematical model based on proper biological principles. Specifically, we use principles identified as fundamental for the elaboration of a theory of organisms, namely i) the default state of cell proliferation with variation and motility and ii) the principle of organization by closure of constraints. This model has a biological component, the cells, and a physical component, a matrix which contains collagen fibers. Cells display agency and move and proliferate unless constrained; they exert mechanical forces that i) act on collagen fibers and ii) on other cells. As fibers organize, they constrain the cells on their ability to move and to proliferate. The model exhibits a circularity that can be interpreted in terms of closure of constraints. Implementing the mathematical model shows that constraints to the default state are sufficient to explain ductal and acinar formation, and points to a target of future research, namely, to inhibitors of cell proliferation and motility generated by the epithelial cells. The success of this model suggests a step-wise approach whereby additional constraints imposed by the tissue and the organism could be examined in silico and rigorously tested by in vitro and in vivo experiments, in accordance with the organicist perspective we embrace. PMID:27544910

Analysis of the coupling efficiency of a tapered space receiver with a calculus mathematical model

NASA Astrophysics Data System (ADS)

Hu, Qinggui; Mu, Yining

2018-03-01

We establish a calculus mathematical model to study the coupling characteristics of tapered optical fibers in a space communications system, and obtained the coupling efficiency equation. Then, using MATLAB software, the solution was calculated. After this, the sample was produced by the mature flame-brush technique. The experiment was then performed, and the results were in accordance with the theoretical analysis. This shows that the theoretical analysis was correct and indicates that a tapered structure could improve its tolerance with misalignment. Project supported by The National Natural Science Foundation of China (grant no. 61275080); 2017 Jilin Province Science and Technology Development Plan-Science and Technology Innovation Fund for Small and Medium Enterprises (20170308029HJ); ‘thirteen five’ science and technology research project of the Department of Education of Jilin 2016 (16JK009).

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.

Locality of the Thomas-Fermi-von Weizsäcker Equations

NASA Astrophysics Data System (ADS)

Nazar, F. Q.; Ortner, C.

2017-06-01

We establish a pointwise stability estimate for the Thomas-Fermi-von Weiz-säcker (TFW) model, which demonstrates that a local perturbation of a nuclear arrangement results also in a local response in the electron density and electrostatic potential. The proof adapts the arguments for existence and uniqueness of solutions to the TFW equations in the thermodynamic limit by Catto et al. (The mathematical theory of thermodynamic limits: Thomas-Fermi type models. Oxford mathematical monographs. The Clarendon Press, Oxford University Press, New York, 1998). To demonstrate the utility of this combined locality and stability result we derive several consequences, including an exponential convergence rate for the thermodynamic limit, partition of total energy into exponentially localised site energies (and consequently, exponential locality of forces), and generalised and strengthened results on the charge neutrality of local defects.

[Establishment of the mathematic model of total quantum statistical moment standard similarity for application to medical theoretical research].

PubMed

He, Fu-yuan; Deng, Kai-wen; Huang, Sheng; Liu, Wen-long; Shi, Ji-lian

2013-09-01

The paper aims to elucidate and establish a new mathematic model: the total quantum statistical moment standard similarity (TQSMSS) on the base of the original total quantum statistical moment model and to illustrate the application of the model to medical theoretical research. The model was established combined with the statistical moment principle and the normal distribution probability density function properties, then validated and illustrated by the pharmacokinetics of three ingredients in Buyanghuanwu decoction and of three data analytical method for them, and by analysis of chromatographic fingerprint for various extracts with different solubility parameter solvents dissolving the Buyanghanwu-decoction extract. The established model consists of four mainly parameters: (1) total quantum statistical moment similarity as ST, an overlapped area by two normal distribution probability density curves in conversion of the two TQSM parameters; (2) total variability as DT, a confidence limit of standard normal accumulation probability which is equal to the absolute difference value between the two normal accumulation probabilities within integration of their curve nodical; (3) total variable probability as 1-Ss, standard normal distribution probability within interval of D(T); (4) total variable probability (1-beta)alpha and (5) stable confident probability beta(1-alpha): the correct probability to make positive and negative conclusions under confident coefficient alpha. With the model, we had analyzed the TQSMS similarities of pharmacokinetics of three ingredients in Buyanghuanwu decoction and of three data analytical methods for them were at range of 0.3852-0.9875 that illuminated different pharmacokinetic behaviors of each other; and the TQSMS similarities (ST) of chromatographic fingerprint for various extracts with different solubility parameter solvents dissolving Buyanghuanwu-decoction-extract were at range of 0.6842-0.999 2 that showed different constituents with various solvent extracts. The TQSMSS can characterize the sample similarity, by which we can quantitate the correct probability with the test of power under to make positive and negative conclusions no matter the samples come from same population under confident coefficient a or not, by which we can realize an analysis at both macroscopic and microcosmic levels, as an important similar analytical method for medical theoretical research.

Enhancing School Mathematics Culturally: A Path of Reconciliation

ERIC Educational Resources Information Center

Aikenhead, Glen S.

2017-01-01

Culturally responsive or place-based school mathematics that focuses on Indigenous students has an established presence in the research literature. This culture-based innovation represents a historical shift from conventional approaches to mathematics education. Moreover, it has demonstratively advanced the academic achievement for both Indigenous…

Measures and Metrics of Information Processing in Complex Systems: A Rope of Sand

ERIC Educational Resources Information Center

James, Ryan Gregory

2013-01-01

How much information do natural systems store and process? In this work we attempt to answer this question in multiple ways. We first establish a mathematical framework where natural systems are represented by a canonical form of edge-labeled hidden fc models called e-machines. Then, utilizing this framework, a variety of measures are defined and…

Mathematics and Physics: The Idea of a Pre-Established Harmony

NASA Astrophysics Data System (ADS)

Kragh, Helge

2015-07-01

For more than a century the notion of a pre-established harmony between the mathematical and physical sciences has played an important role not only in the rhetoric of mathematicians and theoretical physicists, but also as a doctrine guiding much of their research. Strongly mathematized branches of physics, such as the vortex theory of atoms popular in Victorian Britain, were not unknown in the nineteenth century, but it was only in the environment of fin-de-siècle Germany that the idea of a pre-established harmony really took off and became part of the mathematicians' ideology. Important historical figures were in this respect David Hilbert, Hermann Minkowski and, somewhat later, Albert Einstein. Roughly similar ideas can be found also among British theorists, among whom Arthur Eddington, Arthur Milne, and Paul Dirac are singled out. Although largely limited to the period 1870-1940, the paper also considers Max Tegmark's recent hypothesis of the universe (or multiverse) being a one-to-one reflection of mathematical structures.

Mathematizing Process of Junior High School Students to Improve Mathematics Literacy Refers PISA on RCP Learning

NASA Astrophysics Data System (ADS)

Wardono; Mariani, S.; Hendikawati, P.; Ikayani

2017-04-01

Mathematizing process (MP) is the process of modeling a phenomenon mathematically or establish the concept of a phenomenon. There are two mathematizing that is Mathematizing Horizontal (MH) and Mathematizing Vertical (MV). MH as events changes contextual problems into mathematical problems, while MV is the process of formulation of the problem into a variety of settlement mathematics by using some appropriate rules. Mathematics Literacy (ML) is the ability to formulate, implement and interpret mathematics in various contexts, including the capacity to perform reasoning mathematically and using the concepts, procedures, and facts to describe, explain or predict phenomena incident. If junior high school students are conditioned continuously to conduct mathematizing activities on RCP (RME-Card Problem) learning, it will be able to improve ML that refers PISA. The purpose of this research is to know the capability of the MP grade VIII on ML content shape and space with the matter of the cube and beams with RCP learning better than the scientific learning, upgrade MP grade VIII in the issue of the cube and beams with RCP learning better than the scientific learning in terms of cognitive styles reflective and impulsive the MP grade VIII with the approach of the RCP learning in terms of cognitive styles reflective and impulsive This research is the mixed methods model concurrent embedded. The population in this study, i.e., class VIII SMPN 1 Batang with sample two class. Data were taken with the observation, interviews, and tests and analyzed with a different test average of one party the right qualitative and descriptive. The results of this study demonstrate the capability of the MP student with RCP learning better than the scientific learning, upgrade MP with RCP learning better compare with scientific learning in term cognitive style of reflective and impulsive. The subject of the reflective group top, middle, and bottom can meet all the process of MH indicators are then the subject of the reflective upper and intermediate group can meet all the MV indicators but to lower groups can only fulfill some MV indicators. The subject is impulsive upper and middle group can meet all the MH indicators but to lower groups can only meet some MH indicator, then the subject is impulsive group can meet all the MV indicators but for middle and the bottom group can only fulfill some MV indicators.

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

NASA Astrophysics Data System (ADS)

Kosmas, Theocharis; Vagenas, Elias; Vlachos, Dimitrios

2013-02-01

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

Qualitative analysis of a stochastic epidemic model with specific functional response and temporary immunity

NASA Astrophysics Data System (ADS)

Hattaf, Khalid; Mahrouf, Marouane; Adnani, Jihad; Yousfi, Noura

2018-01-01

In this paper, we propose a stochastic delayed epidemic model with specific functional response. The time delay represents temporary immunity period, i.e., time from recovery to becoming susceptible again. We first show that the proposed model is mathematically and biologically well-posed. Moreover, the extinction of the disease and the persistence in the mean are established in the terms of a threshold value R0S which is smaller than the basic reproduction number R0 of the corresponding deterministic system.

Periodicity computation of generalized mathematical biology problems involving delay differential equations.

PubMed

Jasim Mohammed, M; Ibrahim, Rabha W; Ahmad, M Z

2017-03-01

In this paper, we consider a low initial population model. Our aim is to study the periodicity computation of this model by using neutral differential equations, which are recognized in various studies including biology. We generalize the neutral Rayleigh equation for the third-order by exploiting the model of fractional calculus, in particular the Riemann-Liouville differential operator. We establish the existence and uniqueness of a periodic computational outcome. The technique depends on the continuation theorem of the coincidence degree theory. Besides, an example is presented to demonstrate the finding.

Enjoying mathematics or feeling competent in mathematics? Reciprocal effects on mathematics achievement and perceived math effort expenditure.

PubMed

Pinxten, Maarten; Marsh, Herbert W; De Fraine, Bieke; Van Den Noortgate, Wim; Van Damme, Jan

2014-03-01

The multidimensionality of the academic self-concept in terms of domain specificity has been well established in previous studies, whereas its multidimensionality in terms of motivational functions (the so-called affect-competence separation) needs further examination. This study aims at exploring differential effects of enjoyment and competence beliefs on two external validity criteria in the field of mathematics. Data analysed in this study were part of a large-scale longitudinal research project. Following a five-wave design, math enjoyment, math competence beliefs, math achievement, and perceived math effort expenditure measures were repeatedly collected from a cohort of 4,724 pupils in Grades 3-7. Confirmatory factor analysis (CFA) was used to test the internal factor structure of the math self-concept. Additionally, a series of nested models was tested using structural equation modelling to examine longitudinal reciprocal interrelations between math competence beliefs and math enjoyment on the one hand and math achievement and perceived math effort expenditure on the other. Our results showed that CFA models with separate factors for math enjoyment and math competence beliefs fit the data substantially better than models without it. Furthermore, differential relationships between both constructs and the two educational outcomes were observed. Math competence beliefs had positive effects on math achievement and negative effects on perceived math effort expenditure. Math enjoyment had (mild) positive effects on subsequent perceived effort expenditure and math competence beliefs. This study provides further support for the affect-competence separation. Theoretical issues regarding adequate conceptualization and practical consequences for practitioners are discussed. © 2013 The British Psychological Society.

A Review of the “Bolus Guide,” A New Insulin Bolus Dosing Support Tool Based on Selection of Carbohydrate Ranges

PubMed Central

Pańkowska, Ewa

2010-01-01

In this issue of Journal of Diabetes Science and Technology, Shapira and colleagues present new concepts of carbohydrate load estimation in intensive insulin therapy. By using a mathematical model, they attempt to establish how accurately carbohydrate food content should be maintained in order to keep postprandial blood glucose levels in the recommended range. Their mathematical formula, the “bolus guide” (BG), is verified by simulating prandial insulin dosing and responding to proper blood glucose levels. Different variants such as insulin sensitivity factor, insulin-to-carbohydrate ratio, and target blood glucose were taken into this formula in establishing the calculated proper insulin dose. The new approach presented here estimates the carbohydrate content by rearranging the carbohydrate load instead of the simple point estimation that the current bolus calculators (BCs) use. Computerized estimations show that the BG directives, as compared to a BC, result in more glucose levels above 200 mg/dl and thus indicate less hypoglycemia readings. PMID:20663454

Controversy in the allometric application of fixed- versus varying-exponent models: a statistical and mathematical perspective.

PubMed

Tang, Huadong; Hussain, Azher; Leal, Mauricio; Fluhler, Eric; Mayersohn, Michael

2011-02-01

This commentary is a reply to a recent article by Mahmood commenting on the authors' article on the use of fixed-exponent allometry in predicting human clearance. The commentary discusses eight issues that are related to criticisms made in Mahmood's article and examines the controversies (fixed-exponent vs. varying-exponent allometry) from the perspective of statistics and mathematics. The key conclusion is that any allometric method, which is to establish a power function based on a limited number of animal species and to extrapolate the resulting power function to human values (varying-exponent allometry), is infused with fundamental statistical errors. Copyright © 2010 Wiley-Liss, Inc.

Are quantum-mechanical-like models possible, or necessary, outside quantum physics?

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

2014-12-01

This article examines some experimental conditions that invite and possibly require recourse to quantum-mechanical-like mathematical models (QMLMs), models based on the key mathematical features of quantum mechanics, in scientific fields outside physics, such as biology, cognitive psychology, or economics. In particular, I consider whether the following two correlative features of quantum phenomena that were decisive for establishing the mathematical formalism of quantum mechanics play similarly important roles in QMLMs elsewhere. The first is the individuality and discreteness of quantum phenomena, and the second is the irreducibly probabilistic nature of our predictions concerning them, coupled to the particular character of the probabilities involved, as different from the character of probabilities found in classical physics. I also argue that these features could be interpreted in terms of a particular form of epistemology that suspends and even precludes a causal and, in the first place, realist description of quantum objects and processes. This epistemology limits the descriptive capacity of quantum theory to the description, classical in nature, of the observed quantum phenomena manifested in measuring instruments. Quantum mechanics itself only provides descriptions, probabilistic in nature, concerning numerical data pertaining to such phenomena, without offering a physical description of quantum objects and processes. While QMLMs share their use of the quantum-mechanical or analogous mathematical formalism, they may differ by the roles, if any, the two features in question play in them and by different ways of interpreting the phenomena they considered and this formalism itself. This article will address those differences as well.

The secondary drying and the fate of organic solvents for spray dried dispersion drug product.

PubMed

Hsieh, Daniel S; Yue, Hongfei; Nicholson, Sarah J; Roberts, Daniel; Schild, Richard; Gamble, John F; Lindrud, Mark

2015-05-01

To understand the mechanisms of secondary drying of spray-dried dispersion (SDD) drug product and establish a model to describe the fate of organic solvents in such a product. The experimental approach includes characterization of the SDD particles, drying studies of SDD using an integrated weighing balance and mass spectrometer, and the subsequent generation of the drying curve. The theoretical approach includes the establishment of a Fickian diffusion model. The kinetics of solvent removal during secondary drying from the lab scale to a bench scale follows Fickian diffusion model. Excellent agreement is obtained between the experimental data and the prediction from the modeling. The diffusion process is dependent upon temperature. The key to a successful scale up of the secondary drying is to control the drying temperature. The fate of primary solvents including methanol and acetone, and their potential impurity such as benzene can be described by the Fickian diffusion model. A mathematical relationship based upon the ratio of diffusion coefficient was established to predict the benzene concentration from the fate of the primary solvent during the secondary drying process.

Topological soliton solutions for three shallow water waves models

NASA Astrophysics Data System (ADS)

Liu, Jiangen; Zhang, Yufeng; Wang, Yan

2018-07-01

In this article, we investigate three distinct physical structures for shallow water waves models by the improved ansatz method. The method was improved and can be used to obtain more generalized form topological soliton solutions than the original method. As a result, some new exact solutions of the shallow water equations are successfully established and the obtained results are exhibited graphically. The results showed that the improved ansatz method can be applied to solve other nonlinear differential equations arising from mathematical physics.

Equation-free modeling unravels the behavior of complex ecological systems

USGS Publications Warehouse

DeAngelis, Donald L.; Yurek, Simeon

2015-01-01

Ye et al. (1) address a critical problem confronting the management of natural ecosystems: How can we make forecasts of possible future changes in populations to help guide management actions? This problem is especially acute for marine and anadromous fisheries, where the large interannual fluctuations of populations, arising from complex nonlinear interactions among species and with varying environmental factors, have defied prediction over even short time scales. The empirical dynamic modeling (EDM) described in Ye et al.’s report, the latest in a series of papers by Sugihara and his colleagues, offers a promising quantitative approach to building models using time series to successfully project dynamics into the future. With the term “equation-free” in the article title, Ye et al. (1) are suggesting broader implications of their approach, considering the centrality of equations in modern science. From the 1700s on, nature has been increasingly described by mathematical equations, with differential or difference equations forming the basic framework for describing dynamics. The use of mathematical equations for ecological systems came much later, pioneered by Lotka and Volterra, who showed that population cycles might be described in terms of simple coupled nonlinear differential equations. It took decades for Lotka–Volterra-type models to become established, but the development of appropriate differential equations is now routine in modeling ecological dynamics. There is no question that the injection of mathematical equations, by forcing “clarity and precision into conjecture” (2), has led to increased understanding of population and community dynamics. As in science in general, in ecology equations are a key method of communication and of framing hypotheses. These equations serve as compact representations of an enormous amount of empirical data and can be analyzed by the powerful methods of mathematics.

Computer Attitude, Use, Experience, Software Familiarity and Perceived Pedagogical Usefulness: The Case of Mathematics Professors

ERIC Educational Resources Information Center

Yushau, Balarabe

2006-01-01

As the pedagogical-effectiveness of information technology (IT) in mathematics education is carefully established the topic of discourse among mathematicians and mathematics educators is no longer a dispute about whether or not to use IT in the teaching and learning of mathematics but a shift to some debate about the when and how of its usage.…

The Effectiveness of the North Carolina Early Mathematics Placement Test in Preparing High School Students for College-Level Introductory Mathematics Courses

ERIC Educational Resources Information Center

Hilgoe, Ellen; Brinkley, Jason; Hattingh, Johannes; Bernhardt, Robert

2016-01-01

Since its establishment in 1996, the North Carolina Early Mathematics Placement Testing (NC EMPT) Program has provided a low stakes reality check of readiness for college-level mathematics to more than 600,000 high school students statewide. The program strives to help reduce the percentage of incoming college freshmen requiring mathematics…

The North Carolina School of Science and Mathematics.

ERIC Educational Resources Information Center

Eilber, Charles R.

1987-01-01

The North Carolina School of Science and Mathematics was established in 1980 as a resident public high school for juniors and seniors demonstrating ability and interest in science and mathematics. Outlines the admission policy, instructional program, supportive services, and the school's commitment to public service. This was the first publicly…

Student Comprehension of Mathematics through Astronomy

ERIC Educational Resources Information Center

Search, Robert

2016-01-01

The purpose of this study is to examine how knowledge of astronomy can enhance college-level learning situations involving mathematics. The fundamental symbiosis between mathematics and astronomy was established early in the 17th century when Johannes Kepler deduced the 3 basic laws of planetary motion. This mutually harmonious relationship…

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…

A Reflection Framework for Teaching Mathematics

ERIC Educational Resources Information Center

Merritt, Eileen G.; Rimm-Kaufman, Sara E.; Berry, Robert Q., III; Walkowiak, Temple A.; McCracken, Erin R.

2010-01-01

Mathematics teachers confront dozens of daily decisions about how to instruct students. It is well established that high-quality instruction provides benefits for students with diverse learning and family backgrounds. However, it is often difficult for teachers to identify the critical aspects of a successful mathematics lesson as they strive to…

It's Going to Happen Anyway....

ERIC Educational Resources Information Center

Fusaro, B. A.

Within the context of the developments in mathematics and computer science, this paper argues that the emergence of the microcomputer gives mathematics the opportunity to survive as a viable and healthy discipline. Section I traces the development of the computer and the position of established mathematics on the sidelines of this development.…

Seventies, Eighties, Nineties, Noughties.... a Sequence of Concerns

ERIC Educational Resources Information Center

Jackson, Elizabeth

2007-01-01

This paper outlines small scale research regarding mathematics anxiety and potential links to confidence and mathematics subject knowledge for primary teacher education (QTS) students in a HE institution, where the author is a Senior Lecturer in Primary Mathematics Education. The purpose is to establish the existence of such anxiety and related…

Study on the variable cycle engine modeling techniques based on the component method

NASA Astrophysics Data System (ADS)

Zhang, Lihua; Xue, Hui; Bao, Yuhai; Li, Jijun; Yan, Lan

2016-01-01

Based on the structure platform of the gas turbine engine, the components of variable cycle engine were simulated by using the component method. The mathematical model of nonlinear equations correspondeing to each component of the gas turbine engine was established. Based on Matlab programming, the nonlinear equations were solved by using Newton-Raphson steady-state algorithm, and the performance of the components for engine was calculated. The numerical simulation results showed that the model bulit can describe the basic performance of the gas turbine engine, which verified the validity of the model.

Cultural horizons for mathematics

NASA Astrophysics Data System (ADS)

Owens, Kay; Paraides, Patricia; Jannok Nutti, Ylva; Johansson, Gunilla; Bennet, Maria; Doolan, Pat; Peckham, Ray; Hill, John; Doolan, Frank; O'Sullivan, Dominic; Murray, Libbey; Logan, Patricia; McNair, Melissa; Sunnari, Vappu; Murray, Beatrice; Miller, Alissa; Nolan, John; Simpson, Alca; Ohrin, Christine; Doolan, Terry; Doolan, Michelle; Taylor, Paul

2011-06-01

As a result of a number of government reports, there have been numerous systemic changes in Indigenous education in Australia revolving around the importance of partnerships with the community. A forum with our local Dubbo community established the importance of working together and developed a model which placed the child in an ecological perspective that particularly noted the role of Elders and the place of the child in the family. However, there was also the issue of curriculum and mathematics education to be addressed. It was recognised that a colonised curriculum reduces the vision of what might be the potential for Indigenous mathematics education. This paper reports on the sharing that developed between our local community and some researchers and teachers from Sweden, Papua New Guinea and New Zealand. It has implications for recognising the impact of testing regimes, the teaching space, understanding the ways children learn, the curriculum, and teacher education. As a result of these discussions, a critical pedagogy that considers culture and place is presented as an ecocultural perspective on mathematics education. This perspective was seen as critical for the curriculum and learning experiences of Indigenous children.

SU-E-T-17: A Mathematical Model for PinPoint Chamber Correction in Measuring Small Fields

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

Li, T; Zhang, Y; Li, X

2014-06-01

Purpose: For small field dosimetry, such as measuring the cone output factor for stereotactic radiosurgery, ion chambers often result in underestimation of the dose, due to both the volume averaging effect and the lack of electron equilibrium. The purpose of this work is to develop a mathematical model, specifically for the pinpoint chamber, to calculate the correction factors corresponding to different type of small fields, including single cone-based circular field and non-standard composite fields. Methods: A PTW 0.015cc PinPoint chamber was used in the study. Its response in a certain field was modeled as the total contribution of many smallmore » beamlets, each with different response factor depending on the relative strength, radial distance to the chamber axis, and the beam angle. To get these factors, 12 cone-shaped circular fields (5mm,7.5mm, 10mm, 12.5mm, 15mm, 20mm, 25mm, 30mm, 35mm, 40mm, 50mm, 60mm) were irradiated and measured with the PinPoint chamber. For each field size, hundreds of readings were recorded for every 2mm chamber shift in the horizontal plane. These readings were then compared with the theoretical doses as obtained with Monte Carlo calculation. A penalized-least-square optimization algorithm was developed to find out the beamlet response factors. After the parameter fitting, the established mathematical model was validated with the same MC code for other non-circular fields. Results: The optimization algorithm used for parameter fitting was stable and the resulted response factors were smooth in spatial domain. After correction with the mathematical model, the chamber reading matched with the Monte Carlo calculation for all the tested fields to within 2%. Conclusion: A novel mathematical model has been developed for the PinPoint chamber for dosimetric measurement of small fields. The current model is applicable only when the beam axis is perpendicular to the chamber axis. It can be applied to non-standard composite fields. Further validation with other type of detectors is being conducted.« less

An Interactive System of Computer Generated Graphic Displays for Motivating Meaningful Learning of Matrix Operations and Concepts of Matrix Algebra

DTIC Science & Technology

1990-09-01

community’s search for a workable set of standards for school mathematics . In 1989 the National Council of Teachers of Mathematics ( NCTM ) established the...made by the Commission on Standards for School Mathematics to the National Council of Teachers of Mathematics ( NCTM ). Of the 40 students who...Abstract This -s-y evaluated students’ responses to a teaching method designed to involve students and teachers of mathematics in a meaningful learning

The geometric semantics of algebraic quantum mechanics.

PubMed

Cruz Morales, John Alexander; Zilber, Boris

2015-08-06

In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Study on the Effect of water Injection Momentum on the Cooling Effect of Rocket Engine Exhaust Plume

NASA Astrophysics Data System (ADS)

Yang, Kan; Qiang, Yanhui; Zhong, Chenghang; Yu, Shaozhen

2017-10-01

For the study of water injection momentum factors impact on flow field of the rocket engine tail flame, the numerical computation model of gas-liquid two phase flow in the coupling of high temperature and high speed gas flow and low temperature liquid water is established. The accuracy and reliability of the numerical model are verified by experiments. Based on the numerical model, the relationship between the flow rate and the cooling effect is analyzed by changing the water injection momentum of the water spray pipes. And the effective mathematical expression is obtained. What’s more, by changing the number of the water spray and using small flow water injection, the cooling effect is analyzed to check the application range of the mathematical expressions. The results show that: the impact and erosion of the gas flow field could be reduced greatly by water injection, and there are two parts in the gas flow field, which are the slow cooling area and the fast cooling area. In the fast cooling area, the influence of the water flow momentum and nozzle quantity on the cooling effect can be expressed by mathematical functions without causing bifurcation flow for the mainstream gas. The conclusion provides a theoretical reference for the engineering application.

Dynamic hyperbolic geometry: building intuition and understanding mediated by a Euclidean model

NASA Astrophysics Data System (ADS)

Moreno-Armella, Luis; Brady, Corey; Elizondo-Ramirez, Rubén

2018-05-01

This paper explores a deep transformation in mathematical epistemology and its consequences for teaching and learning. With the advent of non-Euclidean geometries, direct, iconic correspondences between physical space and the deductive structures of mathematical inquiry were broken. For non-Euclidean ideas even to become thinkable the mathematical community needed to accumulate over twenty centuries of reflection and effort: a precious instance of distributed intelligence at the cultural level. In geometry education after this crisis, relations between intuitions and geometrical reasoning must be established philosophically, rather than taken for granted. One approach seeks intuitive supports only for Euclidean explorations, viewing non-Euclidean inquiry as fundamentally non-intuitive in nature. We argue for moving beyond such an impoverished approach, using dynamic geometry environments to develop new intuitions even in the extremely challenging setting of hyperbolic geometry. Our efforts reverse the typical direction, using formal structures as a source for a new family of intuitions that emerge from exploring a digital model of hyperbolic geometry. This digital model is elaborated within a Euclidean dynamic geometry environment, enabling a conceptual dance that re-configures Euclidean knowledge as a support for building intuitions in hyperbolic space-intuitions based not directly on physical experience but on analogies extending Euclidean concepts.

Science Education - Deja Vu Revised.

ERIC Educational Resources Information Center

Walsh, John

1982-01-01

Summarizes views expressed and issues raised at the National Convocation on Precollege Education in Mathematics and Science and another meeting to establish a coalition of affiliates for science and mathematics education. (DC)

Modeling of Austenite Grain Growth During Austenitization in a Low Alloy Steel

NASA Astrophysics Data System (ADS)

Dong, Dingqian; Chen, Fei; Cui, Zhenshan

2016-01-01

The main purpose of this work is to develop a pragmatic model to predict austenite grain growth in a nuclear reactor pressure vessel steel. Austenite grain growth kinetics has been investigated under different heating conditions, involving heating temperature, holding time, as well as heating rate. Based on the experimental results, the mathematical model was established by regression analysis. The model predictions present a good agreement with the experimental data. Meanwhile, grain boundary precipitates and pinning effects on grain growth were studied by transmission electron microscopy. It is found that with the increasing of the temperature, the second-phase particles tend to be dissolved and the pinning effects become smaller, which results in a rapid growth of certain large grains with favorable orientation. The results from this study provide the basis for the establishment of large-sized ingot heating specification for SA508-III steel.

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…

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.

[Treatment of surface burns with proteolytic enzymes: mathematic description of lysis kinetics].

PubMed

Domogatskaia, A S; Domogatskiĭ, S P; Ruuge, E K

2003-01-01

The lysis of necrotic tissue by a proteolytic enzyme applied to the surface of a burn wound was studied. A mathematical model was proposed, which describes changes in the thickness of necrotic tissue as a function of the proteolytic activity of the enzyme. The model takes into account the inward-directed diffusion of the enzyme, the counterflow of interstitial fluid (exudates) containing specific inhibitors, and the extracellular matrix proteolysis. It was shown in terms of the quasi-stationary approach that the thickness of the necrotic tissue layer decreases exponentially with time; i.e., the lysis slows down as the thickness of the necrotic tissue layer decreases. The dependence of the characteristic time of this decrease on enzyme concentration was obtained. It was shown that, at high enzyme concentrations (more than 5 mg/ml), the entire time of lysis (after the establishment of quasi-stationary equilibrium) is inversely proportional to the concentration of the enzyme.

A Measuring System for Well Logging Attitude and a Method of Sensor Calibration

PubMed Central

Ren, Yong; Wang, Yangdong; Wang, Mijian; Wu, Sheng; Wei, Biao

2014-01-01

This paper proposes an approach for measuring the azimuth angle and tilt angle of underground drilling tools with a MEMS three-axis accelerometer and a three-axis fluxgate sensor. A mathematical model of well logging attitude angle is deduced based on combining space coordinate transformations and algebraic equations. In addition, a system implementation plan of the inclinometer is given in this paper, which features low cost, small volume and integration. Aiming at the sensor and assembly errors, this paper analyses the sources of errors, and establishes two mathematical models of errors and calculates related parameters to achieve sensor calibration. The results show that this scheme can obtain a stable and high precision azimuth angle and tilt angle of drilling tools, with the deviation of the former less than ±1.4° and the deviation of the latter less than ±0.1°. PMID:24859028

Mathematic modeling the relationship of bacteria number in a dairy product and the color difference measured by a CCD image sensor

NASA Astrophysics Data System (ADS)

Zhou, Zhen; Zhao, Zhigang; Chen, Dongkui; Liu, Yuping

2005-01-01

Although many methods, such as bacteria plate count, flow cytometry and impedance method have been broadly used in the dairy industry to quantitate bacteria numbers around the world, none of them is a quick, low cost and easy one. In this study, we proposed to apply the color difference theory in this field to establish a mathematic model to quantitate bacteria number in fresh milk. Preliminary testing results not only indicate that the application of the color difference theory to the new system is practical, but also confirm the theoretical relationship between the numbers of bacteria, incubation time and color difference. The proof of the principal study in this article further suggests that the novel method has the potential to replace the traditional methods to determine bacteria numbers for the food industry.

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

A measuring system for well logging attitude and a method of sensor calibration.

PubMed

Ren, Yong; Wang, Yangdong; Wang, Mijian; Wu, Sheng; Wei, Biao

2014-05-23

This paper proposes an approach for measuring the azimuth angle and tilt angle of underground drilling tools with a MEMS three-axis accelerometer and a three-axis fluxgate sensor. A mathematical model of well logging attitude angle is deduced based on combining space coordinate transformations and algebraic equations. In addition, a system implementation plan of the inclinometer is given in this paper, which features low cost, small volume and integration. Aiming at the sensor and assembly errors, this paper analyses the sources of errors, and establishes two mathematical models of errors and calculates related parameters to achieve sensor calibration. The results show that this scheme can obtain a stable and high precision azimuth angle and tilt angle of drilling tools, with the deviation of the former less than ±1.4° and the deviation of the latter less than ±0.1°.

A new pneumatic suspension system with independent stiffness and ride height tuning capabilities

NASA Astrophysics Data System (ADS)

Yin, Zhihong; Khajepour, Amir; Cao, Dongpu; Ebrahimi, Babak; Guo, Konghui

2012-12-01

This paper introduces a new pneumatic spring for vehicle suspension systems, allowing independent tuning of stiffness and ride height according to different vehicle operating conditions and driver preferences. The proposed pneumatic spring comprises a double-acting pneumatic cylinder, two accumulators and a tuning subsystem. This paper presents a detailed description of the pneumatic spring and its working principle. The mathematical model is established based on principles of thermo and fluid dynamics. An experimental setup has been designed and fabricated for testing and evaluating the proposed pneumatic spring. The analytical and experimental results confirm the capability of the new pneumatic spring system for independent tuning of stiffness and ride height. The mathematical model is verified and the capabilities of the pneumatic spring are further proved. It is concluded that this new pneumatic spring provides a more flexible suspension design alternative for meeting various conflicting suspension requirements for ride comfort and performance.

Mathematical modelling of cyclic pressure swing adsorption processes

NASA Astrophysics Data System (ADS)

Skvortsov, S. A.; Akulinin, E. I.; Golubyatnikov, O. O.; Dvoretsky, D. S.; Dvoretsky, S. I.

2018-05-01

The paper discusses the results of a numerical analysis of the properties and regimes of the adsorption air separation and oxygen concentration process with a purity of ∼ 40-60%, carried out in a 2-adsorption vacuum-pressure plant with a granular zeolite adsorbent 13X with a productivity of 1.6 · 10-5 m3/s. Computational experiments were carried out using the developed mathematical model and the influence of temperature, pressure, reflux ratio, the duration of the adsorption and desorption stages, the harmonic fluctuations of the inlet pressure during the adsorption stage and the outlet pressure during the desorption stage on the kinetics, and the efficiency of the air separation process by the PSA method were investigated. It is established that the specially organized harmonic fluctuations of the inlet pressure at the stage of adsorption and outlet pressure during the desorption stage lead to an increase in the purity of product oxygen by 4% (vol.).

Improve the Recovery of Fermentable Sugar from Rice Straw by Sonication and Its Mathematical Modeling

NASA Astrophysics Data System (ADS)

Bhattacharyya, Saurav; Dutta, Somenath; Datta, Sidhartha; Bhattacharjee, Chiranjib

2012-08-01

Rice straw is waste renewable agricultural biomass, which contains sufficient amount of fermentable sugars like glucose, galactose fructose, xylose etc. These sugars can be treated with fermentation pathway to produce ethanol. Hydrolysis of pretreated rice straw in dilute sulfuric acid was investigated at different acid concentrations (0.25-0.75 % w/v), and sonication was carried out to improve the extent of sugar extraction. The current work examines the effect of sonication on extraction of total reducing sugar (TRS) and an empirical mathematical model has been established to predict it. Effects of various operating variables of sonication, including amplitude (60-100 %), cycle (0.6-1.0), treatment time (0-15 min) have been analyzed for each acid concentration. Observation shows that on optimization of the sonication conditions (100 % amplitude, 0.8 cycle and 10 min) around 90 % improvement of TRS extraction occurs at 0.5 % (w/v) acid concentration.

Historical perspective on lead biokinetic models.

PubMed Central

Rabinowitz, M

1998-01-01

A historical review of the development of biokinetic model of lead is presented. Biokinetics is interpreted narrowly to mean only physiologic processes happening within the body. Proceeding chronologically, for each epoch, the measurements of lead in the body are presented along with mathematical models in an attempt to trace the convergence of observations from two disparate fields--occupational medicine and radiologic health--into some unified models. Kehoe's early balance studies and the use of radioactive lead tracers are presented. The 1960s saw the joint application of radioactive lead techniques and simple compartmental kinetic models used to establish the exchange rates and residence times of lead in body pools. The applications of stable isotopes to questions of the magnitudes of respired and ingested inputs required the development of a simple three-pool model. During the 1980s more elaborate models were developed. One of their key goals was the establishment of the dose-response relationship between exposure to lead and biologic precursors of adverse health effects. PMID:9860905

Mathematical modeling of the process of determining the standards for process losses in the transfer of thermal energy of the coolant

NASA Astrophysics Data System (ADS)

Akhmetova, I. G.; Chichirova, N. D.

2017-11-01

Currently the actual problem is a precise definition of the normative and actual heat loss. Existing methods - experimental, on metering devices, on the basis of mathematical modeling methods are not without drawbacks. Heat losses establishing during the heat carrier transport has an impact on the tariff structure of heat supply organizations. This quantity determination also promotes proper choice of main and auxiliary equipment power, temperature chart of heat supply networks, as well as the heating system structure choice with the decentralization. Calculation of actual heat loss and their comparison with standard values justifies the performance of works on improvement of the heat networks with the replacement of piping or its insulation. To determine the cause of discrepancies between normative and actual heat losses thermal tests on the magnitude of the actual heat losses in the 124 sections of heat networks in Kazan. As were carried out the result mathematical model of the regulatory definition of heat losses is developed and tested. This model differ from differs the existing according the piping insulation type. The application of this factor will bring the value of calculative normative losses heat energy to their actual value. It is of great importance for enterprises operating distribution networks and because of the conditions of their configuration and extensions do not have the technical ability to produce thermal testing.

Characteristics of mathematics teaching in Shanghai, China: Through the lens of a Malaysian

NASA Astrophysics Data System (ADS)

Lim, Chap Sam

2007-06-01

The mathematical performance of Chinese students, from mainland China, Hong Kong and Taiwan, is widely acclaimed in international comparisons of mathematics achievement. However, in the eyes of the Western educators, the environments established in Chinese schools are deemed relatively unfavourable for mathematics learning. This paper reports on a study that investigates the characteristics of effective mathematics teaching in five Shanghai schools. Findings reveal that those characteristics include (a) teaching with variation; (b) emphasis of precise and elegant mathematical language; (c) emphasis of logical reasoning, mathematical thinking and proofing during teaching; (d) order and serious classroom discipline; (e) strong and coherence teacher-student rapport, and (f) strong collaborative culture amongst mathematics teachers.

Widening and Increasing Post-16 Mathematics Participation: Pathways, Pedagogies and Politics

ERIC Educational Resources Information Center

Noyes, Andrew; Wake, Geoff; Drake, Pat

2011-01-01

This paper explores the potential impact of a national pilot initiative in England aimed at increasing and widening participation in advanced mathematical study through the creation of a new qualification for 16- to 18-year-olds. This proposed qualification pathway--"Use of Mathematics"--sits in parallel with long-established,…

Mathematics Education & Digital Technologies: Facing the Challenge of Networking European Research Teams

ERIC Educational Resources Information Center

Bottino, Rosa Maria; Kynigos, Chronis

2009-01-01

This paper introduces the "IJCML" Special Issue dedicated to digital technologies and mathematics education and, in particular, to the work performed by the European Research Team TELMA (Technology Enhanced Learning in Mathematics). TELMA was one of the initiatives of the Kaleidoscope Network of Excellence established by the European…

Specific Quality Criteria for Research Papers on Adults Learning Mathematics?

ERIC Educational Resources Information Center

Wedege, Tine

2009-01-01

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

Effectiveness of an Interactive Multimedia Learning Package in Developing Attitude towards Mathematics

ERIC Educational Resources Information Center

Muthulakshmi, P.; Veliappan, A.

2016-01-01

The present study has been designed to investigate the effectiveness of an interactive multimedia learning package in developing attitude towards Mathematics. After establishing homogeneity with reference to the students' quarterly marks in Mathematics and the scores of intelligence test, they were divided into 21 learners in control group and 21…

The Mathematics and Computer Science Learning Center (MLC).

ERIC Educational Resources Information Center

Abraham, Solomon T.

The Mathematics and Computer Science Learning Center (MLC) was established in the Department of Mathematics at North Carolina Central University during the fall semester of the 1982-83 academic year. The initial operations of the MLC were supported by grants to the University from the Burroughs-Wellcome Company and the Kenan Charitable Trust Fund.…

...And Gladly Teach: A Ford Foundation Report on the Urban Mathematics Collaboratives.

ERIC Educational Resources Information Center

Ford Foundation, New York, NY.

In February, 1985, the Ford Foundation launched an experimental program to strengthen mathematics education in inner-city high schools. Five grants helped establish urban mathematics collaboratives (UMC) in Cleveland, Minneapolis-St. Paul, Los Angeles, Philadelphia, and San Francisco. Later, additional UMCs were set up in Durham, Memphis, New…

The Effectiveness of Robotics as a Manipulative in Mathematics Instruction: A Mixed Method Study

ERIC Educational Resources Information Center

Sheehy, Leonard

2017-01-01

Addition of fractions is an important foundation for students to experience success in mathematics. This mixed-methods study was conducted to measure the effectiveness of robotics as a mathematics manipulative with seventh grade students. Two groups of students were established: control and treatment. The control group received teacher-centered…

Relating Aspects of Motivation to Facets of Mathematical Competence Varying in Cognitive Demand

ERIC Educational Resources Information Center

Gilbert, Melissa C.

2016-01-01

The author investigated the relationship between aspects of student motivation and performance on mathematical tasks varying in cognitive demand relevant to meeting the expectations of the Common Core State Standards for Mathematics (CCSS-M). A sample of 479 primarily Latino middle school students completed established survey measures of…

Establishing a relationship between maximum torque production of isolated joints to simulate EVA ratchet push-pull maneuver: A case study

NASA Technical Reports Server (NTRS)

Pandya, Abhilash; Maida, James; Hasson, Scott; Greenisen, Michael; Woolford, Barbara

1993-01-01

As manned exploration of space continues, analytical evaluation of human strength characteristics is critical. These extraterrestrial environments will spawn issues of human performance which will impact the designs of tools, work spaces, and space vehicles. Computer modeling is an effective method of correlating human biomechanical and anthropometric data with models of space structures and human work spaces. The aim of this study is to provide biomechanical data from isolated joints to be utilized in a computer modeling system for calculating torque resulting from any upper extremity motions: in this study, the ratchet wrench push-pull operation (a typical extravehicular activity task). Established here are mathematical relationships used to calculate maximum torque production of isolated upper extremity joints. These relationships are a function of joint angle and joint velocity.

Study on the total amount control of atmospheric pollutant based on GIS.

PubMed

Wang, Jian-Ping; Guo, Xi-Kun

2005-08-01

To provide effective environmental management for total amount control of atmospheric pollutants. An atmospheric diffusion model of sulfur dioxide on the surface of the earth was established and tested in Shantou of Guangdong Province on the basis of an overall assessment of regional natural environment, social economic state of development, pollution sources and atmospheric environmental quality. Compared with actual monitoring results in a studied region, simulation values fell within the range of two times of error and were evenly distributed in the two sides of the monitored values. Predicted with the largest emission model method, the largest emission of sulfur dioxide would be 54,279.792 tons per year in 2010. The mathematical model established and revised on the basis of GIS is more rational and suitable for the regional characteristics of total amount control of air pollutants.

Formal Darwinism, the individual-as-maximizing-agent analogy and bet-hedging

PubMed Central

Grafen, A.

1999-01-01

The central argument of The origin of species was that mechanical processes (inheritance of features and the differential reproduction they cause) can give rise to the appearance of design. The 'mechanical processes' are now mathematically represented by the dynamic systems of population genetics, and the appearance of design by optimization and game theory in which the individual plays the part of the maximizing agent. Establishing a precise individual-as-maximizing-agent (IMA) analogy for a population-genetics system justifies optimization approaches, and so provides a modern formal representation of the core of Darwinism. It is a hitherto unnoticed implication of recent population-genetics models that, contrary to a decades-long consensus, an IMA analogy can be found in models with stochastic environments (subject to a convexity assumption), in which individuals maximize expected reproductive value. The key is that the total reproductive value of a species must be considered as constant, so therefore reproductive value should always be calculated in relative terms. This result removes a major obstacle from the theoretical challenge to find a unifying framework which establishes the IMA analogy for all of Darwinian biology, including as special cases inclusive fitness, evolutionarily stable strategies, evolutionary life-history theory, age-structured models and sex ratio theory. This would provide a formal, mathematical justification of fruitful and widespread but 'intentional' terms in evolutionary biology, such as 'selfish', 'altruism' and 'conflict'.

Application of mathematical planning in production of filled emulsion rubbers

NASA Astrophysics Data System (ADS)

Pugacheva, I. N.; Molokanova, L. V.; Popova, L. V.; Repin, P. S.

2018-05-01

The applicability of mathematical planning of experiment in the field of chemistry and chemical engineering, in particular in the industrial production of synthetic rubbers, is considered in the article. Possibility of using secondary material resources, which are waste products of light industry, in the production of elastomeric compositions is studied. The method of obtaining a powdered cellulose additive from wastes containing cellulose fiber is described. The best way of introducing the obtained additive into elastomeric compositions based on the emulsion rubber is established. Optimal conditions for obtaining filled emulsion rubber with the help of a powdered cellulose additive were established basing on the mathematical planning of experiment.

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…

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…

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 Modelling Approach in Mathematics Education

ERIC Educational Resources Information Center

Arseven, Ayla

2015-01-01

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

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

ERIC Educational Resources Information Center

Lowe, James; Carter, Merilyn; Cooper, Tom

2018-01-01

Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…

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

NASA Astrophysics Data System (ADS)

Shahbari, Juhaina Awawdeh

2018-07-01

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

Combining measurements to estimate properties and characterization extent of complex biochemical mixtures; applications to Heparan Sulfate

PubMed Central

Pradines, Joël R.; Beccati, Daniela; Lech, Miroslaw; Ozug, Jennifer; Farutin, Victor; Huang, Yongqing; Gunay, Nur Sibel; Capila, Ishan

2016-01-01

Complex mixtures of molecular species, such as glycoproteins and glycosaminoglycans, have important biological and therapeutic functions. Characterization of these mixtures with analytical chemistry measurements is an important step when developing generic drugs such as biosimilars. Recent developments have focused on analytical methods and statistical approaches to test similarity between mixtures. The question of how much uncertainty on mixture composition is reduced by combining several measurements still remains mostly unexplored. Mathematical frameworks to combine measurements, estimate mixture properties, and quantify remaining uncertainty, i.e. a characterization extent, are introduced here. Constrained optimization and mathematical modeling are applied to a set of twenty-three experimental measurements on heparan sulfate, a mixture of linear chains of disaccharides having different levels of sulfation. While this mixture has potentially over two million molecular species, mathematical modeling and the small set of measurements establish the existence of nonhomogeneity of sulfate level along chains and the presence of abundant sulfate repeats. Constrained optimization yields not only estimations of sulfate repeats and sulfate level at each position in the chains but also bounds on these levels, thereby estimating the extent of characterization of the sulfation pattern which is achieved by the set of measurements. PMID:27112127

Combining measurements to estimate properties and characterization extent of complex biochemical mixtures; applications to Heparan Sulfate.

PubMed

Pradines, Joël R; Beccati, Daniela; Lech, Miroslaw; Ozug, Jennifer; Farutin, Victor; Huang, Yongqing; Gunay, Nur Sibel; Capila, Ishan

2016-04-26

Complex mixtures of molecular species, such as glycoproteins and glycosaminoglycans, have important biological and therapeutic functions. Characterization of these mixtures with analytical chemistry measurements is an important step when developing generic drugs such as biosimilars. Recent developments have focused on analytical methods and statistical approaches to test similarity between mixtures. The question of how much uncertainty on mixture composition is reduced by combining several measurements still remains mostly unexplored. Mathematical frameworks to combine measurements, estimate mixture properties, and quantify remaining uncertainty, i.e. a characterization extent, are introduced here. Constrained optimization and mathematical modeling are applied to a set of twenty-three experimental measurements on heparan sulfate, a mixture of linear chains of disaccharides having different levels of sulfation. While this mixture has potentially over two million molecular species, mathematical modeling and the small set of measurements establish the existence of nonhomogeneity of sulfate level along chains and the presence of abundant sulfate repeats. Constrained optimization yields not only estimations of sulfate repeats and sulfate level at each position in the chains but also bounds on these levels, thereby estimating the extent of characterization of the sulfation pattern which is achieved by the set of measurements.

Combining measurements to estimate properties and characterization extent of complex biochemical mixtures; applications to Heparan Sulfate

NASA Astrophysics Data System (ADS)

Pradines, Joël R.; Beccati, Daniela; Lech, Miroslaw; Ozug, Jennifer; Farutin, Victor; Huang, Yongqing; Gunay, Nur Sibel; Capila, Ishan

2016-04-01

Complex mixtures of molecular species, such as glycoproteins and glycosaminoglycans, have important biological and therapeutic functions. Characterization of these mixtures with analytical chemistry measurements is an important step when developing generic drugs such as biosimilars. Recent developments have focused on analytical methods and statistical approaches to test similarity between mixtures. The question of how much uncertainty on mixture composition is reduced by combining several measurements still remains mostly unexplored. Mathematical frameworks to combine measurements, estimate mixture properties, and quantify remaining uncertainty, i.e. a characterization extent, are introduced here. Constrained optimization and mathematical modeling are applied to a set of twenty-three experimental measurements on heparan sulfate, a mixture of linear chains of disaccharides having different levels of sulfation. While this mixture has potentially over two million molecular species, mathematical modeling and the small set of measurements establish the existence of nonhomogeneity of sulfate level along chains and the presence of abundant sulfate repeats. Constrained optimization yields not only estimations of sulfate repeats and sulfate level at each position in the chains but also bounds on these levels, thereby estimating the extent of characterization of the sulfation pattern which is achieved by the set of measurements.

FNAS/summer faculty fellowship research continuation program. Task 6: Integrated model development for liquid fueled rocket propulsion systems. Task 9: Aspects of model-based rocket engine condition monitoring and control

NASA Technical Reports Server (NTRS)

Santi, L. Michael; Helmicki, Arthur J.

1993-01-01

The objective of Phase I of this research effort was to develop an advanced mathematical-empirical model of SSME steady-state performance. Task 6 of Phase I is to develop component specific modification strategy for baseline case influence coefficient matrices. This report describes the background of SSME performance characteristics and provides a description of the control variable basis of three different gains models. The procedure used to establish influence coefficients for each of these three models is also described. Gains model analysis results are compared to Rocketdyne's power balance model (PBM).

Stochastic user equilibrium model with a tradable credit scheme and application in maximizing network reserve capacity

NASA Astrophysics Data System (ADS)

Han, Fei; Cheng, Lin

2017-04-01

The tradable credit scheme (TCS) outperforms congestion pricing in terms of social equity and revenue neutrality, apart from the same perfect performance on congestion mitigation. This article investigates the effectiveness and efficiency of TCS on enhancing transportation network capacity in a stochastic user equilibrium (SUE) modelling framework. First, the SUE and credit market equilibrium conditions are presented; then an equivalent general SUE model with TCS is established by virtue of two constructed functions, which can be further simplified under a specific probability distribution. To enhance the network capacity by utilizing TCS, a bi-level mathematical programming model is established for the optimal TCS design problem, with the upper level optimization objective maximizing network reserve capacity and lower level being the proposed SUE model. The heuristic sensitivity analysis-based algorithm is developed to solve the bi-level model. Three numerical examples are provided to illustrate the improvement effect of TCS on the network in different scenarios.

Stability analysis of an HIV/AIDS epidemic model with treatment

NASA Astrophysics Data System (ADS)

Cai, Liming; Li, Xuezhi; Ghosh, Mini; Guo, Baozhu

2009-07-01

An HIV/AIDS epidemic model with treatment is investigated. The model allows for some infected individuals to move from the symptomatic phase to the asymptomatic phase by all sorts of treatment methods. We first establish the ODE treatment model with two infective stages. Mathematical analyses establish that the global dynamics of the spread of the HIV infectious disease are completely determined by the basic reproduction number [real]0. If [real]0<=1, the disease-free equilibrium is globally stable, whereas the unique infected equilibrium is globally asymptotically stable if [real]0>1. Then, we introduce a discrete time delay to the model to describe the time from the start of treatment in the symptomatic stage until treatment effects become visible. The effect of the time delay on the stability of the endemically infected equilibrium is investigated. Moreover, the delay model exhibits Hopf bifurcations by using the delay as a bifurcation parameter. Finally, numerical simulations are presented to illustrate the results.

Establishment of a mathematic model for predicting malignancy in solitary pulmonary nodules.

PubMed

Zhang, Man; Zhuo, Na; Guo, Zhanlin; Zhang, Xingguang; Liang, Wenhua; Zhao, Sheng; He, Jianxing

2015-10-01

The aim of this study was to establish a model for predicting the probability of malignancy in solitary pulmonary nodules (SPNs) and provide guidance for the diagnosis and follow-up intervention of SPNs. We retrospectively analyzed the clinical data and computed tomography (CT) images of 294 patients with a clear pathological diagnosis of SPN. Multivariate logistic regression analysis was used to screen independent predictors of the probability of malignancy in the SPN and to establish a model for predicting malignancy in SPNs. Then, another 120 SPN patients who did not participate in the model establishment were chosen as group B and used to verify the accuracy of the prediction model. Multivariate logistic regression analysis showed that there were significant differences in age, smoking history, maximum diameter of nodules, spiculation, clear borders, and Cyfra21-1 levels between subgroups with benign and malignant SPNs (P<0.05). These factors were identified as independent predictors of malignancy in SPNs. The area under the curve (AUC) was 0.910 [95% confidence interval (CI), 0.857-0.963] in model with Cyfra21-1 significantly better than 0.812 (95% CI, 0.763-0.861) in model without Cyfra21-1 (P=0.008). The area under receiver operating characteristic (ROC) curve of our model is significantly higher than the Mayo model, VA model and Peking University People's (PKUPH) model. Our model (AUC =0.910) compared with Brock model (AUC =0.878, P=0.350), the difference was not statistically significant. The model added Cyfra21-1 could improve prediction. The prediction model established in this study can be used to assess the probability of malignancy in SPNs, thereby providing help for the diagnosis of SPNs and the selection of follow-up interventions.

The Interrelationships of Mathematical Precursors in Kindergarten

PubMed Central

Cirino, Paul T.

2011-01-01

This study evaluated the interrelations among cognitive precursors across quantitative, linguistic, and spatial attention domains that have been implicated for math achievement in young children. The dimensionality of the quantity precursors was evaluated in 286 Kindergarteners via latent variable techniques, and the contribution of precursors from each domain was established for small sums addition. Results showed a five factor structure for the quantity precursors with the major distinction between nonsymbolic and symbolic tasks. The overall model demonstrated good fit, and strong predictive power (R2 = 55%) for addition number combinations. Linguistic and spatial attention domains showed indirect relationships with outcomes, with their effects mediated by symbolic quantity measures. These results have implications for the measurement of mathematical precursors, and yield promise for predicting future math performance. PMID:21194711

Broadening participation in Natural Sciences and Mathematics at the University of Maryland Baltimore County

NASA Astrophysics Data System (ADS)

Rous, Philip

2013-03-01

Over the past two decades, UMBC has undertaken a series of efforts to broaden participation in the natural sciences and mathematics, beginning with the establishment of the Meyerhoff program. Using as examples the multiple initiatives that followed, and with a focus on the challenge of increasing access and success of all students who enter as both freshmen and transfer students, I will describe a model of culture change that we have employed repeatedly to understand and guide our efforts in broadening participation. Particular attention will be paid to the concept of cultural capital, the role of innovators and the challenge of scaling small-scale innovations towards institutional change. Supported by the National Science Foundation and the Bill and Melinda Gates Foundation.

Mathematical model of salt cavern leaching for gas storage in high-insoluble salt formations.

PubMed

Li, Jinlong; Shi, Xilin; Yang, Chunhe; Li, Yinping; Wang, Tongtao; Ma, Hongling

2018-01-10

A mathematical model is established to predict the salt cavern development during leaching in high-insoluble salt formations. The salt-brine mass transfer rate is introduced, and the effects of the insoluble sediments on the development of the cavern are included. Considering the salt mass conservation in the cavern, the couple equations of the cavern shape, brine concentration and brine velocity are derived. According to the falling and accumulating rules of the insoluble particles, the governing equations of the insoluble sediments are deduced. A computer program using VC++ language is developed to obtain the numerical solution of these equations. To verify the proposed model, the leaching processes of two salt caverns of Jintan underground gas storage are simulated by the program, using the actual geological and technological parameters. The same simulation is performed by the current mainstream leaching software in China. The simulation results of the two programs are compared with the available field data. It shows that the proposed software is more accurate on the shape prediction of the cavern bottom and roof, which demonstrates the reliability and applicability of the model.

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.

Research on modeling and motion simulation of a spherical space robot with telescopic manipulator based on virtual prototype technology

NASA Astrophysics Data System (ADS)

Shi, Chengkun; Sun, Hanxu; Jia, Qingxuan; Zhao, Kailiang

2009-05-01

For realizing omni-directional movement and operating task of spherical space robot system, this paper describes an innovated prototype and analyzes dynamic characteristics of a spherical rolling robot with telescopic manipulator. Based on the Newton-Euler equations, the kinematics and dynamic equations of the spherical robot's motion are instructed detailedly. Then the motion simulations of the robot in different environments are developed with ADAMS. The simulation results validate the mathematics model of the system. And the dynamic model establishes theoretical basis for the latter job.

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…

South African Grade 9 Mathematics Teachers' Views on the Teaching of Problem Solving

ERIC Educational Resources Information Center

Chirinda, Brantina; Barmby, Patrick

2018-01-01

The South African curriculum emphasizes the teaching of problem solving in mathematics. However, little is known about South African teachers' views on the teaching of mathematical problem solving (MPS). The purpose of this study was to establish Grade 9 South African teachers' views, teaching strategies and the support required in their teaching…

Enjoying Mathematics or Feeling Competent in Mathematics? Reciprocal Effects on Mathematics Achievement and Perceived Math Effort Expenditure

ERIC Educational Resources Information Center

Pinxten, Maarten; Marsh, Herbert W.; De Fraine, Bieke; Van Den Noortgate, Wim; Van Damme, Jan

2014-01-01

Background: The multidimensionality of the academic self-concept in terms of domain specificity has been well established in previous studies, whereas its multidimensionality in terms of motivational functions (the so-called affect-competence separation) needs further examination. Aim: This study aims at exploring differential effects of enjoyment…

Community Partnerships: Pathways to Meaningful Mathematics

ERIC Educational Resources Information Center

Bush, Sarah B.; Karp, Karen S.; Lentz, Tova; Nadler, Jennifer

2013-01-01

This article showcases the benefits of the alliance the authors have established during the past two years with the Barnes Foundation to add more mathematics activities to their repertoire and to integrate more art into their mathematics lessons. Recently, they decided to focus on activities at the K-grade 2 level that could be used as an on-site…

Improving Geometric and Trigonometric Knowledge and Skill for High School Mathematics Teachers: A Professional Development Partnership

ERIC Educational Resources Information Center

Merrill, Chris; Devine, Kevin L.; Brown, Joshua W.; Brown, Ryan A.

2010-01-01

In the summer of 2009, a professional development partnership was established between the Peoria Public School District (PPSD), a local education agency (LEA), and Illinois State University (ISU) to improve geometric and trigonometric knowledge and skill for high school mathematics teachers as part of the Illinois Mathematics and Science…

Judged Similarity of Aptitude and Achievement Tests in Mathematics.

ERIC Educational Resources Information Center

Donlon, Thomas F.

This study attempts to establish the ability of a panel of five judges with varied mathematics background to distinguish between two types of mathematical tests by separating their component items when they are presented in a mixed pool of aptitude and achievement tests. Typically, the two tests show high correlation. The judges showed about 70%…

Eisenhower Southwest Consortium for the Improvement of Mathematics and Science Teaching Cumulative Report for FY96-00.

ERIC Educational Resources Information Center

Southwest Educational Development Lab., Austin, TX. Southwest Consortium for the Improvement of Mathematics and Science Teaching.

This report presents activities, accomplishments, and conclusions of the Eisenhower Southwest Consortium for the Improvement of Mathematics and Science Teaching (SCIMAST) for the fiscal years 1996-2000. SCIMAST was established in 1992 and supports mathematics and science learning in the states of Arkansas, Louisiana, New Mexico, Oklahoma, and…

On the Nature of and Teachers' Goals for Students' Mathematical Argumentation in High School Classrooms

ERIC Educational Resources Information Center

Howell, Tracey H.

2013-01-01

In an era of new standards and emerging accountability systems, an understanding of the supports needed to aid teachers and students in making necessary transitions in mathematics teaching and learning is critical. Given the established research base demonstrating the importance of justification and reasoning in students' mathematics learning and…

Mathematical Experiences and Parental Involvement of Parents Who Are and Who Are Not Mathematicians

ERIC Educational Resources Information Center

Antolin Drešar, Darja; Lipovec, Alenka

2017-01-01

Previous studies suggest that parental involvement in children's mathematics education is more established for parents who feel competent in mathematics. This qualitative study aimed to gain an in-depth insight into the experiences of parental involvement of two different groups of parents: those who are mathematicians and those who are not. Data…

An Interdisciplinary Collaboration between Computer Engineering and Mathematics/Bilingual Education to Develop a Curriculum for Underrepresented Middle School Students

ERIC Educational Resources Information Center

Celedón-Pattichis, Sylvia; LópezLeiva, Carlos Alfonso; Pattichis, Marios S.; Llamocca, Daniel

2013-01-01

There is a strong need in the United States to increase the number of students from underrepresented groups who pursue careers in Science, Technology, Engineering, and Mathematics. Drawing from sociocultural theory, we present approaches to establishing collaborations between computer engineering and mathematics/bilingual education faculty to…

Viscosity Meaurement Technique for Metal Fuels

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

Ban, Heng; Kennedy, Rory

2015-02-09

Metallic fuels have exceptional transient behavior, excellent thermal conductivity, and a more straightforward reprocessing path, which does not separate out pure plutonium from the process stream. Fabrication of fuel containing minor actinides and rare earth (RE) elements for irradiation tests, for instance, U-20Pu-3Am-2Np-1.0RE-15Zr samples at the Idaho National Laboratory, is generally done by melt casting in an inert atmosphere. For the design of a casting system and further scale up development, computational modeling of the casting process is needed to provide information on melt flow and solidification for process optimization. Therefore, there is a need for melt viscosity data, themore » most important melt property that controls the melt flow. The goal of the project was to develop a measurement technique that uses fully sealed melt sample with no Americium vapor loss to determine the viscosity of metallic melts and at temperatures relevant to the casting process. The specific objectives of the project were to: develop mathematical models to establish the principle of the measurement method, design and build a viscosity measurement prototype system based on the established principle, and calibrate the system and quantify the uncertainty range. The result of the project indicates that the oscillation cup technique is applicable for melt viscosity measurement. Detailed mathematical models of innovative sample ampoule designs were developed to not only determine melt viscosity, but also melt density under certain designs. Measurement uncertainties were analyzed and quantified. The result of this project can be used as the initial step toward the eventual goal of establishing a viscosity measurement system for radioactive melts.« less

Choosing Between Public and Private Providers of Depot Maintenance: A Proposed New Approach

DTIC Science & Technology

1997-09-01

Appendix A Mathematical Form of the Model Appendix B Assumed Distributions for Evaluation Factors vm Contents Appendix C Trial Evaluation Workbook ...Figure 4-2. Revised Factor Scale Anchors 4-5 Figure 4-3. Workbook Display Establishing Relevance of Factor 4-5 Figure 4-4. Comparing Results of...Introduction process. To fill voids we conducted additional research in the areas of classical microeconomics , transaction cost economics, public

Mathematical modeling and measurement of electric fields of electrode-based through-the-earth (TTE) communication

NASA Astrophysics Data System (ADS)

Yan, Lincan; Zhou, Chenming; Reyes, Miguel; Whisner, Bruce; Damiano, Nicholas

2017-06-01

There are two types of through-the-earth (TTE) wireless communication in the mining industry: magnetic loop TTE and electrode-based (or linear) TTE. While the magnetic loop systems send signal through magnetic fields, the transmitter of an electrode-based TTE system sends signal directly through the mine overburden by driving an extremely low frequency (ELF) or ultralow frequency (ULF) AC current into the earth. The receiver at the other end (underground or surface) detects the resultant current and receives it as a voltage. A wireless communication link between surface and underground is then established. For electrode-based TTE communications, the signal is transmitted through the established electric field and is received as a voltage detected at the receiver. It is important to understand the electric field distribution within the mine overburden for the purpose of designing and improving the performance of the electrode-based TTE systems. In this paper, a complete explicit solution for all three electric field components for the electrode-based TTE communication was developed. An experiment was conducted using a prototype electrode-based TTE system developed by National Institute for Occupational Safety and Health. The mathematical model was then compared and validated with test data. A reasonable agreement was found between them.

Mathematical modeling and measurement of electric fields of electrode-based through-the-earth (TTE) communication.

PubMed

Yan, Lincan; Zhou, Chenming; Reyes, Miguel; Whisner, Bruce; Damiano, Nicholas

2017-07-12

There are two types of through-the-earth (TTE) wireless communication in the mining industry: magnetic loop TTE and electrode-based (or linear) TTE. While the magnetic loop systems send signal through magnetic fields, the transmitter of an electrode-based TTE system sends signal directly through the mine overburden by driving an extremely low frequency (ELF) or ultralow frequency (ULF) AC current into the earth. The receiver at the other end (underground or surface) detects the resultant current and receives it as a voltage. A wireless communication link between surface and underground is then established. For electrode-based TTE communications, the signal is transmitted through the established electric field and is received as a voltage detected at the receiver. It is important to understand the electric field distribution within the mine overburden for the purpose of designing and improving the performance of the electrode-based TTE systems. In this paper, a complete explicit solution for all three electric field components for the electrode-based TTE communication was developed. An experiment was conducted using a prototype electrode-based TTE system developed by National Institute for Occupational Safety and Health. The mathematical model was then compared and validated with test data. A reasonable agreement was found between them.

Mathematical modeling and measurement of electric fields of electrode-based through-the-earth (TTE) communication

PubMed Central

Yan, Lincan; Zhou, Chenming; Reyes, Miguel; Whisner, Bruce; Damiano, Nicholas

2017-01-01

There are two types of through-the-earth (TTE) wireless communication in the mining industry: magnetic loop TTE and electrode-based (or linear) TTE. While the magnetic loop systems send signal through magnetic fields, the transmitter of an electrode-based TTE system sends signal directly through the mine overburden by driving an extremely low frequency (ELF) or ultralow frequency (ULF) AC current into the earth. The receiver at the other end (underground or surface) detects the resultant current and receives it as a voltage. A wireless communication link between surface and underground is then established. For electrode-based TTE communications, the signal is transmitted through the established electric field and is received as a voltage detected at the receiver. It is important to understand the electric field distribution within the mine overburden for the purpose of designing and improving the performance of the electrode-based TTE systems. In this paper, a complete explicit solution for all three electric field components for the electrode-based TTE communication was developed. An experiment was conducted using a prototype electrode-based TTE system developed by National Institute for Occupational Safety and Health. The mathematical model was then compared and validated with test data. A reasonable agreement was found between them. PMID:28845062

[Study on the quantitative evaluation on the degree of TCM basic syndromes often encountered in patients with primary liver cancer].

PubMed

Li, Dong-tao; Ling, Chang-quan; Zhu, De-zeng

2007-07-01

To establish a quantitative model for evaluating the degree of the TCM basic syndromes often encountered in patients with primary liver cancer (PLC). Medical literatures concerning the clinical investigation and TCM syndrome of PLC were collected and analyzed adopting expert-composed symposium method, and the 100 millimeter scaling was applied in combining with scoring on degree of symptoms to establish a quantitative criterion for symptoms and signs degree classification in patients with PLC. Two models, i.e. the additive model and the additive-multiplicative model, were established by using comprehensive analytic hierarchy process (AHP) as the mathematical tool to estimate the weight of the criterion for evaluating basic syndromes in various layers by specialists. Then the two models were verified in clinical practice and the outcomes were compared with that fuzzy evaluated by specialists. Verification on 459 times/case of PLC showed that the coincidence rate between the outcomes derived from specialists with that from the additive model was 84.53 %, and with that from the additive-multificative model was 62.75 %, the difference between the two showed statistical significance (P<0.01). It could be decided that the additive model is the principle model suitable for quantitative evaluation on the degree of TCM basic syndromes in patients with PLC.

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.

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…

Energy-saving management modelling and optimization for lead-acid battery formation process

NASA Astrophysics Data System (ADS)

Wang, T.; Chen, Z.; Xu, J. Y.; Wang, F. Y.; Liu, H. M.

2017-11-01

In this context, a typical lead-acid battery producing process is introduced. Based on the formation process, an efficiency management method is proposed. An optimization model with the objective to minimize the formation electricity cost in a single period is established. This optimization model considers several related constraints, together with two influencing factors including the transformation efficiency of IGBT charge-and-discharge machine and the time-of-use price. An example simulation is shown using PSO algorithm to solve this mathematic model, and the proposed optimization strategy is proved to be effective and learnable for energy-saving and efficiency optimization in battery producing industries.

Integrated modeling and design for realizing a two-wheeled wheelchair for disabled.

PubMed

Altalmas, Tareq; Aula, Abqori; Ahmad, Salmiah; Tokhi, M O; Akmeliawati, Rini

2016-01-01

Two-wheeled wheelchairs are considered highly nonlinear and complex systems. The systems mimic a double-inverted pendulum scenario and will provide better maneuverability in confined spaces and also to reach higher level of height for pick and place tasks. The challenge resides in modeling and control of the two-wheeled wheelchair to perform comparably to a normal four-wheeled wheelchair. Most common modeling techniques have been accomplished by researchers utilizing the basic Newton's Laws of motion and some have used 3D tools to model the system where the models are much more theoretical and quite far from the practical implementation. This article is aimed at closing the gap between the conventional mathematical modeling approaches where the integrated 3D modeling approach with validation on the actual hardware implementation was conducted. To achieve this, both nonlinear and a linearized model in terms of state space model were obtained from the mathematical model of the system for analysis and, thereafter, a 3D virtual prototype of the wheelchair was developed, simulated, and analyzed. This has increased the confidence level for the proposed platform and facilitated the actual hardware implementation of the two-wheeled wheelchair. Results show that the prototype developed and tested has successfully worked within the specific requirements established.

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 research of breaking rock with liquid-solid two-phase jet flow

NASA Astrophysics Data System (ADS)

Cheng, X. Z.; Ren, F. S.; Fang, T. C.

2018-03-01

Abstracts. Particle impact drilling is an efficient way of breaking rock, which is mainly used in deep drilling and ultra-deep drilling. The differential equation was established based on the theory of Hertz and Newton’s second law, through the analysis of particle impact rock, the depth of particles into the rock was obtained. The mathematical model was established based on the effect of water impact crack. The research results show when water jet speed is more than 40 m/s, rock stability coefficient is more than 1.0, the rock fracture appear. Through the experimental research of particle impact drilling facilities, analysis of cuttings and the crack size which was analyzed through Scanning electron microscope consistent with the theoretical calculation, the validity of the model was verified.

Modeling the dynamics of multipartite quantum systems created departing from two-level systems using general local and non-local interactions

NASA Astrophysics Data System (ADS)

Delgado, Francisco

2017-12-01

Quantum information is an emergent area merging physics, mathematics, computer science and engineering. To reach its technological goals, it is requiring adequate approaches to understand how to combine physical restrictions, computational approaches and technological requirements to get functional universal quantum information processing. This work presents the modeling and the analysis of certain general type of Hamiltonian representing several physical systems used in quantum information and establishing a dynamics reduction in a natural grammar for bipartite processing based on entangled states.

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.

Ultrasensitive dual phosphorylation dephosphorylation cycle kinetics exhibits canonical competition behavior

NASA Astrophysics Data System (ADS)

Huang, Qingdao; Qian, Hong

2009-09-01

We establish a mathematical model for a cellular biochemical signaling module in terms of a planar differential equation system. The signaling process is carried out by two phosphorylation-dephosphorylation reaction steps that share common kinase and phosphatase with saturated enzyme kinetics. The pair of equations is particularly simple in the present mathematical formulation, but they are singular. A complete mathematical analysis is developed based on an elementary perturbation theory. The dynamics exhibits the canonical competition behavior in addition to bistability. Although widely understood in ecological context, we are not aware of a full range of biochemical competition in a simple signaling network. The competition dynamics has broad implications to cellular processes such as cell differentiation and cancer immunoediting. The concepts of homogeneous and heterogeneous multisite phosphorylation are introduced and their corresponding dynamics are compared: there is no bistability in a heterogeneous dual phosphorylation system. A stochastic interpretation is also provided that further gives intuitive understanding of the bistable behavior inside the cells.

Analytic considerations and axiomatic approaches to the concept cell death and cell survival functions in biology and cancer treatment.

PubMed

Gkigkitzis, Ioannis; Haranas, Ioannis; Austerlitz, Carlos

2015-01-01

This study contains a discussion on the connection between current mathematical and biological modeling systems in response to the main research need for the development of a new mathematical theory for study of cell survival after medical treatment and cell biological behavior in general. This is a discussion of suggested future research directions and relations with interdisciplinary science. In an effort to establish the foundations for a possible framework that may be adopted to study and analyze the process of cell survival during treatment, we investigate the organic connection among an axiomatic system foundation, a predator-prey rate equation, and information theoretic signal processing. A new set theoretic approach is also introduced through the definition of cell survival units or cell survival units indicating the use of "proper classes" according to the Zermelo-Fraenkel set theory and the axiom of choice, as the mathematics appropriate for the development of biological theory of cell survival.

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.

Binary logistic regression-Instrument for assessing museum indoor air impact on exhibits.

PubMed

Bucur, Elena; Danet, Andrei Florin; Lehr, Carol Blaziu; Lehr, Elena; Nita-Lazar, Mihai

2017-04-01

This paper presents a new way to assess the environmental impact on historical artifacts using binary logistic regression. The prediction of the impact on the exhibits during certain pollution scenarios (environmental impact) was calculated by a mathematical model based on the binary logistic regression; it allows the identification of those environmental parameters from a multitude of possible parameters with a significant impact on exhibitions and ranks them according to their severity effect. Air quality (NO 2 , SO 2 , O 3 and PM 2.5 ) and microclimate parameters (temperature, humidity) monitoring data from a case study conducted within exhibition and storage spaces of the Romanian National Aviation Museum Bucharest have been used for developing and validating the binary logistic regression method and the mathematical model. The logistic regression analysis was used on 794 data combinations (715 to develop of the model and 79 to validate it) by a Statistical Package for Social Sciences (SPSS 20.0). The results from the binary logistic regression analysis demonstrated that from six parameters taken into consideration, four of them present a significant effect upon exhibits in the following order: O 3 >PM 2.5 >NO 2 >humidity followed at a significant distance by the effects of SO 2 and temperature. The mathematical model, developed in this study, correctly predicted 95.1 % of the cumulated effect of the environmental parameters upon the exhibits. Moreover, this model could also be used in the decisional process regarding the preventive preservation measures that should be implemented within the exhibition space. The paper presents a new way to assess the environmental impact on historical artifacts using binary logistic regression. The mathematical model developed on the environmental parameters analyzed by the binary logistic regression method could be useful in a decision-making process establishing the best measures for pollution reduction and preventive preservation of exhibits.

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…

Integrating science and business models of sustainability for environmentally-challenging industries such as secondary lead smelters: a systematic review and analysis of findings.

PubMed

Genaidy, A M; Sequeira, R; Tolaymat, T; Kohler, J; Wallace, S; Rinder, M

2010-09-01

Secondary lead smelters (SLS) represent an environmentally-challenging industry as they deal with toxic substances posing potential threats to both human and environmental health, consequently, they operate under strict government regulations. Such challenges have resulted in the significant reduction of SLS plants in the last three decades. In addition, the domestic recycling of lead has been on a steep decline in the past 10 years as the amount of lead recovered has remained virtually unchanged while consumption has increased. Therefore, one may wonder whether sustainable development can be achieved among SLS. The primary objective of this study was to determine whether a roadmap for sustainable development can be established for SLS. The following aims were established in support of the study objective: (1) to conduct a systematic review and an analysis of models of sustainable systems with a particular emphasis on SLS; (2) to document the challenges for the U.S. secondary lead smelting industry; and (3) to explore practices and concepts which act as vehicles for SLS on the road to sustainable development. An evidence-based methodology was adopted to achieve the study objective. A comprehensive electronic search was conducted to implement the aforementioned specific aims. Inclusion criteria were established to filter out irrelevant scientific papers and reports. The relevant articles were closely scrutinized and appraised to extract the required information and data for the possible development of a sustainable roadmap. The search process yielded a number of research articles which were utilized in the systematic review. Two types of models emerged: management/business and science/mathematical models. Although the management/business models explored actions to achieve sustainable growth in the industrial enterprise, science/mathematical models attempted to explain the sustainable behaviors and properties aiming at predominantly ecosystem management. As such, there are major disconnects between the science/mathematical and management/business models in terms of aims and goals. Therefore, there is an urgent need to integrate science and business models of sustainability for the industrial enterprises at large and environmentally-challenging industrial sectors in particular. In this paper, we offered examples of practices and concepts which can be used in charting a path towards sustainable development for secondary lead smelters particularly that the waste generated is much greater outside the industrial enterprise than inside. An environmentally-challenging industry such as secondary lead smelters requires a fresh look to chart a path towards sustainable development (i.e., survivability and purposive needs) for all stakeholders (i.e., industrial enterprise, individual stakeholders, and social/ecological systems). Such a path should deal with issues beyond pollution prevention, product stewardship and clean technologies. 2010 Elsevier Ltd. All rights reserved.

Research on energy efficiency design index for sea-going LNG carriers

NASA Astrophysics Data System (ADS)

Lin, Yan; Yu, Yanyun; Guan, Guan

2014-12-01

This paper describes the characteristics of liquefied natural gas (LNG) carriers briefly. The LNG carrier includes power plant selection, vapor treatment, liquid cargo tank type, etc. Two parameters—fuel substitution rate and recovery of boil of gas (BOG) volume to energy efficiency design index (EEDI) formula are added, and EEDI formula of LNG carriers is established based on ship EEDI formula. Then, based on steam turbine propulsion device of LNG carriers, mathematical models of LNG carriers' reference line value are established in this paper. By verification, the EEDI formula of LNG carriers described in this paper can provide a reference for LNG carrier EEDI calculation and green shipbuilding.

PLZT Ceramic Driving Rotary Micro-mirror Based on Photoelectric-electrostatic Mechanism

NASA Astrophysics Data System (ADS)

Tang, Yujuan; Yang, Zhong; Chen, Yusong; Wang, Xinjie

2017-12-01

Based on the anomalous photovoltaic effect of PLZT, a rotary micro-mirror driven by hybrid photoelectric-electrostatic actuation of PLZT ceramic is proposed. Firstly, the mathematical modelling of coupled multi-physics fields of PLZT ceramic is established during illumination and light off phases. Then, the relationship between the rotation angle and the photovoltage of PLZT ceramics is established. In addition, the feasibility of rotary micro-mirror with hybrid photoelectric-electrostatic driving is verified via closed-loop control for photo-induced voltage of PLZT ceramic. The experimental results show that the photo-induced voltage of PLZT ceramics has good dynamic control precision using on-off closed-loop control method.

Methods of Comprehensive Assessment for China’s Energy Sustainability

NASA Astrophysics Data System (ADS)

Xu, Zhijin; Song, Yankui

2018-02-01

In order to assess the sustainable development of China’s energy objectively and accurately, we need to establish a reasonable indicator system for energy sustainability and make a targeted comprehensive assessment with the scientific methods. This paper constructs a comprehensive indicator system for energy sustainability from five aspects of economy, society, environment, energy resources and energy technology based on the theory of sustainable development and the theory of symbiosis. On this basis, it establishes and discusses the assessment models and the general assessment methods for energy sustainability with the help of fuzzy mathematics. It is of some reference for promoting the sustainable development of China’s energy, economy and society.

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…

Information models of software productivity - Limits on productivity growth

NASA Technical Reports Server (NTRS)

Tausworthe, Robert C.

1992-01-01

Research into generalized information-metric models of software process productivity establishes quantifiable behavior and theoretical bounds. The models establish a fundamental mathematical relationship between software productivity and the human capacity for information traffic, the software product yield (system size), information efficiency, and tool and process efficiencies. An upper bound is derived that quantifies average software productivity and the maximum rate at which it may grow. This bound reveals that ultimately, when tools, methodologies, and automated assistants have reached their maximum effective state, further improvement in productivity can only be achieved through increasing software reuse. The reuse advantage is shown not to increase faster than logarithmically in the number of reusable features available. The reuse bound is further shown to be somewhat dependent on the reuse policy: a general 'reuse everything' policy can lead to a somewhat slower productivity growth than a specialized reuse policy.

Mathematics at A-Level. A Discussion Paper on the Applied Content. No. 93.

ERIC Educational Resources Information Center

Mathematical Association, Leicester (England).

In September 1979, the Mathematical Association in England held a weekend seminar on the scope of Applied Mathematics at A-level, and a subcommittee was established to consider the topic at more length. This paper is the first product of the subcommittee's deliberations. Sections 1 and 2 describe the background to current A-level courses: (1) who…

Investigating Relationships between the Usage of Mathematics Learning Support and Performance of At-Risk Students

ERIC Educational Resources Information Center

Berry, Emma; Mac An Bhaird, Ciarán; O'Shea, Ann

2015-01-01

The provision of some level of Mathematics Learning Support is now commonplace in the majority of Higher Education Institutions in the UK and Ireland. Most of these supports were initially established with the aim of trying to address the problem of large numbers of first-year students with weak mathematical backgrounds. The centres provide…

Influences of Technology Integrated Professional Development Course on Mathematics Teachers

ERIC Educational Resources Information Center

Kul, Umit

2018-01-01

The aim of this study was to explore the degree to which a professional development (PD) program designed using GeoGebra influences a group of Turkish middle school teachers' beliefs in relation to mathematics and role of GeoGebra in mathematics education. In order to collect the required data, the PD course was established to provide six teachers…

Mathematical modeling of fed-batch fermentation of Schizochytrium sp. FJU-512 growth and DHA production using a shift control strategy.

PubMed

Zhang, Mingliang; Wu, Weibin; Guo, Xiaolei; Weichen, You; Qi, Feng; Jiang, Xianzhang; Huang, Jianzhong

2018-03-01

To obtain high-cell-density cultures of Schizochytrium sp. FJU-512 for DHA production, two stages of fermentation strategy were used and carbon/nitrogen ratio, DO and temperature were controlled at different levels. The final dry cell weight, total lipid production and DHA yield in 15 l bioreactor reached 103.9, 37.2 and 16.0 g/l, respectively. For the further study of microbial growth and DHA production dynamics, we established a set of kinetic models for the fed-batch production of DHA by Schizochytrium sp. FJU-512 in 15 and 100 l fermenters and a compensatory parameter n was integrated into the model in order to find the optimal mathematical equations. A modified Logistic model was proposed to fit the cell growth data and the following kinetic parameters were obtained: µ m  = 0.0525/h, X m  = 100 g/l and n  = 4.1717 for the 15 l bioreactor, as well as µ m  = 0.0382/h, X m  = 107.4371 g/l and n  = 10 for the 100 l bioreactor. The Luedeking-Piret equations were utilized to model DHA production, yielding values of α  = 0.0648 g/g and β  = 0.0014 g/g/h for the 15 l bioreactor, while the values of α and β obtained for the 100 l fermentation were 0.0209 g/g and 0.0030 g/g/h. The predicted results compared with experimental data showed that the established models had a good fitting precision and were able to exactly depict the dynamic features of the DHA production process.

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

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

Sandhu, S.S.

1997-09-30

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

Mathematical modeling of the adsorption/desorption characteristics of anthocyanins from muscadine (Vitis rotundifolia cv. Noble) juice pomace on Amberlite FPX66 resin in a fixed bed column.

PubMed

Uzdevenes, Chad G; Gao, Chi; Sandhu, Amandeep K; Yagiz, Yavuz; Gu, Liwei

2018-03-24

Muscadine grape pomace, a by-product of juicing and wine-making, contains significant amounts of anthocyanin 3,5-diglucosides, known to be beneficial to human health. The objective of this research was to use mathematical modeling to investigate the adsorption/desorption characteristics of these anthocyanins from muscadine grape pomace on Amberlite FPX66 resin in a fixed bed column. Anthocyanins were extracted using hot water and ultrasound, and the extracts were loaded onto a resin column at five bed depths (5, 6, 8, 10 and 12 cm) using three flow rates (4, 6 and 8 mL min -1 ). It was found that adsorption on the column fitted the bed depth service time (BDST) model and the empty bed residence time (EBRT) model. Desorption was achieved by eluting the column using ethanol at four concentrations (25, 40, 55 and 70% v/v) and could be described with an empirical sigmoid model. The breakthrough curves of anthocyanins fitted the BDST model for all three flow rates with R 2 values of 0.983, 0.992 and 0.984 respectively. The EBRT model was successfully employed to find the operating lines, which allow for column scale-up while still achieving similar results to those found in a laboratory operation. Desorption with 40% (v/v) ethanol achieved the highest recovery rate of anthocyanins at 79.6%. The mathematical models established in this study can be used in designing a pilot/industrial- scale column for the separation and concentration of anthocyanins from muscadine juice pomace. © 2018 Society of Chemical Industry. © 2018 Society of Chemical Industry.

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…

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

Model Predictive Control of LCL Three-level Photovoltaic Grid-connected Inverter

NASA Astrophysics Data System (ADS)

Liang, Cheng; Tian, Engang; Pang, Baobing; Li, Juan; Yang, Yang

2018-05-01

In this paper, neutral point clamped three-level inverter circuit is analyzed to establish a mathematical model of the three-level inverter in the αβ coordinate system. The causes and harms of the midpoint potential imbalance problem are described. The paper use the method of model predictive control to control the entire inverter circuit[1]. The simulation model of the inverter system is built in Matlab/Simulink software. It is convenient to control the grid-connected current, suppress the unbalance of the midpoint potential and reduce the switching frequency by changing the weight coefficient in the cost function. The superiority of the model predictive control in the control method of the inverter system is verified.

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…

Modeling microbial diversity in anaerobic digestion through an extended ADM1 model.

PubMed

Ramirez, Ivan; Volcke, Eveline I P; Rajinikanth, Rajagopal; Steyer, Jean-Philippe

2009-06-01

The anaerobic digestion process comprises a whole network of sequential and parallel reactions, of both biochemical and physicochemical nature. Mathematical models, aiming at understanding and optimization of the anaerobic digestion process, describe these reactions in a structured way, the IWA Anaerobic Digestion Model No. 1 (ADM1) being the most well established example. While these models distinguish between different microorganisms involved in different reactions, to our knowledge they all neglect species diversity between organisms with the same function, i.e. performing the same reaction. Nevertheless, available experimental evidence suggests that the structure and properties of a microbial community may be influenced by process operation and on their turn also determine the reactor functioning. In order to adequately describe these phenomena, mathematical models need to consider the underlying microbial diversity. This is demonstrated in this contribution by extending the ADM1 to describe microbial diversity between organisms of the same functional group. The resulting model has been compared with the traditional ADM1 in describing experimental data of a pilot-scale hybrid Upflow Anaerobic Sludge Filter Bed (UASFB) reactor, as well as in a more detailed simulation study. The presented model is further shown useful in assessing the relationship between reactor performance and microbial community structure in mesophilic CSTRs seeded with slaughterhouse wastewater when facing increasing levels of ammonia.

How can sensitivity analysis improve the robustness of mathematical models utilized by the re/insurance industry?

NASA Astrophysics Data System (ADS)

Noacco, V.; Wagener, T.; Pianosi, F.; Philp, T.

2017-12-01

Insurance companies provide insurance against a wide range of threats, such as natural catastrophes, nuclear incidents and terrorism. To quantify risk and support investment decisions, mathematical models are used, for example to set the premiums charged to clients that protect from financial loss, should deleterious events occur. While these models are essential tools for adequately assessing the risk attached to an insurer's portfolio, their development is costly and their value for decision-making may be limited by an incomplete understanding of uncertainty and sensitivity. Aside from the business need to understand risk and uncertainty, the insurance sector also faces regulation which requires them to test their models in such a way that uncertainties are appropriately captured and that plans are in place to assess the risks and their mitigation. The building and testing of models constitutes a high cost for insurance companies, and it is a time intensive activity. This study uses an established global sensitivity analysis toolbox (SAFE) to more efficiently capture the uncertainties and sensitivities embedded in models used by a leading re/insurance firm, with structured approaches to validate these models and test the impact of assumptions on the model predictions. It is hoped that this in turn will lead to better-informed and more robust business decisions.

A Diverse Community To Study Communities: Integration of Experiments and Mathematical Models To Study Microbial Consortia.

PubMed

Succurro, Antonella; Moejes, Fiona Wanjiku; Ebenhöh, Oliver

2017-08-01

The last few years have seen the advancement of high-throughput experimental techniques that have produced an extraordinary amount of data. Bioinformatics and statistical analyses have become instrumental to interpreting the information coming from, e.g., sequencing data and often motivate further targeted experiments. The broad discipline of "computational biology" extends far beyond the well-established field of bioinformatics, but it is our impression that more theoretical methods such as the use of mathematical models are not yet as well integrated into the research studying microbial interactions. The empirical complexity of microbial communities presents challenges that are difficult to address with in vivo / in vitro approaches alone, and with microbiology developing from a qualitative to a quantitative science, we see stronger opportunities arising for interdisciplinary projects integrating theoretical approaches with experiments. Indeed, the addition of in silico experiments, i.e., computational simulations, has a discovery potential that is, unfortunately, still largely underutilized and unrecognized by the scientific community. This minireview provides an overview of mathematical models of natural ecosystems and emphasizes that one critical point in the development of a theoretical description of a microbial community is the choice of problem scale. Since this choice is mostly dictated by the biological question to be addressed, in order to employ theoretical models fully and successfully it is vital to implement an interdisciplinary view at the conceptual stages of the experimental design. Copyright © 2017 Succurro et al.

Conversations to Transform Geometry Class

ERIC Educational Resources Information Center

Szydlik, Jennifer Earles; Parrott, Amy; Belnap, Jason Knight

2016-01-01

Classroom culture is negotiated and established through both conversations and practices. Traditionally, teachers and researchers have focused primarily on the individual and social construction of mathematical content--that is, students' conceptual understanding and procedural skills--through mathematical actions and practices. This article…

[Basic reproduction rate and its application in schistosomiasis].

PubMed

Yang, Guo-Jing

2013-02-01

A key parameter in the transmission dynamics of schistosomiasis, namely basic reproduction rate (R0) is introduced in this paper, as well as its epidemiological significance, formulas in mathematical models of schistosomiasis transmission dynamics, and its application in the evaluation of schistosomiasis control measures. It suggests that the studies on transmission thresholds such as R0 are of important theoretical guiding significance to the establishment of a schistosomiasis elimination standard in China.

On two special values of temperature factor in hypersonic flow stagnation point

NASA Astrophysics Data System (ADS)

Bilchenko, G. G.; Bilchenko, N. G.

2018-03-01

The hypersonic aircraft permeable cylindrical and spherical surfaces laminar boundary layer heat and mass transfer control mathematical model properties are investigated. The nonlinear algebraic equations systems are obtained for two special values of temperature factor in the hypersonic flow stagnation point. The mappings bijectivity between heat and mass transfer local parameters and controls is established. The computation experiments results are presented: the domains of allowed values “heat-friction” are obtained.

Design Criteria for Low Profile Flange Calculations

NASA Technical Reports Server (NTRS)

Leimbach, K. R.

1973-01-01

An analytical method and a design procedure to develop flanged separable pipe connectors are discussed. A previously established algorithm is the basis for calculating low profile flanges. The characteristics and advantages of the low profile flange are analyzed. The use of aluminum, titanium, and plastics for flange materials is described. Mathematical models are developed to show the mechanical properties of various flange configurations. A computer program for determining the structural stability of the flanges is described.

Effects of femtosecond laser radiation on the skin

NASA Astrophysics Data System (ADS)

Rogov, P. Yu; Bespalov, V. G.

2016-08-01

A mathematical model of linear and nonlinear processes is presented occurring under the influence of femtosecond laser radiation on the skin. There was held an analysis and the numerical solution of an equation system describing the dynamics of the electron and phonon subsystems were received. The results can be used to determine the maximum permissible levels of energy generated by femtosecond laser systems and the establishment of Russian laser safety standards for femtosecond laser systems.

Treatment of the control mechanisms of light airplanes in the flutter clearance process

NASA Technical Reports Server (NTRS)

Breitbach, E. J.

1979-01-01

It has become more and more evident that many difficulties encountered in the course of aircraft flutter analyses can be traced to strong localized nonlinearities in the control mechanisms. To cope with these problems, more reliable mathematical models paying special attention to control system nonlinearities were established by means of modified ground vibration test procedures in combination with suitably adapted modal synthesis approaches. Three different concepts are presented.

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…

Optimization of the 3-Point Bending Failure of Anodized Aluminum Formed in Tartaric/Sulphuric Acid Using Doehlert Design

NASA Astrophysics Data System (ADS)

Bensalah, W.; Feki, M.; De-Petris Wery, M.; Ayedi, H. F.

2015-02-01

The bending failure of anodized aluminum in tartaric/sulphuric acid bath was modeled using Doehlert design. Bath temperature, anodic current density, sulphuric acid, and tartaric acid concentrations were retained as variables. Thickness measurements and 3-point bending experiments were conducted. The deflection at failure ( D f) and the maximum load ( F m) of each sample were, then, deducted from the corresponding flexural responses. The treatment of experimental results has established mathematical models of second degree reflecting the relation of cause and effect between the factors and the studied properties. The optimum path study of thickness, deflection at failure, and maximum load, showed that the three optima were opposite. Multicriteria optimization using the desirability function was achieved in order to maximize simultaneously the three responses. The optimum conditions were: C tar = 18.2 g L-1, T = 17.3 °C, J = 2.37 A dm-2, C sul = 191 g L-1, while the estimated response values were e = 57.7 µm, D f = 5.6 mm, and F m = 835 N. Using the established models, a mathematical correlation was found between deflection at failure and thickness of the anodic oxide layer. Before bending tests, aluminum oxide layer was examined by scanning electron microscopy (SEM) and atomic force microscopy. After tests, the morphology and the composition of the anodic oxide layer were inspected by SEM, optical microscopy, and glow-discharge optical emission spectroscopy.

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

ERIC Educational Resources Information Center

Czocher, Jennifer A.

2016-01-01

This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…

An Experimental Approach to Mathematical Modeling in Biology

ERIC Educational Resources Information Center

Ledder, Glenn

2008-01-01

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

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

ERIC Educational Resources Information Center

Stohlmann, Micah S.

2017-01-01

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

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

ERIC Educational Resources Information Center

Karatas, Ilhan

2014-01-01

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

Mathematical Modeling: A Structured Process

ERIC Educational Resources Information Center

Anhalt, Cynthia Oropesa; Cortez, Ricardo

2015-01-01

Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…

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

ERIC Educational Resources Information Center

Suppes, Patrick

This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…

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

ERIC Educational Resources Information Center

Lingefjard, Thomas; Holmquist, Mikael

2005-01-01

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

Mathematical Modeling in the Undergraduate Curriculum

ERIC Educational Resources Information Center

Toews, Carl

2012-01-01

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

Teachers' Conceptions of Mathematical Modeling

ERIC Educational Resources Information Center

Gould, Heather

2013-01-01

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

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

NASA Astrophysics Data System (ADS)

Irawan, Adi; Mardiyana; Retno Sari Saputro, Dewi

2017-06-01

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

Software Quality Metrics Enhancements. Volume 1

DTIC Science & Technology

1980-04-01

the mathematical relationships which relate metrics to ratings of the various quality factors) for factors which were not validated previously were...function, provides a mathematical relationship between the metrics and the quality factors. (3) Validation of these normalization functions was performed by...samples, further research is needed before a high degree of confidence can be placed on the mathematical relationships established to date l (3.3.3) 6

Development, Evaluation, and Dissemination of an Astrobiology Curriculum for Secondary Students: Establishing a Successful Model for Increasing the Use of Scientific Data by Underrepresented Students.

NASA Astrophysics Data System (ADS)

Arino de La Rubia, L.; Butler, J.; Gary, T.; Stockman, S.; Mumma, M.; Pfiffner, S.; Davis, K.; Edmonds, J.

2009-12-01

The Minority Institution Astrobiology Collaborative began working with the NASA Goddard Center for Astrobiology in 2003 to develop curriculum materials for high school chemistry and Earth science classes based on astrobiology concepts. The Astrobiology in Secondary Classrooms modules are being developed to emphasize interdisciplinary connections in astronomy, biology, chemistry, geoscience, physics, mathematics, and ethics through hands-on activities that address national educational standards. Since this time, more NASA Astrobiology Institute Teams have joined this education and public outreach (EPO)effort. Field-testing of the Astrobiology in Secondary Classrooms materials began in 2007 in five US locations, each with populations that are underrepresented in the career fields of science, technology, engineering, and mathematics.

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.

Modellus: Learning Physics with Mathematical Modelling

NASA Astrophysics Data System (ADS)

Teodoro, Vitor

Computers are now a major tool in research and development in almost all scientific and technological fields. Despite recent developments, this is far from true for learning environments in schools and most undergraduate studies. This thesis proposes a framework for designing curricula where computers, and computer modelling in particular, are a major tool for learning. The framework, based on research on learning science and mathematics and on computer user interface, assumes that: 1) learning is an active process of creating meaning from representations; 2) learning takes place in a community of practice where students learn both from their own effort and from external guidance; 3) learning is a process of becoming familiar with concepts, with links between concepts, and with representations; 4) direct manipulation user interfaces allow students to explore concrete-abstract objects such as those of physics and can be used by students with minimal computer knowledge. Physics is the science of constructing models and explanations about the physical world. And mathematical models are an important type of models that are difficult for many students. These difficulties can be rooted in the fact that most students do not have an environment where they can explore functions, differential equations and iterations as primary objects that model physical phenomena--as objects-to-think-with, reifying the formal objects of physics. The framework proposes that students should be introduced to modelling in a very early stage of learning physics and mathematics, two scientific areas that must be taught in very closely related way, as they were developed since Galileo and Newton until the beginning of our century, before the rise of overspecialisation in science. At an early stage, functions are the main type of objects used to model real phenomena, such as motions. At a later stage, rates of change and equations with rates of change play an important role. This type of equations--differential equations--are the most important mathematical objects used for modelling Natural phenomena. In traditional approaches, they are introduced only at advanced level, because it takes a long time for students to be introduced to the fundamental principles of Calculus. With the new proposed approach, rates of change can be introduced also at early stages on learning if teachers stress semi-quantitative reasoning and use adequate computer tools. In this thesis, there is also presented Modellus, a computer tool for modelling and experimentation. This computer tool has a user interface that allows students to start doing meaningful conceptual and empirical experiments without the need to learn new syntax, as is usual with established tools. The different steps in the process of constructing and exploring models can be done with Modellus, both from physical points of view and from mathematical points of view. Modellus activities show how mathematics and physics have a unity that is very difficult to see with traditional approaches. Mathematical models are treated as concrete-abstract objects: concrete in the sense that they can be manipulated directly with a computer and abstract in the sense that they are representations of relations between variables. Data gathered from two case studies, one with secondary school students and another with first year undergraduate students support the main ideas of the thesis. Also data gathered from teachers (from college and secondary schools), mainly through an email structured questionnaire, shows that teachers agree on the potential of modelling in the learning of physics (and mathematics) and of the most important aspects of the proposed framework to integrate modelling as an essential component of the curriculum. Schools, as all institutions, change at a very slow rate. There are a multitude of reasons for this. And traditional curricula, where the emphasis is on rote learning of facts, can only be changed if schools have access to new and powerful views of learning and to new tools, that support meaningful conceptual learning and are as common and easy to use as pencil and paper.

[Feedforward control strategy and its application in quality improvement of ethanol precipitation process of danhong injection].

PubMed

Yan, Bin-Jun; Guo, Zheng-Tai; Qu, Hai-Bin; Zhao, Bu-Chang; Zhao, Tao

2013-06-01

In this work, a feedforward control strategy basing on the concept of quality by design was established for the manufacturing process of traditional Chinese medicine to reduce the impact of the quality variation of raw materials on drug. In the research, the ethanol precipitation process of Danhong injection was taken as an application case of the method established. Box-Behnken design of experiments was conducted. Mathematical models relating the attributes of the concentrate, the process parameters and the quality of the supernatants produced were established. Then an optimization model for calculating the best process parameters basing on the attributes of the concentrate was built. The quality of the supernatants produced by ethanol precipitation with optimized and non-optimized process parameters were compared. The results showed that using the feedforward control strategy for process parameters optimization can control the quality of the supernatants effectively. The feedforward control strategy proposed can enhance the batch-to-batch consistency of the supernatants produced by ethanol precipitation.

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.…

Mathematical Modeling of Cellular Cross-Talk Between Endothelial and Tumor Cells Highlights Counterintuitive Effects of VEGF-Targeted Therapies.

PubMed

Jain, Harsh; Jackson, Trachette

2018-05-01

Tumor growth and progression are critically dependent on the establishment of a vascular support system. This is often accomplished via the expression of pro-angiogenic growth factors, including members of the vascular endothelial growth factor (VEGF) family of ligands. VEGF ligands are overexpressed in a wide variety of solid tumors and therefore have inspired optimism that inhibition of the different axes of the VEGF pathway-alone or in combination-would represent powerful anti-angiogenic therapies for most cancer types. When considering treatments that target VEGF and its receptors, it is difficult to tease out the differential anti-angiogenic and anti-tumor effects of all combinations experimentally because tumor cells and vascular endothelial cells are engaged in a dynamic cross-talk that impacts key aspects of tumorigenesis, independent of angiogenesis. Here we develop a mathematical model that connects intracellular signaling responsible for both endothelial and tumor cell proliferation and death to population-level cancer growth and angiogenesis. We use this model to investigate the effect of bidirectional communication between endothelial cells and tumor cells on treatments targeting VEGF and its receptors both in vitro and in vivo. Our results underscore the fact that in vitro therapeutic outcomes do not always translate to the in vivo situation. For example, our model predicts that certain therapeutic combinations result in antagonism in vivo that is not observed in vitro. Mathematical modeling in this direction can shed light on the mechanisms behind experimental observations that manipulating VEGF and its receptors is successful in some cases but disappointing in others.

Identifying parameter regions for multistationarity

PubMed Central

Conradi, Carsten; Mincheva, Maya; Wiuf, Carsten

2017-01-01

Mathematical modelling has become an established tool for studying the dynamics of biological systems. Current applications range from building models that reproduce quantitative data to identifying systems with predefined qualitative features, such as switching behaviour, bistability or oscillations. Mathematically, the latter question amounts to identifying parameter values associated with a given qualitative feature. We introduce a procedure to partition the parameter space of a parameterized system of ordinary differential equations into regions for which the system has a unique or multiple equilibria. The procedure is based on the computation of the Brouwer degree, and it creates a multivariate polynomial with parameter depending coefficients. The signs of the coefficients determine parameter regions with and without multistationarity. A particular strength of the procedure is the avoidance of numerical analysis and parameter sampling. The procedure consists of a number of steps. Each of these steps might be addressed algorithmically using various computer programs and available software, or manually. We demonstrate our procedure on several models of gene transcription and cell signalling, and show that in many cases we obtain a complete partitioning of the parameter space with respect to multistationarity. PMID:28972969

Dynamic characteristics of the rotor in a magnetically suspended control moment gyroscope with active magnetic bearing and passive magnetic bearing.

PubMed

Tang, Jiqiang; Xiang, Biao; Zhang, Yongbin

2014-07-01

For a magnetically suspended control moment gyroscope, stiffness and damping of magnetic bearing will influence modal frequency of a rotor. In this paper the relationship between modal frequency and stiffness and damping has been investigated. The mathematic calculation model of axial passive magnetic bearing (PMB) stiffness is developed. And PID control based on internal model control is introduced into control of radial active magnetic bearing (AMB), considering the radial coupling of axial PMB, a mathematic calculation model of stiffness and damping of radial AMB is established. According to modal analysis, the relationship between modal frequency and modal shapes is achieved. Radial vibration frequency is mainly influenced by stiffness of radial AMB; however, when stiffness increases, radial vibration will disappear and a high frequency bending modal will appear. Stiffness of axial PMB mainly affects the axial vibration mode, which will turn into high-order bending modal. Axial PMB causes bigger influence on torsion modal of the rotor. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Mathematical Modeling and Nonlinear Dynamical Analysis of Cell Growth in Response to Antibiotics

NASA Astrophysics Data System (ADS)

Jin, Suoqin; Niu, Lili; Wang, Gang; Zou, Xiufen

2015-06-01

This study is devoted to the revelation of the dynamical mechanisms of cell growth in response to antibiotics. We establish a mathematical model of ordinary differential equations for an antibiotic-resistant growth system with one positive feedback loop. We perform a dynamical analysis of the behavior of this model system. We present adequate sets of conditions that can guarantee the existence and stability of biologically-reasonable steady states. Using bifurcation analysis and numerical simulation, we show that the relative growth rate, which is defined as the ratio of the cell growth rate to the basal cell growth rate in the absence of antibiotics, can exhibit bistable behavior in an extensive range of parameters that correspond to a growth state and a nongrowth state in biology. We discover that both antibiotic and antibiotic resistance genes can cooperatively enhance bistability, whereas the cooperative coefficient of feedback can contribute to the onset of bistability. These results would contribute to a better understanding of not only the evolution of antibiotics but also the emergence of drug resistance in other diseases.

Cytochrome P450 metabolism of the post-lanosterol intermediates explains enigmas of cholesterol synthesis

NASA Astrophysics Data System (ADS)

Ačimovič, Jure; Goyal, Sandeep; Košir, Rok; Goličnik, Marko; Perše, Martina; Belič, Ales; Urlep, Žiga; Guengerich, F. Peter; Rozman, Damjana

2016-06-01

Cholesterol synthesis is among the oldest metabolic pathways, consisting of the Bloch and Kandutch-Russell branches. Following lanosterol, sterols of both branches are proposed to be dedicated to cholesterol. We challenge this dogma by mathematical modeling and with experimental evidence. It was not possible to explain the sterol profile of testis in cAMP responsive element modulator tau (Crem τ) knockout mice with mathematical models based on textbook pathways of cholesterol synthesis. Our model differs in the inclusion of virtual sterol metabolizing enzymes branching from the pathway. We tested the hypothesis that enzymes from the cytochrome P450 (CYP) superfamily can participate in the catalysis of non-classical reactions. We show that CYP enzymes can metabolize multiple sterols in vitro, establishing novel branching points of cholesterol synthesis. In conclusion, sterols of cholesterol synthesis can be oxidized further to metabolites not dedicated to production of cholesterol. Additionally, CYP7A1, CYP11A1, CYP27A1, and CYP46A1 are parts of a broader cholesterol synthesis network.

Cytochrome P450 metabolism of the post-lanosterol intermediates explains enigmas of cholesterol synthesis.

PubMed

Ačimovič, Jure; Goyal, Sandeep; Košir, Rok; Goličnik, Marko; Perše, Martina; Belič, Ales; Urlep, Žiga; Guengerich, F Peter; Rozman, Damjana

2016-06-23

Cholesterol synthesis is among the oldest metabolic pathways, consisting of the Bloch and Kandutch-Russell branches. Following lanosterol, sterols of both branches are proposed to be dedicated to cholesterol. We challenge this dogma by mathematical modeling and with experimental evidence. It was not possible to explain the sterol profile of testis in cAMP responsive element modulator tau (Crem τ) knockout mice with mathematical models based on textbook pathways of cholesterol synthesis. Our model differs in the inclusion of virtual sterol metabolizing enzymes branching from the pathway. We tested the hypothesis that enzymes from the cytochrome P450 (CYP) superfamily can participate in the catalysis of non-classical reactions. We show that CYP enzymes can metabolize multiple sterols in vitro, establishing novel branching points of cholesterol synthesis. In conclusion, sterols of cholesterol synthesis can be oxidized further to metabolites not dedicated to production of cholesterol. Additionally, CYP7A1, CYP11A1, CYP27A1, and CYP46A1 are parts of a broader cholesterol synthesis network.

An Analytical Design Method for a Regenerative Braking Control System for DC-electrified Railway Systems under Light Load Conditions

NASA Astrophysics Data System (ADS)

Saito, Tatsuhito; Kondo, Keiichiro; Koseki, Takafumi

A DC-electrified railway system that is fed by diode rectifiers at a substation is unable to return the electric power to an AC grid. Accordingly, the braking cars have to restrict regenerative braking power when the power consumption of the powering cars is not sufficient. However, the characteristics of a DC-electrified railway system, including the powering cars, is not known, and a mathematical model for designing a controller has not been established yet. Hence, the object of this study is to obtain the mathematical model for an analytical design method of the regenerative braking control system. In the first part of this paper, the static characteristics of this system are presented to show the position of the equilibrium point. The linearization of this system at the equilibrium point is then performed to describe the dynamic characteristics of the system. An analytical design method is then proposed on the basis of these characteristics. The proposed design method is verified by experimental tests with a 1kW class miniature model, and numerical simulations.

Mathematical Modeling of Cellular Metabolism.

PubMed

Berndt, Nikolaus; Holzhütter, Hermann-Georg

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

Prognostic modelling options for remaining useful life estimation by industry

NASA Astrophysics Data System (ADS)

Sikorska, J. Z.; Hodkiewicz, M.; Ma, L.

2011-07-01

Over recent years a significant amount of research has been undertaken to develop prognostic models that can be used to predict the remaining useful life of engineering assets. Implementations by industry have only had limited success. By design, models are subject to specific assumptions and approximations, some of which are mathematical, while others relate to practical implementation issues such as the amount of data required to validate and verify a proposed model. Therefore, appropriate model selection for successful practical implementation requires not only a mathematical understanding of each model type, but also an appreciation of how a particular business intends to utilise a model and its outputs. This paper discusses business issues that need to be considered when selecting an appropriate modelling approach for trial. It also presents classification tables and process flow diagrams to assist industry and research personnel select appropriate prognostic models for predicting the remaining useful life of engineering assets within their specific business environment. The paper then explores the strengths and weaknesses of the main prognostics model classes to establish what makes them better suited to certain applications than to others and summarises how each have been applied to engineering prognostics. Consequently, this paper should provide a starting point for young researchers first considering options for remaining useful life prediction. The models described in this paper are Knowledge-based (expert and fuzzy), Life expectancy (stochastic and statistical), Artificial Neural Networks, and Physical models.

Model of multistep electron transfer in a single-mode polar medium

NASA Astrophysics Data System (ADS)

Feskov, S. V.; Yudanov, V. V.

2017-09-01

A mathematical model of multistep photoinduced electron transfer (PET) in a polar medium with a single relaxation time (Debye solvent) is developed. The model includes the polarization nonequilibrity formed in the vicinity of the donor-acceptor molecular system at the initial steps of photoreaction and its influence on the subsequent steps of PET. It is established that the results from numerical simulation of transient luminescence spectra of photoexcited donor-acceptor complexes (DAC) conform to calculated data obtained on the basis of the familiar experimental technique used to measure the relaxation function of solvent polarization in the vicinity of DAC in the picosecond and subpicosecond ranges.

Study on Heat Transfer Agent Models of Transmission Line and Transformer

NASA Astrophysics Data System (ADS)

Wang, B.; Zhang, P. P.

2018-04-01

When using heat transfer simulation to study the dynamic overload of transmission line and transformer, it needs to establish the mathematical expression of heat transfer. However, the formula is a nonlinear differential equation or equation set and it is not easy to get general solutions. Aiming at this problem, some different temperature change processes caused by different initial conditions are calculated by differential equation and equation set. New agent models are developed according to the characteristics of different temperature change processes. The results show that the agent models have high precision and can solve the problem that the original equation cannot be directly applied in some practical engineers.

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.

Virtual-source diffusion approximation for enhanced near-field modeling of photon-migration in low-albedo medium.

PubMed

Jia, Mengyu; Chen, Xueying; Zhao, Huijuan; Cui, Shanshan; Liu, Ming; Liu, Lingling; Gao, Feng

2015-01-26

Most analytical methods for describing light propagation in turbid medium exhibit low effectiveness in the near-field of a collimated source. Motivated by the Charge Simulation Method in electromagnetic theory as well as the established discrete source based modeling, we herein report on an improved explicit model for a semi-infinite geometry, referred to as "Virtual Source" (VS) diffuse approximation (DA), to fit for low-albedo medium and short source-detector separation. In this model, the collimated light in the standard DA is analogously approximated as multiple isotropic point sources (VS) distributed along the incident direction. For performance enhancement, a fitting procedure between the calculated and realistic reflectances is adopted in the near-field to optimize the VS parameters (intensities and locations). To be practically applicable, an explicit 2VS-DA model is established based on close-form derivations of the VS parameters for the typical ranges of the optical parameters. This parameterized scheme is proved to inherit the mathematical simplicity of the DA approximation while considerably extending its validity in modeling the near-field photon migration in low-albedo medium. The superiority of the proposed VS-DA method to the established ones is demonstrated in comparison with Monte-Carlo simulations over wide ranges of the source-detector separation and the medium optical properties.

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.

Comprehensive manual handling limits for lowering, pushing, pulling and carrying activities.

PubMed

Shoaf, C; Genaidy, A; Karwowski, W; Waters, T; Christensen, D

1997-11-01

The objective of this study was to develop a set of mathematical models for manual lowering, pushing, pulling and carrying activities that would result in establishing load capacity limits to protect the lower back against occupational low-back disorders. In order to establish safe guidelines, a three-stage process was used. First, psychophysical data was used to generate the models' discounting factors and recommended load capacities. Second, biomechanical analysis was used to refine the recommended load capacities. Third, physiological criteria were used to validate the models' discounting factors. Both task and personal factors were considered in the models' development. When compared to the results from prior psychophysical research for these activities, the developed load capacity values are lower than previously established limits. The results of this study allowed the authors to validate the hypothesis proposed and tested by Karwowski (1983) that states that the combination of physiological and biomechanical stresses should lead to the overall measure of task acceptability or the psychophysical stress. This study also found that some of the discounting factors for the task frequency parameters recommended in the prior psychophysical research should not be used as several of the high frequency factors violated physiological limits.

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;…

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.

Boolean Dynamic Modeling Approaches to Study Plant Gene Regulatory Networks: Integration, Validation, and Prediction.

PubMed

Velderraín, José Dávila; Martínez-García, Juan Carlos; Álvarez-Buylla, Elena R

2017-01-01

Mathematical models based on dynamical systems theory are well-suited tools for the integration of available molecular experimental data into coherent frameworks in order to propose hypotheses about the cooperative regulatory mechanisms driving developmental processes. Computational analysis of the proposed models using well-established methods enables testing the hypotheses by contrasting predictions with observations. Within such framework, Boolean gene regulatory network dynamical models have been extensively used in modeling plant development. Boolean models are simple and intuitively appealing, ideal tools for collaborative efforts between theorists and experimentalists. In this chapter we present protocols used in our group for the study of diverse plant developmental processes. We focus on conceptual clarity and practical implementation, providing directions to the corresponding technical literature.

Space ecosynthesis: An approach to the design of closed ecosystems for use in space

NASA Technical Reports Server (NTRS)

Macelroy, R. D.; Averner, M. M.

1978-01-01

The use of closed ecological systems for the regeneration of wastes, air, and water is discussed. It is concluded that such systems, if they are to be used for the support of humans in space, will require extensive mechanical and physico-chemical support. The reason for this is that the buffering capacity available in small systems is inadequate, and that natural biological and physical regulatory mechanisms rapidly become inoperative. It is proposed that mathematical models of the dynamics of a closed ecological system may provide the best means of studying the initial problems of ecosystem closure. A conceptual and mathematical model of a closed ecosystem is described which treats the biological components as a farm, calculates the rates of flow of elements through the system by mass-balance techniques and control theory postulates, and can evaluate the requirements for mechanical buffering activities. It is suggested that study of the closure of ecosystems can significantly aid in the establishment of general principles of ecological systems.

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…

Dynamical Analysis of an SEIT Epidemic Model with Application to Ebola Virus Transmission in Guinea.

PubMed

Li, Zhiming; Teng, Zhidong; Feng, Xiaomei; Li, Yingke; Zhang, Huiguo

2015-01-01

In order to investigate the transmission mechanism of the infectious individual with Ebola virus, we establish an SEIT (susceptible, exposed in the latent period, infectious, and treated/recovery) epidemic model. The basic reproduction number is defined. The mathematical analysis on the existence and stability of the disease-free equilibrium and endemic equilibrium is given. As the applications of the model, we use the recognized infectious and death cases in Guinea to estimate parameters of the model by the least square method. With suitable parameter values, we obtain the estimated value of the basic reproduction number and analyze the sensitivity and uncertainty property by partial rank correlation coefficients.

Parameter estimation and sensitivity analysis for a mathematical model with time delays of leukemia

NASA Astrophysics Data System (ADS)

Cândea, Doina; Halanay, Andrei; Rǎdulescu, Rodica; Tǎlmaci, Rodica

2017-01-01

We consider a system of nonlinear delay differential equations that describes the interaction between three competing cell populations: healthy, leukemic and anti-leukemia T cells involved in Chronic Myeloid Leukemia (CML) under treatment with Imatinib. The aim of this work is to establish which model parameters are the most important in the success or failure of leukemia remission under treatment using a sensitivity analysis of the model parameters. For the most significant parameters of the model which affect the evolution of CML disease during Imatinib treatment we try to estimate the realistic values using some experimental data. For these parameters, steady states are calculated and their stability is analyzed and biologically interpreted.

Just do it: flipped lecture, determinants and debate

NASA Astrophysics Data System (ADS)

Kensington-Miller, Barbara; Novak, Julia; Evans, Tanya

2016-08-01

This paper describes a case study of two pure mathematicians who flipped their lecture to teach matrix determinants in two large mathematics service courses (one at Stage I and the other at Stage II). The purpose of the study was to transform the passive lecture into an active learning opportunity and to introduce valuable mathematical skills, such as debate, argument and disagreement. The students were told in advance to use the online material to prepare, which had a short handout on matrix determinants posted, as the lesson would be interactive and would rely on them having studied this. At the beginning of the lesson, the two mathematicians worked together to model the skill of professional disagreement, one arguing for the cofactor expansion method and the other for the row reduction method. After voting for their preferred method, the students worked in small groups on examples to defend their choice. Each group elected a spokesperson and a political style debate followed as the students argued the pros and cons of each technique. Although one lecture does not establish whether the flipped lecture model is preferable for student instruction, the paper presents a case study for pursuing this approach and for further research on incorporating this style of teaching in Science, Technology, Engineering and Mathematics subjects.

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.

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…

The Application of HOS to PLRS

DTIC Science & Technology

1977-11-01

of "older," more established fields, like philosophy or mathematics , and more recently, linguistics. But when working with large systems, there is...property of natural language, which is eliminated by using formal, mathematical specifications. 3.4.2.2 Network Management Processing: The Network...the format: y = f(x) That is, we must immediately begin thinking of the problem in terms of mathematical functions (mappings) acting on some input(s

An interdisciplinary collaboration between computer engineering and mathematics/bilingual education to develop a curriculum for underrepresented middle school students

NASA Astrophysics Data System (ADS)

Celedón-Pattichis, Sylvia; LópezLeiva, Carlos Alfonso; Pattichis, Marios S.; Llamocca, Daniel

2013-12-01

There is a strong need in the United States to increase the number of students from underrepresented groups who pursue careers in Science, Technology, Engineering, and Mathematics. Drawing from sociocultural theory, we present approaches to establishing collaborations between computer engineering and mathematics/bilingual education faculty to address this need. We describe our work through the Advancing Out-of-School Learning in Mathematics and Engineering project by illustrating how an integrated curriculum that is based on mathematics with applications in image and video processing can be designed and how it can be implemented with middle school students from underrepresented groups.

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…

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.

Inert gas transport in blood and tissues.

PubMed

Baker, A Barry; Farmery, Andrew D

2011-04-01

This article establishes the basic mathematical models and the principles and assumptions used for inert gas transfer within body tissues-first, for a single compartment model and then for a multicompartment model. From these, and other more complex mathematical models, the transport of inert gases between lungs, blood, and other tissues is derived and compared to known experimental studies in both animals and humans. Some aspects of airway and lung transfer are particularly important to the uptake and elimination of inert gases, and these aspects of gas transport in tissues are briefly described. The most frequently used inert gases are those that are administered in anesthesia, and the specific issues relating to the uptake, transport, and elimination of these gases and vapors are dealt with in some detail showing how their transfer depends on various physical and chemical attributes, particularly their solubilities in blood and different tissues. Absorption characteristics of inert gases from within gas cavities or tissue bubbles are described, and the effects other inhaled gas mixtures have on the composition of these gas cavities are discussed. Very brief consideration is given to the effects of hyper- and hypobaric conditions on inert gas transport. © 2011 American Physiological Society. Compr Physiol 1:569-592, 2011.

Mathematical model for Dengue with three states of infection

NASA Astrophysics Data System (ADS)

Hincapie, Doracelly; Ospina, Juan

2012-06-01

A mathematical model for dengue with three states of infection is proposed and analyzed. The model consists in a system of differential equations. The three states of infection are respectively asymptomatic, partially asymptomatic and fully asymptomatic. The model is analyzed using computer algebra software, specifically Maple, and the corresponding basic reproductive number and the epidemic threshold are computed. The resulting basic reproductive number is an algebraic synthesis of all epidemic parameters and it makes clear the possible control measures. The microscopic structure of the epidemic parameters is established using the quantum theory of the interactions between the atoms and radiation. In such approximation, the human individual is represented by an atom and the mosquitoes are represented by radiation. The force of infection from the mosquitoes to the humans is considered as the transition probability from the fundamental state of atom to excited states. The combination of computer algebra software and quantum theory provides a very complete formula for the basic reproductive number and the possible control measures tending to stop the propagation of the disease. It is claimed that such result may be important in military medicine and the proposed method can be applied to other vector-borne diseases.

The mathematics of tanning

PubMed Central

Thingnes, Josef; Øyehaug, Leiv; Hovig, Eivind; Omholt, Stig W

2009-01-01

Background The pigment melanin is produced by specialized cells, called melanocytes. In healthy skin, melanocytes are sparsely spread among the other cell types in the basal layer of the epidermis. Sun tanning results from an UV-induced increase in the release of melanin to neighbouring keratinocytes, the major cell type component of the epidermis as well as redistribution of melanin among these cells. Here we provide a mathematical conceptualization of our current knowledge of the tanning response, in terms of a dynamic model. The resolution level of the model is tuned to available data, and its primary focus is to describe the tanning response following UV exposure. Results The model appears capable of accounting for available experimental data on the tanning response in different skin and photo types. It predicts that the thickness of the epidermal layer and how far the melanocyte dendrites grow out in the epidermal layers after UV exposure influence the tanning response substantially. Conclusion Despite the paucity of experimental validation data the model is constrained enough to serve as a foundation for the establishment of a theoretical-experimental research programme aimed at elucidating the more fine-grained regulatory anatomy underlying the tanning response. PMID:19505344

Modelling of the batch biosorption system: study on exchange of protons with cell wall-bound mineral ions.

PubMed

Mishra, Vishal

2015-01-01

The interchange of the protons with the cell wall-bound calcium and magnesium ions at the interface of solution/bacterial cell surface in the biosorption system at various concentrations of protons has been studied in the present work. A mathematical model for establishing the correlation between concentration of protons and active sites was developed and optimized. The sporadic limited residence time reactor was used to titrate the calcium and magnesium ions at the individual data point. The accuracy of the proposed mathematical model was estimated using error functions such as nonlinear regression, adjusted nonlinear regression coefficient, the chi-square test, P-test and F-test. The values of the chi-square test (0.042-0.017), P-test (<0.001-0.04), sum of square errors (0.061-0.016), root mean square error (0.01-0.04) and F-test (2.22-19.92) reported in the present research indicated the suitability of the model over a wide range of proton concentrations. The zeta potential of the bacterium surface at various concentrations of protons was observed to validate the denaturation of active sites.

[Mathematical modeling for conditionality of cardiovascular disease by housing conditions].

PubMed

Meshkov, N A

2014-01-01

There was studied the influence of living conditions (housing area per capita, availability of housing water supply, sewerage and central heating) on the morbidity of the cardiovascular diseases in child and adult population. With the method of regression analysis the morbidity rate was established to significantly decrease with the increase in the area of housing, constructed models are statistically significant, respectively, p = 0.01 and p = 0.02. There was revealed the relationship of the morbidity rate of cardiovascular diseases in children and adults with the supply with housing central heating (p = 0.02 and p = 0.009).

Derivation and application of a mathematical model for long bone growth.

PubMed

Seetharam, Suneil; Bhatia, Sujata K

2012-01-01

The objective of this work was to develop a mathematical model of long bone growth and to gain insights regarding growth disorders. A cell balance (mass balance of moving cells) assessment was performed on the three regions of the growth plate, to determine the variables (including number of proliferating cells, and division rate of proliferating cells) that influence tibia growth rate. Once this relationship was established, clinical data were used to understand how tibia growth rate and number of proliferating cells change with time. These equations were then inserted into the model to determine how cell division rate changes with time. The model was utilized to determine the influence of growth time, and to measure changes in vitamin C deficiency, Indian hedgehog (IHH) expression, and bone morphogenetic protein-2 (BMP-2) implants on tibia length. According to the model, a 10-month discrepancy in growth time between the two tibias is required to produce clinically significant leg asymmetry. In addition, vitamin C deficiency, IHH overexpression, and BMP-2 implants can all affect tibia length. These bioactive molecules have the greatest effect on tibia growth rate when these perturbations occur early in life for extended periods of time. The results are significant for modeling and predicting the effects of perturbations, including bioactive implants, on long bone growth.

Building new computational models to support health behavior change and maintenance: new opportunities in behavioral research.

PubMed

Spruijt-Metz, Donna; Hekler, Eric; Saranummi, Niilo; Intille, Stephen; Korhonen, Ilkka; Nilsen, Wendy; Rivera, Daniel E; Spring, Bonnie; Michie, Susan; Asch, David A; Sanna, Alberto; Salcedo, Vicente Traver; Kukakfa, Rita; Pavel, Misha

2015-09-01

Adverse and suboptimal health behaviors and habits are responsible for approximately 40 % of preventable deaths, in addition to their unfavorable effects on quality of life and economics. Our current understanding of human behavior is largely based on static "snapshots" of human behavior, rather than ongoing, dynamic feedback loops of behavior in response to ever-changing biological, social, personal, and environmental states. This paper first discusses how new technologies (i.e., mobile sensors, smartphones, ubiquitous computing, and cloud-enabled processing/computing) and emerging systems modeling techniques enable the development of new, dynamic, and empirical models of human behavior that could facilitate just-in-time adaptive, scalable interventions. The paper then describes concrete steps to the creation of robust dynamic mathematical models of behavior including: (1) establishing "gold standard" measures, (2) the creation of a behavioral ontology for shared language and understanding tools that both enable dynamic theorizing across disciplines, (3) the development of data sharing resources, and (4) facilitating improved sharing of mathematical models and tools to support rapid aggregation of the models. We conclude with the discussion of what might be incorporated into a "knowledge commons," which could help to bring together these disparate activities into a unified system and structure for organizing knowledge about behavior.

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

Non-linear behaviour of electrical parameters in porous, water-saturated rocks: a model to predict pore size distribution

NASA Astrophysics Data System (ADS)

Hallbauer-Zadorozhnaya, Valeriya; Santarato, Giovanni; Abu Zeid, Nasser

2015-08-01

In this paper, two separate but related goals are tackled. The first one is to demonstrate that in some saturated rock textures the non-linear behaviour of induced polarization (IP) and the violation of Ohm's law not only are real phenomena, but they can also be satisfactorily predicted by a suitable physical-mathematical model, which is our second goal. This model is based on Fick's second law. As the model links the specific dependence of resistivity and chargeability of a laboratory sample to the injected current and this in turn to its pore size distribution, it is able to predict pore size distribution from laboratory measurements, in good agreement with mercury injection capillary pressure test results. This fact opens up the possibility for hydrogeophysical applications on a macro scale. Mathematical modelling shows that the chargeability acquired in the field under normal conditions, that is at low current, will always be very small and approximately proportional to the applied current. A suitable field test site for demonstrating the possible reliance of both resistivity and chargeability on current was selected and a specific measuring strategy was established. Two data sets were acquired using different injected current strengths, while keeping the charging time constant. Observed variations of resistivity and chargeability are in agreement with those predicted by the mathematical model. These field test data should however be considered preliminary. If confirmed by further evidence, these facts may lead to changing the procedure of acquiring field measurements in future, and perhaps may encourage the design and building of a new specific geo-resistivity meter. This paper also shows that the well-known Marshall and Madden's equations based on Fick's law cannot be solved without specific boundary conditions.

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.

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.

Social Justice in the Mathematics Classroom

ERIC Educational Resources Information Center

Wright, Pete

2016-01-01

Despite increases in educational attainment in London, too many mathematics lessons remain focused on factual recall and procedural understanding,resulting in disaffection among learners. This study reports on the establishment of a research group, comprising five teacher researchers and myself, which aimed to challenge this situation through…

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…

Establishment of a rotor model basis

NASA Technical Reports Server (NTRS)

Mcfarland, R. E.

1982-01-01

Radial-dimension computations in the RSRA's blade-element model are modified for both the acquisition of extensive baseline data and for real-time simulation use. The baseline data, which are for the evaluation of model changes, use very small increments and are of high quality. The modifications to the real-time simulation model are for accuracy improvement, especially when a minimal number of blade segments is required for real-time synchronization. An accurate technique for handling tip loss in discrete blade models is developed. The mathematical consistency and convergence properties of summation algorithms for blade forces and moments are examined and generalized integration coefficients are applied to equal-annuli midpoint spacing. Rotor conditions identified as 'constrained' and 'balanced' are used and the propagation of error is analyzed.

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.

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…

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.

Bridging the gap between evidence and policy for infectious diseases: How models can aid public health decision-making.

PubMed

Knight, Gwenan M; Dharan, Nila J; Fox, Gregory J; Stennis, Natalie; Zwerling, Alice; Khurana, Renuka; Dowdy, David W

2016-01-01

The dominant approach to decision-making in public health policy for infectious diseases relies heavily on expert opinion, which often applies empirical evidence to policy questions in a manner that is neither systematic nor transparent. Although systematic reviews are frequently commissioned to inform specific components of policy (such as efficacy), the same process is rarely applied to the full decision-making process. Mathematical models provide a mechanism through which empirical evidence can be methodically and transparently integrated to address such questions. However, such models are often considered difficult to interpret. In addition, models provide estimates that need to be iteratively re-evaluated as new data or considerations arise. Using the case study of a novel diagnostic for tuberculosis, a framework for improved collaboration between public health decision-makers and mathematical modellers that could lead to more transparent and evidence-driven policy decisions for infectious diseases in the future is proposed. The framework proposes that policymakers should establish long-term collaborations with modellers to address key questions, and that modellers should strive to provide clear explanations of the uncertainty of model structure and outputs. Doing so will improve the applicability of models and clarify their limitations when used to inform real-world public health policy decisions. Copyright © 2015 The Authors. Published by Elsevier Ltd.. All rights reserved.

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

Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling.

PubMed

Wu, Hulin; Lu, Tao; Xue, Hongqi; Liang, Hua

2014-04-02

The gene regulation network (GRN) is a high-dimensional complex system, which can be represented by various mathematical or statistical models. The ordinary differential equation (ODE) model is one of the popular dynamic GRN models. High-dimensional linear ODE models have been proposed to identify GRNs, but with a limitation of the linear regulation effect assumption. In this article, we propose a sparse additive ODE (SA-ODE) model, coupled with ODE estimation methods and adaptive group LASSO techniques, to model dynamic GRNs that could flexibly deal with nonlinear regulation effects. The asymptotic properties of the proposed method are established and simulation studies are performed to validate the proposed approach. An application example for identifying the nonlinear dynamic GRN of T-cell activation is used to illustrate the usefulness of the proposed method.

BiGG Models: A platform for integrating, standardizing and sharing genome-scale models

DOE PAGES

King, Zachary A.; Lu, Justin; Drager, Andreas; ...

2015-10-17

In this study, genome-scale metabolic models are mathematically structured knowledge bases that can be used to predict metabolic pathway usage and growth phenotypes. Furthermore, they can generate and test hypotheses when integrated with experimental data. To maximize the value of these models, centralized repositories of high-quality models must be established, models must adhere to established standards and model components must be linked to relevant databases. Tools for model visualization further enhance their utility. To meet these needs, we present BiGG Models (http://bigg.ucsd.edu), a completely redesigned Biochemical, Genetic and Genomic knowledge base. BiGG Models contains more than 75 high-quality, manually-curated genome-scalemore » metabolic models. On the website, users can browse, search and visualize models. BiGG Models connects genome-scale models to genome annotations and external databases. Reaction and metabolite identifiers have been standardized across models to conform to community standards and enable rapid comparison across models. Furthermore, BiGG Models provides a comprehensive application programming interface for accessing BiGG Models with modeling and analysis tools. As a resource for highly curated, standardized and accessible models of metabolism, BiGG Models will facilitate diverse systems biology studies and support knowledge-based analysis of diverse experimental data.« less

BiGG Models: A platform for integrating, standardizing and sharing genome-scale models

PubMed Central

King, Zachary A.; Lu, Justin; Dräger, Andreas; Miller, Philip; Federowicz, Stephen; Lerman, Joshua A.; Ebrahim, Ali; Palsson, Bernhard O.; Lewis, Nathan E.

2016-01-01

Genome-scale metabolic models are mathematically-structured knowledge bases that can be used to predict metabolic pathway usage and growth phenotypes. Furthermore, they can generate and test hypotheses when integrated with experimental data. To maximize the value of these models, centralized repositories of high-quality models must be established, models must adhere to established standards and model components must be linked to relevant databases. Tools for model visualization further enhance their utility. To meet these needs, we present BiGG Models (http://bigg.ucsd.edu), a completely redesigned Biochemical, Genetic and Genomic knowledge base. BiGG Models contains more than 75 high-quality, manually-curated genome-scale metabolic models. On the website, users can browse, search and visualize models. BiGG Models connects genome-scale models to genome annotations and external databases. Reaction and metabolite identifiers have been standardized across models to conform to community standards and enable rapid comparison across models. Furthermore, BiGG Models provides a comprehensive application programming interface for accessing BiGG Models with modeling and analysis tools. As a resource for highly curated, standardized and accessible models of metabolism, BiGG Models will facilitate diverse systems biology studies and support knowledge-based analysis of diverse experimental data. PMID:26476456

A mathematical prediction model incorporating molecular subtype for risk of non-sentinel lymph node metastasis in sentinel lymph node-positive breast cancer patients: a retrospective analysis and nomogram development.

PubMed

Wang, Na-Na; Yang, Zheng-Jun; Wang, Xue; Chen, Li-Xuan; Zhao, Hong-Meng; Cao, Wen-Feng; Zhang, Bin

2018-04-25

Molecular subtype of breast cancer is associated with sentinel lymph node status. We sought to establish a mathematical prediction model that included breast cancer molecular subtype for risk of positive non-sentinel lymph nodes in breast cancer patients with sentinel lymph node metastasis and further validate the model in a separate validation cohort. We reviewed the clinicopathologic data of breast cancer patients with sentinel lymph node metastasis who underwent axillary lymph node dissection between June 16, 2014 and November 16, 2017 at our hospital. Sentinel lymph node biopsy was performed and patients with pathologically proven sentinel lymph node metastasis underwent axillary lymph node dissection. Independent risks for non-sentinel lymph node metastasis were assessed in a training cohort by multivariate analysis and incorporated into a mathematical prediction model. The model was further validated in a separate validation cohort, and a nomogram was developed and evaluated for diagnostic performance in predicting the risk of non-sentinel lymph node metastasis. Moreover, we assessed the performance of five different models in predicting non-sentinel lymph node metastasis in training cohort. Totally, 495 cases were eligible for the study, including 291 patients in the training cohort and 204 in the validation cohort. Non-sentinel lymph node metastasis was observed in 33.3% (97/291) patients in the training cohort. The AUC of MSKCC, Tenon, MDA, Ljubljana, and Louisville models in training cohort were 0.7613, 0.7142, 0.7076, 0.7483, and 0.671, respectively. Multivariate regression analysis indicated that tumor size (OR = 1.439; 95% CI 1.025-2.021; P = 0.036), sentinel lymph node macro-metastasis versus micro-metastasis (OR = 5.063; 95% CI 1.111-23.074; P = 0.036), the number of positive sentinel lymph nodes (OR = 2.583, 95% CI 1.714-3.892; P < 0.001), and the number of negative sentinel lymph nodes (OR = 0.686, 95% CI 0.575-0.817; P < 0.001) were independent statistically significant predictors of non-sentinel lymph node metastasis. Furthermore, luminal B (OR = 3.311, 95% CI 1.593-6.884; P = 0.001) and HER2 overexpression (OR = 4.308, 95% CI 1.097-16.912; P = 0.036) were independent and statistically significant predictor of non-sentinel lymph node metastasis versus luminal A. A regression model based on the results of multivariate analysis was established to predict the risk of non-sentinel lymph node metastasis, which had an AUC of 0.8188. The model was validated in the validation cohort and showed excellent diagnostic performance. The mathematical prediction model that incorporates five variables including breast cancer molecular subtype demonstrates excellent diagnostic performance in assessing the risk of non-sentinel lymph node metastasis in sentinel lymph node-positive patients. The prediction model could be of help surgeons in evaluating the risk of non-sentinel lymph node involvement for breast cancer patients; however, the model requires further validation in prospective studies.

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.

Ecological quality boundary-setting procedures: the Gulf of Riga case study.

PubMed

Aigars, Juris; Müller-Karulis, Bärbel; Martin, Georg; Jermakovs, Vadims

2008-03-01

Two approaches for setting ecological class boundaries, response curves and a simplified mathematical boundary-setting protocol, were tested for coastal, transitional and open waters in the Gulf of Riga, Baltic Sea. The simplified mathematical boundary-setting protocol defines acceptable ecological status based on expert judgment by a uniform relative deviation from reference conditions. In contrast, response curves derive class boundary definitions from observed changes in biological quality elements along environmental pressure gradients for class boundary definitions. Identification of relevant environmental pressures for the construction of response curves was based on a conceptual model of eutrophication in the Gulf of Riga. Response curves were successfully established for summer chlorophyll a and transparency, as well as for macrozoobenthos abundance in the Central Gulf, macrozoobenthos biotic coefficient in the Southern Gulf, and maximum depth of phytobenthos in the Northern Gulf. In the Gulf of Riga response curves almost always permitted a larger deviation from reference conditions than the 50% deviation applied for the simplified mathematical boundary-setting protocol. The case study clearly demonstrated that class boundary definitions should take into account the sensitivity of the target water body. Also, the class boundaries for different ecological quality elements were internally more consistent than those derived by the simplified mathematical boundary-setting protocol.

Developing Mathematical Habits of Mind

ERIC Educational Resources Information Center

Mark, June; Cuoco, Al; Goldenberg, E. Paul; Sword, Sarah

2010-01-01

"Mathematical habits of mind" include reasoning by continuity, looking at extreme cases, performing thought experiments, and using abstraction that mathematicians use in their work. Current recommendations emphasize the critical nature of developing these habits of mind: "Once this kind of thinking is established, students can apply it in the…

Establishing a Community of Discourse through Social Norms

ERIC Educational Resources Information Center

Mullins, Sara Brooke

2018-01-01

While researchers, educators, state and national organizations, and policy makers are taking strides to help transform traditional mathematics classrooms into inquiry-based classrooms, they fail to address how to bridge the gap between creating discussions to developing mathematical discourse. One key component for producing inquiry-based…

Dynamic modeling method for infrared smoke based on enhanced discrete phase model

NASA Astrophysics Data System (ADS)

Zhang, Zhendong; Yang, Chunling; Zhang, Yan; Zhu, Hongbo

2018-03-01

The dynamic modeling of infrared (IR) smoke plays an important role in IR scene simulation systems and its accuracy directly influences the system veracity. However, current IR smoke models cannot provide high veracity, because certain physical characteristics are frequently ignored in fluid simulation; simplifying the discrete phase as a continuous phase and ignoring the IR decoy missile-body spinning. To address this defect, this paper proposes a dynamic modeling method for IR smoke, based on an enhanced discrete phase model (DPM). A mathematical simulation model based on an enhanced DPM is built and a dynamic computing fluid mesh is generated. The dynamic model of IR smoke is then established using an extended equivalent-blackbody-molecule model. Experiments demonstrate that this model realizes a dynamic method for modeling IR smoke with higher veracity.

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,…

Image-based quantification and mathematical modeling of spatial heterogeneity in ESC colonies.

PubMed

Herberg, Maria; Zerjatke, Thomas; de Back, Walter; Glauche, Ingmar; Roeder, Ingo

2015-06-01

Pluripotent embryonic stem cells (ESCs) have the potential to differentiate into cells of all three germ layers. This unique property has been extensively studied on the intracellular, transcriptional level. However, ESCs typically form clusters of cells with distinct size and shape, and establish spatial structures that are vital for the maintenance of pluripotency. Even though it is recognized that the cells' arrangement and local interactions play a role in fate decision processes, the relations between transcriptional and spatial patterns have not yet been studied. We present a systems biology approach which combines live-cell imaging, quantitative image analysis, and multiscale, mathematical modeling of ESC growth. In particular, we develop quantitative measures of the morphology and of the spatial clustering of ESCs with different expression levels and apply them to images of both in vitro and in silico cultures. Using the same measures, we are able to compare model scenarios with different assumptions on cell-cell adhesions and intercellular feedback mechanisms directly with experimental data. Applying our methodology to microscopy images of cultured ESCs, we demonstrate that the emerging colonies are highly variable regarding both morphological and spatial fluorescence patterns. Moreover, we can show that most ESC colonies contain only one cluster of cells with high self-renewing capacity. These cells are preferentially located in the interior of a colony structure. The integrated approach combining image analysis with mathematical modeling allows us to reveal potential transcription factor related cellular and intercellular mechanisms behind the emergence of observed patterns that cannot be derived from images directly. © 2015 International Society for Advancement of Cytometry.

Mathematical biomarkers for the autonomic regulation of cardiovascular system.

PubMed

Campos, Luciana A; Pereira, Valter L; Muralikrishna, Amita; Albarwani, Sulayma; Brás, Susana; Gouveia, Sónia

2013-10-07

Heart rate and blood pressure are the most important vital signs in diagnosing disease. Both heart rate and blood pressure are characterized by a high degree of short term variability from moment to moment, medium term over the normal day and night as well as in the very long term over months to years. The study of new mathematical algorithms to evaluate the variability of these cardiovascular parameters has a high potential in the development of new methods for early detection of cardiovascular disease, to establish differential diagnosis with possible therapeutic consequences. The autonomic nervous system is a major player in the general adaptive reaction to stress and disease. The quantitative prediction of the autonomic interactions in multiple control loops pathways of cardiovascular system is directly applicable to clinical situations. Exploration of new multimodal analytical techniques for the variability of cardiovascular system may detect new approaches for deterministic parameter identification. A multimodal analysis of cardiovascular signals can be studied by evaluating their amplitudes, phases, time domain patterns, and sensitivity to imposed stimuli, i.e., drugs blocking the autonomic system. The causal effects, gains, and dynamic relationships may be studied through dynamical fuzzy logic models, such as the discrete-time model and discrete-event model. We expect an increase in accuracy of modeling and a better estimation of the heart rate and blood pressure time series, which could be of benefit for intelligent patient monitoring. We foresee that identifying quantitative mathematical biomarkers for autonomic nervous system will allow individual therapy adjustments to aim at the most favorable sympathetic-parasympathetic balance.

Mathematical biomarkers for the autonomic regulation of cardiovascular system

PubMed Central

Campos, Luciana A.; Pereira, Valter L.; Muralikrishna, Amita; Albarwani, Sulayma; Brás, Susana; Gouveia, Sónia

2013-01-01

Heart rate and blood pressure are the most important vital signs in diagnosing disease. Both heart rate and blood pressure are characterized by a high degree of short term variability from moment to moment, medium term over the normal day and night as well as in the very long term over months to years. The study of new mathematical algorithms to evaluate the variability of these cardiovascular parameters has a high potential in the development of new methods for early detection of cardiovascular disease, to establish differential diagnosis with possible therapeutic consequences. The autonomic nervous system is a major player in the general adaptive reaction to stress and disease. The quantitative prediction of the autonomic interactions in multiple control loops pathways of cardiovascular system is directly applicable to clinical situations. Exploration of new multimodal analytical techniques for the variability of cardiovascular system may detect new approaches for deterministic parameter identification. A multimodal analysis of cardiovascular signals can be studied by evaluating their amplitudes, phases, time domain patterns, and sensitivity to imposed stimuli, i.e., drugs blocking the autonomic system. The causal effects, gains, and dynamic relationships may be studied through dynamical fuzzy logic models, such as the discrete-time model and discrete-event model. We expect an increase in accuracy of modeling and a better estimation of the heart rate and blood pressure time series, which could be of benefit for intelligent patient monitoring. We foresee that identifying quantitative mathematical biomarkers for autonomic nervous system will allow individual therapy adjustments to aim at the most favorable sympathetic-parasympathetic balance. PMID:24109456

Modeling of carbonate reservoir variable secondary pore space based on CT images

NASA Astrophysics Data System (ADS)

Nie, X.; Nie, S.; Zhang, J.; Zhang, C.; Zhang, Z.

2017-12-01

Digital core technology has brought convenience to us, and X-ray CT scanning is one of the most common way to obtain 3D digital cores. However, it can only provide the original information of the only samples being scanned, and we can't modify the porosity of the scanned cores. For numerical rock physical simulations, a series of cores with variable porosities are needed to determine the relationship between the physical properties and porosity. In carbonate rocks, the secondary pore space including dissolution pores, caves and natural fractures is the key reservoir space, which makes the study of carbonate secondary porosity very important. To achieve the variation of porosities in one rock sample, based on CT scanned digital cores, according to the physical and chemical properties of carbonate rocks, several mathematical methods are chosen to simulate the variation of secondary pore space. We use the erosion and dilation operations of mathematical morphology method to simulate the pore space changes of dissolution pores and caves. We also use the Fractional Brownian Motion model to generate natural fractures with different widths and angles in digital cores to simulate fractured carbonate rocks. The morphological opening-and-closing operations in mathematical morphology method are used to simulate distribution of fluid in the pore space. The established 3D digital core models with different secondary porosities and water saturation status can be used in the study of the physical property numerical simulations of carbonate reservoir rocks.

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.

Chronic Stereotype Threat Is Associated With Mathematical Achievement on Representative Sample of Secondary Schoolgirls: The Role of Gender Identification, Working Memory, and Intellectual Helplessness

PubMed Central

Bedyńska, Sylwia; Krejtz, Izabela; Sedek, Grzegorz

2018-01-01

Stereotype threat affects performance in many different groups across many different domains. Despite a large body of experimental research on situational stereotype threat, little attention has been paid to the consequences of repeated experience of stereotype threat. Using structural equation modeling on data from a representative sample of girls from secondary schools, the current research examined the relations of chronic stereotype threat with mathematical achievement, and effectiveness of working memory functions. Moving beyond past theory, this study examined a new mechanism by which chronic stereotype threat decreases school achievement – namely intellectual helplessness. We assumed that repeated experience of stereotype threat works as intellectual helplessness training. After the phase of cognitive mobilization, cognitive exhaustion appears, because the individual has no gain from intense cognitive effort. Corroborating previous research on acute stereotype threat, we demonstrated that chronic stereotype threat is negatively associated with mathematical achievement. Additionally, it was also associated with lower effectiveness of working memory functions, which seems to show depletion of working memory as an effect of chronic stereotype threat. The results also demonstrated that both mediational paths from chronic stereotype threat to mathematical achievement: through working memory depletion and through intellectual helplessness were significant but only for girls that were highly identified with their gender group. In sum, we extended a well-established model of acute stereotype threat to its chronic version and suggested a new mechanism of chronic stereotype threat, which involves intellectual helplessness. Implications for stereotype threat theory and educational practice are discussed. PMID:29666599

Chronic Stereotype Threat Is Associated With Mathematical Achievement on Representative Sample of Secondary Schoolgirls: The Role of Gender Identification, Working Memory, and Intellectual Helplessness.

PubMed

Bedyńska, Sylwia; Krejtz, Izabela; Sedek, Grzegorz

2018-01-01

Stereotype threat affects performance in many different groups across many different domains. Despite a large body of experimental research on situational stereotype threat, little attention has been paid to the consequences of repeated experience of stereotype threat. Using structural equation modeling on data from a representative sample of girls from secondary schools, the current research examined the relations of chronic stereotype threat with mathematical achievement, and effectiveness of working memory functions. Moving beyond past theory, this study examined a new mechanism by which chronic stereotype threat decreases school achievement - namely intellectual helplessness. We assumed that repeated experience of stereotype threat works as intellectual helplessness training. After the phase of cognitive mobilization, cognitive exhaustion appears, because the individual has no gain from intense cognitive effort. Corroborating previous research on acute stereotype threat, we demonstrated that chronic stereotype threat is negatively associated with mathematical achievement. Additionally, it was also associated with lower effectiveness of working memory functions, which seems to show depletion of working memory as an effect of chronic stereotype threat. The results also demonstrated that both mediational paths from chronic stereotype threat to mathematical achievement: through working memory depletion and through intellectual helplessness were significant but only for girls that were highly identified with their gender group. In sum, we extended a well-established model of acute stereotype threat to its chronic version and suggested a new mechanism of chronic stereotype threat, which involves intellectual helplessness. Implications for stereotype threat theory and educational practice are discussed.

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 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…

A review of design and modeling of magnetorheological valve

NASA Astrophysics Data System (ADS)

Abd Fatah, Abdul Yasser; Mazlan, Saiful Amri; Koga, Tsuyoshi; Zamzuri, Hairi; Zeinali, Mohammadjavad; Imaduddin, Fitrian

2015-01-01

Following recent rapid development of researches in utilizing Magnetorheological (MR) fluid, a smart material that can be magnetically controlled to change its apparent viscosity instantaneously, a lot of applications have been established to exploit the benefits and advantages of using the MR fluid. One of the most important applications for MR fluid in devices is the MR valve, where it uses the popular flow or valve mode among the available working modes for MR fluid. As such, MR valve is widely applied in a lot of hydraulic actuation and vibration reduction devices, among them are dampers, actuators and shock absorbers. This paper presents a review on MR valve, discusses on several design configurations and the mathematical modeling for the MR valve. Therefore, this review paper classifies the MR valve based on the coil configuration and geometrical arrangement of the valve, and focusing on four different mathematical models for MR valve: Bingham plastic, Herschel-Bulkley, bi-viscous and Herschel-Bulkley with pre-yield viscosity (HBPV) models for calculating yield stress and pressure drop in the MR valve. Design challenges and opportunities for application of MR fluid and MR valve are also highlighted in this review. Hopefully, this review paper can provide basic knowledge on design and modeling of MR valve, complementing other reviews on MR fluid, its applications and technologies.

Fuzzy differential inclusions in atmospheric and medical cybernetics.

PubMed

Majumdar, Kausik Kumar; Majumder, Dwijesh Dutta

2004-04-01

Uncertainty management in dynamical systems is receiving attention in artificial intelligence, particularly in the fields of qualitative and model based reasoning. Fuzzy dynamical systems occupy a very important position in the class of uncertain systems. It is well established that the fuzzy dynamical systems represented by a set of fuzzy differential inclusions (FDI) are very convenient tools for modeling and simulation of various uncertain systems. In this paper, we discuss about the mathematical modeling of two very complex natural phenomena by means of FDIs. One of them belongs to the atmospheric cybernetics (the term has been used in a broad sense) of the genesis of a cyclonic storm (cyclogenesis), and the other belongs to the bio-medical cybernetics of the evolution of tumor in a human body. Since a discussion of the former already appears in a previous paper by the first author, here, we present very briefly a theoretical formalism of cyclone formation. On the other hand, we treat the latter system more elaborately. We solve the FDIs with the help of an algorithm developed in this paper to numerically simulate the mathematical models. From the simulation results thus obtained, we have drawn a number of interesting conclusions, which have been verified, and this vindicates the validity of our models.

Mathematical Model of Solid Food Pasteurization by Ohmic Heating: Influence of Process Parameters

PubMed Central

2014-01-01

Pasteurization of a solid food undergoing ohmic heating has been analysed by means of a mathematical model, involving the simultaneous solution of Laplace's equation, which describes the distribution of electrical potential within a food, the heat transfer equation, using a source term involving the displacement of electrical potential, the kinetics of inactivation of microorganisms likely to be contaminating the product. In the model, thermophysical and electrical properties as function of temperature are used. Previous works have shown the occurrence of heat loss from food products to the external environment during ohmic heating. The current model predicts that, when temperature gradients are established in the proximity of the outer ohmic cell surface, more cold areas are present at junctions of electrodes with lateral sample surface. For these reasons, colder external shells are the critical areas to be monitored, instead of internal points (typically geometrical center) as in classical pure conductive heat transfer. Analysis is carried out in order to understand the influence of pasteurisation process parameters on this temperature distribution. A successful model helps to improve understanding of these processing phenomenon, which in turn will help to reduce the magnitude of the temperature differential within the product and ultimately provide a more uniformly pasteurized product. PMID:24574874

Mathematical model of solid food pasteurization by ohmic heating: influence of process parameters.

PubMed

Marra, Francesco

2014-01-01

Pasteurization of a solid food undergoing ohmic heating has been analysed by means of a mathematical model, involving the simultaneous solution of Laplace's equation, which describes the distribution of electrical potential within a food, the heat transfer equation, using a source term involving the displacement of electrical potential, the kinetics of inactivation of microorganisms likely to be contaminating the product. In the model, thermophysical and electrical properties as function of temperature are used. Previous works have shown the occurrence of heat loss from food products to the external environment during ohmic heating. The current model predicts that, when temperature gradients are established in the proximity of the outer ohmic cell surface, more cold areas are present at junctions of electrodes with lateral sample surface. For these reasons, colder external shells are the critical areas to be monitored, instead of internal points (typically geometrical center) as in classical pure conductive heat transfer. Analysis is carried out in order to understand the influence of pasteurisation process parameters on this temperature distribution. A successful model helps to improve understanding of these processing phenomenon, which in turn will help to reduce the magnitude of the temperature differential within the product and ultimately provide a more uniformly pasteurized product.

Compression-bending of multi-component semi-rigid columns in response to axial loads and conjugate reciprocal extension-prediction of mechanical behaviours and implications for structural design.

PubMed

Lau, Ernest W

2013-01-01

The mathematical modelling of column buckling or beam bending under an axial or transverse load is well established. However, the existent models generally assume a high degree of symmetry in the structure of the column and minor longitudinal and transverse displacements. The situation when the column is made of several components with different mechanical properties asymmetrically distributed in the transverse section, semi-rigid, and subjected to multiple axial loads with significant longitudinal and transverse displacements through compression and bending has not been well characterised. A more comprehensive theoretical model allowing for these possibilities and assuming a circular arc contour for the bend is developed, and used to establish the bending axes, balance between compression and bending, and equivalent stiffness of the column. In certain situations, such as with pull cable catheters commonly used for minimally invasive surgical procedures, the compression loads are applied via cables running through channels inside a semi-rigid column. The model predicts the mathematical relationships between the radius of curvature of the bend and the tension in and normal force exerted by such cables. Conjugate extension with reciprocal compression-bending is a special structural arrangement for a semi-rigid column such that extension of one segment is linked to compression-bending of another by inextensible cables running between them. Leads are cords containing insulated electrical conductor coil and cables between the heart muscle and cardiac implantable electronic devices. Leads can behave like pull cable catheters through differential component pulling, providing a possible mechanism for inside-out abrasion and conductor cable externalisation. Certain design features may predispose to this mode of structural failure. Copyright © 2012 Elsevier Ltd. All rights reserved.

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…

Design and Performance Analysis of a new Rotary Hydraulic Joint

NASA Astrophysics Data System (ADS)

Feng, Yong; Yang, Junhong; Shang, Jianzhong; Wang, Zhuo; Fang, Delei

2017-07-01

To improve the driving torque of the robots joint, a wobble plate hydraulic joint is proposed, and the structure and working principle are described. Then mathematical models of kinematics and dynamics was established. On the basis of this, dynamic simulation and characteristic analysis are carried out. Results show that the motion curve of the joint is continuous and the impact is small. Moreover the output torque of the joint characterized by simple structure and easy processing is large and can be rotated continuously.

Analysis of material particle motion and optimizing parameters of vibration of two-mass GZS vibratory feeder

NASA Astrophysics Data System (ADS)

Nguyen, Van Xo; Golikov, N. S.

2018-05-01

The structure and kinematics of the two-mass GZS vibratory feeder operation are considered. It is established that the movement of the material's particles on the feeder surface determines its capacity. The development and analysis of the mathematical model of material's particle movement on the two-mass GZS vibratory feeder surface are shown. The results of Matlab optimization of material particles velocity function are given that allows setting rational kinematics of the feeder.

Research and application of genetic algorithm in path planning of logistics distribution vehicle

NASA Astrophysics Data System (ADS)

Wang, Yong; Zhou, Heng; Wang, Ying

2017-08-01

The core of the logistics distribution system is the vehicle routing planning, research path planning problem, provide a better solution has become an important issue. In order to provide the decision support for logistics and distribution operations, this paper studies the problem of vehicle routing with capacity constraints (CVRP). By establishing a mathematical model, the genetic algorithm is used to plan the path of the logistics vehicle to meet the minimum logistics and transportation costs.

The Application of FAHP in Decisions of Pavement Maintenance

NASA Astrophysics Data System (ADS)

Wu, Zhaorong

2017-04-01

In this paper, a method of building the fuzzy complementary judgement matrix and checking consistency is introduced based on the knowledge of the basic theory of FAHP and the procedure to establish the mathematical model corresponded. The scope and the advantages in the problems of multi-objective decisions have also been discussed. The availability of its use in the management system in pavement maintenance is demonstrated by analyzing the optimization for maintenance. Meanwhile, the faulty is also pointed out.

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.

Numerical and Analytical Study of Nonlinear Effects of Transonic Flow Past a Wing Airfoil in Oscillation of its Surface Element

NASA Astrophysics Data System (ADS)

Aul'chenko, S. M.; Zamuraev, V. P.; Kalinina, A. P.

2014-05-01

The present work is devoted to a criterial analysis and mathematical modeling of the influence of forced oscillations of surface elements of a wing airfoil on the shock-wave structure of transonic flow past it. Parameters that govern the regimes of interaction of the oscillatory motion of airfoil sections with the breakdown compression shock have been established. The qualitative and quantitative influence of these parameters on the wave resistance of the airfoil has been investigated.

Axelrod's Metanorm Games on Networks

PubMed Central

Galán, José M.; Łatek, Maciej M.; Rizi, Seyed M. Mussavi

2011-01-01

Metanorms is a mechanism proposed to promote cooperation in social dilemmas. Recent experimental results show that network structures that underlie social interactions influence the emergence of norms that promote cooperation. We generalize Axelrod's analysis of metanorms dynamics to interactions unfolding on networks through simulation and mathematical modeling. Network topology strongly influences the effectiveness of the metanorms mechanism in establishing cooperation. In particular, we find that average degree, clustering coefficient and the average number of triplets per node play key roles in sustaining or collapsing cooperation. PMID:21655211

Heat storage capability of a rolling cylinder using Glauber's salt

NASA Technical Reports Server (NTRS)

Herrick, C. S.; Zarnoch, K. P.

1980-01-01

The rolling cylinder phase change heat storage concept was developed to the point where a prototype design is completed and a cost analysis is prepared. A series of experimental and analytical tasks are defined to establish the thermal, mechanical, and materials behavior of rolling cylinder devices. These tasks include: analyses of internal and external heat transfer; performance and lifetime testing of the phase change materials; corrosion evaluation; development of a mathematical model; and design of a prototype and associated test equipment.

System for computer controlled shifting of an automatic transmission

DOEpatents

Patil, Prabhakar B.

1989-01-01

In an automotive vehicle having an automatic transmission that driveably connects a power source to the driving wheels, a method to control the application of hydraulic pressure to a clutch, whose engagement produces an upshift and whose disengagement produces a downshift, the speed of the power source, and the output torque of the transmission. The transmission output shaft torque and the power source speed are the controlled variables. The commanded power source torque and commanded hydraulic pressure supplied to the clutch are the control variables. A mathematical model is formulated that describes the kinematics and dynamics of the powertrain before, during and after a gear shift. The model represents the operating characteristics of each component and the structural arrangement of the components within the transmission being controlled. Next, a close loop feedback control is developed to determine the proper control law or compensation strategy to achieve an acceptably smooth gear ratio change, one in which the output torque disturbance is kept to a minimum and the duration of the shift is minimized. Then a computer algorithm simulating the shift dynamics employing the mathematical model is used to study the effects of changes in the values of the parameters established from a closed loop control of the clutch hydraulic and the power source torque on the shift quality. This computer simulation is used also to establish possible shift control strategies. The shift strategies determine from the prior step are reduced to an algorithm executed by a computer to control the operation of the power source and the transmission.

Closed loop computer control for an automatic transmission

DOEpatents

Patil, Prabhakar B.

1989-01-01

In an automotive vehicle having an automatic transmission that driveably connects a power source to the driving wheels, a method to control the application of hydraulic pressure to a clutch, whose engagement produces an upshift and whose disengagement produces a downshift, the speed of the power source, and the output torque of the transmission. The transmission output shaft torque and the power source speed are the controlled variables. The commanded power source torque and commanded hydraulic pressure supplied to the clutch are the control variables. A mathematical model is formulated that describes the kinematics and dynamics of the powertrain before, during and after a gear shift. The model represents the operating characteristics of each component and the structural arrangement of the components within the transmission being controlled. Next, a close loop feedback control is developed to determine the proper control law or compensation strategy to achieve an acceptably smooth gear ratio change, one in which the output torque disturbance is kept to a minimum and the duration of the shift is minimized. Then a computer algorithm simulating the shift dynamics employing the mathematical model is used to study the effects of changes in the values of the parameters established from a closed loop control of the clutch hydraulic and the power source torque on the shift quality. This computer simulation is used also to establish possible shift control strategies. The shift strategies determined from the prior step are reduced to an algorithm executed by a computer to control the operation of the power source and the transmission.

Mathematical models of cytotoxic effects in endpoint tumor cell line assays: critical assessment of the application of a single parametric value as a standard criterion to quantify the dose-response effects and new unexplored proposal formats.

PubMed

Calhelha, Ricardo C; Martínez, Mireia A; Prieto, M A; Ferreira, Isabel C F R

2017-10-23

The development of convenient tools for describing and quantifying the effects of standard and novel therapeutic agents is essential for the research community, to perform more precise evaluations. Although mathematical models and quantification criteria have been exchanged in the last decade between different fields of study, there are relevant methodologies that lack proper mathematical descriptions and standard criteria to quantify their responses. Therefore, part of the relevant information that can be drawn from the experimental results obtained and the quantification of its statistical reliability are lost. Despite its relevance, there is not a standard form for the in vitro endpoint tumor cell lines' assays (TCLA) that enables the evaluation of the cytotoxic dose-response effects of anti-tumor drugs. The analysis of all the specific problems associated with the diverse nature of the available TCLA used is unfeasible. However, since most TCLA share the main objectives and similar operative requirements, we have chosen the sulforhodamine B (SRB) colorimetric assay for cytotoxicity screening of tumor cell lines as an experimental case study. In this work, the common biological and practical non-linear dose-response mathematical models are tested against experimental data and, following several statistical analyses, the model based on the Weibull distribution was confirmed as the convenient approximation to test the cytotoxic effectiveness of anti-tumor compounds. Then, the advantages and disadvantages of all the different parametric criteria derived from the model, which enable the quantification of the dose-response drug-effects, are extensively discussed. Therefore, model and standard criteria for easily performing the comparisons between different compounds are established. The advantages include a simple application, provision of parametric estimations that characterize the response as standard criteria, economization of experimental effort and enabling rigorous comparisons among the effects of different compounds and experimental approaches. In all experimental data fitted, the calculated parameters were always statistically significant, the equations proved to be consistent and the correlation coefficient of determination was, in most of the cases, higher than 0.98.

Colored Petri net modeling and simulation of signal transduction pathways.

PubMed

Lee, Dong-Yup; Zimmer, Ralf; Lee, Sang Yup; Park, Sunwon

2006-03-01

Presented herein is a methodology for quantitatively analyzing the complex signaling network by resorting to colored Petri nets (CPN). The mathematical as well as Petri net models for two basic reaction types were established, followed by the extension to a large signal transduction system stimulated by epidermal growth factor (EGF) in an application study. The CPN models based on the Petri net representation and the conservation and kinetic equations were used to examine the dynamic behavior of the EGF signaling pathway. The usefulness of Petri nets is demonstrated for the quantitative analysis of the signal transduction pathway. Moreover, the trade-offs between modeling capability and simulation efficiency of this pathway are explored, suggesting that the Petri net model can be invaluable in the initial stage of building a dynamic model.

A novel water poverty index model for evaluation of Chinese regional water security

NASA Astrophysics Data System (ADS)

Gong, L.; Jin, C. L.; Li, Y. X.; Zhou, Z. L.

2017-08-01

This study proposed an improved Water Poverty Index (WPI) model employed in evaluating Chinese regional water security. Firstly, the Chinese WPI index system was constructed, in which the indicators were obtained according to China River reality. A new mathematical model was then established for WPI values calculation on the basis of Center for Ecology and Hydrology (CEH) model. Furthermore, this new model was applied in Shiyanghe River (located in western China). It turned out that the Chinese index system could clearly reflect the indicators threatening security of river water and the Chinese WPI model is feasible. This work has also developed a Water Security Degree (WSD) standard which is able to be regarded as a scientific basis for further water resources utilization and water security warning mechanism formulation.

Nonlinear mathematical modeling and sensitivity analysis of hydraulic drive unit

NASA Astrophysics Data System (ADS)

Kong, Xiangdong; Yu, Bin; Quan, Lingxiao; Ba, Kaixian; Wu, Liujie

2015-09-01

The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity indexes values of four measurable parameters, such as supply pressure, proportional gain, initial position of servo cylinder piston and load force, are verified experimentally on test platform of hydraulic drive unit, and the experimental research shows that the sensitivity analysis results obtained through simulation are approximate to the test results. This research indicates each parameter sensitivity characteristics of hydraulic drive unit, the performance-affected main parameters and secondary parameters are got under different working conditions, which will provide the theoretical foundation for the control compensation and structure optimization of hydraulic drive unit.

Measuring Near-Infrared Spectroscopy Derived Cerebral Autoregulation in Neonates: From Research Tool Toward Bedside Multimodal Monitoring

PubMed Central

Thewissen, Liesbeth; Caicedo, Alexander; Lemmers, Petra; Van Bel, Frank; Van Huffel, Sabine; Naulaers, Gunnar

2018-01-01

Introduction: Cerebral autoregulation (CAR), the ability of the human body to maintain cerebral blood flow (CBF) in a wide range of perfusion pressures, can be calculated by describing the relation between arterial blood pressure (ABP) and cerebral oxygen saturation measured by near-infrared spectroscopy (NIRS). In literature, disturbed CAR is described in different patient groups, using multiple measurement techniques and mathematical models. Furthermore, it is unclear to what extent cerebral pathology and outcome can be explained by impaired CAR. Aim and methods: In order to summarize CAR studies using NIRS in neonates, a systematic review was performed in the PUBMED and EMBASE database. To provide a general overview of the clinical framework used to study CAR, the different preprocessing methods and mathematical models are described and explained. Furthermore, patient characteristics, definition of impaired CAR and the outcome according to this definition is described organized for the different patient groups. Results: Forty-six articles were included in this review. Four patient groups were established: preterm infants during the transitional period, neonates receiving specific medication/treatment, neonates with congenital heart disease and neonates with hypoxic-ischemic encephalopathy (HIE) treated with therapeutic hypothermia. Correlation, coherence and transfer function (TF) gain are the mathematical models most frequently used to describe CAR. The definition of impaired CAR is depending on the mathematical model used. The incidence of intraventricular hemorrhage in preterm infants is the outcome variable most frequently correlated with impaired CAR. Hypotension, disease severity, dopamine treatment, injury on magnetic resonance imaging (MRI) and long term outcome are associated with impaired CAR. Prospective interventional studies are lacking in all research areas. Discussion and conclusion: NIRS derived CAR measurement is an important research tool to improve knowledge about central hemodynamic fluctuations during the transitional period, cerebral pharmacodynamics of frequently used medication (sedatives-inotropes) and cerebral effects of specific therapies in neonatology. Uniformity regarding measurement techniques and mathematical models is needed. Multimodal monitoring databases of neonatal intensive care patients of multiple centers, together with identical outcome parameters are needed to compare different techniques and make progress in this field. Real-time bedside monitoring of CAR, together with conventional monitoring, seems a promising technique to improve individual patient care. PMID:29868521

Bifurcation analysis and global dynamics of a mathematical model of antibiotic resistance in hospitals.

PubMed

Cen, Xiuli; Feng, Zhilan; Zheng, Yiqiang; Zhao, Yulin

2017-12-01

Antibiotic-resistant bacteria have posed a grave threat to public health by causing a number of nosocomial infections in hospitals. Mathematical models have been used to study transmission dynamics of antibiotic-resistant bacteria within a hospital and the measures to control antibiotic resistance in nosocomial pathogens. Studies presented in Lipstich et al. (Proc Natl Acad Sci 97(4):1938-1943, 2000) and Lipstich and Bergstrom (Infection control in the ICU environment. Kluwer, Boston, 2002) have provided valuable insights in understanding the transmission of antibiotic-resistant bacteria in a hospital. However, their results are limited to numerical simulations of a few different scenarios without analytical analyses of the models in broader parameter regions that are biologically feasible. Bifurcation analysis and identification of the global stability conditions can be very helpful for assessing interventions that are aimed at limiting nosocomial infections and stemming the spread of antibiotic-resistant bacteria. In this paper we study the global dynamics of the mathematical model of antibiotic resistance in hospitals considered in Lipstich et al. (2000) and Lipstich and Bergstrom (2002). The invasion reproduction number [Formula: see text] of antibiotic-resistant bacteria is derived, and the relationship between [Formula: see text] and two control reproduction numbers of sensitive bacteria and resistant bacteria ([Formula: see text] and [Formula: see text]) is established. More importantly, we prove that a backward bifurcation may occur at [Formula: see text] when the model includes superinfection, which is not mentioned in Lipstich and Bergstrom (2002). More specifically, there exists a new threshold [Formula: see text], such that if [Formula: see text], then the system can have two positive interior equilibria, which leads to an interesting bistable phenomenon. This may have critical implications for controlling the antibiotic-resistance in a hospital.

Mathematics and Science Faculty Service Learning Handbook.

ERIC Educational Resources Information Center

Wozniak, Jacci

Resources developed by "Campus Compact," a coalition of over 550 colleges and universities established to create and enhance service learning opportunities for students, are presented in this handbook for mathematics and science faculty. A brief introduction defines service learning and provides a continuum of types of service learning, such as…

Artistic Ways of Knowing in Gifted Education: Encouraging Every Student to Think Like an Artist

ERIC Educational Resources Information Center

Haroutounian, Joanne

2017-01-01

After decades of fluctuating presence in gifted education, the arts are surprisingly establishing themselves in academic classrooms, spurred by arts integration with science, technology, engineering, and mathematics (STEM) curricula or science, technology, engineering, art, and mathematics (STEAM). This renewed interest provides the opportunity to…

Values and Norms of Proof for Mathematicians and Students

ERIC Educational Resources Information Center

Dawkins, Paul Christian; Weber, Keith

2017-01-01

In this theoretical paper, we present a framework for conceptualizing proof in terms of mathematical values, as well as the norms that uphold those values. In particular, proofs adhere to the values of establishing a priori truth, employing decontextualized reasoning, increasing mathematical understanding, and maintaining consistent standards for…

Cases on Technology Integration in Mathematics Education

ERIC Educational Resources Information Center

Polly, Drew, Ed.

2015-01-01

Common Core education standards establish a clear set of specific ideas and skills that all students should be able to comprehend at each grade level. In an effort to meet these standards, educators are turning to technology for improved learning outcomes. "Cases on Technology Integration in Mathematics Education" provides a compilation…

Numerical calculation of primary slot leakage inductance of a Single-sided HTS linear induction motor used for linear metro

NASA Astrophysics Data System (ADS)

Li, Dong; Wen, Yinghong; Li, Weili; Fang, Jin; Cao, Junci; Zhang, Xiaochen; Lv, Gang

2017-03-01

In the paper, the numerical method calculating asymmetric primary slot leakage inductances of Single-sided High-Temperature Superconducting (HTS) Linear Induction Motor (HTS LIM) is presented. The mathematical and geometric models of three-dimensional nonlinear transient electromagnetic field are established and the boundary conditions are also given. The established model is solved by time-stepping Finite Element Method (FEM). Then, the three-phase asymmetric primary slot leakage inductances under different operation conditions are calculated by using the obtained electromagnetic field distribution. The influences of the special effects such as longitudinal end effects, transversal edge effects, etc. on the primary slot leakage inductance are investigated. The presented numerical method is validated by experiments carried out on a 3.5 kW prototype with copper wires which has the same structures with the HTS LIM.

The motion and control of a complex three-body space tethered system

NASA Astrophysics Data System (ADS)

Shi, Gefei; Zhu, Zhanxia; Chen, Shiyu; Yuan, Jianping; Tang, Biwei

2017-11-01

This paper is mainly devoted to investigating the dynamics and stability control of a three body-tethered satellite system which contains a main satellite and two subsatellites connected by two straight, massless and inextensible tethers. Firstly, a detailed mathematical model is established in the central gravitational field. Then, the dynamic characteristics of the established system are investigated and analyzed. Based on the dynamic analysis, a novel sliding mode prediction model (SMPM) control strategy is proposed to suppress the motion of the built tethered system. The numerical results show that the proposed underactuated control law is highly effective in suppressing the attitude/libration motion of the underactuated three-body tethered system. Furthermore, cases of different target angles are also examined and analyzed. The simulation results reveal that even if the final equilibrium states differ from different selections of the target angles, the whole system can still be maintained in acceptable areas.

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.

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.

Analysis of the Multi Strategy Goal Programming for Micro-Grid Based on Dynamic ant Genetic Algorithm

NASA Astrophysics Data System (ADS)

Qiu, J. P.; Niu, D. X.

Micro-grid is one of the key technologies of the future energy supplies. Take economic planning. reliability, and environmental protection of micro grid as a basis for the analysis of multi-strategy objective programming problems for micro grid which contains wind power, solar power, and battery and micro gas turbine. Establish the mathematical model of each power generation characteristics and energy dissipation. and change micro grid planning multi-objective function under different operating strategies to a single objective model based on AHP method. Example analysis shows that in combination with dynamic ant mixed genetic algorithm can get the optimal power output of this model.

Research on NC laser combined cutting optimization model of sheet metal parts

NASA Astrophysics Data System (ADS)

Wu, Z. Y.; Zhang, Y. L.; Li, L.; Wu, L. H.; Liu, N. B.

2017-09-01

The optimization problem for NC laser combined cutting of sheet metal parts was taken as the research object in this paper. The problem included two contents: combined packing optimization and combined cutting path optimization. In the problem of combined packing optimization, the method of “genetic algorithm + gravity center NFP + geometric transformation” was used to optimize the packing of sheet metal parts. In the problem of combined cutting path optimization, the mathematical model of cutting path optimization was established based on the parts cutting constraint rules of internal contour priority and cross cutting. The model played an important role in the optimization calculation of NC laser combined cutting.

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.

"Photographing money" task pricing

NASA Astrophysics Data System (ADS)

Jia, Zhongxiang

2018-05-01

"Photographing money" [1]is a self-service model under the mobile Internet. The task pricing is reasonable, related to the success of the commodity inspection. First of all, we analyzed the position of the mission and the membership, and introduced the factor of membership density, considering the influence of the number of members around the mission on the pricing. Multivariate regression of task location and membership density using MATLAB to establish the mathematical model of task pricing. At the same time, we can see from the life experience that membership reputation and the intensity of the task will also affect the pricing, and the data of the task success point is more reliable. Therefore, the successful point of the task is selected, and its reputation, task density, membership density and Multiple regression of task positions, according to which a nhew task pricing program. Finally, an objective evaluation is given of the advantages and disadvantages of the established model and solution method, and the improved method is pointed out.

Infrared characteristics and flow field of the exhaust plume outside twin engine nozzle

NASA Astrophysics Data System (ADS)

Feng, Yun-song

2016-01-01

For mastery of infrared radiation characteristics and flow field of exhaust plume of twin engine nozzles, first, a physical model of the double rectangular nozzles is established with the Gambit, and the mathematical model of flow field is determined. Secondly, software Fluent6.3 is used to simulated the 3-D exterior flow field of the twin engine nozzles, and the datum of flow field, such as temperature, pressure and density, are obtained. Finally, based on the plume temperature, the exhaust plume space is divided. The exhaust plume is equivalent to a gray-body. A calculating model of the plume infrared radiation is established, and the plume infrared radiation characteristics are calculated by the software MATLAB, then the spatial distribution curves are drawn. The result improves that with the height increasing the temperature, press and infrared radiant intensity diminish. Compared with engine afterburning condition, temperature and infrared radiant intensity increases and press has no obvious change.

On the extinction probability in models of within-host infection: the role of latency and immunity.

PubMed

Yan, Ada W C; Cao, Pengxing; McCaw, James M

2016-10-01

Not every exposure to virus establishes infection in the host; instead, the small amount of initial virus could become extinct due to stochastic events. Different diseases and routes of transmission have a different average number of exposures required to establish an infection. Furthermore, the host immune response and antiviral treatment affect not only the time course of the viral load provided infection occurs, but can prevent infection altogether by increasing the extinction probability. We show that the extinction probability when there is a time-dependent immune response depends on the chosen form of the model-specifically, on the presence or absence of a delay between infection of a cell and production of virus, and the distribution of latent and infectious periods of an infected cell. We hypothesise that experimentally measuring the extinction probability when the virus is introduced at different stages of the immune response, alongside the viral load which is usually measured, will improve parameter estimates and determine the most suitable mathematical form of the model.

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.

Complex systems as lenses on learning and teaching

NASA Astrophysics Data System (ADS)

Hurford, Andrew C.

From metaphors to mathematized models, the complexity sciences are changing the ways disciplines view their worlds, and ideas borrowed from complexity are increasingly being used to structure conversations and guide research on teaching and learning. The purpose of this corpus of research is to further those conversations and to extend complex systems ideas, theories, and modeling to curricula and to research on learning and teaching. A review of the literatures of learning and of complexity science and a discussion of the intersections between those disciplines are provided. The work reported represents an evolving model of learning qua complex system and that evolution is the result of iterative cycles of design research. One of the signatures of complex systems is the presence of scale invariance and this line of research furnishes empirical evidence of scale invariant behaviors in the activity of learners engaged in participatory simulations. The offered discussion of possible causes for these behaviors and chaotic phase transitions in human learning favors real-time optimization of decision-making as the means for producing such behaviors. Beyond theoretical development and modeling, this work includes the development of teaching activities intended to introduce pre-service mathematics and science teachers to complex systems. While some of the learning goals for this activity focused on the introduction of complex systems as a content area, we also used complex systems to frame perspectives on learning. Results of scoring rubrics and interview responses from students illustrate attributes of the proposed model of complex systems learning and also how these pre-service teachers made sense of the ideas. Correlations between established theories of learning and a complex adaptive systems model of learning are established and made explicit, and a means for using complex systems ideas for designing instruction is offered. It is a fundamental assumption of this research and researcher that complex systems ideas and understandings can be appropriated from more complexity-developed disciplines and put to use modeling and building increasingly productive understandings of learning and teaching.

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.

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.

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.

Generating A Strobed Laser Light Sheet

NASA Technical Reports Server (NTRS)

Leighty, Bradley D.; Franke, John M.; Rhodes, David B.; Jones, Stephen B.

1994-01-01

An optoelectronic system generating synchronous, strobed sheet of laser light developed for use in making visible flow of air about model helicopter rotor. Used in wind-tunnel tests to determine actual locations of vortices for comparison with locations predicted by mathematical models to validate models. Each blade tip produces vortex. By establishing successive vortex locations, researcher determines trajectory of vortex pattern. Light-sheet strobe circuits provide selection of blade positions, strobe-pulse durations, and multiple pulses per revolution for rotors having two to nine blades. To make flow visible, vaporizing propylene glycol injected upstream of model. System also provides calibrated trigger delay of strobe pulses, adjustable strobe-pulse durations, selectable number of blades, and slip-sync mode to make flow visible as though in slow motion.

Modeling an internal gear pump

NASA Astrophysics Data System (ADS)

Chen, Zongbin; Xu, Rongwu; He, Lin; Liao, Jian

2018-05-01

Considering the nature and characteristics of construction waste piles, this paper analyzed the factors affecting the stability of the slope of construction waste piles, and established the system of the assessment indexes for the slope failure risks of construction waste piles. Based on the basic principles and methods of fuzzy mathematics, the factor set and the remark set were established. The membership grade of continuous factor indexes is determined using the "ridge row distribution" function, while that for the discrete factor indexes was determined by the Delphi Method. For the weight of factors, the subjective weight was determined by the Analytic Hierarchy Process (AHP) and objective weight by the entropy weight method. And the distance function was introduced to determine the combination coefficient. This paper established a fuzzy comprehensive assessment model of slope failure risks of construction waste piles, and assessed pile slopes in the two dimensions of hazard and vulnerability. The root mean square of the hazard assessment result and vulnerability assessment result was the final assessment result. The paper then used a certain construction waste pile slope as the example for analysis, assessed the risks of the four stages of a landfill, verified the assessment model and analyzed the slope's failure risks and preventive measures against a slide.

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.