Closed-form summations of Dowker's and related trigonometric sums

NASA Astrophysics Data System (ADS)

Cvijović, Djurdje; Srivastava, H. M.

2012-09-01

Through a unified and relatively simple approach which uses complex contour integrals, particularly convenient integration contours and calculus of residues, closed-form summation formulas for 12 very general families of trigonometric sums are deduced. One of them is a family of cosecant sums which was first summed in closed form in a series of papers by Dowker (1987 Phys. Rev. D 36 3095-101 1989 J. Math. Phys. 30 770-3 1992 J. Phys. A: Math. Gen. 25 2641-8), whose method has inspired our work in this area. All of the formulas derived here involve the higher-order Bernoulli polynomials. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.

The Identities Hidden in the Matching Laws, and Their Uses

ERIC Educational Resources Information Center

Thorne, David R.

2010-01-01

Various theoretical equations have been proposed to predict response rate as a function of the rate of reinforcement. If both the rate and probability of reinforcement are considered, a simple identity, defining equation, or "law" holds. This identity places algebraic constraints on the allowable forms of our mathematical models and can help…

Stimulating Mathematical Reasoning with Simple Open-Ended Tasks

ERIC Educational Resources Information Center

West, John

2018-01-01

The importance of mathematical reasoning is unquestioned and providing opportunities for students to become involved in mathematical reasoning is paramount. The open-ended tasks presented incorporate mathematical content explored through the contexts of problem solving and reasoning. This article presents a number of simple tasks that may be…

A simple model for indentation creep

NASA Astrophysics Data System (ADS)

Ginder, Ryan S.; Nix, William D.; Pharr, George M.

2018-03-01

A simple model for indentation creep is developed that allows one to directly convert creep parameters measured in indentation tests to those observed in uniaxial tests through simple closed-form relationships. The model is based on the expansion of a spherical cavity in a power law creeping material modified to account for indentation loading in a manner similar to that developed by Johnson for elastic-plastic indentation (Johnson, 1970). Although only approximate in nature, the simple mathematical form of the new model makes it useful for general estimation purposes or in the development of other deformation models in which a simple closed-form expression for the indentation creep rate is desirable. Comparison to a more rigorous analysis which uses finite element simulation for numerical evaluation shows that the new model predicts uniaxial creep rates within a factor of 2.5, and usually much better than this, for materials creeping with stress exponents in the range 1 ≤ n ≤ 7. The predictive capabilities of the model are evaluated by comparing it to the more rigorous analysis and several sets of experimental data in which both the indentation and uniaxial creep behavior have been measured independently.

Simple linear and multivariate regression models.

PubMed

Rodríguez del Águila, M M; Benítez-Parejo, N

2011-01-01

In biomedical research it is common to find problems in which we wish to relate a response variable to one or more variables capable of describing the behaviour of the former variable by means of mathematical models. Regression techniques are used to this effect, in which an equation is determined relating the two variables. While such equations can have different forms, linear equations are the most widely used form and are easy to interpret. The present article describes simple and multiple linear regression models, how they are calculated, and how their applicability assumptions are checked. Illustrative examples are provided, based on the use of the freely accessible R program. Copyright © 2011 SEICAP. Published by Elsevier Espana. All rights reserved.

Causality

NASA Astrophysics Data System (ADS)

Pearl, Judea

2000-03-01

Written by one of the pre-eminent researchers in the field, this book provides a comprehensive exposition of modern analysis of causation. It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, philosophy, cognitive science, and the health and social sciences. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artifical intelligence, business, epidemiology, social science and economics. Students in these areas will find natural models, simple identification procedures, and precise mathematical definitions of causal concepts that traditional texts have tended to evade or make unduly complicated. This book will be of interest to professionals and students in a wide variety of fields. Anyone who wishes to elucidate meaningful relationships from data, predict effects of actions and policies, assess explanations of reported events, or form theories of causal understanding and causal speech will find this book stimulating and invaluable.

An implicit semianalytic numerical method for the solution of nonequilibrium chemistry problems

NASA Technical Reports Server (NTRS)

Graves, R. A., Jr.; Gnoffo, P. A.; Boughner, R. E.

1974-01-01

The first order differential equation form systems of equations. They are solved by a simple and relatively accurate implicit semianalytic technique which is derived from a quadrature solution of the governing equation. This method is mathematically simpler than most implicit methods and has the exponential nature of the problem embedded in the solution.

[Quality assurance of the renal applications software].

PubMed

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

2007-01-01

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

Receptors as a master key for synchronization of rhythms

NASA Astrophysics Data System (ADS)

Nagano, Seido

2004-03-01

A simple, but general scheme to achieve synchronization of rhythms was derived. The scheme has been inductively generalized from the modelling study of cellular slime mold. It was clarified that biological receptors work as apparatuses that can convert external stimulus to the form of nonlinear interaction within individual oscillators. Namely, the mathematical model receptor works as a nonlinear coupling apparatus between nonlinear oscillators. Thus, synchronization is achieved as a result of competition between two kinds of non-linearities, and to achieve synchronization, even a small external stimulation via model receptors can change the characteristics of individual oscillators significantly. The derived scheme is very simple mathematically, but it is a very powerful scheme as numerically demonstrated. The biological receptor scheme should significantly help understanding of synchronization phenomena in biology since groups of limit cycle oscillators and receptors are ubiquitous in biological systems. Reference: S. Nagano, Phys Rev. E67, 056215(2003)

Modeling and simulation for fewer-axis grinding of complex surface

NASA Astrophysics Data System (ADS)

Li, Zhengjian; Peng, Xiaoqiang; Song, Ci

2017-10-01

As the basis of fewer-axis grinding of complex surface, the grinding mathematical model is of great importance. A mathematical model of the grinding wheel was established, and then coordinate and normal vector of the wheel profile could be calculated. Through normal vector matching at the cutter contact point and the coordinate system transformation, the grinding mathematical model was established to work out the coordinate of the cutter location point. Based on the model, interference analysis was simulated to find out the right position and posture of workpiece for grinding. Then positioning errors of the workpiece including the translation positioning error and the rotation positioning error were analyzed respectively, and the main locating datum was obtained. According to the analysis results, the grinding tool path was planned and generated to grind the complex surface, and good form accuracy was obtained. The grinding mathematical model is simple, feasible and can be widely applied.

A bivariate rational interpolation with a bi-quadratic denominator

NASA Astrophysics Data System (ADS)

Duan, Qi; Zhang, Huanling; Liu, Aikui; Li, Huaigu

2006-10-01

In this paper a new rational interpolation with a bi-quadratic denominator is developed to create a space surface using only values of the function being interpolated. The interpolation function has a simple and explicit rational mathematical representation. When the knots are equally spaced, the interpolating function can be expressed in matrix form, and this form has a symmetric property. The concept of integral weights coefficients of the interpolation is given, which describes the "weight" of the interpolation points in the local interpolating region.

Modeling and control of flexible space platforms with articulated payloads

NASA Technical Reports Server (NTRS)

Graves, Philip C.; Joshi, Suresh M.

1989-01-01

The first steps in developing a methodology for spacecraft control-structure interaction (CSI) optimization are identification and classification of anticipated missions, and the development of tractable mathematical models in each mission class. A mathematical model of a generic large flexible space platform (LFSP) with multiple independently pointed rigid payloads is considered. The objective is not to develop a general purpose numerical simulation, but rather to develop an analytically tractable mathematical model of such composite systems. The equations of motion for a single payload case are derived, and are linearized about zero steady-state. The resulting model is then extended to include multiple rigid payloads, yielding the desired analytical form. The mathematical models developed clearly show the internal inertial/elastic couplings, and are therefore suitable for analytical and numerical studies. A simple decentralized control law is proposed for fine pointing the payloads and LFSP attitude control, and simulation results are presented for an example problem. The decentralized controller is shown to be adequate for the example problem chosen, but does not, in general, guarantee stability. A centralized dissipative controller is then proposed, requiring a symmetric form of the composite system equations. Such a controller guarantees robust closed loop stability despite unmodeled elastic dynamics and parameter uncertainties.

A Bayesian Modeling Approach for Estimation of a Shape-Free Groundwater Age Distribution using Multiple Tracers

DOE PAGES

Massoudieh, Arash; Visser, Ate; Sharifi, Soroosh; ...

2013-10-15

The mixing of groundwaters with different ages in aquifers, groundwater age is more appropriately represented by a distribution rather than a scalar number. To infer a groundwater age distribution from environmental tracers, a mathematical form is often assumed for the shape of the distribution and the parameters of the mathematical distribution are estimated using deterministic or stochastic inverse methods. We found that the prescription of the mathematical form limits the exploration of the age distribution to the shapes that can be described by the selected distribution. In this paper, the use of freeform histograms as groundwater age distributions is evaluated.more » A Bayesian Markov Chain Monte Carlo approach is used to estimate the fraction of groundwater in each histogram bin. This method was able to capture the shape of a hypothetical gamma distribution from the concentrations of four age tracers. The number of bins that can be considered in this approach is limited based on the number of tracers available. The histogram method was also tested on tracer data sets from Holten (The Netherlands; 3H, 3He, 85Kr, 39Ar) and the La Selva Biological Station (Costa-Rica; SF 6, CFCs, 3H, 4He and 14C), and compared to a number of mathematical forms. According to standard Bayesian measures of model goodness, the best mathematical distribution performs better than the histogram distributions in terms of the ability to capture the observed tracer data relative to their complexity. Among the histogram distributions, the four bin histogram performs better in most of the cases. The Monte Carlo simulations showed strong correlations in the posterior estimates of bin contributions, indicating that these bins cannot be well constrained using the available age tracers. The fact that mathematical forms overall perform better than the freeform histogram does not undermine the benefit of the freeform approach, especially for the cases where a larger amount of observed data is available and when the real groundwater distribution is more complex than can be represented by simple mathematical forms.« less

A Bayesian Modeling Approach for Estimation of a Shape-Free Groundwater Age Distribution using Multiple Tracers

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

Massoudieh, Arash; Visser, Ate; Sharifi, Soroosh

The mixing of groundwaters with different ages in aquifers, groundwater age is more appropriately represented by a distribution rather than a scalar number. To infer a groundwater age distribution from environmental tracers, a mathematical form is often assumed for the shape of the distribution and the parameters of the mathematical distribution are estimated using deterministic or stochastic inverse methods. We found that the prescription of the mathematical form limits the exploration of the age distribution to the shapes that can be described by the selected distribution. In this paper, the use of freeform histograms as groundwater age distributions is evaluated.more » A Bayesian Markov Chain Monte Carlo approach is used to estimate the fraction of groundwater in each histogram bin. This method was able to capture the shape of a hypothetical gamma distribution from the concentrations of four age tracers. The number of bins that can be considered in this approach is limited based on the number of tracers available. The histogram method was also tested on tracer data sets from Holten (The Netherlands; 3H, 3He, 85Kr, 39Ar) and the La Selva Biological Station (Costa-Rica; SF 6, CFCs, 3H, 4He and 14C), and compared to a number of mathematical forms. According to standard Bayesian measures of model goodness, the best mathematical distribution performs better than the histogram distributions in terms of the ability to capture the observed tracer data relative to their complexity. Among the histogram distributions, the four bin histogram performs better in most of the cases. The Monte Carlo simulations showed strong correlations in the posterior estimates of bin contributions, indicating that these bins cannot be well constrained using the available age tracers. The fact that mathematical forms overall perform better than the freeform histogram does not undermine the benefit of the freeform approach, especially for the cases where a larger amount of observed data is available and when the real groundwater distribution is more complex than can be represented by simple mathematical forms.« less

Pictorial Representations of Simple Arithmetic Problems Are Not Always Helpful: A Cognitive Load Perspective

ERIC Educational Resources Information Center

van Lieshout, Ernest C. D. M.; Xenidou-Dervou, Iro

2018-01-01

At the start of mathematics education children are often presented with addition and subtraction problems in the form of pictures. They are asked to solve the problems by filling in corresponding number sentences. One type of problem concerns the representation of an increase or a decrease in a depicted amount. A decrease is, however, more…

An accessible four-dimensional treatment of Maxwell's equations in terms of differential forms

NASA Astrophysics Data System (ADS)

Sá, Lucas

2017-03-01

Maxwell’s equations are derived in terms of differential forms in the four-dimensional Minkowski representation, starting from the three-dimensional vector calculus differential version of these equations. Introducing all the mathematical and physical concepts needed (including the tool of differential forms), using only knowledge of elementary vector calculus and the local vector version of Maxwell’s equations, the equations are reduced to a simple and elegant set of two equations for a unified quantity, the electromagnetic field. The treatment should be accessible for students taking a first course on electromagnetism.

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

PubMed

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

2014-12-11

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

A simple algorithm to estimate the effective regional atmospheric parameters for thermal-inertia mapping

USGS Publications Warehouse

Watson, K.; Hummer-Miller, S.

1981-01-01

A method based solely on remote sensing data has been developed to estimate those meteorological effects which are required for thermal-inertia mapping. It assumes that the atmospheric fluxes are spatially invariant and that the solar, sky, and sensible heat fluxes can be approximated by a simple mathematical form. Coefficients are determined from least-squares method by fitting observational data to our thermal model. A comparison between field measurements and the model-derived flux shows the type of agreement which can be achieved. An analysis of the limitations of the method is also provided. ?? 1981.

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

ERIC Educational Resources Information Center

Johnston, Peter R.

2013-01-01

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

Comment on the asymptotics of a distribution-free goodness of fit test statistic.

PubMed

Browne, Michael W; Shapiro, Alexander

2015-03-01

In a recent article Jennrich and Satorra (Psychometrika 78: 545-552, 2013) showed that a proof by Browne (British Journal of Mathematical and Statistical Psychology 37: 62-83, 1984) of the asymptotic distribution of a goodness of fit test statistic is incomplete because it fails to prove that the orthogonal component function employed is continuous. Jennrich and Satorra (Psychometrika 78: 545-552, 2013) showed how Browne's proof can be completed satisfactorily but this required the development of an extensive and mathematically sophisticated framework for continuous orthogonal component functions. This short note provides a simple proof of the asymptotic distribution of Browne's (British Journal of Mathematical and Statistical Psychology 37: 62-83, 1984) test statistic by using an equivalent form of the statistic that does not involve orthogonal component functions and consequently avoids all complicating issues associated with them.

Microcomputer-Assisted Mathematics: From Simple Interest to e.

ERIC Educational Resources Information Center

Kimberling, Clark

1985-01-01

The progression from simple interest to compound interest leads naturally and quickly to the number e, involving mathematical discovery learning through writing programs. Several programs are given, with suggestions for a teaching sequence. (MNS)

Matrix De Rham Complex and Quantum A-infinity algebras

NASA Astrophysics Data System (ADS)

Barannikov, S.

2014-04-01

I establish the relation of the non-commutative BV-formalism with super-invariant matrix integration. In particular, the non-commutative BV-equation, defining the quantum A ∞-algebras, introduced in Barannikov (Modular operads and non-commutative Batalin-Vilkovisky geometry. IMRN, vol. 2007, rnm075. Max Planck Institute for Mathematics 2006-48, 2007), is represented via de Rham differential acting on the supermatrix spaces related with Bernstein-Leites simple associative algebras with odd trace q( N), and gl( N| N). I also show that the matrix Lagrangians from Barannikov (Noncommutative Batalin-Vilkovisky geometry and matrix integrals. Isaac Newton Institute for Mathematical Sciences, Cambridge University, 2006) are represented by equivariantly closed differential forms.

Kinematic analysis of asymmetric folds in competent layers using mathematical modelling

NASA Astrophysics Data System (ADS)

Aller, J.; Bobillo-Ares, N. C.; Bastida, F.; Lisle, R. J.; Menéndez, C. O.

2010-08-01

Mathematical 2D modelling of asymmetric folds is carried out by applying a combination of different kinematic folding mechanisms: tangential longitudinal strain, flexural flow and homogeneous deformation. The main source of fold asymmetry is discovered to be due to the superimposition of a general homogeneous deformation on buckle folds that typically produces a migration of the hinge point. Forward modelling is performed mathematically using the software 'FoldModeler', by the superimposition of simple shear or a combination of simple shear and irrotational strain on initial buckle folds. The resulting folds are Ramsay class 1C folds, comparable to those formed by symmetric flattening, but with different length of limbs and layer thickness asymmetry. Inverse modelling is made by fitting the natural fold to a computer-simulated fold. A problem of this modelling is the search for the most appropriate homogeneous deformation to be superimposed on the initial fold. A comparative analysis of the irrotational and rotational deformations is made in order to find the deformation which best simulates the shapes and attitudes of natural folds. Modelling of recumbent folds suggests that optimal conditions for their development are: a) buckling in a simple shear regime with a sub-horizontal shear direction and layering gently dipping towards this direction; b) kinematic amplification due to superimposition of a combination of simple shear and irrotational strain with a sub-vertical maximum shortening direction for the latter component. The modelling shows that the amount of homogeneous strain necessary for the development of recumbent folds is much less when an irrotational strain component is superimposed at this stage that when the superimposed strain is only simple shear. In nature, the amount of the irrotational strain component probably increases during the development of the fold as a consequence of the increasing influence of the gravity due to the tectonic superimposition of rocks.

The topology of fullerenes

PubMed Central

Schwerdtfeger, Peter; Wirz, Lukas N; Avery, James

2015-01-01

Fullerenes are carbon molecules that form polyhedral cages. Their bond structures are exactly the planar cubic graphs that have only pentagon and hexagon faces. Strikingly, a number of chemical properties of a fullerene can be derived from its graph structure. A rich mathematics of cubic planar graphs and fullerene graphs has grown since they were studied by Goldberg, Coxeter, and others in the early 20th century, and many mathematical properties of fullerenes have found simple and beautiful solutions. Yet many interesting chemical and mathematical problems in the field remain open. In this paper, we present a general overview of recent topological and graph theoretical developments in fullerene research over the past two decades, describing both solved and open problems. WIREs Comput Mol Sci 2015, 5:96–145. doi: 10.1002/wcms.1207 Conflict of interest: The authors have declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website. PMID:25678935

Simulating Bone Loss in Microgravity Using Mathematical Formulations of Bone Remodeling

NASA Technical Reports Server (NTRS)

Pennline, James A.

2009-01-01

Most mathematical models of bone remodeling are used to simulate a specific bone disease, by disrupting the steady state or balance in the normal remodeling process, and to simulate a therapeutic strategy. In this work, the ability of a mathematical model of bone remodeling to simulate bone loss as a function of time under the conditions of microgravity is investigated. The model is formed by combining a previously developed set of biochemical, cellular dynamics, and mechanical stimulus equations in the literature with two newly proposed equations; one governing the rate of change of the area of cortical bone tissue in a cross section of a cylindrical section of bone and one governing the rate of change of calcium in the bone fluid. The mechanical stimulus comes from a simple model of stress due to a compressive force on a cylindrical section of bone which can be reduced to zero to mimic the effects of skeletal unloading in microgravity. The complete set of equations formed is a system of first order ordinary differential equations. The results of selected simulations are displayed and discussed. Limitations and deficiencies of the model are also discussed as well as suggestions for further research.

Spectrophotometric Method for the Determination of Two Coformulated Drugs with Highly Different Concentrations. Application on Vildagliptin and Metformin Hydrochloride

NASA Astrophysics Data System (ADS)

Zaazaa, H. E.; Elzanfaly, E. S.; Soudi, A. T.; Salem, M. Y.

2016-03-01

A new smart simple validated spectrophotometric method was developed for the determination of two drugs one of which is in a very low concentration compared to the other. The method is based on spiking and dilution then simple mathematical manipulation of the absorbance spectra. This method was applied for the determination of a binary mixture of vildagliptin and metformin hydrochloride in the ratio 50:850 in laboratory prepared mixtures containing both drugs in this ratio and in pharmaceutical dosage form with good recoveries. The developed method was validated according to ICH guidelines and can be used for routine quality control testing.

A Mathematical Model of a Simple Amplifier Using a Ferroelectric Transistor

NASA Technical Reports Server (NTRS)

Sayyah, Rana; Hunt, Mitchell; MacLeod, Todd C.; Ho, Fat D.

2009-01-01

This paper presents a mathematical model characterizing the behavior of a simple amplifier using a FeFET. The model is based on empirical data and incorporates several variables that affect the output, including frequency, load resistance, and gate-to-source voltage. Since the amplifier is the basis of many circuit configurations, a mathematical model that describes the behavior of a FeFET-based amplifier will help in the integration of FeFETs into many other circuits.

A cluster bootstrap for two-loop MHV amplitudes

DOE PAGES

Golden, John; Spradlin, Marcus

2015-02-02

We apply a bootstrap procedure to two-loop MHV amplitudes in planar N=4 super-Yang-Mills theory. We argue that the mathematically most complicated part (the Λ 2 B 2 coproduct component) of the n-particle amplitude is uniquely determined by a simple cluster algebra property together with a few physical constraints (dihedral symmetry, analytic structure, supersymmetry, and well-defined collinear limits). Finally, we present a concise, closed-form expression which manifests these properties for all n.

Falling head ponded infiltration in the nonlinear limit

NASA Astrophysics Data System (ADS)

Triadis, D.

2014-12-01

The Green and Ampt infiltration solution represents only an extreme example of behavior within a larger class of very nonlinear, delta function diffusivity soils. The mathematical analysis of these soils is greatly simplified by the existence of a sharp wetting front below the soil surface. Solutions for more realistic delta function soil models have recently been presented for infiltration under surface saturation without ponding. After general formulation of the problem, solutions for a full suite of delta function soils are derived for ponded surface water depleted by infiltration. Exact expressions for the cumulative infiltration as a function of time, or the drainage time as a function of the initial ponded depth may take implicit or parametric forms, and are supplemented by simple asymptotic expressions valid for small times, and small and large initial ponded depths. As with surface saturation without ponding, the Green-Ampt model overestimates the effect of the soil hydraulic conductivity. At the opposing extreme, a low-conductivity model is identified that also takes a very simple mathematical form and appears to be more accurate than the Green-Ampt model for larger ponded depths. Between these two, the nonlinear limit of Gardner's soil is recommended as a physically valid first approximation. Relative discrepancies between different soil models are observed to reach a maximum for intermediate values of the dimensionless initial ponded depth, and in general are smaller than for surface saturation without ponding.

Simple Example of Backtest Overfitting (SEBO)

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

In the field of mathematical finance, a "backtest" is the usage of historical market data to assess the performance of a proposed trading strategy. It is a relatively simple matter for a present-day computer system to explore thousands, millions or even billions of variations of a proposed strategy, and pick the best performing variant as the "optimal" strategy "in sample" (i.e., on the input dataset). Unfortunately, such an "optimal" strategy often performs very poorly "out of sample" (i.e. on another dataset), because the parameters of the invest strategy have been oversit to the in-sample data, a situation known as "backtestmore » overfitting". While the mathematics of backtest overfitting has been examined in several recent theoretical studies, here we pursue a more tangible analysis of this problem, in the form of an online simulator tool. Given a input random walk time series, the tool develops an "optimal" variant of a simple strategy by exhaustively exploring all integer parameter values among a handful of parameters. That "optimal" strategy is overfit, since by definition a random walk is unpredictable. Then the tool tests the resulting "optimal" strategy on a second random walk time series. In most runs using our online tool, the "optimal" strategy derived from the first time series performs poorly on the second time series, demonstrating how hard it is not to overfit a backtest. We offer this online tool, "Simple Example of Backtest Overfitting (SEBO)", to facilitate further research in this area.« less

New Challenges in the Teaching of Mathematics.

ERIC Educational Resources Information Center

Bourguignon, Jean Pierre

The manifold but discrete presence of mathematics in many objects or services imposes new constraints to the teaching of mathematics. If citizens need to be comfortable in various situations with a variety of mathematical tools, the learning of mathematics requires that one starts with simple concepts. This paper proposes some solutions to solve…

Building Mathematical Models of Simple Harmonic and Damped Motion.

ERIC Educational Resources Information Center

Edwards, Thomas

1995-01-01

By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)

A Mathematical Diet Model

ERIC Educational Resources Information Center

Toumasis, Charalampos

2004-01-01

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

Applying a Conceptual Mini Game for Supporting Simple Mathematical Calculation Skills: Students' Perceptions and Considerations

ERIC Educational Resources Information Center

Panagiotakopoulos, Chris T.

2011-01-01

Mathematics is an area of study that particularly lacks student enthusiasm. Nevertheless, with the help of educational games, any phobias concerning mathematics can be considerably decreased and mathematics can become more appealing. In this study, an educational game addressing mathematics was designed, developed and evaluated by a sample of 33…

Multiple-generator errors are unavoidable under model misspecification.

PubMed

Jewett, D L; Zhang, Z

1995-08-01

Model misspecification poses a major problem for dipole source localization (DSL) because it causes insidious multiple-generator errors (MulGenErrs) to occur in the fitted dipole parameters. This paper describes how and why this occurs, based upon simple algebraic considerations. MulGenErrs must occur, to some degree, in any DSL analysis of real data because there is model misspecification and mathematically the equations used for the simultaneously active generators must be of a different form than the equations for each generator active alone.

Mathematical model of the solar radiation force and torques acting on the components of a spacecraft

NASA Technical Reports Server (NTRS)

Georgevic, R. M.

1971-01-01

General expressions for the solar radiation force and torques are derived in the vectorial form for any given reflecting surface, provided that the reflecting characteristics of the surface, as well as the value of the solar constant, are known. An appropriate choice of a spacecraft-fixed frame of reference leads to relatively simple expressions for the solar radiation forces and torques in terms of the functions of the sun-spacecraft-earth angle.

Spontaneous knotting of an agitated string.

PubMed

Raymer, Dorian M; Smith, Douglas E

2007-10-16

It is well known that a jostled string tends to become knotted; yet the factors governing the "spontaneous" formation of various knots are unclear. We performed experiments in which a string was tumbled inside a box and found that complex knots often form within seconds. We used mathematical knot theory to analyze the knots. Above a critical string length, the probability P of knotting at first increased sharply with length but then saturated below 100%. This behavior differs from that of mathematical self-avoiding random walks, where P has been proven to approach 100%. Finite agitation time and jamming of the string due to its stiffness result in lower probability, but P approaches 100% with long, flexible strings. We analyzed the knots by calculating their Jones polynomials via computer analysis of digital photos of the string. Remarkably, almost all were identified as prime knots: 120 different types, having minimum crossing numbers up to 11, were observed in 3,415 trials. All prime knots with up to seven crossings were observed. The relative probability of forming a knot decreased exponentially with minimum crossing number and Möbius energy, mathematical measures of knot complexity. Based on the observation that long, stiff strings tend to form a coiled structure when confined, we propose a simple model to describe the knot formation based on random "braid moves" of the string end. Our model can qualitatively account for the observed distribution of knots and dependence on agitation time and string length.

[Mathematical model of oblique three-dimensional intertrochanteric detorsion varus-forming osteotomy of the femur by the Bernbeck method in surgical treatment of congenital hip dysplasia in children].

PubMed

Bohatyrewicz, A

1992-01-01

Whenever the conservative procedure fails to bring about congruence of the dysplastic hip joint, an operative procedure becomes indispensable. In Orthopaedic Clinic of the Pomeranian Medical Academy in Szczecin we implement the oblique three-dimensional intertrochanteric detorsion and varus forming osteotomy after Bernbeck in order to correct the proximal end of the femoral bone. Precise determination of the plane to be cut, prior to the operative procedure, simplifies and shortens the operation itself and facilitates the achieving of the planned angular values in all three planes. Mathematical model of osteotomy according to Bernbeck considering required angles of correction as well as angles determining the plane of osteotomy was worked out. In collaboration of the Szczecin Technical University, a simple computer program was elaborated which allowed the presentation of the results in the form of tables. With the help of tables the optimal cutting plane was chosen and created correct biomechanical and anatomical conditions as well as optimal conditions for stable osteosynthesis of dissected fragments of the femoral bone. That type of osteotomy is useful in most operative correcrions of the dysplastic hip joint (not great varus formation connected with relatively extensive detorsion). The achieved congruence in the 22 dysplastic hip joints operated on was the most important condition for their later physiological development. Short post-operative observations confirm the value of described mathematic model.

Mathematical Foundation for Plane Covering Using Hexagons

NASA Technical Reports Server (NTRS)

Johnson, Gordon G.

1999-01-01

This work is to indicate the development and mathematical underpinnings of the algorithms previously developed for covering the plane and the addressing of the elements of the covering. The algorithms are of interest in that they provides a simple systematic way of increasing or decreasing resolution, in the sense that if we have the covering in place and there is an image superimposed upon the covering, then we may view the image in a rough form or in a very detailed form with minimal effort. Such ability allows for quick searches of crude forms to determine a class in which to make a detailed search. In addition, the addressing algorithms provide an efficient way to process large data sets that have related subsets. The algorithms produced were based in part upon the work of D. Lucas "A Multiplication in N Space" which suggested a set of three vectors, any two of which would serve as a bases for the plane and also that the hexagon is the natural geometric object to be used in a covering with a suggested bases. The second portion is a refinement of the eyeball vision system, the globular viewer.

Mathematical Gossip: Relevance and Context in the Mathematics Classroom

ERIC Educational Resources Information Center

Callingham, Rosemary

2004-01-01

Using mathematical gossip in the classroom allows teachers to expand their students' horizons, and provide pathways to improvement of understanding. The expansion of a simple idea into another mathematical context can enrich a student's learning. In particular it may help to bridge the gap between purely procedural approaches and a conceptual…

Strategic competence of senior secondary school students in solving mathematics problem based on cognitive style

NASA Astrophysics Data System (ADS)

Syukriani, Andi; Juniati, Dwi; Siswono, Tatag Yuli Eko

2017-08-01

The purpose of this study was to explore the strategic competence of senior secondary school students in solving mathematics problems. Terdapat dua subjek, satu bergaya kognitif field-independent dan satu bergaya kognitif field-dependent tetapi keduanya memiliki tingkat prestasi belajar matematika yang setara. There were two subjects, one field-independent cognitive style and one field-dependent cognitive style. They had an equivalent high level of mathematics achievement. Keduanya dipilih berdasarkan hasil tes kompetensi matematika dan GEFT (Group Embedded Figures Test). Subjects were selected based on the test results of mathematics competence and GEFT (Group Embedded Figures Test). Kompetensi strategis dapat merangsang perkembangan otonomi dan fleksibilitas dalam diri siswa karena merupakan keterampilan yang sangat dibutuhkan di sepanjang abad 21. Gaya kognitif merupakan kecenderungan siswa dalam mengolah informasi sangat mempengaruhi performance dalam menyelesaikan masalah matematika. Strategic competence can stimulate the development of autonomy and flexibility of students and they are skills which are needed in the 21st century. Cognitive style is the tendency of students in processing informations and it greatly affects the performance in solving mathematics problems. Hasil penelitian menunjukkan bahwa subjek FI cenderung analitis baik pada pembentukan bayangannya maupun pada gambar yang dibuatnya untuk memproses informasi berdasarkan dengan struktur pengetahuannya sendiri (Internally directed). The research result showed that subject FI tended to be analytical both in forming the mental imagination and the picture to process information in accordance with his own knowledge structure (internally directed). Subjek FD kurang analitis dan tidak dapat mengenal bentuk sederhana (konsep matematika) dari bentuk yang kompleks (Exeternally directed) sehingga menerima ide sebagaimana yang disajikan. Subject FD was less analytical and unable to recognize simple form (mathematical concept) of a complex form (Externally directed), so he received the idea as presented. Hasil penelitian ini penting sebagai bahan masukan untuk guru dan pengembang ilmu pendidikan matematika untuk meningkatkan fleksibilitas (Flexibility) siswa dalam keberagaman karakteristiknya melalui penelitian terkait dengan pengembangan bahan instruksi, perangkat dan model pembelajaran matematika. The results of this research are important as input for teachers and mathematics education developers to increase the flexibility of students in the characteristics diversity through the research related to the development of instruction materials and mathematics learning model. Penelitian selanjutnya, sebaiknya melihat bagaimana FI dan FD dapat memberikan penjelasan dan pembenaran atas strategi yang telah diusahakan supaya terlihat lebih jelas bagaimana perbedaan FI dan FD dalam mengkontruksi konsep matematika pada pengalaman belajarnya Further research should study about how the explanation and justification for the strategy that has been attempted in order to look more clearly how constructing mathematical concepts in their learning experience.

Dimensional analysis yields the general second-order differential equation underlying many natural phenomena: the mathematical properties of a phenomenon's data plot then specify a unique differential equation for it.

PubMed

Kepner, Gordon R

2014-08-27

This study uses dimensional analysis to derive the general second-order differential equation that underlies numerous physical and natural phenomena described by common mathematical functions. It eschews assumptions about empirical constants and mechanisms. It relies only on the data plot's mathematical properties to provide the conditions and constraints needed to specify a second-order differential equation that is free of empirical constants for each phenomenon. A practical example of each function is analyzed using the general form of the underlying differential equation and the observable unique mathematical properties of each data plot, including boundary conditions. This yields a differential equation that describes the relationship among the physical variables governing the phenomenon's behavior. Complex phenomena such as the Standard Normal Distribution, the Logistic Growth Function, and Hill Ligand binding, which are characterized by data plots of distinctly different sigmoidal character, are readily analyzed by this approach. It provides an alternative, simple, unifying basis for analyzing each of these varied phenomena from a common perspective that ties them together and offers new insights into the appropriate empirical constants for describing each phenomenon.

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

USGS Publications Warehouse

Lamb, Berton Lee; Burkardt, Nina

2008-01-01

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

A new fractional nonlocal model and its application in free vibration of Timoshenko and Euler-Bernoulli beams

NASA Astrophysics Data System (ADS)

Rahimi, Zaher; Sumelka, Wojciech; Yang, Xiao-Jun

2017-11-01

The application of fractional calculus in fractional models (FMs) makes them more flexible than integer models inasmuch they can conclude all of integer and non-integer operators. In other words FMs let us use more potential of mathematics to modeling physical phenomena due to the use of both integer and fractional operators to present a better modeling of problems, which makes them more flexible and powerful. In the present work, a new fractional nonlocal model has been proposed, which has a simple form and can be used in different problems due to the simple form of numerical solutions. Then the model has been used to govern equations of the motion of the Timoshenko beam theory (TBT) and Euler-Bernoulli beam theory (EBT). Next, free vibration of the Timoshenko and Euler-Bernoulli simply-supported (S-S) beam has been investigated. The Galerkin weighted residual method has been used to solve the non-linear governing equations.

Is the Reaction Equilibrium Composition in Non-ideal Mixtures Uniquely Determined by the Initial Composition?

NASA Astrophysics Data System (ADS)

Sefcik, Jan

1998-05-01

Reaction equilibrium can be mathematically described by the equilibrium equation and the reaction equilibrium composition can be calculated by solving this equation. It can be proved by non-elementary thermodynamic arguments that for a generic system with given initial composition, temperature and pressure there is a unique stable equilibrium state corresponding to the global minimum of the Gibbs free energy function. However, when the concept of equilibrium is introduced in undergraduate chemistry and chemical engineering courses, such arguments are generally not accessible. When there is a single reaction equilibrium among mixture components and the components form an ideal mixture, it has been demonstrated by a simple, elegant mathematical argument that there is a unique composition satisfying the equilibrium equation. It has been also suggested that this particular argument extends to non-ideal mixtures by simply incorporating activity coefficients. We show that the argument extension to non-ideal systems is not generally valid. Increasing non-ideality can result in non-monotonicity of the function crucial for the simple uniqueness argument, and only later it leads to non-uniqueness and hence phase separation. The main feature responsible for this is a composition dependence of activity coefficients in non-ideal mixtures.

Mathematical thinking and origami

NASA Astrophysics Data System (ADS)

Wares, Arsalan

2016-01-01

The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and calculus.

Electro-osmotic flow of semidilute polyelectrolyte solutions.

PubMed

Uematsu, Yuki; Araki, Takeaki

2013-09-07

We investigate electro-osmosis in aqueous solutions of polyelectrolytes using mean-field equations. A solution of positively charged polyelectrolytes is confined between two negatively charged planar surfaces, and an electric field is applied parallel to the surfaces. When electrostatic attraction between the polymer and the surface is strong, the polymers adhere to the surface, forming a highly viscous adsorption layer that greatly suppresses the electro-osmosis. Conversely, electro-osmosis is enhanced by depleting the polymers from the surfaces. We also found that the electro-osmotic flow is invertible when the electrostatic potential decays to its bulk value with the opposite sign. These behaviors are well explained by a simple mathematical form of the electro-osmotic coefficient.

Method to compute the stress-energy tensor for a quantum field outside a black hole that forms from collapse

NASA Astrophysics Data System (ADS)

Anderson, Paul; Evans, Charles

2017-01-01

A method to compute the stress-energy tensor for a quantized massless minimally coupled scalar field outside the event horizon of a 4-D black hole that forms from the collapse of a spherically symmetric null shell is given. The method is illustrated in the corresponding 2-D case which is mathematically similar but is simple enough that the calculations can be done analytically. The approach to the Unruh state at late times is discussed. National Science Foundation Grant No. PHY-1505875 to Wake Forest University and National Science Foundation Grant No. PHY-1506182 to the University of North Carolina, Chapel Hill

Mathematical model to estimate risk of calcium-containing renal stones

NASA Technical Reports Server (NTRS)

Pietrzyk, R. A.; Feiveson, A. H.; Whitson, P. A.

1999-01-01

BACKGROUND/AIMS: Astronauts exposed to microgravity during the course of spaceflight undergo physiologic changes that alter the urinary environment so as to increase the risk of renal stone formation. This study was undertaken to identify a simple method with which to evaluate the potential risk of renal stone development during spaceflight. METHOD: We used a large database of urinary risk factors obtained from 323 astronauts before and after spaceflight to generate a mathematical model with which to predict the urinary supersaturation of calcium stone forming salts. RESULT: This model, which involves the fewest possible analytical variables (urinary calcium, citrate, oxalate, phosphorus, and total volume), reliably and accurately predicted the urinary supersaturation of the calcium stone forming salts when compared to results obtained from a group of 6 astronauts who collected urine during flight. CONCLUSIONS: The use of this model will simplify both routine medical monitoring during spaceflight as well as the evaluation of countermeasures designed to minimize renal stone development. This model also can be used for Earth-based applications in which access to analytical resources is limited.

Conditions and Linear Stability Analysis at the Transition to Synchronization of Three Coupled Phase Oscillators in a Ring

NASA Astrophysics Data System (ADS)

El-Nashar, Hassan F.

2017-06-01

We consider a system of three nonidentical coupled phase oscillators in a ring topology. We explore the conditions that must be satisfied in order to obtain the phases at the transition to a synchrony state. These conditions lead to the correct mathematical expressions of phases that aid to find a simple analytic formula for critical coupling when the oscillators transit to a synchronization state having a common frequency value. The finding of a simple expression for the critical coupling allows us to perform a linear stability analysis at the transition to the synchronization stage. The obtained analytic forms of the eigenvalues show that the three coupled phase oscillators with periodic boundary conditions transit to a synchrony state when a saddle-node bifurcation occurs.

Dynamics of a particle with friction and delay

NASA Astrophysics Data System (ADS)

Monteiro Marques, Manuel D. P.; Dzonou, Raoul

2018-03-01

We are interested in the motion of a simple mechanical system having a finite number of degrees of freedom subjected to a unilateral constraint with dry friction and delay effects (with maximal duration τ > 0). At the contact point, we characterize the friction by a Coulomb law associated with a friction cone. Starting from a formulation of the problem that was given by Jean-Jacques Moreau in the form of a second-order differential inclusion in the sense of measures, we consider a sweeping process algorithm that converges towards a solution to the dynamical contact problem. The mathematical machinery as well as the general plan of the existence proof may seem much too heavy in order to treat just this simple case, but they have proved useful in more complex settings. xml:lang="fr"

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Techniques for Accelerating Iterative Methods for the Solution of Mathematical Problems

DTIC Science & Technology

1989-07-01

m, we can find a solu ion to the problem by using generalized inverses. Hence, ;= Ih.i = GAi = G - where G is of the form (18). A simple choice for V...have understood why I was not available for many of their activities and not home many of the nights. Their love is forever. I have saved the best for...Xk) Extrapolation applied to terms xP through Xk F Operator on x G Iteration function Ik Identity matrix of rank k Solution of the problem or the limit

Remodeling a tissue: subtraction adds insight.

PubMed

Axelrod, Jeffrey D

2012-11-27

Sculpting a body plan requires both patterning of gene expression and translating that pattern into morphogenesis. Developmental biologists have made remarkable strides in understanding gene expression patterning, but despite a long history of fascination with the mechanics of morphogenesis, knowledge of how patterned gene expression drives the emergence of even simple shapes and forms has grown at a slower pace. The successful merging of approaches from cell biology, developmental biology, imaging, engineering, and mathematical and computational sciences is now accelerating progress toward a fuller and better integrated understanding of the forces shaping morphogenesis.

A simple mathematical model of gradual Darwinian evolution: emergence of a Gaussian trait distribution in adaptation along a fitness gradient.

PubMed

Biktashev, Vadim N

2014-04-01

We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while far from evolutionary stable equilibrium. The model admits exact analytical solution. In particular, Gaussian distribution of the trait emerges from generic initial conditions.

Functional diversity through the mean trait dissimilarity: resolving shortcomings with existing paradigms and algorithms.

PubMed

de Bello, Francesco; Carmona, Carlos P; Lepš, Jan; Szava-Kovats, Robert; Pärtel, Meelis

2016-04-01

While an increasing number of indices for estimating the functional trait diversity of biological communities are being proposed, there is a growing demand by ecologists to clarify their actual implications and simplify index selection. Several key indices relate to mean trait dissimilarity between species within biological communities. Among them, the most widely used include (a) the mean species pairwise dissimilarity (MPD) and (b) the Rao quadratic entropy (and related indices). These indices are often regarded as redundant and promote the unsubstantiated yet widely held view that Rao is a form of MPD. Worryingly, existing R functions also do not always simplify the use and differentiation of these indices. In this paper, we show various distinctions between these two indices that warrant mathematical and biological consideration. We start by showing an existing form of MPD that considers species abundances and is different from Rao both mathematically and conceptually. We then show that the mathematical relationship between MPD and Rao can be presented simply as Rao = MPD × Simpson, where the Simpson diversity index is defined as 1 - dominance. We further show that this relationship is maintained for both species abundances and presence/absence. This evidence dismantles the paradigm that the Rao diversity is an abundance-weighted form of MPD and indicates that both indices can differ substantially at low species diversities. We discuss the different interpretations of trait diversity patterns in biological communities provided by Rao and MPD and then provide a simple R function, called "melodic," which avoids the unintended results that arise from existing mainstream functions.

Games for Developing Mathematical Strategy.

ERIC Educational Resources Information Center

Williford, Harold

1992-01-01

The three middle school games described in this article focus on problem solving and mathematical reasoning skills. Included are Solomon's game, nine mens' morris, and nim-with-cards which all offer not only high student interest and strong mathematical value but also simple rules, ease of construction, and attractiveness for repeated play.…

Student Attrition in Mathematics E-Learning

ERIC Educational Resources Information Center

Smith, Glenn Gordon; Ferguson, David

2005-01-01

Qualitative studies indicate that mathematics does not work well in e-learning. The current study used quantitative methods to investigate more objectively the extent of problems with mathematics in e-learning. The authors used student attrition as a simple measure of student satisfaction and course viability in two studies, one investigating…

Connecting Dynamic Representations of Simple Mathematical Objects with the Construction and Exploration of Conic Sections

ERIC Educational Resources Information Center

Santos-Trigo, Manuel; Espinosa-Perez, Hugo; Reyes-Rodriguez, Aaron

2008-01-01

Different technological artefacts may offer distinct opportunities for students to develop resources and strategies to formulate, comprehend and solve mathematical problems. In particular, the use of dynamic software becomes relevant to assemble geometric configurations that may help students reconstruct and examine mathematical relationships. In…

Learning to Calculate and Learning Mathematics.

ERIC Educational Resources Information Center

Fearnley-Sander, Desmond

1980-01-01

A calculator solution of a simple computational problem is discussed with emphasis on its ramifications for the understanding of some fundamental theorems of pure mathematics and techniques of computing. (Author/MK)

The Topographical Mapping in Drosophila Central Complex Network and Its Signal Routing

PubMed Central

Chang, Po-Yen; Su, Ta-Shun; Shih, Chi-Tin; Lo, Chung-Chuan

2017-01-01

Neural networks regulate brain functions by routing signals. Therefore, investigating the detailed organization of a neural circuit at the cellular levels is a crucial step toward understanding the neural mechanisms of brain functions. To study how a complicated neural circuit is organized, we analyzed recently published data on the neural circuit of the Drosophila central complex, a brain structure associated with a variety of functions including sensory integration and coordination of locomotion. We discovered that, except for a small number of “atypical” neuron types, the network structure formed by the identified 194 neuron types can be described by only a few simple mathematical rules. Specifically, the topological mapping formed by these neurons can be reconstructed by applying a generation matrix on a small set of initial neurons. By analyzing how information flows propagate with or without the atypical neurons, we found that while the general pattern of signal propagation in the central complex follows the simple topological mapping formed by the “typical” neurons, some atypical neurons can substantially re-route the signal pathways, implying specific roles of these neurons in sensory signal integration. The present study provides insights into the organization principle and signal integration in the central complex. PMID:28443014

Using mathematical software to design power electronic converters

NASA Astrophysics Data System (ADS)

Hinov, Nikolay; Hranov, Tsveti

2017-12-01

In the paper is presented mathematical software, which was used for design of power electronic devices. Examined to different example, which are applied to designing electronic converters. In this way, it is possible to play different combinations of the circuit elements by simple means, thus optimizing according to certain criteria and limitations. Free software with a simple and intuitive interface is selected. No special user training is required to work with it and no further training is required. The use of mathematical software greatly facilitates the design, assists and makes it attractive and accessible to a wider range of students and specialists in power electronics training.

Relationships between autofocus methods for SAR and self-survey techniques for SONAR. [Synthetic Aperture Radar (SAR)

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

Wahl, D.E.; Jakowatz, C.V. Jr.; Ghiglia, D.C.

1991-01-01

Autofocus methods in SAR and self-survey techniques in SONAR have a common mathematical basis in that they both involve estimation and correction of phase errors introduced by sensor position uncertainties. Time delay estimation and correlation methods have been shown to be effective in solving the self-survey problem for towed SONAR arrays. Since it can be shown that platform motion errors introduce similar time-delay estimation problems in SAR imaging, the question arises as to whether such techniques could be effectively employed for autofocus of SAR imagery. With a simple mathematical model for motion errors in SAR, we will show why suchmore » correlation/time-delay techniques are not nearly as effective as established SAR autofocus algorithms such as phase gradient autofocus or sub-aperture based methods. This analysis forms an important bridge between signal processing methodologies for SAR and SONAR. 5 refs., 4 figs.« less

The Torsion of Members Having Sections Common in Aircraft Construction

NASA Technical Reports Server (NTRS)

Trayer, George W; March, H W

1930-01-01

Within recent years a great variety of approximate torsion formulas and drafting-room processes have been advocated. In some of these, especially where mathematical considerations are involved, the results are extremely complex and are not generally intelligible to engineers. The principal object of this investigation was to determine by experiment and theoretical investigation how accurate the more common of these formulas are and on what assumptions they are founded and, if none of the proposed methods proved to be reasonable accurate in practice, to produce simple, practical formulas from reasonably correct assumptions, backed by experiment. A second object was to collect in readily accessible form the most useful of known results for the more common sections. Formulas for all the important solid sections that have yielded to mathematical treatment are listed. Then follows a discussion of the torsion of tubular rods with formulas both rigorous and approximate.

Searching fundamental information in ordinary differential equations. Nondimensionalization technique.

PubMed

Sánchez Pérez, J F; Conesa, M; Alhama, I; Alhama, F; Cánovas, M

2017-01-01

Classical dimensional analysis and nondimensionalization are assumed to be two similar approaches in the search for dimensionless groups. Both techniques, simplify the study of many problems. The first approach does not need to know the mathematical model, being sufficient a deep understanding of the physical phenomenon involved, while the second one begins with the governing equations and reduces them to their dimensionless form by simple mathematical manipulations. In this work, a formal protocol is proposed for applying the nondimensionalization process to ordinary differential equations, linear or not, leading to dimensionless normalized equations from which the resulting dimensionless groups have two inherent properties: In one hand, they are physically interpreted as balances between counteracting quantities in the problem, and on the other hand, they are of the order of magnitude unity. The solutions provided by nondimensionalization are more precise in every case than those from dimensional analysis, as it is illustrated by the applications studied in this work.

The mathematical relationship between Zipf’s law and the hierarchical scaling law

NASA Astrophysics Data System (ADS)

Chen, Yanguang

2012-06-01

The empirical studies of city-size distribution show that Zipf's law and the hierarchical scaling law are linked in many ways. The rank-size scaling and hierarchical scaling seem to be two different sides of the same coin, but their relationship has never been revealed by strict mathematical proof. In this paper, the Zipf's distribution of cities is abstracted as a q-sequence. Based on this sequence, a self-similar hierarchy consisting of many levels is defined and the numbers of cities in different levels form a geometric sequence. An exponential distribution of the average size of cities is derived from the hierarchy. Thus we have two exponential functions, from which follows a hierarchical scaling equation. The results can be statistically verified by simple mathematical experiments and observational data of cities. A theoretical foundation is then laid for the conversion from Zipf's law to the hierarchical scaling law, and the latter can show more information about city development than the former. Moreover, the self-similar hierarchy provides a new perspective for studying networks of cities as complex systems. A series of mathematical rules applied to cities such as the allometric growth law, the 2n principle and Pareto's law can be associated with one another by the hierarchical organization.

Using emergent order to shape a space society

NASA Technical Reports Server (NTRS)

Graps, Amara L.

1993-01-01

A fast-growing movement in the scientific community is reshaping the way that we view the world around us. The short-hand name for this movement is 'chaos'. Chaos is a science of the global, nonlinear nature of systems. The center of this set of ideas is that simple, deterministic systems can breed complexity. Systems as complex as the human body, ecology, the mind or a human society. While it is true that simple laws can breed complexity, the other side is that complex systems can breed order. It is the latter that I will focus on in this paper. In the past, nonlinear was nearly synonymous with unsolvable because no general analytic solutions exist. Mathematically, an essential difference exists between linear and nonlinear systems. For linear systems, you just break up the complicated system into many simple pieces and patch together the separated solutions for each piece to form a solution to the full problem. In contrast, solutions to a nonlinear system cannot be added to form a new solution. The system must be treated in its full complexity. While it is true that no general analytical approach exists for reducing a complex system such as a society, it can be modeled. The technical involves a mathematical construct called phase space. In this space stable structures can appear which I use as analogies for the stable structures that appear in a complex system such as an ecology, the mind or a society. The common denominator in all of these systems is that they rely on a process called feedback loops. Feedback loops link the microscopic (individual) parts to the macroscopic (global) parts. The key, then, in shaping a space society, is in effectively using feedback loops. This paper will illustrate how one can model a space society by using methods that chaoticists have developed over the last hundred years. And I will show that common threads exist in the modeling of biological, economical, philosophical, and sociological systems.

Changing Beliefs about Teaching in Large Undergraduate Mathematics Classes

ERIC Educational Resources Information Center

Kensington-Miller, Barbara; Sneddon, Jamie; Yoon, Caroline; Stewart, Sepideh

2013-01-01

Many lecturers use teacher-centred styles of teaching in large undergraduate mathematics classes, often believing in the effectiveness of such pedagogy. Changing these beliefs about how mathematics should be taught is not a simple process and many academic staff are reluctant to change their ways of lecturing due to tradition and ease. This study…

And So It Grows: Using a Computer-Based Simulation of a Population Growth Model to Integrate Biology & Mathematics

ERIC Educational Resources Information Center

Street, Garrett M.; Laubach, Timothy A.

2013-01-01

We provide a 5E structured-inquiry lesson so that students can learn more of the mathematics behind the logistic model of population biology. By using models and mathematics, students understand how population dynamics can be influenced by relatively simple changes in the environment.

A Simple Model for a SARS Epidemic

ERIC Educational Resources Information Center

Ang, Keng Cheng

2004-01-01

In this paper, we examine the use of an ordinary differential equation in modelling the SARS outbreak in Singapore. The model provides an excellent example of using mathematics in a real life situation. The mathematical concepts involved are accessible to students with A level Mathematics backgrounds. Data for the SARS epidemic in Singapore are…

Math in Plain English: Literacy Strategies for the Mathematics Classroom

ERIC Educational Resources Information Center

Benjamin, Amy

2011-01-01

Do word problems and math vocabulary confuse students in your mathematics classes? Do simple keywords like "value" and "portion" seem to mislead them? Many words that students already know can have a different meaning in mathematics. To grasp that difference, students need to connect English literacy skills to math. Successful students speak,…

The NCTM High School Curriculum Project: Why It Matters to You

ERIC Educational Resources Information Center

Martin, W. Gary

2009-01-01

This article discusses "Focus in High School Mathematics: Reasoning and Sense Making", a new (2009) publication of the National Council of Teachers of Mathematics (NCTM). Its message is simple: Reasoning and sense making provide a focus for high school mathematics that will give students a foundation for their future success. The publication…

BOOK REVIEW: Symmetry and the Monster: One of the Greatest Quests of Mathematics

NASA Astrophysics Data System (ADS)

Szabo, R. J.

2007-04-01

The book Symmetry and the Monster: One of the Greatest Quests of Mathematics describes historical events leading up to the discovery of the Monster sporadic group, the largest simple sporadic group. It also expounds the significance and deep relationships between this group and other areas of mathematics and theoretical physics. It begins, in the prologue, with a nice overview of some of the mathematical drama surrounding the discovery of the Monster and its subsequent relationship to number theory (the so-called Moonshine conjectures). From a historical perspective, the book traces back to the roots of group theory, Galois theory, and steadily runs through time through the many famous mathematicians who contributed to group theory, including Lie, Killing and Cartan. Throughout, the author has provided a very nice and deep insight into the sociological and scientific problems at the time, and gives the reader a very prominent inside view of the real people behind the mathematics. The book should be an enjoyable read to anyone with an interest in the history of mathematics. For the non-mathematician the book makes a good, and mostly successful, attempt at being non-technical. Technical mathematical jargon is replaced with more heuristic, intuitive terminology, making the mathematical descriptions in the book fairly easy going. A glossary\\hspace{0.25pc} of\\hspace{0.25pc} terminology for noindent the more scientifically inclined is included in various footnotes throughout the book and in a comprehensive listing at the end of the book. Some more technical material is also included in the form of appendices at the end of the book. Some aspects of physics are also explained in a simple, intuitive way. The author further attempts at various places to give the non-specialist a glimpse into what mathematical proof is all about, and explains the difficulties and technicalities involved in this very nicely (for instance, he mentions the various 100+ page articles that appeared in the hey-day of finite group theory, indicating the enormous technical nature of the subject). The book nicely paints a dramatic landscape leading up to the discovery of the Monster group, and the problems that remain to this day in trying to understand its significance. One can really take from this book a feel of the mathematics leading up to its appearance, and the importance of the classification problem which was responsible for this. One also really gets an appreciation of the efforts and commitments of the mathematicians who contributed to the subject. All in all, this book achieves a nice balance between providing a beautiful historical account of group theory, and explaining the classification problem for finite groups in a way that is accessible to non-scientists. This should prove to be a good read for both the layperson interested in mathematics or mathematical physics, and also both mathematicians and physicists alike.

Method for the simulation of blood platelet shape and its evolution during activation

PubMed Central

Muliukov, Artem R.; Litvinenko, Alena L.; Nekrasov, Vyacheslav M.; Chernyshev, Andrei V.; Maltsev, Valeri P.

2018-01-01

We present a simple physically based quantitative model of blood platelet shape and its evolution during agonist-induced activation. The model is based on the consideration of two major cytoskeletal elements: the marginal band of microtubules and the submembrane cortex. Mathematically, we consider the problem of minimization of surface area constrained to confine the marginal band and a certain cellular volume. For resting platelets, the marginal band appears as a peripheral ring, allowing for the analytical solution of the minimization problem. Upon activation, the marginal band coils out of plane and forms 3D convoluted structure. We show that its shape is well approximated by an overcurved circle, a mathematical concept of closed curve with constant excessive curvature. Possible mechanisms leading to such marginal band coiling are discussed, resulting in simple parametric expression for the marginal band shape during platelet activation. The excessive curvature of marginal band is a convenient state variable which tracks the progress of activation. The cell surface is determined using numerical optimization. The shapes are strictly mathematically defined by only three parameters and show good agreement with literature data. They can be utilized in simulation of platelets interaction with different physical fields, e.g. for the description of hydrodynamic and mechanical properties of platelets, leading to better understanding of platelets margination and adhesion and thrombus formation in blood flow. It would also facilitate precise characterization of platelets in clinical diagnosis, where a novel optical model is needed for the correct solution of inverse light-scattering problem. PMID:29518073

Mathematical neuroscience: from neurons to circuits to systems.

PubMed

Gutkin, Boris; Pinto, David; Ermentrout, Bard

2003-01-01

Applications of mathematics and computational techniques to our understanding of neuronal systems are provided. Reduction of membrane models to simplified canonical models demonstrates how neuronal spike-time statistics follow from simple properties of neurons. Averaging over space allows one to derive a simple model for the whisker barrel circuit and use this to explain and suggest several experiments. Spatio-temporal pattern formation methods are applied to explain the patterns seen in the early stages of drug-induced visual hallucinations.

Reciprocal Relationships between Mathematics Anxiety and Attitude towards Mathematics in Elementary Students

ERIC Educational Resources Information Center

Haciomeroglu, Guney

2017-01-01

This current study examined the reciprocal relationship between anxiety and attitude towards mathematics in elementary students. Two instruments (attitudes towards mathematics inventory short form [ATMI-Short Form] and the Revised Fennema-Sherman Mathematics Anxiety Scale [Revised-FSMAS]) were administered to 310 fourth grade elementary students.…

High School Forum: Brief Introduction to the Three Laws of Thermodynamics

ERIC Educational Resources Information Center

Herron, J. Dudley

1975-01-01

Because thermodynamics is usually presented in a highly mathematical context, many students fail to comprehend even its intuitive aspects. Provides simple explanations, without complicated mathematics, for the three thermodynamics laws. (MLH)

Zonal and tesseral harmonic coefficients for the geopotential function, from zero to 18th order

NASA Technical Reports Server (NTRS)

Kirkpatrick, J. C.

1976-01-01

Zonal and tesseral harmonic coefficients for the geopotential function are usually tabulated in normalized form to provide immediate information as to the relative significance of the coefficients in the gravity model. The normalized form of the geopotential coefficients cannot be used for computational purposes unless the gravity model has been modified to receive them. This modification is usually not done because the absolute or unnormalized form of the coefficients can be obtained from the simple mathematical relationship that relates the two forms. This computation can be quite tedious for hand calculation, especially for the higher order terms, and can be costly in terms of storage and execution time for machine computation. In this report, zonal and tesseral harmonic coefficients for the geopotential function are tabulated in absolute or unnormalized form. The report is designed to be used as a ready reference for both hand and machine calculation to save the user time and effort.

A survey on the effectiveness of using GeoGebra software towards lecturers' conceptual knowledge and procedural mathematics

NASA Astrophysics Data System (ADS)

Wan Salleh, Masturah; Sulaiman, Hajar

2013-04-01

The use of technology in the teaching of mathematics at the university level has long been introduced; but many among the lecturers, especially those that have taught for many years, still opt for a traditional teaching method, that is, by lecture talk. One reason is that lecturers themselves were not exposed to the technologies available and how it can assist in the teaching and learning procedures (T&L) in mathematics. GeoGebra is a mathematical software which is open and free and has just recently been introduced in Malaysia. Compared with the software Cabri Geometry and Geometer's Sketchpad (GSP), which only focus on geometry, GeoGebra is able to connect geometry, algebra and numerical representation. Realizing this, the researchers have conducted a study to expose the university lecturers on the use of GeoGebra in T&L. The researchers chose to do the research on mathematics lecturers at the Department of Computer Science and Mathematics (JSKM), Universiti Teknologi Mara (UiTM), Penang. The objective of this study is to determine whether an exposure to GeoGebra software can affect the conceptual knowledge and procedural teaching of mathematics at the university level. This study is a combination of descriptive and qualitative. One session was conducted in an open workshop for all the 45 lecturers. From that total, four people were selected as a sample. The sample was selected by using a simple random sampling method. This study used materials in the form of modules during the workshop. In terms of conceptual knowledge, the results showed that the GeoGebra software is appropriate, relevant and highly effective for in-depth understanding of the selected topics. While the procedural aspects of teaching, it can be one of the teaching aids and considerably facilitate the lecturers.

Individualized Math Problems in Simple Equations. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this volume require solution of linear equations, systems…

Interactions between Language and Mathematics with Deaf Students: Defining the "Language-Mathematics" Equation.

ERIC Educational Resources Information Center

Hillegeist, Eleanor; Epstein, Kenneth

The study examined the relationship between language and mathematics with 11 classes of deaf students taking Algebra 1 or Algebra 2 at the Gallaudet University School of Preparatory Studies. Specifically, the study attempted to predict the difficulty of a variety of relatively simple algebra problems based on the abstractness of the math and the…

Models of Individual Trajectories in Computer-Assisted Instruction for Deaf Students. Technical Report No. 214.

ERIC Educational Resources Information Center

Suppes, P.; And Others

From some simple and schematic assumptions about information processing, a stochastic differential equation is derived for the motion of a student through a computer-assisted elementary mathematics curriculum. The mathematics strands curriculum of the Institute for Mathematical Studies in the Social Sciences is used to test: (1) the theory and (2)…

Incorporating Learning Motivation and Self-Concept in Mathematical Communicative Ability

ERIC Educational Resources Information Center

Rajagukguk, Waminton

2016-01-01

This research is trying to determine of the mathematical concepts, instead by integrating the learning motivation (X[subscript 1]) and self-concept (X[subscript 2]) can contribute to the mathematical communicative ability (Y). The test instruments showed the following results: (1) simple regressive equation Y on X[subscript 1] was Y = 32.891 +…

Modeling of the minimum variable blank holder force based on forming limit diagram (FLD) in deep drawing process

NASA Astrophysics Data System (ADS)

Candra, S.; Batan, I. M. L.; Berata, W.; Pramono, A. S.

2017-11-01

This paper presents the mathematical approach of minimum blank holder force to prevent wrinkling in deep drawing process of the cylindrical cup. Based on the maximum of minor-major strain ratio, the slab method was applied to determine the modeling of minimum variable blank holder force (VBHF) and it compared to FE simulation. The Tin steel sheet of T4-CA grade, with the thickness of 0.2 mm was used in this study. The modeling of minimum VBHF can be used as a simple reference to prevent wrinkling in deep drawing.

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.

Modeling RNA interference in mammalian cells

PubMed Central

2011-01-01

Background RNA interference (RNAi) is a regulatory cellular process that controls post-transcriptional gene silencing. During RNAi double-stranded RNA (dsRNA) induces sequence-specific degradation of homologous mRNA via the generation of smaller dsRNA oligomers of length between 21-23nt (siRNAs). siRNAs are then loaded onto the RNA-Induced Silencing multiprotein Complex (RISC), which uses the siRNA antisense strand to specifically recognize mRNA species which exhibit a complementary sequence. Once the siRNA loaded-RISC binds the target mRNA, the mRNA is cleaved and degraded, and the siRNA loaded-RISC can degrade additional mRNA molecules. Despite the widespread use of siRNAs for gene silencing, and the importance of dosage for its efficiency and to avoid off target effects, none of the numerous mathematical models proposed in literature was validated to quantitatively capture the effects of RNAi on the target mRNA degradation for different concentrations of siRNAs. Here, we address this pressing open problem performing in vitro experiments of RNAi in mammalian cells and testing and comparing different mathematical models fitting experimental data to in-silico generated data. We performed in vitro experiments in human and hamster cell lines constitutively expressing respectively EGFP protein or tTA protein, measuring both mRNA levels, by quantitative Real-Time PCR, and protein levels, by FACS analysis, for a large range of concentrations of siRNA oligomers. Results We tested and validated four different mathematical models of RNA interference by quantitatively fitting models' parameters to best capture the in vitro experimental data. We show that a simple Hill kinetic model is the most efficient way to model RNA interference. Our experimental and modeling findings clearly show that the RNAi-mediated degradation of mRNA is subject to saturation effects. Conclusions Our model has a simple mathematical form, amenable to analytical investigations and a small set of parameters with an intuitive physical meaning, that makes it a unique and reliable mathematical tool. The findings here presented will be a useful instrument for better understanding RNAi biology and as modelling tool in Systems and Synthetic Biology. PMID:21272352

A simple mathematical method to estimate ammonia emission from in-house windrowing of poultry litter.

PubMed

Ro, Kyoung S; Szogi, Ariel A; Moore, Philip A

2018-05-12

In-house windrowing between flocks is an emerging sanitary management practice to partially disinfect the built-up litter in broiler houses. However, this practice may also increase ammonia (NH 3 ) emission from the litter due to the increase in litter temperature. The objectives of this study were to develop mathematical models to estimate NH 3 emission rates from broiler houses practicing in-house windrowing between flocks. Equations to estimate mass-transfer areas form different shapes windrowed litter (triangular, rectangular, and semi-cylindrical prisms) were developed. Using these equations, the heights of windrows yielding the smallest mass-transfer area were estimated. Smaller mass-transfer area is preferred as it reduces both emission rates and heat loss. The heights yielding the minimum mass-transfer area were 0.8 and 0.5 m for triangular and rectangular windrows, respectively. Only one height (0.6 m) was theoretically possible for semi-cylindrical windrows because the base and the height were not independent. Mass-transfer areas were integrated with published process-based mathematical models to estimate the total house NH 3 emission rates during in-house windrowing of poultry litter. The NH 3 emission rate change calculated from the integrated model compared well with the observed values except for the very high NH 3 initial emission rate from mechanically disturbing the litter to form the windrows. This approach can be used to conveniently estimate broiler house NH 3 emission rates during in-house windrowing between flocks by simply measuring litter temperatures.

Modeling Unipolar and Bipolar Stimulation of Cardiac Tissue

NASA Astrophysics Data System (ADS)

Galappaththige, Suran Kokila

Out of all non-communicable diseases, heart diseases have become the leading cause of death and disease burden worldwide. Heart diseases describe a variety of circumstances that affect your heart. One common condition is the heart rhythm problem often called an arrhythmia. The rhythmic beating of the human heart can be altered due to various reasons. This inconsistency in beating can lead to a lethal form of arrhythmia that we call ventricular fibrillation. We treat fibrillation by applying an electrical shock to the heart using a unipolar electrode or bipolar electrodes. To build better pace makers and defibrillators, we must understand how the heart responds to an electrical shock. One way to study cardiac arrhythmias is using a mathematical model. The computational biology of the heart is one of the most important recent applications of mathematical modeling in biology. By using mathematical models, we can understand the mechanisms responsible of the heart's electrical behavior. We investigate if the time-independent, inwardly rectifying potassium current through the cell membrane inhibits the hyperpolarization after a stimulus electrical pulse is applied to the resting heart tissue. The inhibition of hyperpolarization is due to long duration stimulus pulses, but not short duration pulses. We also investigate the minimum conditions required for the dip in strength-interval curves using a simple but not so simple parsimonious ionic current model coupled with the bidomain model. Unipolar anodal stimulations still results in the dip in the strength-interval curves and this explains the minimum conditions for this phenomenon to occur. Bipolar stimulation of cardiac tissue using the parsimonious ionic current model revels that the strength-interval curves are sensitive to the separation between electrodes and the electrode orientation relative to the fiber direction. One of the ionic currents in the parsimonious ionic current model mimics the time-independent inwardly rectifying potassium current and this study examines the importance of this current in mathematical models that describe cardiac electrical behavior.

What Mathematics Education Can Learn from Art: The Assumptions, Values, and Vision of Mathematics Education

ERIC Educational Resources Information Center

Dietiker, Leslie

2015-01-01

Elliot Eisner proposed that educational challenges can be met by applying an artful lens. This article draws from Eisner's proposal to consider the assumptions, values, and vision of mathematics education by theorizing mathematics curriculum as an art form. By conceptualizing mathematics curriculum (both in written and enacted forms) as stories…

The Use of Digital Technology in Finding Multiple Paths to Solve and Extend an Equilateral Triangle Task

ERIC Educational Resources Information Center

Santos-Trigo, Manuel; Reyes-Rodriguez, Aaron

2016-01-01

Mathematical tasks are crucial elements for teachers to orient, foster and assess students' processes to comprehend and develop mathematical knowledge. During the process of working and solving a task, searching for or discussing multiple solution paths becomes a powerful strategy for students to engage in mathematical thinking. A simple task that…

Teacher and Student Use of Gesture and Access to Secondary Mathematics for Students with Learning Disabilities: An Exploratory Study

ERIC Educational Resources Information Center

Hord, Casey; Marita, Samantha; Walsh, Jennifer B.; Tomaro, Taylor-Marie; Gordon, Kiyana; Saldanha, Rene L.

2016-01-01

The researchers conducted an exploratory qualitative case study to describe the gesturing processes of tutors and students when engaging in secondary mathematics. The use of gestures ranged in complexity from simple gestures, such as pointing and moving the pointing finger in an arching motion to demonstrate mathematics relationships within…

Mathematics, thermodynamics, and modeling to address ten common misconceptions about protein structure, folding, and stability.

PubMed

Robic, Srebrenka

2010-01-01

To fully understand the roles proteins play in cellular processes, students need to grasp complex ideas about protein structure, folding, and stability. Our current understanding of these topics is based on mathematical models and experimental data. However, protein structure, folding, and stability are often introduced as descriptive, qualitative phenomena in undergraduate classes. In the process of learning about these topics, students often form incorrect ideas. For example, by learning about protein folding in the context of protein synthesis, students may come to an incorrect conclusion that once synthesized on the ribosome, a protein spends its entire cellular life time in its fully folded native confirmation. This is clearly not true; proteins are dynamic structures that undergo both local fluctuations and global unfolding events. To prevent and address such misconceptions, basic concepts of protein science can be introduced in the context of simple mathematical models and hands-on explorations of publicly available data sets. Ten common misconceptions about proteins are presented, along with suggestions for using equations, models, sequence, structure, and thermodynamic data to help students gain a deeper understanding of basic concepts relating to protein structure, folding, and stability.

A mathematical function for the description of nutrient-response curve

PubMed Central

Ahmadi, Hamed

2017-01-01

Several mathematical equations have been proposed to modeling nutrient-response curve for animal and human justified on the goodness of fit and/or on the biological mechanism. In this paper, a functional form of a generalized quantitative model based on Rayleigh distribution principle for description of nutrient-response phenomena is derived. The three parameters governing the curve a) has biological interpretation, b) may be used to calculate reliable estimates of nutrient response relationships, and c) provide the basis for deriving relationships between nutrient and physiological responses. The new function was successfully applied to fit the nutritional data obtained from 6 experiments including a wide range of nutrients and responses. An evaluation and comparison were also done based simulated data sets to check the suitability of new model and four-parameter logistic model for describing nutrient responses. This study indicates the usefulness and wide applicability of the new introduced, simple and flexible model when applied as a quantitative approach to characterizing nutrient-response curve. This new mathematical way to describe nutritional-response data, with some useful biological interpretations, has potential to be used as an alternative approach in modeling nutritional responses curve to estimate nutrient efficiency and requirements. PMID:29161271

Decomposition-Based Failure Mode Identification Method for Risk-Free Design of Large Systems

NASA Technical Reports Server (NTRS)

Tumer, Irem Y.; Stone, Robert B.; Roberts, Rory A.; Clancy, Daniel (Technical Monitor)

2002-01-01

When designing products, it is crucial to assure failure and risk-free operation in the intended operating environment. Failures are typically studied and eliminated as much as possible during the early stages of design. The few failures that go undetected result in unacceptable damage and losses in high-risk applications where public safety is of concern. Published NASA and NTSB accident reports point to a variety of components identified as sources of failures in the reported cases. In previous work, data from these reports were processed and placed in matrix form for all the system components and failure modes encountered, and then manipulated using matrix methods to determine similarities between the different components and failure modes. In this paper, these matrices are represented in the form of a linear combination of failures modes, mathematically formed using Principal Components Analysis (PCA) decomposition. The PCA decomposition results in a low-dimensionality representation of all failure modes and components of interest, represented in a transformed coordinate system. Such a representation opens the way for efficient pattern analysis and prediction of failure modes with highest potential risks on the final product, rather than making decisions based on the large space of component and failure mode data. The mathematics of the proposed method are explained first using a simple example problem. The method is then applied to component failure data gathered from helicopter, accident reports to demonstrate its potential.

A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks

PubMed Central

Schaffer, Evan S.; Ostojic, Srdjan; Abbott, L. F.

2013-01-01

Firing-rate models provide an attractive approach for studying large neural networks because they can be simulated rapidly and are amenable to mathematical analysis. Traditional firing-rate models assume a simple form in which the dynamics are governed by a single time constant. These models fail to replicate certain dynamic features of populations of spiking neurons, especially those involving synchronization. We present a complex-valued firing-rate model derived from an eigenfunction expansion of the Fokker-Planck equation and apply it to the linear, quadratic and exponential integrate-and-fire models. Despite being almost as simple as a traditional firing-rate description, this model can reproduce firing-rate dynamics due to partial synchronization of the action potentials in a spiking model, and it successfully predicts the transition to spike synchronization in networks of coupled excitatory and inhibitory neurons. PMID:24204236

Galileo's Mathematical Language of Nature.

ERIC Educational Resources Information Center

Forinash, Kyle; Rumsey, William; Lang, Chris

2000-01-01

Undergraduate students do not always make a clear distinction between physics and mathematics, particularly early in their studies. Offers a simple historical example and show how it can be used to illustrate some of the important differences and relationships between the two. (Author/SAH)

Origami, geometry and art

NASA Astrophysics Data System (ADS)

Wares, Arsalan; Elstak, Iwan

2017-02-01

The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra and geometry, like other branches of mathematics, are interrelated.

PENDISC: a simple method for constructing a mathematical model from time-series data of metabolite concentrations.

PubMed

Sriyudthsak, Kansuporn; Iwata, Michio; Hirai, Masami Yokota; Shiraishi, Fumihide

2014-06-01

The availability of large-scale datasets has led to more effort being made to understand characteristics of metabolic reaction networks. However, because the large-scale data are semi-quantitative, and may contain biological variations and/or analytical errors, it remains a challenge to construct a mathematical model with precise parameters using only these data. The present work proposes a simple method, referred to as PENDISC (Parameter Estimation in a N on- DImensionalized S-system with Constraints), to assist the complex process of parameter estimation in the construction of a mathematical model for a given metabolic reaction system. The PENDISC method was evaluated using two simple mathematical models: a linear metabolic pathway model with inhibition and a branched metabolic pathway model with inhibition and activation. The results indicate that a smaller number of data points and rate constant parameters enhances the agreement between calculated values and time-series data of metabolite concentrations, and leads to faster convergence when the same initial estimates are used for the fitting. This method is also shown to be applicable to noisy time-series data and to unmeasurable metabolite concentrations in a network, and to have a potential to handle metabolome data of a relatively large-scale metabolic reaction system. Furthermore, it was applied to aspartate-derived amino acid biosynthesis in Arabidopsis thaliana plant. The result provides confirmation that the mathematical model constructed satisfactorily agrees with the time-series datasets of seven metabolite concentrations.

Local Normative Data on easyCBM[R] Reading and Mathematics: Fall 2009. Technical Report # 0918

ERIC Educational Resources Information Center

Tindal, Gerald; Alonzo, Julie; Anderson, Daniel

2009-01-01

We developed equivalent, alternate forms of easyCBM[R] in reading (n=20 forms) and mathematics (n=13 forms) with different skills reflective of the National Reading Panel (NRP) and the National Council of Teachers of Mathematics (NCTM), respectively. We then took three forms to use as screening measures in the fall, winter, and spring so educators…

American Mathematics from 1940 to the Day Before Yesterday

ERIC Educational Resources Information Center

Ewing, J. H.; And Others

1976-01-01

Ten recent results in pure mathematics are described, covering the continuum hypothesis, Diophantine equations, simple groups, resolution of singularities, Weil conjectures, Lie groups, Poincare conjecture, exotic spheres, differential equations, and the index theorem. Proofs are omitted, but references are provided. (DT)

Mathematics forBioMathics.

PubMed

Hoffman, William C

2013-09-01

The essence of biological phenomena appears in form and function: "Form follows function." Mathematically, G × M → M, where G contains the parameters of the action and M is the form. The Mathematics for this purpose is largely available and is well described in a recent book (Felix et al., 2008). Copyright © 2013. Published by Elsevier Ltd.

THE MATHEMATICAL ANALYSIS OF A SIMPLE DUEL

DTIC Science & Technology

The principles and techniques of simple Markov processes are used to analyze a simple duel to determine the limiting state probabilities (i.e., the...probabilities of occurrence of the various possible outcomes of the duel ). The duel is one in which A fires at B at a rate of r sub A shots per minute

The molecular and mathematical basis of Waddington's epigenetic landscape: a framework for post-Darwinian biology?

PubMed

Huang, Sui

2012-02-01

The Neo-Darwinian concept of natural selection is plausible when one assumes a straightforward causation of phenotype by genotype. However, such simple 1:1 mapping must now give place to the modern concepts of gene regulatory networks and gene expression noise. Both can, in the absence of genetic mutations, jointly generate a diversity of inheritable randomly occupied phenotypic states that could also serve as a substrate for natural selection. This form of epigenetic dynamics challenges Neo-Darwinism. It needs to incorporate the non-linear, stochastic dynamics of gene networks. A first step is to consider the mathematical correspondence between gene regulatory networks and Waddington's metaphoric 'epigenetic landscape', which actually represents the quasi-potential function of global network dynamics. It explains the coexistence of multiple stable phenotypes within one genotype. The landscape's topography with its attractors is shaped by evolution through mutational re-wiring of regulatory interactions - offering a link between genetic mutation and sudden, broad evolutionary changes. Copyright © 2012 WILEY Periodicals, Inc.

Microwave heating and joining of ceramic cylinders: A mathematical model

NASA Technical Reports Server (NTRS)

Booty, Michael R.; Kriegsmann, Gregory A.

1994-01-01

A thin cylindrical ceramic sample is placed in a single mode microwave applicator in such a way that the electric field strength is allowed to vary along its axis. The sample can either be a single rod or two rods butted together. We present a simple mathematical model which describes the microwave heating process. It is built on the assumption that the Biot number of the material is small, and that the electric field is known and uniform throughout the cylinder's cross-section. The model takes the form of a nonlinear parabolic equation of reaction-diffusion type, with a spatially varying reaction term that corresponds to the spatial variation of the electromagnetic field strength in the waveguide. The equation is analyzed and a solution is found which develops a hot spot near the center of the cylindrical sample and which then propagates outwards until it stabilizes. The propagation and stabilization phenomenon concentrates the microwave energy in a localized region about the center where elevated temperatures may be desirable.

Mathematics anxiety affects counting but not subitizing during visual enumeration.

PubMed

Maloney, Erin A; Risko, Evan F; Ansari, Daniel; Fugelsang, Jonathan

2010-02-01

Individuals with mathematics anxiety have been found to differ from their non-anxious peers on measures of higher-level mathematical processes, but not simple arithmetic. The current paper examines differences between mathematics anxious and non-mathematics anxious individuals in more basic numerical processing using a visual enumeration task. This task allows for the assessment of two systems of basic number processing: subitizing and counting. Mathematics anxious individuals, relative to non-mathematics anxious individuals, showed a deficit in the counting but not in the subitizing range. Furthermore, working memory was found to mediate this group difference. These findings demonstrate that the problems associated with mathematics anxiety exist at a level more basic than would be predicted from the extant literature. Copyright 2009 Elsevier B.V. All rights reserved.

Sharing Teaching Ideas.

ERIC Educational Resources Information Center

Tunis, Harry B., Ed.

1993-01-01

Two teaching ideas integrate mathematics and business. The first discusses consumer deception by such ploys as false bottoms on containers and simple rather than compound interest on investments. The second describes a business mathematics course in which students are motivated by contracting for certain jobs and potential bonuses. (MDH)

The Nature of Feedback Given to Elementary Student Teachers from University Supervisors after Observations of Mathematics Lessons

ERIC Educational Resources Information Center

Schwartz, Catherine; Walkowiak, Temple A.; Poling, Lisa; Richardson, Kerri; Polly, Drew

2018-01-01

This research explores the frequency and nature of mathematics-specific feedback given to elementary student teachers by university supervisors across a collection of post-lesson observation forms. Approximately one-third of the forms (n = 250) analysed from five large universities had no comments related to mathematics. Forms that did have…

Design of two blackbody sources for millimeter and sub-millimeter wave Fourier transform spectrometry

NASA Astrophysics Data System (ADS)

Colin, Angel

2014-03-01

This paper describes an experimental setup for the spectral calibration of bolometric detectors used in radioastronomy. The system is composed of a Martin-Puplett interferometer with two identical artificial blackbody sources operating in the vacuum mode at 77 K and 300 K simultaneously. One source is integrated into a liquid nitrogen cryostat, and the other one into a vacuum chamber at room temperature. The sources were designed with a combination of conical with cylindrical geometries thus forming an orthogonal configuration to match the internal optics of the interfermometer. With a simple mathematical model we estimated emissivities of ε 0.995 for each source.

Genetic models of homosexuality: generating testable predictions

PubMed Central

Gavrilets, Sergey; Rice, William R

2006-01-01

Homosexuality is a common occurrence in humans and other species, yet its genetic and evolutionary basis is poorly understood. Here, we formulate and study a series of simple mathematical models for the purpose of predicting empirical patterns that can be used to determine the form of selection that leads to polymorphism of genes influencing homosexuality. Specifically, we develop theory to make contrasting predictions about the genetic characteristics of genes influencing homosexuality including: (i) chromosomal location, (ii) dominance among segregating alleles and (iii) effect sizes that distinguish between the two major models for their polymorphism: the overdominance and sexual antagonism models. We conclude that the measurement of the genetic characteristics of quantitative trait loci (QTLs) found in genomic screens for genes influencing homosexuality can be highly informative in resolving the form of natural selection maintaining their polymorphism. PMID:17015344

Shape Control in Multivariate Barycentric Rational Interpolation

NASA Astrophysics Data System (ADS)

Nguyen, Hoa Thang; Cuyt, Annie; Celis, Oliver Salazar

2010-09-01

The most stable formula for a rational interpolant for use on a finite interval is the barycentric form [1, 2]. A simple choice of the barycentric weights ensures the absence of (unwanted) poles on the real line [3]. In [4] we indicate that a more refined choice of the weights in barycentric rational interpolation can guarantee comonotonicity and coconvexity of the rational interpolant in addition to a polefree region of interest. In this presentation we generalize the above to the multivariate case. We use a product-like form of univariate barycentric rational interpolants and indicate how the location of the poles and the shape of the function can be controlled. This functionality is of importance in the construction of mathematical models that need to express a certain trend, such as in probability distributions, economics, population dynamics, tumor growth models etc.

Calibration artefacts in radio interferometry - II. Ghost patterns for irregular arrays

NASA Astrophysics Data System (ADS)

Wijnholds, S. J.; Grobler, T. L.; Smirnov, O. M.

2016-04-01

Calibration artefacts, like the self-calibration bias, usually emerge when data are calibrated using an incomplete sky model. In the first paper of this series, in which we analysed calibration artefacts in data from the Westerbork Synthesis Radio Telescope, we showed that these artefacts take the form of spurious positive and negative sources, which we refer to as ghosts or ghost sources. We also developed a mathematical framework with which we could predict the ghost pattern of an east-west interferometer for a simple two-source test case. In this paper, we extend our analysis to more general array layouts. This provides us with a useful method for the analysis of ghosts that we refer to as extrapolation. Combining extrapolation with a perturbation analysis, we are able to (1) analyse the ghost pattern for a two-source test case with one modelled and one unmodelled source for an arbitrary array layout, (2) explain why some ghosts are brighter than others, (3) define a taxonomy allowing us to classify the different ghosts, (4) derive closed form expressions for the fluxes and positions of the brightest ghosts, and (5) explain the strange two-peak structure with which some ghosts manifest during imaging. We illustrate our mathematical predictions using simulations of the KAT-7 (seven-dish Karoo Array Telescope) array. These results show the explanatory power of our mathematical model. The insights gained in this paper provide a solid foundation to study calibration artefacts in arbitrary, I.e. more complicated than the two-source example discussed here, incomplete sky models or full synthesis observations including direction-dependent effects.

Ancient Paradoxes Can Extend Mathematical Thinking

ERIC Educational Resources Information Center

Czocher, Jennifer A.; Moss, Diana L.

2017-01-01

This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…

Active Learning Strategies for the Mathematics Classroom

ERIC Educational Resources Information Center

Kerrigan, John

2018-01-01

Active learning involves students engaging with course content beyond lecture: through writing, applets, simulations, games, and more (Prince, 2004). As mathematics is often viewed as a subject area that is taught using more traditional methods (Goldsmith & Mark, 1999), there are actually many simple ways to make undergraduate mathematics…

Sunspots and Their Simple Harmonic Motion

ERIC Educational Resources Information Center

Ribeiro, C. I.

2013-01-01

In this paper an example of a simple harmonic motion, the apparent motion of sunspots due to the Sun's rotation, is described, which can be used to teach this subject to high-school students. Using real images of the Sun, students can calculate the star's rotation period with the simple harmonic motion mathematical expression.

The Parker-Sochacki Method--A Powerful New Method for Solving Systems of Differential Equations

NASA Astrophysics Data System (ADS)

Rudmin, Joseph W.

2001-04-01

The Parker-Sochacki Method--A Powerful New Method for Solving Systems of Differential Equations Joseph W. Rudmin (Physics Dept, James Madison University) A new system of solving systems of differential equations will be presented, which has been developed by J. Edgar Parker and James Sochacki, of the James Madison University Mathematics Department. The method produces MacClaurin Series solutions to systems of differential equations, with the coefficients in either algebraic or numerical form. The method yields high-degree solutions: 20th degree is easily obtainable. It is conceptually simple, fast, and extremely general. It has been applied to over a hundred systems of differential equations, some of which were previously unsolved, and has yet to fail to solve any system for which the MacClaurin series converges. The method is non-recursive: each coefficient in the series is calculated just once, in closed form, and its accuracy is limited only by the digital accuracy of the computer. Although the original differential equations may include any mathematical functions, the computational method includes ONLY the operations of addition, subtraction, and multiplication. Furthermore, it is perfectly suited to parallel -processing computer languages. Those who learn this system will never use Runge-Kutta or predictor-corrector methods again. Examples will be presented, including the classical many-body problem.

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

NASA Astrophysics Data System (ADS)

Tsonis, A.

2017-12-01

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

Perspectives on the mathematics of biological patterning and morphogenesis

NASA Astrophysics Data System (ADS)

Garikipati, Krishna

2017-02-01

A central question in developmental biology is how size and position are determined. The genetic code carries instructions on how to control these properties in order to regulate the pattern and morphology of structures in the developing organism. Transcription and protein translation mechanisms implement these instructions. However, this cannot happen without some manner of sampling of epigenetic information on the current patterns and morphological forms of structures in the organism. Any rigorous description of space- and time-varying patterns and morphological forms reduces to one among various classes of spatio-temporal partial differential equations. Reaction-transport equations represent one such class. Starting from simple Fickian diffusion, the incorporation of reaction, phase segregation and advection terms can represent many of the patterns seen in the animal and plant kingdoms. Morphological form, requiring the development of three-dimensional structure, also can be represented by these equations of mass transport, albeit to a limited degree. The recognition that physical forces play controlling roles in shaping tissues leads to the conclusion that (nonlinear) elasticity governs the development of morphological form. In this setting, inhomogeneous growth drives the elasticity problem. The combination of reaction-transport equations with those of elasto-growth makes accessible a potentially unlimited spectrum of patterning and morphogenetic phenomena in developmental biology. This perspective communication is a survey of the partial differential equations of mathematical physics that have been proposed to govern patterning and morphogenesis in developmental biology. Several numerical examples are included to illustrate these equations and the corresponding physics, with the intention of providing physical insight wherever possible.

A Simple Model of Circuit Design.

DTIC Science & Technology

1980-05-01

mathematicians who discover mathematical ideas (i.cnat>, programmers who write code <Manna> <Barstow>, physicists who solve mechanics problems <de Kiecr-l...rules and shows how - they result in the design of circuits. ’l’he design rules must not only capture the purely mathematical constralints given by VICs...K VI.. *? and KCI, but also how those constraints can implement mechanism. Mathematical constraints tell us an amplifier’s input and output voltages

Number Sense Made Simple Using Number Patterns

ERIC Educational Resources Information Center

Su, Hui Fang Huang; Marinas, Carol; Furner, Joseph

2011-01-01

This article highlights investigating intriguing number patterns utilising an emerging technology called the Square Tool. Mathematics teachers of grades K-12 will find the Square Tool useful in making connections and bridging the gap from the concrete to the abstract. Pattern recognition helps students discover various mathematical concepts. With…

Matter Gravitates, but Does Gravity Matter?

ERIC Educational Resources Information Center

Groetsch, C. W.

2011-01-01

The interplay of physical intuition, computational evidence, and mathematical rigor in a simple trajectory model is explored. A thought experiment based on the model is used to elicit student conjectures on the influence of a physical parameter; a mathematical model suggests a computational investigation of the conjectures, and rigorous analysis…

An Excel-lent Card Trick

ERIC Educational Resources Information Center

Zullo, Holly S.

2011-01-01

Card tricks based on mathematical principles can be a great way to get students interested in exploring some important mathematical ideas. In this article, the author discusses a simple spreadsheet implementation that shows students why the card trick works and allows them to explore several variations. As an added bonus, students are introduced…

Deaf College Students' Mathematical Skills Relative to Morphological Knowledge, Reading Level, and Language Proficiency

ERIC Educational Resources Information Center

Kelly, Ronald R.; Gaustad, Martha G.

2007-01-01

This study of deaf college students examined specific relationships between their mathematics performance and their assessed skills in reading, language, and English morphology. Simple regression analyses showed that deaf college students' language proficiency scores, reading grade level, and morphological knowledge regarding word segmentation and…

Not Just for Computation: Basic Calculators Can Advance the Process Standards

ERIC Educational Resources Information Center

Moss, Laura J.; Grover, Barbara W.

2007-01-01

Simple nongraphing calculators can be powerful tools to enhance students' conceptual understanding of mathematics concepts. Students have opportunities to develop (1) a broad repertoire of problem-solving strategies by observing multiple solution strategies; (2) respect for other students' abilities and ways of thinking about mathematics; (3) the…

Harmony Theory: A Mathematical Framework for Stochastic Parallel Processing.

ERIC Educational Resources Information Center

Smolensky, Paul

This paper presents preliminary results of research founded on the hypothesis that in real environments there exist regularities that can be idealized as mathematical structures that are simple enough to be analyzed. The author considered three steps in analyzing the encoding of modularity of the environment. First, a general information…

Sustainability Education: The What and How for Mathematics

ERIC Educational Resources Information Center

Hamilton, Jason; Pfaff, Thomas J.

2014-01-01

In this article we provide a simple way to think about the concept of sustainability and provide a number of examples for incorporating sustainability education into commonly taught mathematics courses. Scientific assessments have concluded that ecosystem services (the benefits that humans derive from the functioning of Earth's natural…

Mathematical demography of spotted owls in the Pacific Northwest

Treesearch

B.R. Noon; C.M. Biles

1990-01-01

We examined the mathematical demography of northern spotted owls (Strix occidentalis caurina) using simple deterministic population models. Our goals were to gain insights into the life history strategy, to determine demographic attributes most affecting changes in population size, and to provide guidelines for effective management of spotted owl...

Simple analytical relations for ship bow waves

NASA Astrophysics Data System (ADS)

Noblesse, Francis; Delhommeau, G.?Rard; Guilbaud, Michel; Hendrix, Dane; Yang, Chi

Simple analytical relations for the bow wave generated by a ship in steady motion are given. Specifically, simple expressions that define the height of a ship bow wave, the distance between the ship stem and the crest of the bow wave, the rise of water at the stem, and the bow wave profile, explicitly and without calculations, in terms of the ship speed, draught, and waterline entrance angle, are given. Another result is a simple criterion that predicts, also directly and without calculations, when a ship in steady motion cannot generate a steady bow wave. This unsteady-flow criterion predicts that a ship with a sufficiently fine waterline, specifically with waterline entrance angle 2, may generate a steady bow wave at any speed. However, a ship with a fuller waterline (25E) can only generate a steady bow wave if the ship speed is higher than a critical speed, defined in terms of αE by a simple relation. No alternative criterion for predicting when a ship in steady motion does not generate a steady bow wave appears to exist. A simple expression for the height of an unsteady ship bow wave is also given. In spite of their remarkable simplicity, the relations for ship bow waves obtained in the study (using only rudimentary physical and mathematical considerations) are consistent with experimental measurements for a number of hull forms having non-bulbous wedge-shaped bows with small flare angle, and with the authors' measurements and observations for a rectangular flat plate towed at a yaw angle.

Travelling wave ultrasonic motors, Part I: Working principle and mathematical modelling of the stator

NASA Astrophysics Data System (ADS)

Hagedorn, P.; Wallaschek, J.

1992-05-01

Travelling wave ultrasonic motors have recently been attracting considerable attention: they may possibly soon replace—at least in certain areas—small electromagnetic motors. This development has been made possible by recent advances in power electronics, material research and digital control, which allow utilization of the piezoelectric effect for low power motors. In these motors the mechanical energy is generated with frequencies of the order of 40 kHz via piezo-elements producing bending waves in a stator, which has approximately the form of a circular plate. The rotor is then driven by the stator via contact forces, and with an extremely simple mechanism frequency reductions of 1:40 000 and more are obtained between the stator vibration and the rotor motion. As a consequence, one can work in the 40 kHz range on the electrical side, while a low frequency rotation is obtained on the mechanical side, as is desirable for many applications. In the present paper, which is the first of a series, the working principle of travelling wave ultrasonic motors is reviewed, and the main phenomena are mathematically modelled. In further papers a detailed mathematical description of the stator vibration and a first model of the contact problem will be given.

Error analysis of mathematics students who are taught by using the book of mathematics learning strategy in solving pedagogical problems based on Polya’s four-step approach

NASA Astrophysics Data System (ADS)

Halomoan Siregar, Budi; Dewi, Izwita; Andriani, Ade

2018-03-01

The purpose of this study is to analyse the types of students errors and causes of them in solving of pedagogic problems. The type of this research is qualitative descriptive, conducted on 34 students of mathematics education in academic year 2017 to 2018. The data in this study is obtained through interviews and tests. Furthermore, the data is then analyzed through three stages: 1) data reduction, 2) data description, and 3) conclusions. The data is reduced by organizing and classifying them in order to obtain meaningful information. After reducing, then the data presented in a simple form of narrative, graphics, and tables to illustrate clearly the errors of students. Based on the information then drawn a conclusion. The results of this study indicate that the students made various errors: 1) they made a mistake in answer what being asked at the problem, because they misunderstood the problem, 2) they fail to plan the learning process based on constructivism, due to lack of understanding of how to design the learning, 3) they determine an inappropriate learning tool, because they did not understand what kind of learning tool is relevant to use.

Deaf college students' mathematical skills relative to morphological knowledge, reading level, and language proficiency.

PubMed

Kelly, Ronald R; Gaustad, Martha G

2007-01-01

This study of deaf college students examined specific relationships between their mathematics performance and their assessed skills in reading, language, and English morphology. Simple regression analyses showed that deaf college students' language proficiency scores, reading grade level, and morphological knowledge regarding word segmentation and meaning were all significantly correlated with both the ACT Mathematics Subtest and National Technical Institute for the Deaf (NTID) Mathematics Placement Test scores. Multiple regression analyses identified the best combination from among these potential independent predictors of students' performance on both the ACT and NTID mathematics tests. Additionally, the participating deaf students' grades in their college mathematics courses were significantly and positively associated with their reading grade level and their knowledge of morphological components of words.

Progress in recognizing typeset mathematics

NASA Astrophysics Data System (ADS)

Fateman, Richard J.; Tokuyasu, Taku A.

1996-03-01

Printed mathematics has a number of features which distinguish it from conventional text. These include structure in two dimensions (fractions, exponents, limits), frequent font changes, symbols with variable shape (quotient bars), and substantially differing notational conventions from source to source. When compounded with more generic problems such as noise and merged or broken characters, printed mathematics offers a challenging arena for recognition. Our project was initially driven by the goal of scanning and parsing some 5,000 pages of elaborate mathematics (tables of definite integrals). While our prototype system demonstrates success on translating noise-free typeset equations into Lisp expressions appropriate for further processing, a more semantic top-down approach appears necessary for higher levels of performance. Such an approach may benefit the incorporation of these programs into a more general document processing viewpoint. We intend to release to the public our somewhat refined prototypes as utility programs in the hope that they will be of general use in the construction of custom OCR packages. These utilities are quite fast even as originally prototyped in Lisp, where they may be of particular interest to those working on 'intelligent' optical processing. Some routines have been re-written in C++ as well. Additional programs providing formula recognition and parsing also form a part of this system. It is important however to realize that distinct conflicting grammars are needed to cover variations in contemporary and historical typesetting, and thus a single simple solution is not possible.

Simple Spreadsheet Models For Interpretation Of Fractured Media Tracer Tests

EPA Science Inventory

An analysis of a gas-phase partitioning tracer test conducted through fractured media is discussed within this paper. The analysis employed matching eight simple mathematical models to the experimental data to determine transport parameters. All of the models tested; two porous...

A simple technique to increase profits in wood products marketing

Treesearch

George B. Harpole

1971-01-01

Mathematical models can be used to solve quickly some simple day-to-day marketing problems. This note explains how a sawmill production manager, who has an essentially fixed-capacity mill, can solve several optimization problems by using pencil and paper, a forecast of market prices, and a simple algorithm. One such problem is to maximize profits in an operating period...

Nonlinear Dynamics of Biofilm Growth on Sediment Surfaces

NASA Astrophysics Data System (ADS)

Molz, F. J.; Murdoch, L. C.; Faybishenko, B.

2013-12-01

Bioclogging often begins with the establishment of small colonies (microcolonies), which then form biofilms on the surfaces of a porous medium. These biofilm-porous media surfaces are not simple coatings of single microbes, but complex assemblages of cooperative and competing microbes, interacting with their chemical environment. This leads one to ask: what are the underlying dynamics involved with biofilm growth? To begin answering this question, we have extended the work of Kot et al. (1992, Bull. Mathematical Bio.) from a fully mixed chemostat to an idealized, one-dimensional, biofilm environment, taking into account a simple predator-prey microbial competition, with the prey feeding on a specified food source. With a variable (periodic) food source, Kot et al. (1992) were able to demonstrate chaotic dynamics in the coupled substrate-prey-predator system. Initially, deterministic chaos was thought by many to be mainly a mathematical phenomenon. However, several recent publications (e.g., Becks et al, 2005, Nature Letters; Graham et al. 2007, Int. Soc Microb. Eco. J.; Beninca et al., 2008, Nature Letters; Saleh, 2011, IJBAS) have brought together, using experimental studies and relevant mathematics, a breakthrough discovery that deterministic chaos is present in relatively simple biochemical systems. Two of us (Faybishenko and Molz, 2013, Procedia Environ. Sci)) have numerically analyzed a mathematical model of rhizosphere dynamics (Kravchenko et al., 2004, Microbiology) and detected patterns of nonlinear dynamical interactions supporting evidence of synchronized synergetic oscillations of microbial populations, carbon and oxygen concentrations driven by root exudation into a fully mixed system. In this study, we have extended the application of the Kot et al. model to investigate a spatially-dependent biofilm system. We will present the results of numerical simulations obtained using COMSOL Multi-Physics software, which we used to determine the nature of the complex dynamics. We found that complex dynamics occur even with a constant food supply maintained at the upstream boundary of the biofilm. Results will be presented along with a description of the model, including 3 coupled partial differential equations and examples of the localized and propagating nonlinear dynamics inherent in the system. Contrary to a common opinion that chaos in many mechanical systems is a type of instability, appearing when energy is added, we hypothesize, based on the results of our modeling, that chaos in biofilm dynamics and other microbial ecosystems is driven by a competitive decrease in the food supply (i.e., chemical energy). We also hypothesize that, somewhat paradoxically, this, in turn, may support a long-term system stability that could cause bioclogging in porous media.

Mathematics and complex systems.

PubMed

Foote, Richard

2007-10-19

Contemporary researchers strive to understand complex physical phenomena that involve many constituents, may be influenced by numerous forces, and may exhibit unexpected or emergent behavior. Often such "complex systems" are macroscopic manifestations of other systems that exhibit their own complex behavior and obey more elemental laws. This article proposes that areas of mathematics, even ones based on simple axiomatic foundations, have discernible layers, entirely unexpected "macroscopic" outcomes, and both mathematical and physical ramifications profoundly beyond their historical beginnings. In a larger sense, the study of mathematics itself, which is increasingly surpassing the capacity of researchers to verify "by hand," may be the ultimate complex system.

Helping Students with Emotional and Behavioral Disorders Solve Mathematics Word Problems

ERIC Educational Resources Information Center

Alter, Peter

2012-01-01

The author presents a strategy for helping students with emotional and behavioral disorders become more proficient at solving math word problems. Math word problems require students to go beyond simple computation in mathematics (e.g., adding, subtracting, multiplying, and dividing) and use higher level reasoning that includes recognizing relevant…

Finding Quality Geometry Apps: Not as Simple as a[superscript 2] + b[superscript 2] = c[superscript 2

ERIC Educational Resources Information Center

Larkin, Kevin

2016-01-01

Trying to find quality apps for use in mathematics classes can be time consuming and bewildering. This article outlines a process for evaluating apps and provides teachers with access to comprehensive qualitative evaluations of 53 geometrical apps based on pedagogical, mathematical and cognitive fidelities.

Great Lakes modeling: Are the mathematics outpacing the data and our understanding of the system?

EPA Science Inventory

Mathematical modeling in the Great Lakes has come a long way from the pioneering work done by Manhattan College in the 1970s, when the models operated on coarse computational grids (often lake-wide) and used simple eutrophication formulations. Moving forward 40 years, we are now...

Answering Junior Ant's "Why" for Pythagoras' Theorem

ERIC Educational Resources Information Center

Pask, Colin

2002-01-01

A seemingly simple question in a cartoon about Pythagoras' Theorem is shown to lead to questions about the nature of mathematical proof and the profound relationship between mathematics and science. It is suggested that an analysis of the issues involved could provide a good vehicle for classroom discussions or projects for senior students.…

The Development from Effortful to Automatic Processing in Mathematical Cognition.

ERIC Educational Resources Information Center

Kaye, Daniel B.; And Others

This investigation capitalizes upon the information processing models that depend upon measurement of latency of response to a mathematical problem and the decomposition of reaction time (RT). Simple two term addition problems were presented with possible solutions for true-false verification, and accuracy and RT to response were recorded. Total…

"Autograph" in the KS3 Classroom

ERIC Educational Resources Information Center

Catley, Alan

2006-01-01

In this article, the author shows some simple examples of ways in which "Autograph" can enhance learning in the KS3 curriculum. He began using version 2 with A-level students to help them visualise concepts in pure mathematics. He has "Autograph" projected to the front board to keep learners focused on mathematical activity…

Modelling a Simple Mechanical System.

ERIC Educational Resources Information Center

Morland, Tim

1999-01-01

Provides an example of the modeling power of Mathematics, demonstrated in a piece of A-Level student coursework which was undertaken as part of the MEI Structured Mathematics scheme. A system of two masses and two springs oscillating in one dimension is found to be accurately modeled by a system of linear differential equations. (Author/ASK)

Origami, Geometry and Art

ERIC Educational Resources Information Center

Wares, Arsalan; Elstak, Iwan

2017-01-01

The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…

The Force-Frequency Relationship: Insights from Mathematical Modeling

ERIC Educational Resources Information Center

Puglisi, Jose L.; Negroni, Jorge A.; Chen-Izu, Ye; Bers, Donald M.

2013-01-01

The force-frequency relationship has intrigued researchers since its discovery by Bowditch in 1871. Many attempts have been made to construct mathematical descriptions of this phenomenon, beginning with the simple formulation of Koch-Wesser and Blinks in 1963 to the most sophisticated ones of today. This property of cardiac muscle is amplified by…

Industrial Prep, Volume Four, Junior Year--Contents: Mathematics and Guidance.

ERIC Educational Resources Information Center

Hackensack Public Schools, NJ.

As part of a 3-year comprehensive interdisciplinary program in industrial preparation for vocational students, this 11th Grade teaching guide consists of units on technical mathematics and guidance. Designed as supportive material for related physics and English curriculums, the first four sections of Volume 4 on algebra, vectors, simple machines,…

SIMPLE METHOD FOR THE REPRESENTATION, QUANTIFICATION, AND COMPARISON OF THE VOLUMES AND SHAPES OF CHEMICAL COMPOUNDS

EPA Science Inventory

A conceptually and computationally simple method for the definition, display, quantification, and comparison of the shapes of three-dimensional mathematical molecular models is presented. Molecular or solvent-accessible volume and surface area can also be calculated. Algorithms, ...

Mathematics and Astronomy: Inquire Based Scientific Education at School

NASA Astrophysics Data System (ADS)

de Castro, Ana I. Gómez

2010-10-01

Mathematics is the language of science however, in secondary and high school education students are not made aware of the strong implications behind this statement. This is partially caused because mathematical training and the modelling of nature are not taught together. Astronomy provides firm scientific grounds for this joint training; the mathematics needed is simple, the data can be acquired with simple instrumentation in any place on the planet and the physics is rich with a broad range of levels. In addition, astronomy and space exploration are extremely appealing to young (14-17 years old) students helping to motivate them to study science doing science, i.e. to introduce Inquiry Based Scientific Education (IBSE). Since 1997 a global consortium is being developed to introduce IBSE techniques in secondary/high school education on a global scale: the Global Hands-On Universe association (www.globalhou.org) making use of the astronomical universe as a training lab. This contribution is a brief update on the current activities of the HOU consortium. Relevant URLS: www.globalhou.org, www.euhou.net, www.houspain.com.

Physics and Mathematics as Interwoven Disciplines in Science Education

NASA Astrophysics Data System (ADS)

Galili, Igal

2018-03-01

The relationship between physics and mathematics is reviewed upgrading the common in physics classes' perspective of mathematics as a toolkit for physics. The nature of the physics-mathematics relationship is considered along a certain historical path. The triadic hierarchical structure of discipline-culture helps to identify different ways in which mathematics is used in physics and to appreciate its contribution, to recognize the difference between mathematics and physics as disciplines in approaches, values, methods, and forms. We mentioned certain forms of mathematical knowledge important for physics but often missing in school curricula. The geometrical mode of codification of mathematical knowledge is compared with the analytical one in context of teaching school physics and mathematics; their complementarity is exemplified. Teaching may adopt the examples facilitating the claims of the study to reach science literacy and meaningful learning.

The Mine Locomotive Wireless Network Strategy Based on Successive Interference Cancellation

PubMed Central

Wu, Liaoyuan; Han, Jianghong; Wei, Xing; Shi, Lei; Ding, Xu

2015-01-01

We consider a wireless network strategy based on successive interference cancellation (SIC) for mine locomotives. We firstly build the original mathematical model for the strategy which is a non-convex model. Then, we examine this model intensively, and figure out that there are certain regulations embedded in it. Based on these findings, we are able to reformulate the model into a new form and design a simple algorithm which can assign each locomotive with a proper transmitting scheme during the whole schedule procedure. Simulation results show that the outcomes obtained through this algorithm are improved by around 50% compared with those that do not apply the SIC technique. PMID:26569240

Clairvoyant fusion: a new methodology for designing robust detection algorithms

NASA Astrophysics Data System (ADS)

Schaum, Alan

2016-10-01

Many realistic detection problems cannot be solved with simple statistical tests for known alternative probability models. Uncontrollable environmental conditions, imperfect sensors, and other uncertainties transform simple detection problems with likelihood ratio solutions into composite hypothesis (CH) testing problems. Recently many multi- and hyperspectral sensing CH problems have been addressed with a new approach. Clairvoyant fusion (CF) integrates the optimal detectors ("clairvoyants") associated with every unspecified value of the parameters appearing in a detection model. For problems with discrete parameter values, logical rules emerge for combining the decisions of the associated clairvoyants. For many problems with continuous parameters, analytic methods of CF have been found that produce closed-form solutions-or approximations for intractable problems. Here the principals of CF are reviewed and mathematical insights are described that have proven useful in the derivation of solutions. It is also shown how a second-stage fusion procedure can be used to create theoretically superior detection algorithms for ALL discrete parameter problems.

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

EPA Science Inventory

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

Mathematical and Numerical Analysis of Model Equations on Interactions of the HIV/AIDS Virus and the Immune System

NASA Astrophysics Data System (ADS)

Parumasur, N.; Willie, R.

2008-09-01

We consider a simple HIV/AIDs finite dimensional mathematical model on interactions of the blood cells, the HIV/AIDs virus and the immune system for consistence of the equations to the real biomedical situation that they model. A better understanding to a cure solution to the illness modeled by the finite dimensional equations is given. This is accomplished through rigorous mathematical analysis and is reinforced by numerical analysis of models developed for real life cases.

Sines and Cosines. Part 3 of 3

NASA Technical Reports Server (NTRS)

Apostol, Tom M. (Editor)

1994-01-01

In this 'Project Mathematics' series video, the addition formulas of sines and cosines are explained and their real life applications are demonstrated. Both film footage and computer animation is used. Several mathematical concepts are discussed and include: Ptolemy's theorem concerned with quadrilaterals; the difference between a central angle and an inscribed angle; sines and chord lengths; special angles; subtraction formulas; and a application to simple harmonic motion. A brief history of the city Alexandria, its mathematicians, and their contribution to the field of mathematics is shown.

Mathematical form models of tree trunks

Treesearch

Rudolfs Ozolins

2000-01-01

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

Development of a Short Form of the Attitudes toward Mathematics Inventory

ERIC Educational Resources Information Center

Lim, Siew Yee; Chapman, Elaine

2013-01-01

Existing instruments designed to measure mathematics attitudes were too long, dated, or assessed with only western samples. To address this issue, a shortened version of the Attitudes Toward Mathematics Inventory (short ATMI) which measures four subscales--;enjoyment of mathematics, motivation to do mathematics, self-confidence in mathematics, and…

Orientations toward Mathematical Processes of Prospective Secondary Mathematics Teachers as Related to Work with Tasks

ERIC Educational Resources Information Center

Cannon, Tenille

2016-01-01

Mathematics can be conceptualized in different ways. Policy documents such as the National Council of Teachers of Mathematics (NCTM) (2000) and the Common Core State Standards Initiative (CCSSI) (2010), classify mathematics in terms of mathematical content (e.g., quadratic functions, Pythagorean theorem) and mathematical activity in the form of…

Relating the Stored Magnetic Energy of a Parallel-Plate Inductor to the Work of External Forces

ERIC Educational Resources Information Center

Gauthier, N.

2007-01-01

Idealized models are often used in introductory physics courses. For one, such models involve simple mathematics, which is a definite plus since complex mathematical manipulations quickly become an obstacle rather than a tool for a beginner. Idealized models facilitate a student's understanding and grasp of a given physical phenomenon, yet they…

Getting to the Bottom of a Ladder Problem

ERIC Educational Resources Information Center

McCartney, Mark

2002-01-01

In this paper, the author introduces a simple problem relating to a pair of ladders. A mathematical model of the problem produces an equation which can be solved in a number of ways using mathematics appropriate to "A" level students or first year undergraduates. The author concludes that the ladder problem can be used in class to develop and…

Improving the Effectiveness of Mathematics Teaching through Active Reflection

ERIC Educational Resources Information Center

Driscoll, Kerryn

2015-01-01

A small study of active reflection was undertaken with 21 primary students in a Prep and Year 1 classroom. To provide feedback from the students on their views about their personal learning and ways they could be better supported to learn mathematics a simple survey was supplemented by one-to-one interviews. Students' perceptions of their learning…

Research Reporting Sections, Annual Meeting of the National Council of Teachers of Mathematics (57th, Boston, Massachusetts, April 18-21, 1979).

ERIC Educational Resources Information Center

Higgins, Jon L., Ed.

This document provides abstracts of 20 research reports. Topics covered include: children's comprehension of simple story problems; field independence and group instruction; problem-solving competence and memory; spatial visualization and the use of manipulative materials; effects of games on mathematical skills; problem-solving ability and right…

Stickybear's Math Splash: Adventures in Math Fun for Ages 5-10! School Version with Lesson Plans. [CD-ROM].

ERIC Educational Resources Information Center

Highsmith, Joni Bitman

Stickybear's Math Splash is a CD-ROM-based software tool for teaching mathematics skills beyond simple number recognition to elementary students. The accompanying printed lesson plans are designed to complement mathematics skills with other methods and areas of emphasis including kinesthetic learning, listening skills, decision making skills, and…

Calling for the Development of Children's Number Sense in Primary Schools in Malaysia

ERIC Educational Resources Information Center

Kuldas, Seffetullah; Sinnakaudan, Santi; Hashim, Shahabuddin; Ghazali, Munirah

2017-01-01

Although the early development of children's number sense is a strong predictor of their later mathematics achievements, it has been overlooked in primary schools in Malaysia. Mainly attributable to underdeveloped number sense of Malaysian primary and secondary school children, their inability to handle simple mathematics tasks, which require the…

Second-Degree Price Discrimination: A Graphical and Mathematical Approach

ERIC Educational Resources Information Center

Gotlibovski, Chemi; Kahana, Nava

2009-01-01

The authors use a relatively simple diagram accompanied by mathematical analysis to compare two pricing strategies: price-quantity packages and a two-part tariff. This is done both from the monopolist's point of view and from the welfare point of view. The authors show that in the case of two consumer types, the price-quantity packages strategy…

Developing Essential Understanding of Rational Numbers for Teaching Mathematics in Grades 3-5. Essential Understandings

ERIC Educational Resources Information Center

Clarke, Carne; Fisher, William; Marks, Rick; Ross, Sharon; Zbiek, Rose Mary

2010-01-01

This book focuses on essential knowledge for teachers about rational numbers. It is organized around four big ideas, supported by multiple smaller, interconnected ideas--essential understandings. Taking teachers beyond a simple introduction to rational numbers, the book will broaden and deepen their mathematical understanding of one of the most…

A Simple Interactive Software Package for Plotting, Animating, and Calculating

ERIC Educational Resources Information Center

Engelhardt, Larry

2012-01-01

We introduce a new open source (free) software package that provides a simple, highly interactive interface for carrying out certain mathematical tasks that are commonly encountered in physics. These tasks include plotting and animating functions, solving systems of coupled algebraic equations, and basic calculus (differentiating and integrating…

Children's Criteria for Representational Adequacy in the Perception of Simple Sonic Stimuli

ERIC Educational Resources Information Center

Verschaffel, Lieven; Reybrouck, Mark; Jans, Christine; Van Dooren, Wim

2010-01-01

This study investigates children's metarepresentational competence with regard to listening to and making sense of simple sonic stimuli. Using diSessa's (2003) work on metarepresentational competence in mathematics and sciences as theoretical and empirical background, it aims to assess children's criteria for representational adequacy of graphical…

A Simple Mechanical Model for the Isotropic Harmonic Oscillator

ERIC Educational Resources Information Center

Nita, Gelu M.

2010-01-01

A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels. (Contains 2 figures.)

Eye Movements Reveal Students' Strategies in Simple Equation Solving

ERIC Educational Resources Information Center

Susac, Ana; Bubic, Andreja; Kaponja, Jurica; Planinic, Maja; Palmovic, Marijan

2014-01-01

Equation rearrangement is an important skill required for problem solving in mathematics and science. Eye movements of 40 university students were recorded while they were rearranging simple algebraic equations. The participants also reported on their strategies during equation solving in a separate questionnaire. The analysis of the behavioral…

Coexistence trend contingent to Mediterranean oaks with different leaf habits.

PubMed

Di Paola, Arianna; Paquette, Alain; Trabucco, Antonio; Mereu, Simone; Valentini, Riccardo; Paparella, Francesco

2017-05-01

In a previous work we developed a mathematical model to explain the co-occurrence of evergreen and deciduous oak groups in the Mediterranean region, regarded as one of the distinctive features of Mediterranean biodiversity. The mathematical analysis showed that a stabilizing mechanism resulting from niche difference (i.e. different water use and water stress tolerance) between groups allows their coexistence at intermediate values of suitable soil water content. A simple formal derivation of the model expresses this hypothesis in a testable form linked uniquely to the actual evapotranspiration of forests community. In the present work we ascertain whether this simplified conclusion possesses some degree of explanatory power by comparing available data on oaks distributions and remotely sensed evapotranspiration (MODIS product) in a large-scale survey embracing the western Mediterranean area. Our findings confirmed the basic assumptions of model addressed on large scale, but also revealed asymmetric responses to water use and water stress tolerance between evergreen and deciduous oaks that should be taken into account to increase the understating of species interactions and, ultimately, improve the modeling capacity to explain co-occurrence.

What Physicists Mean By the Equals Sign in Undergraduate Education

NASA Astrophysics Data System (ADS)

Kornick, Kellianne; Alaee, Dina; Sayre, Eleanor; Franklin, Scott

2017-01-01

Mathematical syntax allows for the description of meaningful concepts in the physical sciences, and having nuanced proficiency in mathematical formalism is closely tied to communication and understanding of physical principles. The concept of equality is especially important, as it constrains and dictates the relationships between two equated expressions, and a student with detailed understanding of these relationships can derive physical meaning from syntactical expressions mediated by equals signs by knowing the ``meaning'' of equals signs. We delineate types of equals signs as used in undergraduate textbooks and develop a categorization scheme in order to investigate how equals signs are used paradigmatically and culturally in textbooks to convey physical meaning. We classify equals signs into general clusters (causal, definitional, assignment, balancing, and ``just math''), each cluster containing more detailed types. We investigate differences across various topics and between introductory and upper-division textbooks. We found that upper division textbooks are more likely to use balancing, definitional, and more complex kinds of assignment forms, while introductory texts have much higher frequencies of simple assignment and ``just math'' types.

Separation of Dirac's Hamiltonian by Van Vleck transformation

NASA Astrophysics Data System (ADS)

Jørgensen, Flemming

2017-01-01

The now classic Foldy-Wouthuysen transformation (FWT) was introduced as successive unitary transformations. This fundamental idea has become the standard in later developments such as the Douglas-Kroll transformation (DKT) - but it is not the only possibility. FWT can be seen as a simple special case of the general Van Vleck transformation (VVT) which besides the successive version has another, known as the canonical because of a series of nice mathematical properties discovered gradually over time. The aim of the present paper is to compare the two approaches - which give identical results in the lower orders, but not in the higher. After having recapitalised both, we apply them to Dirac's Hamiltonian for the electron in a constant electromagnetic field, written with so few assumptions about the operators that the mathematical techniques stand out separated from the terminology of relativistic quantum mechanics. FWT for a free particle is dealt with by a recent geometric approach to VVT. The original FWT is continued through the next non-zero orders. DKT is considered with special weight on equivalent formulations of the generalised and the optimised forms introduced by Wolf, Reiher and Hess.

League tables and school effectiveness: a mathematical model.

PubMed Central

Hoyle, Rebecca B; Robinson, James C

2003-01-01

'School performance tables', an alphabetical list of secondary schools along with aggregates of their pupils' performances in national tests, have been published in the UK since 1992. Inevitably, the media have responded by publishing ranked 'league tables'. Despite concern over the potentially divisive effect of such tables, the current government has continued to publish this information in the same form. The effect of this information on standards and on the social make-up of the community has been keenly debated. Since there is no control group available that would allow us to investigate this issue directly, we present here a simple mathematical model. Our results indicate that, while random fluctuations from year to year can cause large distortions in the league-table positions, some schools still establish themselves as 'desirable'. To our surprise, we found that 'value-added' tables were no more accurate than tables based on raw exam scores, while a different method of drawing up the tables, in which exam results are averaged over a period of time, appears to give a much more reliable measure of school performance. PMID:12590748

Intangible heritage for sustainable future: mathematics in the paddy field

NASA Astrophysics Data System (ADS)

Dewanto, Stanley P.; Kusuma, Dianne A.; Nurani Ruchjana, Budi; Setiawan Abdullah, Atje

2017-10-01

Mathematics, as the only general language, can describe all phenomena on earth. Mathematics not only helps us to understand these phenomena, but it also can sustain human activities, consequently ensure that the future development is sustainable. Indonesia, with high cultural diversity, should aware to have its understanding, skills, and philosophies developed by certain societies, with long histories of interaction with their natural surroundings, which will provide a foundation for locally appropriate sustainable development. This paper discussed the condition and situation on certain area in Cigugur, Indonesia, and what skills, knowledge, and concept can be transmitted, regarding simple mathematics (arithmetic). Some examples are provided.

A Descriptive Study Examining the Impact of Digital Writing Environments on Communication and Mathematical Reasoning for Students with Learning Disabilities

ERIC Educational Resources Information Center

Huscroft-D'Angelo, Jacqueline; Higgins, Kristina N.; Crawford, Lindy L.

2014-01-01

Proficiency in mathematics, including mathematical reasoning skills, requires students to communicate their mathematical thinking. Mathematical reasoning involves making sense of mathematical concepts in a logical way to form conclusions or judgments, and is often underdeveloped in students with learning disabilities. Technology-based environments…

Mathematical modeling of solid cancer growth with angiogenesis

PubMed Central

2012-01-01

Background Cancer arises when within a single cell multiple malfunctions of control systems occur, which are, broadly, the system that promote cell growth and the system that protect against erratic growth. Additional systems within the cell must be corrupted so that a cancer cell, to form a mass of any real size, produces substances that promote the growth of new blood vessels. Multiple mutations are required before a normal cell can become a cancer cell by corruption of multiple growth-promoting systems. Methods We develop a simple mathematical model to describe the solid cancer growth dynamics inducing angiogenesis in the absence of cancer controlling mechanisms. Results The initial conditions supplied to the dynamical system consist of a perturbation in form of pulse: The origin of cancer cells from normal cells of an organ of human body. Thresholds of interacting parameters were obtained from the steady states analysis. The existence of two equilibrium points determine the strong dependency of dynamical trajectories on the initial conditions. The thresholds can be used to control cancer. Conclusions Cancer can be settled in an organ if the following combination matches: better fitness of cancer cells, decrease in the efficiency of the repairing systems, increase in the capacity of sprouting from existing vascularization, and higher capacity of mounting up new vascularization. However, we show that cancer is rarely induced in organs (or tissues) displaying an efficient (numerically and functionally) reparative or regenerative mechanism. PMID:22300422

Reconstruction of extended Petri nets from time series data and its application to signal transduction and to gene regulatory networks

PubMed Central

2011-01-01

Background Network inference methods reconstruct mathematical models of molecular or genetic networks directly from experimental data sets. We have previously reported a mathematical method which is exclusively data-driven, does not involve any heuristic decisions within the reconstruction process, and deliveres all possible alternative minimal networks in terms of simple place/transition Petri nets that are consistent with a given discrete time series data set. Results We fundamentally extended the previously published algorithm to consider catalysis and inhibition of the reactions that occur in the underlying network. The results of the reconstruction algorithm are encoded in the form of an extended Petri net involving control arcs. This allows the consideration of processes involving mass flow and/or regulatory interactions. As a non-trivial test case, the phosphate regulatory network of enterobacteria was reconstructed using in silico-generated time-series data sets on wild-type and in silico mutants. Conclusions The new exact algorithm reconstructs extended Petri nets from time series data sets by finding all alternative minimal networks that are consistent with the data. It suggested alternative molecular mechanisms for certain reactions in the network. The algorithm is useful to combine data from wild-type and mutant cells and may potentially integrate physiological, biochemical, pharmacological, and genetic data in the form of a single model. PMID:21762503

Investigation of the Effects of Mathematical Thinking States of Form Teachers on Their Mathematics Teaching Anxieties

ERIC Educational Resources Information Center

Yorulmaz, Alper; Altintas, Sedat; Sidekli, Sabri

2017-01-01

The state of mathematical thinking is considered to have an effect on the formation of anxiety regarding teaching mathematics. It is hypothesized that with the formation of mathematical thinking, the anxiety in teachers regarding teaching mathematics will be reduced. Since mathematical thinking is a skill acquired starting from the early years of…

A study of students' learning styles and mathematics anxiety amongst form four students in Kerian Perak

NASA Astrophysics Data System (ADS)

Esa, Suraya; Mohamed, Nurul Akmal

2017-05-01

This study aims to identify the relationship between students' learning styles and mathematics anxiety amongst Form Four students in Kerian, Perak. The study involves 175 Form Four students as respondents. The instrument which is used to assess the students' learning styles and mathematic anxiety is adapted from the Grasha's Learning Styles Inventory and the Mathematics Anxiety Scale (MAS) respectively. The types of learning styles used are independent, avoidant, collaborative, dependent, competitive and participant. The collected data is processed by SPSS (Statistical Packages for Social Sciences 16.0). The data is analysed by using descriptive statistics and inferential statistics that include t-test and Pearson correlation. The results show that majority of the students adopt collaborative learning style and the students have moderate level of mathematics anxiety. Moreover, it is found that there is significant difference between learning style avoidant, collaborative, dependent and participant based on gender. Amongst all students' learning style, there exists a weak but significant correlation between avoidant, independent and participant learning style and mathematics anxiety. It is very important for the teachers need to be concerned about the effects of learning styles on mathematics anxiety. Therefore, the teachers should understand mathematics anxiety and implement suitable learning strategies in order for the students to overcome their mathematics anxiety.

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

PubMed

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

2017-01-01

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

Educating in Place: Mathematics and Technology

ERIC Educational Resources Information Center

Klein, Robert

2007-01-01

Mathematics education discourse routinely promotes the idea that mathematics is everywhere. That mathematics is everywhere seems a reasonable implication of "We all use math everyday." Modern technology, mostly in the form of computational devices and control systems, is often cited as evidence of the omnipresence of mathematics.…

Validation of the replica trick for simple models

NASA Astrophysics Data System (ADS)

Shinzato, Takashi

2018-04-01

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

Similarity of the Multidimensional Space Defined by Parallel Forms of a Mathematics Test.

ERIC Educational Resources Information Center

Reckase, Mark D.; And Others

The purpose of the paper is to determine whether test forms of the Mathematics Usage Test (AAP Math) of the American College Testing Program are parallel in a multidimensional sense. The AAP Math is an achievement test of mathematics concepts acquired by high school students by the end of their third year. To determine the dimensionality of the…

Obtaining Laws through Quantifying Experiments: Justifications of Pre-Service Physics Teachers in the Case of Electric Current, Voltage and Resistance

ERIC Educational Resources Information Center

Mäntylä, Terhi; Hämäläinen, Ari

2015-01-01

The language of physics is mathematics, and physics ideas, laws and models describing phenomena are usually represented in mathematical form. Therefore, an understanding of how to navigate between phenomena and the models representing them in mathematical form is important for a physics teacher so that the teacher can make physics understandable…

Adaptation of the Mathematics and Technology Attitudes Scale (MTAS) into Turkish: Validity and Reliability Studies for Middle School Students

ERIC Educational Resources Information Center

Tabuk, Mesut

2018-01-01

The paper aims to present the adaptation study of "The Mathematics and Technology Attitudes Scale (MTAS)" into Turkish. The original form MTAS was developed by Pierce, Stacey and Barkatsas (2007) in order to investigate the effect of five different variables in learning mathematics with technology. The original form of the attitudes…

Enhancing Interpretation of Natural Phenomena through a Mathematical Apparatus: A Proposal of an Interactive Unit in Optics

ERIC Educational Resources Information Center

Sokolowski, Andrzej

2012-01-01

This paper integrates technology, in the form of a physics simulation; science concepts, via image formation by lenses; and a mathematics apparatus, in the form of rational functions. All constituents merge into an instructional unit that can be embedded into a high school or undergraduate mathematics or physics course. The cognitive purpose of…

Facilitating Student Understanding of Buffering by an Integration of Mathematics and Chemical Concepts

ERIC Educational Resources Information Center

Curtright, Robert; Emry, Randall; Heaton, Ruth M.; Markwell, John

2004-01-01

We describe a simple undergraduate exercise involving the titration of a weak acid by a strong base using a pH meter and a micropipette. Students then use their data and carry out graphical analyses with a spreadsheet. The analyses involve using mathematical concepts such as first-derivative and semi-log plots and provide an opportunity for…

Posing Complex Problems Requiring Multiplicative Thinking Prompts Students to Use Sophisticated Strategies and Build Mathematical Connections

ERIC Educational Resources Information Center

Downton, Ann; Sullivan, Peter

2017-01-01

While the general planning advice offered to mathematics teachers seems to be to start with simple examples and build complexity progressively, the research reported in this article is a contribution to the body of literature that argues the reverse. That is, posing of appropriately complex tasks may actually prompt the use of more sophisticated…

Issues in Combining the Use of Various Tools in Solving Mathematical Problems--Why Is Copy-Paste Often Useless

ERIC Educational Resources Information Center

Lokar, Matija; Libbrecht, Paul

2017-01-01

Mathematical formulae are information objects that can be entered in a computer, visualized, and evaluated. Thus, by the majority of (mostly occasional) users it is also expected that they are transferable through the simple copy-paste procedure. This transfer is particularly interesting when users are involved in tasks that span different…

Teaching with Technology: Exploring the Use of Robotics to Teach Mathematics

ERIC Educational Resources Information Center

Attard, Catherine

2012-01-01

In this article, the author explores the value of using simple robotics such as BeeBots and ProBots to enhance the teaching and learning of mathematics in the primary classroom. Before making the decision to use such technologies, it is important that they be evaluated in terms of their affordances and constraints. In other words, teachers need to…

Aberrant Functional Activation in School Age Children At-Risk for Mathematical Disability: A Functional Imaging Study of Simple Arithmetic Skill

ERIC Educational Resources Information Center

Davis, Nicole; Cannistraci, Christopher J.; Rogers, Baxter P.; Gatenby, J. Christopher; Fuchs, Lynn S.; Anderson, Adam W.; Gore, John C.

2009-01-01

We used functional magnetic resonance imaging (fMRI) to explore the patterns of brain activation associated with different levels of performance in exact and approximate calculation tasks in well-defined cohorts of children with mathematical calculation difficulties (MD) and typically developing controls. Both groups of children activated the same…

Design and Use Online Platforms to Learn Mathematics and the Use of Them in Simulations of Problems in Applied Sciences

ERIC Educational Resources Information Center

Méndez-Fragoso, Ricardo; Villavicencio-Torres, Mirna; Martínez-Moreno, Josué

2017-01-01

In this contribution, we show the practical use of the computer to visualise simple computational simulations to show phenomena that occur in everyday life, or require an abstract understanding for being unintuitive phenomena. The relationship of the mathematics to different scientific disciplines motivates us to devise different treatments to…

Appreciation of Mathematics through Origami

ERIC Educational Resources Information Center

Wares, Arsalan

2013-01-01

The purpose of this classroom note is to provide an example of how a simple origami box can be used to explore important mathematical concepts in geometry like surface area. This article describes how an origami box can be folded from a rectangular sheet of paper, then it goes on to describe how its surface area can be determined in terms of the…

Mathematics Curriculum Based Measurement to Predict State Test Performance: A Comparison of Measures and Methods

ERIC Educational Resources Information Center

Stevens, Olinger; Leigh, Erika

2012-01-01

Scope and Method of Study: The purpose of the study is to use an empirical approach to identify a simple, economical, efficient, and technically adequate performance measure that teachers can use to assess student growth in mathematics. The current study has been designed to expand the body of research for math CBM to further examine technical…

Science and Mathematics in Astronomy

NASA Technical Reports Server (NTRS)

Woolack, Edward

2009-01-01

A brief historical introduction to the development of observational astronomy will be presented. The close historical relationship between the successful application of mathematical concepts and advances in astronomy will be presented. A variety of simple physical demonstrations, hands-on group activities, and puzzles will be used to understand how the properties of light can be used to understand the contents of our universe.

Mathematical study on robust tissue pattern formation in growing epididymal tubule.

PubMed

Hirashima, Tsuyoshi

2016-10-21

Tissue pattern formation during development is a reproducible morphogenetic process organized by a series of kinetic cellular activities, leading to the building of functional and stable organs. Recent studies focusing on mechanical aspects have revealed physical mechanisms on how the cellular activities contribute to the formation of reproducible tissue patterns; however, the understanding for what factors achieve the reproducibility of such patterning and how it occurs is far from complete. Here, I focus on a tube pattern formation during murine epididymal development, and show that two factors influencing physical design for the patterning, the proliferative zone within the tubule and the viscosity of tissues surrounding to the tubule, control the reproducibility of epididymal tubule pattern, using a mathematical model based on experimental data. Extensive numerical simulation of the simple mathematical model revealed that a spatially localized proliferative zone within the tubule, observed in experiments, results in more reproducible tubule pattern. Moreover, I found that the viscosity of tissues surrounding to the tubule imposes a trade-off regarding pattern reproducibility and spatial accuracy relating to the region where the tubule pattern is formed. This indicates an existence of optimality in material properties of tissues for the robust patterning of epididymal tubule. The results obtained by numerical analysis based on experimental observations provide a general insight on how physical design realizes robust tissue pattern formation. Copyright © 2016 Elsevier Ltd. All rights reserved.

Perceptual learning modules in mathematics: enhancing students' pattern recognition, structure extraction, and fluency.

PubMed

Kellman, Philip J; Massey, Christine M; Son, Ji Y

2010-04-01

Learning in educational settings emphasizes declarative and procedural knowledge. Studies of expertise, however, point to other crucial components of learning, especially improvements produced by experience in the extraction of information: perceptual learning (PL). We suggest that such improvements characterize both simple sensory and complex cognitive, even symbolic, tasks through common processes of discovery and selection. We apply these ideas in the form of perceptual learning modules (PLMs) to mathematics learning. We tested three PLMs, each emphasizing different aspects of complex task performance, in middle and high school mathematics. In the MultiRep PLM, practice in matching function information across multiple representations improved students' abilities to generate correct graphs and equations from word problems. In the Algebraic Transformations PLM, practice in seeing equation structure across transformations (but not solving equations) led to dramatic improvements in the speed of equation solving. In the Linear Measurement PLM, interactive trials involving extraction of information about units and lengths produced successful transfer to novel measurement problems and fraction problem solving. Taken together, these results suggest (a) that PL techniques have the potential to address crucial, neglected dimensions of learning, including discovery and fluent processing of relations; (b) PL effects apply even to complex tasks that involve symbolic processing; and (c) appropriately designed PL technology can produce rapid and enduring advances in learning. Copyright © 2009 Cognitive Science Society, Inc.

Communicational Perspectives on Learning and Teaching Mathematics: Prologue

ERIC Educational Resources Information Center

Tabach, Michal; Nachlieli, Talli

2016-01-01

This special issue comprises five studies which vary in their focus and mathematical content, yet they all share an underlying communicational theoretical framework--commognition. Within this framework, learning mathematics is defined as a change in one's mathematical discourse, that is, in the form of communication known as mathematical. Teaching…

Simple Games . . . or Are They?

ERIC Educational Resources Information Center

Arn, Susan Kyle

2006-01-01

Students today begin using computers and playing video games as early as two years old. The technology behind these games is more complicated than most people can imagine. In this article, the author presents some simple number games which seem easy at the beginning, but as the games are repeated, mathematical content becomes more of the focus…

Simple Examples of the Interpretation of Changes in Kinetic and Potential Energy under Galilean Transformations

ERIC Educational Resources Information Center

Ginsberg, Edw S.

2018-01-01

The compatibility of the Newtonian formulation of mechanical energy and the transformation equations of Galilean relativity is demonstrated for three simple examples of motion treated in most introductory physics courses (free fall, a frictionless inclined plane, and a mass/spring system). Only elementary concepts and mathematics, accessible to…

Teaching the Concept of Breakdown Point in Simple Linear Regression.

ERIC Educational Resources Information Center

Chan, Wai-Sum

2001-01-01

Most introductory textbooks on simple linear regression analysis mention the fact that extreme data points have a great influence on ordinary least-squares regression estimation; however, not many textbooks provide a rigorous mathematical explanation of this phenomenon. Suggests a way to fill this gap by teaching students the concept of breakdown…

Variations of anthropogenic CO2 in urban area deduced by radiocarbon concentration in modern tree rings.

PubMed

Rakowski, Andrzej Z; Nakamura, Toshio; Pazdur, Anna

2008-10-01

Radiocarbon concentration in the atmosphere is significantly lower in areas where man-made emissions of carbon dioxide occur. This phenomenon is known as Suess effect, and is caused by the contamination of clean air with non-radioactive carbon from fossil fuel combustion. The effect is more strongly observed in industrial and densely populated urban areas. Measurements of carbon isotope concentrations in a study area can be compared to those from areas of clear air in order to estimate the amount of carbon dioxide emission from fossil fuel combustion by using a simple mathematical model. This can be calculated using the simple mathematical model. The result of the mathematical model followed in this study suggests that the use of annual rings of trees to obtain the secular variations of 14C concentration of atmospheric CO2 can be useful and efficient for environmental monitoring and modeling of the carbon distribution in local scale.

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.

Combining Automated Theorem Provers with Symbolic Algebraic Systems: Position Paper

NASA Technical Reports Server (NTRS)

Schumann, Johann; Koga, Dennis (Technical Monitor)

1999-01-01

In contrast to pure mathematical applications where automated theorem provers (ATPs) are quite capable, proof tasks arising form real-world applications from the area of Software Engineering show quite different characteristics: they usually do not only contain much arithmetic (albeit often quite simple one), but they also often contain reasoning about specific structures (e.g. graphics, sets). Thus, an ATP must be capable of performing reasoning together with a fair amount of simplification, calculation and solving. Therefore, powerful simplifiers and other (symbolic and semi-symbolic) algorithms seem to be ideally suited to augment ATPs. In the following we shortly describe two major points of interest in combining SASs (symbolic algebraic systems) with top-down automated theorem provers (here: SETHEO [Let92, GLMS94]).

Three-dimensional analysis of tokamaks and stellarators

PubMed Central

Garabedian, Paul R.

2008-01-01

The NSTAB equilibrium and stability code and the TRAN Monte Carlo transport code furnish a simple but effective numerical simulation of essential features of present tokamak and stellarator experiments. When the mesh size is comparable to the island width, an accurate radial difference scheme in conservation form captures magnetic islands successfully despite a nested surface hypothesis imposed by the mathematics. Three-dimensional asymmetries in bifurcated numerical solutions of the axially symmetric tokamak problem are relevant to the observation of unstable neoclassical tearing modes and edge localized modes in experiments. Islands in compact stellarators with quasiaxial symmetry are easier to control, so these configurations will become good candidates for magnetic fusion if difficulties with safety and stability are encountered in the International Thermonuclear Experimental Reactor (ITER) project. PMID:18768807

Transient sequences in a hypernetwork generated by an adaptive network of spiking neurons.

PubMed

Maslennikov, Oleg V; Shchapin, Dmitry S; Nekorkin, Vladimir I

2017-06-28

We propose a model of an adaptive network of spiking neurons that gives rise to a hypernetwork of its dynamic states at the upper level of description. Left to itself, the network exhibits a sequence of transient clustering which relates to a traffic in the hypernetwork in the form of a random walk. Receiving inputs the system is able to generate reproducible sequences corresponding to stimulus-specific paths in the hypernetwork. We illustrate these basic notions by a simple network of discrete-time spiking neurons together with its FPGA realization and analyse their properties.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'. © 2017 The Author(s).

Symmetries in geometrical optics: theory

NASA Astrophysics Data System (ADS)

Szilagyi, M.; Mui, P. H.

1995-12-01

A study of light and charged-particle optical systems with inversion, reflection, rotation, translation, and/or glide symmetries is presented. The constraints imposed by the various symmetries on the first-order properties of a lens are investigated. In particular, the mathematical structures of the deflection vectors and the transfer matrices are described for various symmetrical systems. In the course of studying the translation and the glide symmetries, a simple technique for characterizing a general system of N identical components in series (or cascade) is also developed, based on the linear algebra theory of factoring matrices into Jordan canonical forms. Applications of these results are presented in a follow-up paper [J. Opt. Soc. Am. 12, XXXX (1995)]. Copyright (c) 1995 Optical Society of America

Numerical implementation of the S-matrix algorithm for modeling of relief diffraction gratings

NASA Astrophysics Data System (ADS)

Yaremchuk, Iryna; Tamulevičius, Tomas; Fitio, Volodymyr; Gražulevičiūte, Ieva; Bobitski, Yaroslav; Tamulevičius, Sigitas

2013-11-01

A new numerical implementation is developed to calculate the diffraction efficiency of relief diffraction gratings. In the new formulation, vectors containing the expansion coefficients of electric and magnetic fields on boundaries of the grating layer are expressed by additional constants. An S-matrix algorithm has been systematically described in detail and adapted to a simple matrix form. This implementation is suitable for the study of optical characteristics of periodic structures by using modern object-oriented programming languages and different standard mathematical software. The modeling program has been developed on the basis of this numerical implementation and tested by comparison with other commercially available programs and experimental data. Numerical examples are given to show the usefulness of the new implementation.

Hating School, Loving Mathematics: On the Ideological Function of Critique and Reform in Mathematics Education

ERIC Educational Resources Information Center

Lundin, Sverker

2012-01-01

Students' engagement with fictions in the form of "word problems" plays an important role in classroom practice as well as in theories of mathematical learning. Drawing on the Dutch historian Johan Huizinga and the Austrian philosopher Robert Pfaller, I show that this activity can be seen as a form of "play" or "game," where it is pretended that…

Mathematics in the Early Years.

ERIC Educational Resources Information Center

Copley, Juanita V., Ed.

Noting that young children are capable of surprisingly complex forms of mathematical thinking and learning, this book presents a collection of articles depicting children discovering mathematical ideas, teachers fostering students' informal mathematical knowledge, adults asking questions and listening to answers, and researchers examining…

Research on Mathematics Teachers as Partners in Task Design

ERIC Educational Resources Information Center

Jones, Keith; Pepin, Birgit

2016-01-01

Mathematical tasks and tools, including tasks in the form of digital tools, are key resources in mathematics teaching and in mathematics teacher education. Even so, the "design" of mathematical tasks is perceived in different ways: sometimes seen as something distinct from the teaching and learning process, and sometimes as integral to…

The Emergence of Objects from Mathematical Practices

ERIC Educational Resources Information Center

Font, Vicenc; Godino, Juan D.; Gallardo, Jesus

2013-01-01

The nature of mathematical objects, their various types, the way in which they are formed, and how they participate in mathematical activity are all questions of interest for philosophy and mathematics education. Teaching in schools is usually based, implicitly or explicitly, on a descriptive/realist view of mathematics, an approach which is not…

Investigating Rural Pre-Service Teachers' Mathematics Anxiety Using the Revised Mathematics Anxiety Scale (RMARS)

ERIC Educational Resources Information Center

Wilson, Sue

2013-01-01

Engaging successfully in the modern technological society requires a command of mathematics. Hence, successfully engaging with mathematics has social, economic and political implications. There has been a history over a long period of time of significant numbers of people not forming productive relationships with learning mathematics. Failure in…

Development, triploblastism, physics of wetting and the Cambrian explosion.

PubMed

Fleury, Vincent

2013-09-01

The Cambrian explosion is characterized by the sudden outburst of organized animal plans, which occurred circa 530 M years ago. Around that time, many forms of animal life appeared, including several which have since disappeared. There is no general consensus about "why" this happened, and why it had any form of suddenness. However, all organized animal plans share a common feature: they are triploblastic, i.e., composed of 3 layers of tissue, endoderm, ectoderm and mesoderm. I show here that, within simple hypotheses, the formation of the mesoderm has intrinsically a physical exponential dynamics, leading rapidly to triploblastism, and eventually, to animal formation. A novel physico-mathematical framework including epithelium-mesenchyme transition, visco-elastic constitutive equations, and conservation laws, is presented which allows one to describe gastrulation as a self-wetting phenomenon of a soft solid onto itself. This phenomenon couples differentiation and migration during gastrulation, and leads in a closed form to an exponential scaling law for the formation of the mesoderm. Therefore, the Cambrian explosion might have started, actually, by a true viscoelastic "explosion": the exponential run-away of mesenchymal cells.

Secondary Teachers' Conception of Various Forms of Complex Numbers

ERIC Educational Resources Information Center

Karakok, Gulden; Soto-Johnson, Hortensia; Dyben, Stephenie Anderson

2015-01-01

This study explores in-service high school mathematics teachers' conception of various forms of complex numbers and ways in which they transition between different representations of these forms. One 90-min interview was conducted with three high school mathematics teachers after they completed three professional development sessions, each 4 h, on…

Visual Form Perception Can Be a Cognitive Correlate of Lower Level Math Categories for Teenagers.

PubMed

Cui, Jiaxin; Zhang, Yiyun; Cheng, Dazhi; Li, Dawei; Zhou, Xinlin

2017-01-01

Numerous studies have assessed the cognitive correlates of performance in mathematics, but little research has been conducted to systematically examine the relations between visual perception as the starting point of visuospatial processing and typical mathematical performance. In the current study, we recruited 223 seventh graders to perform a visual form perception task (figure matching), numerosity comparison, digit comparison, exact computation, approximate computation, and curriculum-based mathematical achievement tests. Results showed that, after controlling for gender, age, and five general cognitive processes (choice reaction time, visual tracing, mental rotation, spatial working memory, and non-verbal matrices reasoning), visual form perception had unique contributions to numerosity comparison, digit comparison, and exact computation, but had no significant relation with approximate computation or curriculum-based mathematical achievement. These results suggest that visual form perception is an important independent cognitive correlate of lower level math categories, including the approximate number system, digit comparison, and exact computation.

Strategy Choices in Simple and Complex Addition: Contributions of Working Memory and Counting Knowledge for Children with Mathematical Disability

ERIC Educational Resources Information Center

Geary, David C.; Hoard, Mary K.; Byrd-Craven, Jennifer; DeSoto, M. Catherine

2004-01-01

Groups of first-grade (mean age = 82 months), third-grade (mean age = 107 months), and fifth-grade (mean age = 131 months) children with a learning disability in mathematics (MD, n=58) and their normally achieving peers (n = 91) were administered tasks that assessed their knowledge of counting principles, working memory, and the strategies used to…

Development of mathematical models of environmental physiology

NASA Technical Reports Server (NTRS)

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

1971-01-01

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

Using Blended Learning to Facilitate the Mathematical thought Processes of Primary School Learners in a Computer Laboratory: A Case Study in Calculating Simple Areas

ERIC Educational Resources Information Center

Naidoo, N.; Naidoo, R.

2007-01-01

Primary school learners' first encounters with mathematics in a traditional learning environment often create lifelong "math phobia."(Papert 1980) The situation in a country emerging from an oppressive education system designed to educationally disempower the majority of the population is much worse. The typical scenario in a previously…

Assessing Quantitative Learning With The Math You Need When You Need It

NASA Astrophysics Data System (ADS)

Wenner, J. M.; Baer, E. M.; Burn, H.

2008-12-01

We present new data from a pilot project using the The Math You Need, When You Need It (TMYN) web resources in conjunction with several introductory geoscience courses. TMYN is a series of NSF-supported, NAGT-sponsored, web-based modular resources designed to help students learn (or relearn) mathematical skills essential for success in introductory geoscience courses. TMYN presents mathematical topics that are relevant to introductory geoscience based on a survey of more than 75 geoscience faculty members. To date, modules include unit conversions, many aspects of graphing, density calculations, rearranging equations and other simple mathematical concepts commonly used in the geosciences. The modular nature of the resources make it simple to select the units that are appropriate for a given course. In the fall of 2008, nine TMYN modules were tested in three courses taught at Highline Community College (Geology 101) and University of Wisconsin Oshkosh (Physical and Environmental Geology). Over 300 students participated in the study by taking pre- and post-tests and completing modules relevant to their course. Feedback about the use of these modules has been mixed. Initial results confirm anecdotal evidence that students initially have difficulty applying mathematical concepts to geologic problems. Furthermore, pre- test results indicate that, although instructors assume that students can perform simple mathematical manipulations, many students arrive in courses without the skills to apply mathematical concepts in problem solving situations. TMYN resources effectively provide support for learning quantitative problem solving and a mechanism for students to engage in self-teaching. Although we have seen mixed results due to a range of instructor engagement with the material, TMYN can have significant effect on students who are math phobic or "can't do math" because they can work at their own pace to overcome affective obstacles such as fear and dislike of mathematics. TMYN is most effective when instructors make explicit connections between material in the modules and course content. Instructors who participated in the study in Fall 2008 reacted positively to the use of TMYN in introductory geoscience courses because the resources require minimal class and prep time. Furthermore, when instructors can hold students responsible for the quantitative concepts covered with TMYN, they feel more comfortable including quantitative information without significant loss of geologic content.

Bringing metabolic networks to life: convenience rate law and thermodynamic constraints

PubMed Central

Liebermeister, Wolfram; Klipp, Edda

2006-01-01

Background Translating a known metabolic network into a dynamic model requires rate laws for all chemical reactions. The mathematical expressions depend on the underlying enzymatic mechanism; they can become quite involved and may contain a large number of parameters. Rate laws and enzyme parameters are still unknown for most enzymes. Results We introduce a simple and general rate law called "convenience kinetics". It can be derived from a simple random-order enzyme mechanism. Thermodynamic laws can impose dependencies on the kinetic parameters. Hence, to facilitate model fitting and parameter optimisation for large networks, we introduce thermodynamically independent system parameters: their values can be varied independently, without violating thermodynamical constraints. We achieve this by expressing the equilibrium constants either by Gibbs free energies of formation or by a set of independent equilibrium constants. The remaining system parameters are mean turnover rates, generalised Michaelis-Menten constants, and constants for inhibition and activation. All parameters correspond to molecular energies, for instance, binding energies between reactants and enzyme. Conclusion Convenience kinetics can be used to translate a biochemical network – manually or automatically - into a dynamical model with plausible biological properties. It implements enzyme saturation and regulation by activators and inhibitors, covers all possible reaction stoichiometries, and can be specified by a small number of parameters. Its mathematical form makes it especially suitable for parameter estimation and optimisation. Parameter estimates can be easily computed from a least-squares fit to Michaelis-Menten values, turnover rates, equilibrium constants, and other quantities that are routinely measured in enzyme assays and stored in kinetic databases. PMID:17173669

Exploring Measurement Error with Cookies: A Real and Virtual Approach via Interactive Excel

ERIC Educational Resources Information Center

Sinex, Scott A; Gage, Barbara A.; Beck, Peggy J.

2007-01-01

A simple, guided-inquiry investigation using stacked sandwich cookies is employed to develop a simple linear mathematical model and to explore measurement error by incorporating errors as part of the investigation. Both random and systematic errors are presented. The model and errors are then investigated further by engaging with an interactive…

Grass Grows, the Cow Eats: A Simple Grazing Systems Model with Emergent Properties

ERIC Educational Resources Information Center

Ungar, Eugene David; Seligman, Noam G.; Noy-Meir, Imanuel

2004-01-01

We describe a simple, yet intellectually challenging model of grazing systems that introduces basic concepts in ecology and systems analysis. The practical is suitable for high-school and university curricula with a quantitative orientation, and requires only basic skills in mathematics and spreadsheet use. The model is based on Noy-Meir's (1975)…

Cooperative Team Networks

DTIC Science & Technology

2016-06-01

team processes, such as identifying motifs of dynamic communication exchanges which goes well beyond simple dyadic and triadic configurations; as well...new metrics and ways to formulate team processes, such as identifying motifs of dynamic communication exchanges which goes well beyond simple dyadic ...sensing, communication , information, and decision networks - Darryl Ahner (AFIT: Air Force Inst Tech) Panel Session: Mathematical Models of

Turning Points of the Spherical Pendulum and the Golden Ratio

ERIC Educational Resources Information Center

Essen, Hanno; Apazidis, Nicholas

2009-01-01

We study the turning point problem of a spherical pendulum. The special cases of the simple pendulum and the conical pendulum are noted. For simple initial conditions the solution to this problem involves the golden ratio, also called the golden section, or the golden number. This number often appears in mathematics where you least expect it. To…

Student teachers’ mathematical questioning and courage in metaphorical thinking learning

NASA Astrophysics Data System (ADS)

Hendriana, H.; Hidayat, W.; Ristiana, M. G.

2018-01-01

This study was designed in the form of experiments with control group design and post-test only which aimed to examine the role of metaphorical thinking learning in the mathematical questioning ability of student teachers based on the level of mathematical courage. The population of this study was student teachers of mathematics education study program in West Java Province, while the sample of this study was 152 student teachers which were set purposively and then randomly to be included in the experimental class and control class. Based on the results and discussion, it was concluded that: (a) the mathematical questioning ability of student teachers who received Metaphorical Thinking learning was better than those who received conventional learning seen from mathematical courage level; (b) learning and mathematical courage level factors affected the achievement of student teachers’ mathematical questioning ability. In addition, there was no interaction effect between learning and mathematical courage level (high, medium, and low) simultaneously in developing student teachers’ mathematical questioning ability; (c) achievement of mastering mathematical questioning ability of student teacher was still not well achieved on indicator of problem posing in the form of non-routine question and open question.

Learning Abstract Physical Concepts from Experience: Design and Use of an RC Circuit

NASA Astrophysics Data System (ADS)

Parra, Alfredo; Ordenes, Jorge; de la Fuente, Milton

2018-05-01

Science learning for undergraduate students requires grasping a great number of theoretical concepts in a rather short time. In our experience, this is especially difficult when students are required to simultaneously use abstract concepts, mathematical reasoning, and graphical analysis, such as occurs when learning about RC circuits. We present a simple experimental model in this work that allows students to easily design, build, and analyze RC circuits, thus providing an opportunity to test personal ideas, build graphical descriptions, and explore the meaning of the respective mathematical models, ultimately gaining a better grasp of the concepts involved. The result suggests that the simple setup indeed helps untrained students to visualize the essential points of this kind of circuit.

The correlation structure of several popular pseudorandom number generators

NASA Technical Reports Server (NTRS)

Neuman, F.; Merrick, R.; Martin, C. F.

1973-01-01

One of the desirable properties of a pseudorandom number generator is that the sequence of numbers it generates should have very low autocorrelation for all shifts except for zero shift and those that are multiples of its cycle length. Due to the simple methods of constructing random numbers, the ideal is often not quite fulfilled. A simple method of examining any random generator for previously unsuspected regularities is discussed. Once they are discovered it is often easy to derive the mathematical relationships, which describe the mathematical relationships, which describe the regular behavior. As examples, it is shown that high correlation exists in mixed and multiplicative congruential random number generators and prime moduli Lehmer generators for shifts a fraction of their cycle lengths.

Local Norms and Test Characteristics for Selected Forms of the M.A.A. Placement Test.

ERIC Educational Resources Information Center

Melancon, Janet G.; Thompson, Bruce

The psychometric integrity of selected items from the Mathematics Association of America (MAA) placement tests for college students was investigated. Two alternative and parallel versions of the test were developed (Form A and Form B) for this study. Data for 539 students seeking admission into an undergraduate mathematics curriculum at a private…

Bilingual Teaching Research and Practice of Complex Function Theory

ERIC Educational Resources Information Center

Ma, Lixin

2011-01-01

Mathematics bilingual teaching is assisted in Chinese with English teaching, and gradually enables students to independently use English to learn, study, reflect and exchange Mathematics. In order to better carry out mathematics teaching, department of mathematics in Dezhou University forms discussion groups and launches bilingual teaching…

Forming Positive Identities to Enhance Mathematics Learning among Adolescents

ERIC Educational Resources Information Center

Mkhize, Duduzile Rosemary

2017-01-01

Learners' participation in mathematics decreases during their transition from primary to high school. This is despite adolescents' cognitive growth equipping them with enhanced cognitive ability; to learn mathematics. Hence low participation in mathematics does not result from cognitive deficiency. Rather, lack of motivation to learn mathematics…

Equating Two Forms of a Criterion-Referenced Test by Using Norm Referenced Data: An Illustration of Two Methods.

ERIC Educational Resources Information Center

Garcia-Quintana, Roan A.; Johnson, Lynne M.

Three different computational procedures for equating two forms of a test were applied to a pair of mathematics tests to compare the results of the three procedures. The tests that were being equated were two forms of the SRA Mastery Mathematics Tests. The common, linking test used for equating was the Comprehensive Tests of Basic Skills, Form S,…

[Digital processing and evaluation of ultrasound images].

PubMed

Borchers, J; Klews, P M

1993-10-01

With the help of workstations and PCs, on-site image processing has become possible. If the images are not available in digital form the video signal has to be A/D converted. In the case of colour images the colour channels R (red), G (green) and B (blue) have to be digitized separately. "Truecolour" imaging calls for an 8 bit resolution per channel, leading to 24 bits per pixel. Out of a pool of 2(24) possible values only the relevant 128 gray values and 64 shades of red and blue respectively needed for a colour-coded ultrasound image have to be isolated. Digital images can be changed and evaluated with the help of readily available image evaluation programmes. It is mandatory that during image manipulation the gray scale and colour pixels and LUTs (Look-Up-Table) must be worked on separately. Using relatively simple LUT manipulations astonishing image improvements are possible. Application of simple mathematical operations can lead to completely new clinical results. For example, by subtracting two consecutive colour flow images in time and special LUT operations, local acceleration of blood flow can be visualized (Colour Acceleration Imaging).

Analytical and numerical construction of equivalent cables.

PubMed

Lindsay, K A; Rosenberg, J R; Tucker, G

2003-08-01

The mathematical complexity experienced when applying cable theory to arbitrarily branched dendrites has lead to the development of a simple representation of any branched dendrite called the equivalent cable. The equivalent cable is an unbranched model of a dendrite and a one-to-one mapping of potentials and currents on the branched model to those on the unbranched model, and vice versa. The piecewise uniform cable, with a symmetrised tri-diagonal system matrix, is shown to represent the canonical form for an equivalent cable. Through a novel application of the Laplace transform it is demonstrated that an arbitrary branched model of a dendrite can be transformed to the canonical form of an equivalent cable. The characteristic properties of the equivalent cable are extracted from the matrix for the transformed branched model. The one-to-one mapping follows automatically from the construction of the equivalent cable. The equivalent cable is used to provide a new procedure for characterising the location of synaptic contacts on spinal interneurons.

The skewed weak lensing likelihood: why biases arise, despite data and theory being sound

NASA Astrophysics Data System (ADS)

Sellentin, Elena; Heymans, Catherine; Harnois-Déraps, Joachim

2018-07-01

We derive the essentials of the skewed weak lensing likelihood via a simple hierarchical forward model. Our likelihood passes four objective and cosmology-independent tests which a standard Gaussian likelihood fails. We demonstrate that sound weak lensing data are naturally biased low, since they are drawn from a skewed distribution. This occurs already in the framework of Lambda cold dark matter. Mathematically, the biases arise because noisy two-point functions follow skewed distributions. This form of bias is already known from cosmic microwave background analyses, where the low multipoles have asymmetric error bars. Weak lensing is more strongly affected by this asymmetry as galaxies form a discrete set of shear tracer particles, in contrast to a smooth shear field. We demonstrate that the biases can be up to 30 per cent of the standard deviation per data point, dependent on the properties of the weak lensing survey and the employed filter function. Our likelihood provides a versatile framework with which to address this bias in future weak lensing analyses.

The skewed weak lensing likelihood: why biases arise, despite data and theory being sound.

NASA Astrophysics Data System (ADS)

Sellentin, Elena; Heymans, Catherine; Harnois-Déraps, Joachim

2018-04-01

We derive the essentials of the skewed weak lensing likelihood via a simple Hierarchical Forward Model. Our likelihood passes four objective and cosmology-independent tests which a standard Gaussian likelihood fails. We demonstrate that sound weak lensing data are naturally biased low, since they are drawn from a skewed distribution. This occurs already in the framework of ΛCDM. Mathematically, the biases arise because noisy two-point functions follow skewed distributions. This form of bias is already known from CMB analyses, where the low multipoles have asymmetric error bars. Weak lensing is more strongly affected by this asymmetry as galaxies form a discrete set of shear tracer particles, in contrast to a smooth shear field. We demonstrate that the biases can be up to 30% of the standard deviation per data point, dependent on the properties of the weak lensing survey and the employed filter function. Our likelihood provides a versatile framework with which to address this bias in future weak lensing analyses.

Mathematical model for determining the effects of intracytoplasmic inclusions on volume and density of microorganisms.

PubMed Central

Mas, J; Pedrós-Alió, C; Guerrero, R

1985-01-01

Procaryotic microorganisms accumulate several polymers in the form of intracellular inclusions as a strategy to increase survival in a changing environment. Such inclusions avoid osmotic pressure increases by tightly packaging certain macromolecules into the inclusion. In the present paper, a model describing changes in volume and density of the microbial cell as a function of the weight of the macromolecule forming the inclusion is derived from simple theoretical principles. The model is then tested by linear regression with experimental data from glycogen accumulation in Escherichia coli, poly-beta-hydroxybutyrate accumulation in Alcaligenes eutrophus, and sulfur accumulation in Chromatium spp. The model predicts a certain degree of hydration of the polymer in the inclusion and explains both the linear relationship between volume of the cell and weight of the polymer and the hyperbolic relationship between density of the cell and weight of the polymer. Other implications of the model are also discussed. PMID:3902798

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.

The Eye of a Mathematical Physicist

NASA Astrophysics Data System (ADS)

Hepp, Klaus

2009-03-01

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

The Functional Use of a Mathematical Sign

ERIC Educational Resources Information Center

Berger, Margot

2004-01-01

The question of how a mathematics student at university-level makes sense of a new mathematical sign, presented to her or him in the form of a definition, is a fundamental problem in mathematics education. Using an analogy with Vygotsky's theory (1986, 1994) of how a child learns a new word, I argue that a learner uses a new mathematical sign both…

Sundanese Ethnomathematics: Mathematical Activities in Estimating, Measuring, and Making Patterns

ERIC Educational Resources Information Center

Muhtadi, Dedi; Sukirwan; Warsito; Prahmana, Rully Charitas Indra

2017-01-01

Mathematics is a form of culture integrated in all aspects of society, wherever there are, including the sundanese ethnic communities. This enables the mathematical concepts embedded in cultural practices and recognizes that all people develop a special way of doing mathematics called ethnomathematics activities. Sundanese ethnomathematics is…

A Preschool Program for Preventing Learning Difficulties in Arithmetic.

ERIC Educational Resources Information Center

Dunlap, William P.

Described are many concrete readiness activities within ten broad categories that are designed to provide children with a solid foundation for mathematics and that help prevent learning difficulties in mathematics. Preschool mathematical experiences form the foundation for all studies in mathematics. Without a sufficient number of appropriate…

Factors That Explains Student Anxiety toward Mathematics

ERIC Educational Resources Information Center

García-Santillán, Arturo; Escalera-Chávez, Milka Elena; Moreno-García, Elena; Santana-Villegas, Josefina del Carmen

2016-01-01

The aim of this research is to test whether anxiety toward mathematics is made up of a five-factor structure: anxiety toward evaluation, anxiety toward temporality, anxiety toward understanding of mathematical problems, anxiety toward numbers and operations, and anxiety toward mathematical situations in real life. Our study sample was formed of…

A Guided Reinvention of Ring, Integral Domain, and Field

ERIC Educational Resources Information Center

Cook, John Paul

2012-01-01

Abstract algebra enjoys a prestigious position in mathematics and the undergraduate mathematics curriculum. A typical abstract algebra course aims to provide students with a glimpse into the elegance of mathematics by exposing them to structures that form its foundation--it arguably approximates the actual practice of mathematics better than any…

On Fences, Forms and Mathematical Modeling

ERIC Educational Resources Information Center

Lege, Jerry

2009-01-01

The white picket fence is an integral component of the iconic American townscape. But, for mathematics students, it can be a mathematical challenge. Picket fences in a variety of styles serve as excellent sources to model constant, step, absolute value, and sinusoidal functions. "Principles and Standards for School Mathematics" (NCTM 2000)…

Delivering Online Professional Development in Mathematics to Rural Educators

ERIC Educational Resources Information Center

Cady, Jo; Rearden, Kristin

2009-01-01

Rural school districts struggle to attract, retain, and support highly qualified mathematics teachers. A series of four online professional development courses in the form of integrated mathematics content and pedagogy courses was designed to meet the professional development needs of rural middle school mathematics teachers. Changes in teachers'…

Mathematics Teaching as Praxis

ERIC Educational Resources Information Center

Grootenboer, Peter; Edwards-Groves, Christine

2014-01-01

In this paper we argue that mathematics teaching can be conceptualised as a form of praxis. Viewing mathematics teaching as praxis foregrounds the moral nature of teaching and the educational practices that are developed in response to the educational needs in particular sites. The case for praxis in mathematics education is then made by drawing…

Teaching Preschoolers to Count: Effective Strategies for Achieving Early Mathematics Milestones

ERIC Educational Resources Information Center

Jacobi-Vessels, Jill L.; Brown, E. Todd; Molfese, Victoria J.; Do, Ahn

2016-01-01

Attention to early childhood mathematics instructional strategies has sharpened due to the relatively poor mathematics performance of U.S. students in comparison to students from other countries and research evidence that early mathematics skills impact later achievement. Early Childhood counting skills form the foundation for subsequent…

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…

Analysis of junior high school students' attempt to solve a linear inequality problem

NASA Astrophysics Data System (ADS)

Taqiyuddin, Muhammad; Sumiaty, Encum; Jupri, Al

2017-08-01

Linear inequality is one of fundamental subjects within junior high school mathematics curricula. Several studies have been conducted to asses students' perform on linear inequality. However, it can hardly be found that linear inequality problems are in the form of "ax + b < dx + e" with "a, d ≠ 0", and "a ≠ d" as it can be seen on the textbook used by Indonesian students and several studies. This condition leads to the research questions concerning students' attempt on solving a simple linear inequality problem in this form. In order to do so, the written test was administered to 58 students from two schools in Bandung followed by interviews. The other sources of the data are from teachers' interview and mathematics books used by students. After that, the constant comparative method was used to analyse the data. The result shows that the majority approached the question by doing algebraic operations. Interestingly, most of them did it incorrectly. In contrast, algebraic operations were correctly used by some of them. Moreover, the others performed expected-numbers solution, rewriting the question, translating the inequality into words, and blank answer. Furthermore, we found that there is no one who was conscious of the existence of all-numbers solution. It was found that this condition is reasonably due to how little the learning components concern about why a procedure of solving a linear inequality works and possibilities of linear inequality solution.

Spectrophotometric resolution of the severely overlapped spectra of clotrimazole with dexamethasone in cream dosage form by mathematical manipulation steps.

PubMed

Lotfy, Hayam Mahmoud; Fayez, Yasmin Mohammed; Tawakkol, Shereen Mostafa; Fahmy, Nesma Mahmoud; Shehata, Mostafa Abd El-Atty

2018-09-05

Several spectrophotometric techniques were recently conducted for the determination of binary mixtures of clotrimazole (CLT) and dexamethasone acetate (DA) without any separation procedure. The methods were based on generation of ratio spectra of mixture then applying simple mathematic manipulation. The zero order absorption spectra of both drugs could be obtained by the constant center (CC) method. The concentration of both CLT and DA could be obtained by constant value via amplitude difference (CV-AD) method depending on ratio spectra, Ratio difference (RD) method where the difference between the amplitudes at two wavelengths (ΔP) on the ratio spectra could eliminate the contribution of the interfering substance and bring the concentration of the other, and the derivative ratio (DD 1 ) method where the derivative of the ratio spectra was able to determine the drug of interest without any interference of the other one. While the concentration of DA could be measured after graphical manipulation as concentration using the novel advanced concentration value method (ACV). Calibration graphs were linear in the range of 75-550 μg/mL for CLT and 2-20 μg/mL for DA. The methods applied to the binary mixture under study were successfully applied for the simultaneous determination of the two drugs in synthetic mixtures and in their combined form Mycuten-D cream. The results obtained were compared statistically to each other and to the official methods. Copyright © 2018 Elsevier B.V. All rights reserved.

The Relative Importance of Children's Criteria for Representational Adequacy in the Perception of Simple Sonic Stimuli

ERIC Educational Resources Information Center

Verschaffel, Lieven; Reybrouck, Mark; Degraeuwe, Goedele; Van Dooren, Wim

2013-01-01

This study investigates children's metarepresentational competence (MRC) with regard to listening to and making sense of simple sonic stimuli. Using diSessa's (2002) seminal work on MRC in mathematics and sciences as background, it aims to assess the relative importance children attribute to several criteria for representational adequacy…

Pizza Again? On the Division of Polygons into Sections with a Common Origin

ERIC Educational Resources Information Center

Sinitsky, Ilya; Stupel, Moshe; Sinitsky, Marina

2018-01-01

The paper explores the division of a polygon into equal-area pieces using line segments originating at a common point. The mathematical background of the proposed method is very simple and belongs to secondary school geometry. Simple examples dividing a square into two, four or eight congruent pieces provide a starting point to discovering how to…

Projectiles, pendula, and special relativity

NASA Astrophysics Data System (ADS)

Price, Richard H.

2005-05-01

The kind of flat-earth gravity used in introductory physics appears in an accelerated reference system in special relativity. From this viewpoint, we work out the special relativistic description of a ballistic projectile and a simple pendulum, two examples of simple motion driven by earth-surface gravity. The analysis uses only the basic mathematical tools of special relativity typical of a first-year university course.

Cortical circuits for mathematical knowledge: evidence for a major subdivision within the brain's semantic networks.

PubMed

Amalric, Marie; Dehaene, Stanislas

2017-02-19

Is mathematical language similar to natural language? Are language areas used by mathematicians when they do mathematics? And does the brain comprise a generic semantic system that stores mathematical knowledge alongside knowledge of history, geography or famous people? Here, we refute those views by reviewing three functional MRI studies of the representation and manipulation of high-level mathematical knowledge in professional mathematicians. The results reveal that brain activity during professional mathematical reflection spares perisylvian language-related brain regions as well as temporal lobe areas classically involved in general semantic knowledge. Instead, mathematical reflection recycles bilateral intraparietal and ventral temporal regions involved in elementary number sense. Even simple fact retrieval, such as remembering that 'the sine function is periodical' or that 'London buses are red', activates dissociated areas for math versus non-math knowledge. Together with other fMRI and recent intracranial studies, our results indicated a major separation between two brain networks for mathematical and non-mathematical semantics, which goes a long way to explain a variety of facts in neuroimaging, neuropsychology and developmental disorders.This article is part of a discussion meeting issue 'The origins of numerical abilities'. © 2017 The Author(s).

77 FR 76604 - Submission for OMB Review; Comment Request

Federal Register 2010, 2011, 2012, 2013, 2014

2012-12-28

... currently approved collection. Title: Form 5304-SIMPLE; Form 5305-SIMPLE; Notice 98-4. Abstract: Forms 5304-SIMPLE and 5035-SIMPLE are used by an employer to permit employees to make salary reduction contributions to a savings incentive match plan (SIMPLE IRA) described in Code section 408(p). These forms are not...

Cutting Materials in Half: A Graph Theory Approach for Generating Crystal Surfaces and Its Prediction of 2D Zeolites

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

Witman, Matthew; Ling, Sanliang; Boyd, Peter

Scientific interest in two-dimensional (2D) materials, ranging from graphene and other single layer materials to atomically thin crystals, is quickly increasing for a large variety of technological applications. While in silico design approaches have made a large impact in the study of 3D crystals, algorithms designed to discover atomically thin 2D materials from their parent 3D materials are by comparison more sparse. Here, we hypothesize that determining how to cut a 3D material in half (i.e., which Miller surface is formed) by severing a minimal number of bonds or a minimal amount of total bond energy per unit area canmore » yield insight into preferred crystal faces. We answer this question by implementing a graph theory technique to mathematically formalize the enumeration of minimum cut surfaces of crystals. While the algorithm is generally applicable to different classes of materials, we focus on zeolitic materials due to their diverse structural topology and because 2D zeolites have promising catalytic and separation performance compared to their 3D counterparts. We report here a simple descriptor based only on structural information that predicts whether a zeolite is likely to be synthesizable in the 2D form and correctly identifies the expressed surface in known layered 2D zeolites. The discovery of this descriptor allows us to highlight other zeolites that may also be synthesized in the 2D form that have not been experimentally realized yet. Finally, our method is general since the mathematical formalism can be applied to find the minimum cut surfaces of other crystallographic materials such as metal-organic frameworks, covalent-organic frameworks, zeolitic-imidazolate frameworks, metal oxides, etc.« less

Cutting Materials in Half: A Graph Theory Approach for Generating Crystal Surfaces and Its Prediction of 2D Zeolites.

PubMed

Witman, Matthew; Ling, Sanliang; Boyd, Peter; Barthel, Senja; Haranczyk, Maciej; Slater, Ben; Smit, Berend

2018-02-28

Scientific interest in two-dimensional (2D) materials, ranging from graphene and other single layer materials to atomically thin crystals, is quickly increasing for a large variety of technological applications. While in silico design approaches have made a large impact in the study of 3D crystals, algorithms designed to discover atomically thin 2D materials from their parent 3D materials are by comparison more sparse. We hypothesize that determining how to cut a 3D material in half (i.e., which Miller surface is formed) by severing a minimal number of bonds or a minimal amount of total bond energy per unit area can yield insight into preferred crystal faces. We answer this question by implementing a graph theory technique to mathematically formalize the enumeration of minimum cut surfaces of crystals. While the algorithm is generally applicable to different classes of materials, we focus on zeolitic materials due to their diverse structural topology and because 2D zeolites have promising catalytic and separation performance compared to their 3D counterparts. We report here a simple descriptor based only on structural information that predicts whether a zeolite is likely to be synthesizable in the 2D form and correctly identifies the expressed surface in known layered 2D zeolites. The discovery of this descriptor allows us to highlight other zeolites that may also be synthesized in the 2D form that have not been experimentally realized yet. Finally, our method is general since the mathematical formalism can be applied to find the minimum cut surfaces of other crystallographic materials such as metal-organic frameworks, covalent-organic frameworks, zeolitic-imidazolate frameworks, metal oxides, etc.

Cutting Materials in Half: A Graph Theory Approach for Generating Crystal Surfaces and Its Prediction of 2D Zeolites

PubMed Central

2018-01-01

Scientific interest in two-dimensional (2D) materials, ranging from graphene and other single layer materials to atomically thin crystals, is quickly increasing for a large variety of technological applications. While in silico design approaches have made a large impact in the study of 3D crystals, algorithms designed to discover atomically thin 2D materials from their parent 3D materials are by comparison more sparse. We hypothesize that determining how to cut a 3D material in half (i.e., which Miller surface is formed) by severing a minimal number of bonds or a minimal amount of total bond energy per unit area can yield insight into preferred crystal faces. We answer this question by implementing a graph theory technique to mathematically formalize the enumeration of minimum cut surfaces of crystals. While the algorithm is generally applicable to different classes of materials, we focus on zeolitic materials due to their diverse structural topology and because 2D zeolites have promising catalytic and separation performance compared to their 3D counterparts. We report here a simple descriptor based only on structural information that predicts whether a zeolite is likely to be synthesizable in the 2D form and correctly identifies the expressed surface in known layered 2D zeolites. The discovery of this descriptor allows us to highlight other zeolites that may also be synthesized in the 2D form that have not been experimentally realized yet. Finally, our method is general since the mathematical formalism can be applied to find the minimum cut surfaces of other crystallographic materials such as metal–organic frameworks, covalent-organic frameworks, zeolitic-imidazolate frameworks, metal oxides, etc. PMID:29532024

Cutting Materials in Half: A Graph Theory Approach for Generating Crystal Surfaces and Its Prediction of 2D Zeolites

DOE PAGES

Witman, Matthew; Ling, Sanliang; Boyd, Peter; ...

2018-02-06

Scientific interest in two-dimensional (2D) materials, ranging from graphene and other single layer materials to atomically thin crystals, is quickly increasing for a large variety of technological applications. While in silico design approaches have made a large impact in the study of 3D crystals, algorithms designed to discover atomically thin 2D materials from their parent 3D materials are by comparison more sparse. Here, we hypothesize that determining how to cut a 3D material in half (i.e., which Miller surface is formed) by severing a minimal number of bonds or a minimal amount of total bond energy per unit area canmore » yield insight into preferred crystal faces. We answer this question by implementing a graph theory technique to mathematically formalize the enumeration of minimum cut surfaces of crystals. While the algorithm is generally applicable to different classes of materials, we focus on zeolitic materials due to their diverse structural topology and because 2D zeolites have promising catalytic and separation performance compared to their 3D counterparts. We report here a simple descriptor based only on structural information that predicts whether a zeolite is likely to be synthesizable in the 2D form and correctly identifies the expressed surface in known layered 2D zeolites. The discovery of this descriptor allows us to highlight other zeolites that may also be synthesized in the 2D form that have not been experimentally realized yet. Finally, our method is general since the mathematical formalism can be applied to find the minimum cut surfaces of other crystallographic materials such as metal-organic frameworks, covalent-organic frameworks, zeolitic-imidazolate frameworks, metal oxides, etc.« less

The Adaptation of the Mathematics Anxiety Rating Scale-Elementary Form into Turkish, Language Validity, and Preliminary Psychometric Investigation

ERIC Educational Resources Information Center

Baloglu, Mustafa; Balgalmis, Esra

2010-01-01

The purpose of the present study was to adapt the Mathematics Anxiety Rating Scale- Elementary Form (MARS-E, Suinn, 1988) into Turkish by first doing the translation of its items and then the preliminary psychometric investigation of the Turkish form. The study included four different samples: 30 bilingual language experts, 50 Turkish language…

Visual Form Perception Can Be a Cognitive Correlate of Lower Level Math Categories for Teenagers

PubMed Central

Cui, Jiaxin; Zhang, Yiyun; Cheng, Dazhi; Li, Dawei; Zhou, Xinlin

2017-01-01

Numerous studies have assessed the cognitive correlates of performance in mathematics, but little research has been conducted to systematically examine the relations between visual perception as the starting point of visuospatial processing and typical mathematical performance. In the current study, we recruited 223 seventh graders to perform a visual form perception task (figure matching), numerosity comparison, digit comparison, exact computation, approximate computation, and curriculum-based mathematical achievement tests. Results showed that, after controlling for gender, age, and five general cognitive processes (choice reaction time, visual tracing, mental rotation, spatial working memory, and non-verbal matrices reasoning), visual form perception had unique contributions to numerosity comparison, digit comparison, and exact computation, but had no significant relation with approximate computation or curriculum-based mathematical achievement. These results suggest that visual form perception is an important independent cognitive correlate of lower level math categories, including the approximate number system, digit comparison, and exact computation. PMID:28824513

A Simple Colorimeter.

ERIC Educational Resources Information Center

Martinez-Anton, J. C.; And Others

1995-01-01

Describes a system that demonstrates how a color may be generated and specified in mathematical terms. Illustrates the mixing of primary colors as well as the concepts of saturation, luminance, and illumination. (JRH)

Data-driven outbreak forecasting with a simple nonlinear growth model

PubMed Central

Lega, Joceline; Brown, Heidi E.

2016-01-01

Recent events have thrown the spotlight on infectious disease outbreak response. We developed a data-driven method, EpiGro, which can be applied to cumulative case reports to estimate the order of magnitude of the duration, peak and ultimate size of an ongoing outbreak. It is based on a surprisingly simple mathematical property of many epidemiological data sets, does not require knowledge or estimation of disease transmission parameters, is robust to noise and to small data sets, and runs quickly due to its mathematical simplicity. Using data from historic and ongoing epidemics, we present the model. We also provide modeling considerations that justify this approach and discuss its limitations. In the absence of other information or in conjunction with other models, EpiGro may be useful to public health responders. PMID:27770752

A new formulation for anisotropic radiative transfer problems. I - Solution with a variational technique

NASA Technical Reports Server (NTRS)

Cheyney, H., III; Arking, A.

1976-01-01

The equations of radiative transfer in anisotropically scattering media are reformulated as linear operator equations in a single independent variable. The resulting equations are suitable for solution by a variety of standard mathematical techniques. The operators appearing in the resulting equations are in general nonsymmetric; however, it is shown that every bounded linear operator equation can be embedded in a symmetric linear operator equation and a variational solution can be obtained in a straightforward way. For purposes of demonstration, a Rayleigh-Ritz variational method is applied to three problems involving simple phase functions. It is to be noted that the variational technique demonstrated is of general applicability and permits simple solutions for a wide range of otherwise difficult mathematical problems in physics.

Computer simulation of two electrophoretic columns coupled for isoelectric focusing in simple buffers

NASA Technical Reports Server (NTRS)

Tsai, Amos; Mosher, Richard A.; Bier, Milan

1986-01-01

Computer simulation is used to analyze a system of two electrophoretic columns coupled by mixing the anolyte of one with the catholyte of the other. A mathematical model is presented which is used to predict the pH gradients formed by monovalent buffers in this system, when the currents in the columns are unequal. In the column with the higher current a pH gradient is created which increases from anode to cathode and is potentially useful for isoelectric focusing. The breadth of this gradient is dependent upon the ratio of the currents. The function of the second column is the compensation of buffer migration which occurs in the first column, thereby maintaining constant electrolyte composition. The effects of buffer pKs and mobilities are evaluated.

Complexity and diversity.

PubMed

Doebeli, Michael; Ispolatov, Iaroslav

2010-04-23

The mechanisms for the origin and maintenance of biological diversity are not fully understood. It is known that frequency-dependent selection, generating advantages for rare types, can maintain genetic variation and lead to speciation, but in models with simple phenotypes (that is, low-dimensional phenotype spaces), frequency dependence needs to be strong to generate diversity. However, we show that if the ecological properties of an organism are determined by multiple traits with complex interactions, the conditions needed for frequency-dependent selection to generate diversity are relaxed to the point where they are easily satisfied in high-dimensional phenotype spaces. Mathematically, this phenomenon is reflected in properties of eigenvalues of quadratic forms. Because all living organisms have at least hundreds of phenotypes, this casts the potential importance of frequency dependence for the origin and maintenance of diversity in a new light.

Point and path performance of light aircraft: A review and analysis

NASA Technical Reports Server (NTRS)

Smetana, F. O.; Summey, D. C.; Johnson, W. D.

1973-01-01

The literature on methods for predicting the performance of light aircraft is reviewed. The methods discussed in the review extend from the classical instantaneous maximum or minimum technique to techniques for generating mathematically optimum flight paths. Classical point performance techniques are shown to be adequate in many cases but their accuracies are compromised by the need to use simple lift, drag, and thrust relations in order to get closed form solutions. Also the investigation of the effect of changes in weight, altitude, configuration, etc. involves many essentially repetitive calculations. Accordingly, computer programs are provided which can fit arbitrary drag polars and power curves with very high precision and which can then use the resulting fits to compute the performance under the assumption that the aircraft is not accelerating.

Helping parents to motivate adolescents in mathematics and science: an experimental test of a utility-value intervention.

PubMed

Harackiewicz, Judith M; Rozek, Christopher S; Hulleman, Chris S; Hyde, Janet S

2012-08-01

The pipeline toward careers in science, technology, engineering, and mathematics (STEM) begins to leak in high school, when some students choose not to take advanced mathematics and science courses. We conducted a field experiment testing whether a theory-based intervention that was designed to help parents convey the importance of mathematics and science courses to their high school-aged children would lead them to take more mathematics and science courses in high school. The three-part intervention consisted of two brochures mailed to parents and a Web site, all highlighting the usefulness of STEM courses. This relatively simple intervention led students whose parents were in the experimental group to take, on average, nearly one semester more of science and mathematics in the last 2 years of high school, compared with the control group. Parents are an untapped resource for increasing STEM motivation in adolescents, and the results demonstrate that motivational theory can be applied to this important pipeline problem.

McDonald's vs Father Christmas

ERIC Educational Resources Information Center

Pratt, Dave; Simpson, Amanda

2004-01-01

Mathematics in textbooks and indeed in conventional classrooms is often presented as exercises or worksheets in which the mathematics itself has been processed into a form that is easily digested. This McDonald's version of mathematics ensures that the mathematical skill or technique is laid bare and typically the sole focus of attention. In this…

Leveling of Critical Thinking Abilities of Students of Mathematics Education in Mathematical Problem Solving

ERIC Educational Resources Information Center

Rasiman

2015-01-01

This research aims to determine the leveling of critical thinking abilities of students of mathematics education in mathematical problem solving. It includes qualitative-explorative study that was conducted at University of PGRI Semarang. The generated data in the form of information obtained problem solving question and interview guides. The…

Working Memory and Language: Skill-Specific or Domain-General Relations to Mathematics?

ERIC Educational Resources Information Center

Purpura, David J.; Ganley, Colleen M.

2014-01-01

Children's early mathematics skills develop in a cumulative fashion; foundational skills form a basis for the acquisition of later skills. However, non-mathematical factors such as working memory and language skills have also been linked to mathematical development at a broad level. Unfortunately, little research has been conducted to evaluate the…

Reflections on a Technology-Rich Mathematics Classroom

ERIC Educational Resources Information Center

Hodges, Thomas E.; Conner, Elizabeth

2011-01-01

Integrating technology into the mathematics classroom means more than just new teaching tools--it is an opportunity to redefine what it means to teach and learn mathematics. Yet deciding when a particular form of technology may be appropriate for a specific mathematics topic can be difficult. Such decisions center on what is commonly being…

Approaches to Studying the Enacted Mathematics Curriculum. Research in Mathematics Education

ERIC Educational Resources Information Center

Heck, Dan, Ed.; Chval, Kathryn, Ed.; Weiss, Iris, Ed.; Ziebarth, Steven W., Ed.

2012-01-01

Curriculum materials are among the most pervasive and powerful influences on school mathematics. In many mathematics classes, student assignments, the questions the teacher asks, the ways students are grouped, the forms of assessment, and much more originate in curriculum materials. At the same time, teachers have considerable latitude in how they…

Analysing the Mathematical Experience: Posing the "What Is Mathematics?" Question

ERIC Educational Resources Information Center

Padula, Janice

2011-01-01

In this paper, different schools of thought are discussed and compared to encourage lively classroom discussion and interest in mathematics for high achieving Form 12 students and first (or higher) year university students enrolled in a mathematics degree program. In particular the work and views of two mathematicians, Kurt Godel (1931) and Ian…

Opinions of Secondary School Mathematics Teachers on Mathematical Modelling

ERIC Educational Resources Information Center

Tutak, Tayfun; Güder, Yunus

2013-01-01

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

GENASIS Mathematics : Object-oriented manifolds, operations, and solvers for large-scale physics simulations

NASA Astrophysics Data System (ADS)

Cardall, Christian Y.; Budiardja, Reuben D.

2018-01-01

The large-scale computer simulation of a system of physical fields governed by partial differential equations requires some means of approximating the mathematical limit of continuity. For example, conservation laws are often treated with a 'finite-volume' approach in which space is partitioned into a large number of small 'cells,' with fluxes through cell faces providing an intuitive discretization modeled on the mathematical definition of the divergence operator. Here we describe and make available Fortran 2003 classes furnishing extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon, along with individual 'unit test' programs and larger example problems demonstrating their use. These classes inaugurate the Mathematics division of our developing astrophysics simulation code GENASIS (Gen eral A strophysical Si mulation S ystem), which will be expanded over time to include additional meshing options, mathematical operations, solver types, and solver variations appropriate for many multiphysics applications.

pyomocontrib_simplemodel v. 1.0

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

Hart, William

2017-03-02

Pyomo supports the formulation and analysis of mathematical models for complex optimization applications. This library extends the API of Pyomo to include a simple modeling representation: a list of objectives and constraints.

Optimal quality control of bakers' yeast fed-batch culture using population dynamics.

PubMed

Dairaku, K; Izumoto, E; Morikawa, H; Shioya, S; Takamatsu, T

1982-12-01

An optimal quality control policy for the overall specific growth rate of bakers' yeast, which maximizes the fermentative activity in the making of bread, was obtained by direct searching based on the mathematical model proposed previously. The mathematical model had described the age distribution of bakers' yeast which had an essential relationship to the ability of fermentation in the making of bread. The mathematical model is a simple aging model with two periods: Nonbudding and budding. Based on the result obtained by direct searching, the quality control of bakers' yeast fed-batch culture was performed and confirmed to be experimentally valid.

Dannie Heineman Prize for Mathematical Physics: Applying mathematical techniques to solve important problems in quantum theory

NASA Astrophysics Data System (ADS)

Bender, Carl

2017-01-01

The theory of complex variables is extremely useful because it helps to explain the mathematical behavior of functions of a real variable. Complex variable theory also provides insight into the nature of physical theories. For example, it provides a simple and beautiful picture of quantization and it explains the underlying reason for the divergence of perturbation theory. By using complex-variable methods one can generalize conventional Hermitian quantum theories into the complex domain. The result is a new class of parity-time-symmetric (PT-symmetric) theories whose remarkable physical properties have been studied and verified in many recent laboratory experiments.

A simple mathematical model of society collapse applied to Easter Island

NASA Astrophysics Data System (ADS)

Bologna, M.; Flores, J. C.

2008-02-01

In this paper we consider a mathematical model for the evolution and collapse of the Easter Island society. Based on historical reports, the available primary resources consisted almost exclusively in the trees, then we describe the inhabitants and the resources as an isolated dynamical system. A mathematical, and numerical, analysis about the Easter Island community collapse is performed. In particular, we analyze the critical values of the fundamental parameters and a demographic curve is presented. The technological parameter, quantifying the exploitation of the resources, is calculated and applied to the case of another extinguished civilization (Copán Maya) confirming the consistency of the adopted model.

Introduction to Solar Motion Geometry on the Basis of a Simple Model

ERIC Educational Resources Information Center

Khavrus, Vyacheslav; Shelevytsky, Ihor

2010-01-01

By means of a simple mathematical model developed by the authors, the apparent movement of the Sun can be studied for arbitrary latitudes. Using this model, it is easy to gain insight into various phenomena, such as the passage of the seasons, dependences of position and time of sunrise or sunset on a specific day of year, day duration for…

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

PubMed Central

Wang, Li; Sun, Yuhua; Zhou, Xinlin

2016-01-01

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

Educational Technologies and Mathematics: Signature Pedagogies and Learner Impacts

ERIC Educational Resources Information Center

Passey, Don

2012-01-01

In this article the author focuses on signature pedagogies that are associated with different forms of educational technologies. The author categorizes forms of technologies that support the teaching and learning of mathematics in different ways, and identifies signature pedagogies associated with each category. Outcomes and impacts of different…

Reversible Reasoning and the Working Backwards Problem Solving Strategy

ERIC Educational Resources Information Center

Ramful, Ajay

2015-01-01

Making sense of mathematical concepts and solving mathematical problems may demand different forms of reasoning. These could be either domain-based, such as algebraic, geometric or statistical reasoning, while others are more general such as inductive/deductive reasoning. This article aims at giving visibility to a particular form of reasoning…

Defective Number Module or Impaired Access? Numerical Magnitude Processing in First Graders with Mathematical Difficulties

ERIC Educational Resources Information Center

De Smedt, Bert; Gilmore, Camilla K.

2011-01-01

This study examined numerical magnitude processing in first graders with severe and mild forms of mathematical difficulties, children with mathematics learning disabilities (MLD) and children with low achievement (LA) in mathematics, respectively. In total, 20 children with MLD, 21 children with LA, and 41 regular achievers completed a numerical…

Influence of a Mathematics Teachers' Circle on Elementary Teachers' Use of Problem Solving

ERIC Educational Resources Information Center

Garner, Mary L.; Watson, Virginia; Rogers, Beth; Head, Catherine

2017-01-01

Math teachers' circles are a form of professional development that is recommended by the Conference Board of the Mathematical Sciences in their publication Mathematical Education of Teachers II (2012). However, little research has been published on how effective math teachers' circles are in advancing the mathematical knowledge of teachers and…

Hybrid Task Design: Connecting Learning Opportunities Related to Critical Thinking and Statistical Thinking

ERIC Educational Resources Information Center

Kuntze, Sebastian; Aizikovitsh-Udi, Einav; Clarke, David

2017-01-01

Stimulating thinking related to mathematical content is the focus of many tasks in the mathematics classroom. Beyond such content-related thinking, promoting forms of higher order thinking is among the goals of mathematics instruction as well. So-called hybrid tasks focus on combining both goals: they aim at fostering mathematical thinking and…

Contents or Ideology? A Case Study of Mathematical Teaching in North Korea

ERIC Educational Resources Information Center

Karp, Alexander; Lee, JungHang

2010-01-01

This article addresses mathematics education in one of the most closed countries in the world, North Korea. It is known that ideology permeates all aspects of life in North Korea, but how exactly do the ideological and substantive mathematical components interact in mathematics education there? What concrete form does this interaction take in…

A Longitudinal Assessment of Early Acceleration of Students in Mathematics on Growth in Mathematics Achievement

ERIC Educational Resources Information Center

Ma, X.

2005-01-01

Early acceleration of students in mathematics (in the form of early access to formal abstract algebra) has been a controversial educational issue. The current study examined the rate of growth in mathematics achievement of accelerated gifted, honors, and regular students across the entire secondary years (Grades 7-12), in comparison to their…

The Academic and the Everyday in Mathematicians' Talk: The Case of the Hyper-Bagel

ERIC Educational Resources Information Center

Barwell, Richard

2013-01-01

Mathematics curricula increasingly emphasise the importance of mathematical communication. Students are seen as progressing from the use of a more informal or everyday form of communication to a more mathematical approach. There have, however, been very few studies of how mathematicians actually talk about mathematics. This paper reports analysis…

Low Performance on Mathematical Tasks in Preschoolers: The Importance of Domain-General and Domain-Specific Abilities

ERIC Educational Resources Information Center

Costa, H. M.; Nicholson, B.; Donlan, C.; Van Herwegen, J.

2018-01-01

Background: Different domain-specific and domain-general cognitive precursors play a key role in the development of mathematical abilities. The contribution of these domains to mathematical ability changes during development. Primary school-aged children who show mathematical difficulties form a heterogeneous group, but it is not clear whether…

Much More than It's Cooked-up to Be: Reflections on Doing Math and Teachers' Professional Learning

ERIC Educational Resources Information Center

Taton, Joshua A.

2015-01-01

The author argues that students' persistent struggles with mathematics suggest a new form of professional development for teachers is needed. The author draws on a model of professional learning in literacy education to propose an analogous model for mathematics education: teachers of mathematics need to produce mathematical ideas, themselves, in…

Surface-Height Determination of Crevassed Glaciers-Mathematical Principles of an Autoadaptive Density-Dimension Algorithm and Validation Using ICESat-2 Simulator (SIMPL) Data

NASA Technical Reports Server (NTRS)

Herzfeld, Ute C.; Trantow, Thomas M.; Harding, David; Dabney, Philip W.

2017-01-01

Glacial acceleration is a main source of uncertainty in sea-level-change assessment. Measurement of ice-surface heights with a spatial and temporal resolution that not only allows elevation-change calculation, but also captures ice-surface morphology and its changes is required to aid in investigations of the geophysical processes associated with glacial acceleration.The Advanced Topographic Laser Altimeter System aboard NASAs future ICESat-2 Mission (launch 2017) will implement multibeam micropulse photon-counting lidar altimetry aimed at measuring ice-surface heights at 0.7-m along-track spacing. The instrument is designed to resolve spatial and temporal variability of rapidly changing glaciers and ice sheets and the Arctic sea ice. The new technology requires the development of a new mathematical algorithm for the retrieval of height information.We introduce the density-dimension algorithm (DDA) that utilizes the radial basis function to calculate a weighted density as a form of data aggregation in the photon cloud and considers density an additional dimension as an aid in auto-adaptive threshold determination. The auto-adaptive capability of the algorithm is necessary to separate returns from noise and signal photons under changing environmental conditions. The algorithm is evaluated using data collected with an ICESat-2 simulator instrument, the Slope Imaging Multi-polarization Photon-counting Lidar, over the heavily crevassed Giesecke Braer in Northwestern Greenland in summer 2015. Results demonstrate that ICESat-2 may be expected to provide ice-surface height measurements over crevassed glaciers and other complex ice surfaces. The DDA is generally applicable for the analysis of airborne and spaceborne micropulse photon-counting lidar data over complex and simple surfaces.

The `Miracle' of Applicability? The Curious Case of the Simple Harmonic Oscillator

NASA Astrophysics Data System (ADS)

Bangu, Sorin; Moir, Robert H. C.

2018-05-01

The paper discusses to what extent the conceptual issues involved in solving the simple harmonic oscillator model fit Wigner's famous point that the applicability of mathematics borders on the miraculous. We argue that although there is ultimately nothing mysterious here, as is to be expected, a careful demonstration that this is so involves unexpected difficulties. Consequently, through the lens of this simple case we derive some insight into what is responsible for the appearance of mystery in more sophisticated examples of the Wigner problem.

The `Miracle' of Applicability? The Curious Case of the Simple Harmonic Oscillator

NASA Astrophysics Data System (ADS)

Bangu, Sorin; Moir, Robert H. C.

2018-03-01

The paper discusses to what extent the conceptual issues involved in solving the simple harmonic oscillator model fit Wigner's famous point that the applicability of mathematics borders on the miraculous. We argue that although there is ultimately nothing mysterious here, as is to be expected, a careful demonstration that this is so involves unexpected difficulties. Consequently, through the lens of this simple case we derive some insight into what is responsible for the appearance of mystery in more sophisticated examples of the Wigner problem.

The S-Matrix and Acoustic Signal Structure in Simple and Compound Waveguides.

DTIC Science & Technology

1982-12-01

RD-A125 583 THE S-MATRIX AND ACOUSTIC SIGNAL STRUCTURE IN SIMPLE- L/1 AND COMPOUND WAVEGUIDES(U) UTAH UNIV SALT LAKE CITY DEPT OF MATHEMATICS C H...WILCOX DEC 82 TSR-45 UNCLASSIFIED N6@8i4-76-C-8276 F/G 12/1 NL IEINEIIIIIIEIhllhlllllllIflllllflflflflflEN L-- U5-12 III,2,0 III.J --IL.,5 MICROCOP ...RESLUIO TETCHRNATIONA BUREA OF 20NADS16 THE S-MATRIX AND ACOUSTIC SIGNAL STRUCTURE IN SIMPLE AND COMPOUND WAVEGUIDES C. H. Wilcox Technical Simmary Report

Computer Classification of Triangles and Quadrilaterals--A Challenging Application

ERIC Educational Resources Information Center

Dennis, J. Richard

1978-01-01

Two computer exercises involving the classification of geometric figures are given. The mathematics required is relatively simple but comes from several areas--synthetic geometry, analytic geometry, and linear algebra. (MN)

A Simple Optical Waveguide Experiment.

ERIC Educational Resources Information Center

Phelps, J.; Sambles, J. R.

1989-01-01

Describes a thin film rectangular dielectric waveguide and its laboratory use. Discusses the theory of uniaxial thin film waveguides with mathematical expressions and the laboratory procedures for a classroom experiment with diagrams. (Author/YP)

Human evaluation in association to the mathematical analysis of arch forms: Two-dimensional study.

PubMed

Zabidin, Nurwahidah; Mohamed, Alizae Marny; Zaharim, Azami; Marizan Nor, Murshida; Rosli, Tanti Irawati

2018-03-01

To evaluate the relationship between human evaluation of the dental-arch form, to complete a mathematical analysis via two different methods in quantifying the arch form, and to establish agreement with the fourth-order polynomial equation. This study included 64 sets of digitised maxilla and mandible dental casts obtained from a sample of dental arch with normal occlusion. For human evaluation, a convenient sample of orthodontic practitioners ranked the photo images of dental cast from the most tapered to the less tapered (square). In the mathematical analysis, dental arches were interpolated using the fourth-order polynomial equation with millimetric acetate paper and AutoCAD software. Finally, the relations between human evaluation and mathematical objective analyses were evaluated. Human evaluations were found to be generally in agreement, but only at the extremes of tapered and square arch forms; this indicated general human error and observer bias. The two methods used to plot the arch form were comparable. The use of fourth-order polynomial equation may be facilitative in obtaining a smooth curve, which can produce a template for individual arch that represents all potential tooth positions for the dental arch. Copyright © 2018 CEO. Published by Elsevier Masson SAS. All rights reserved.

Forming conjectures within a spreadsheet environment

NASA Astrophysics Data System (ADS)

Calder, Nigel; Brown, Tony; Hanley, Una; Darby, Susan

2006-12-01

This paper is concerned with the use of spreadsheets within mathematical investigational tasks. Considering the learning of both children and pre-service teaching students, it examines how mathematical phenomena can be seen as a function of the pedagogical media through which they are encountered. In particular, it shows how pedagogical apparatus influence patterns of social interaction, and how this interaction shapes the mathematical ideas that are engaged with. Notions of conjecture, along with the particular faculty of the spreadsheet setting, are considered with regard to the facilitation of mathematical thinking. Employing an interpretive perspective, a key focus is on how alternative pedagogical media and associated discursive networks influence the way that students form and test informal conjectures.

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

PubMed

Marill, Keith A

2004-01-01

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

Phase demodulation method from a single fringe pattern based on correlation with a polynomial form.

PubMed

Robin, Eric; Valle, Valéry; Brémand, Fabrice

2005-12-01

The method presented extracts the demodulated phase from only one fringe pattern. Locally, this method approaches the fringe pattern morphology with the help of a mathematical model. The degree of similarity between the mathematical model and the real fringe is estimated by minimizing a correlation function. To use an optimization process, we have chosen a polynomial form such as a mathematical model. However, the use of a polynomial form induces an identification procedure with the purpose of retrieving the demodulated phase. This method, polynomial modulated phase correlation, is tested on several examples. Its performance, in terms of speed and precision, is presented on very noised fringe patterns.

Understanding space weather with new physical, mathematical and philosophical approaches

NASA Astrophysics Data System (ADS)

Mateev, Lachezar; Velinov, Peter; Tassev, Yordan

2016-07-01

The actual problems of solar-terrestrial physics, in particular of space weather are related to the prediction of the space environment state and are solved by means of different analyses and models. The development of these investigations can be considered also from another side. This is the philosophical and mathematical approach towards this physical reality. What does it constitute? We have a set of physical processes which occur in the Sun and interplanetary space. All these processes interact with each other and simultaneously participate in the general process which forms the space weather. Let us now consider the Leibniz's monads (G.W. von Leibniz, 1714, Monadologie, Wien; Id., 1710, Théodicée, Amsterdam) and use some of their properties. There are total 90 theses for monads in the Leibniz's work (1714), f.e. "(1) The Monad, of which we shall here speak, is nothing but a simple substance, which enters into compounds. By 'simple' is meant 'without parts'. (Theod. 10.); … (56) Now this connexion or adaptation of all created things to each and of each to all, means that each simple substance has relations which express all the others, and, consequently, that it is a perpetual living mirror of the universe. (Theod. 130, 360.); (59) … this universal harmony, according to which every substance exactly expresses all others through the relations it has with them. (63) … every Monad is, in its own way, a mirror of the universe, and the universe is ruled according to a perfect order. (Theod. 403.)", etc. Let us introduce in the properties of monads instead of the word "monad" the word "process". We obtain the following statement: Each process reflects all other processes and all other processes reflect this process. This analogy is not formal at all, it reflects accurately the relation between the physical processes and their unity. The category monad which in the Leibniz's Monadology reflects generally the philosophical sense is fully identical with the physical one, in our case. The corresponding mathematical relations are needed for the application of this analogy in the solar-terrestrial physics and space weather. For this purpose in the contemporary categories theory in the algebra a whole field for it exists - the theory of monads (M. Barr, Ch. Wells, 1985, Toposes, Triples and Theories, Springer-Verlag, 278, p. 82). This theory is generated by analogous elements as in the Leibniz's Monadology. As it is known the categories theory and in particular the monad theory (also named triple or triad theory) tends to make axioms in mathematics. This approach would be very useful for such complex systems and processes as these in the solar-terrestrial physics and space weather. Here some methods for algebraic data structures could be introduced. Or some imperative programs can be embedded in a purely functional program for modeling, respectively. All these problems are principally considered in the proposed report.

Tutorial on Fourier space coverage for scattering experiments, with application to SAR

NASA Astrophysics Data System (ADS)

Deming, Ross W.

2010-04-01

The Fourier Diffraction Theorem relates the data measured during electromagnetic, optical, or acoustic scattering experiments to the spatial Fourier transform of the object under test. The theorem is well-known, but since it is based on integral equations and complicated mathematical expansions, the typical derivation may be difficult for the non-specialist. In this paper, the theorem is derived and presented using simple geometry, plus undergraduatelevel physics and mathematics. For practitioners of synthetic aperture radar (SAR) imaging, the theorem is important to understand because it leads to a simple geometric and graphical understanding of image resolution and sampling requirements, and how they are affected by radar system parameters and experimental geometry. Also, the theorem can be used as a starting point for imaging algorithms and motion compensation methods. Several examples are given in this paper for realistic scenarios.

Rules of Thumb for Depth of Investigation, Pseudo-Position and Resolution of the Electrical Resistivity Method from Analysis of the Moments of the Sensitivity Function for a Homogeneous Half-Space

NASA Astrophysics Data System (ADS)

Butler, S. L.

2017-12-01

The electrical resistivity method is now highly developed with 2D and even 3D surveys routinely performed and with available fast inversion software. However, rules of thumb, based on simple mathematical formulas, for important quantities like depth of investigation, horizontal position and resolution have not previously been available and would be useful for survey planning, preliminary interpretation and general education about the method. In this contribution, I will show that the sensitivity function for the resistivity method for a homogeneous half-space can be analyzed in terms of its first and second moments which yield simple mathematical formulas. The first moment gives the sensitivity-weighted center of an apparent resistivity measurement with the vertical center being an estimate of the depth of investigation. I will show that this depth of investigation estimate works at least as well as previous estimates based on the peak and median of the depth sensitivity function which must be calculated numerically for a general four electrode array. The vertical and horizontal first moments can also be used as pseudopositions when plotting 1, 2 and 3D pseudosections. The appropriate horizontal plotting point for a pseudosection was not previously obvious for nonsymmetric arrays. The second moments of the sensitivity function give estimates of the spatial extent of the region contributing to an apparent resistivity measurement and hence are measures of the resolution. These also have simple mathematical formulas.

Dosimetry in x-ray-based breast imaging

PubMed Central

Dance, David R; Sechopoulos, Ioannis

2016-01-01

The estimation of the mean glandular dose to the breast (MGD) for x-ray based imaging modalities forms an essential part of quality control and is needed for risk estimation and for system design and optimisation. This review considers the development of methods for estimating the MGD for mammography, digital breast tomosynthesis (DBT) and dedicated breast CT (DBCT). Almost all of the methodology used employs Monte Carlo calculated conversion factors to relate the measurable quantity, generally the incident air kerma, to the MGD. After a review of the size and composition of the female breast, the various mathematical models used are discussed, with particular emphasis on models for mammography. These range from simple geometrical shapes, to the more recent complex models based on patient DBCT examinations. The possibility of patient-specific dose estimates is considered as well as special diagnostic views and the effect of breast implants. Calculations using the complex models show that the MGD for mammography is overestimated by about 30% when the simple models are used. The design and uses of breast-simulating test phantoms for measuring incident air kerma are outlined and comparisons made between patient and phantom-based dose estimates. The most widely used national and international dosimetry protocols for mammography are based on different simple geometrical models of the breast, and harmonisation of these protocols using more complex breast models is desirable. PMID:27617767

Dosimetry in x-ray-based breast imaging

NASA Astrophysics Data System (ADS)

Dance, David R.; Sechopoulos, Ioannis

2016-10-01

The estimation of the mean glandular dose to the breast (MGD) for x-ray based imaging modalities forms an essential part of quality control and is needed for risk estimation and for system design and optimisation. This review considers the development of methods for estimating the MGD for mammography, digital breast tomosynthesis (DBT) and dedicated breast CT (DBCT). Almost all of the methodology used employs Monte Carlo calculated conversion factors to relate the measurable quantity, generally the incident air kerma, to the MGD. After a review of the size and composition of the female breast, the various mathematical models used are discussed, with particular emphasis on models for mammography. These range from simple geometrical shapes, to the more recent complex models based on patient DBCT examinations. The possibility of patient-specific dose estimates is considered as well as special diagnostic views and the effect of breast implants. Calculations using the complex models show that the MGD for mammography is overestimated by about 30% when the simple models are used. The design and uses of breast-simulating test phantoms for measuring incident air kerma are outlined and comparisons made between patient and phantom-based dose estimates. The most widely used national and international dosimetry protocols for mammography are based on different simple geometrical models of the breast, and harmonisation of these protocols using more complex breast models is desirable.

The application of brain-based learning principles aided by GeoGebra to improve mathematical representation ability

NASA Astrophysics Data System (ADS)

Priatna, Nanang

2017-08-01

The use of Information and Communication Technology (ICT) in mathematics instruction will help students in building conceptual understanding. One of the software products used in mathematics instruction is GeoGebra. The program enables simple visualization of complex geometric concepts and helps improve students' understanding of geometric concepts. Instruction applying brain-based learning principles is one oriented at the efforts of naturally empowering the brain potentials which enable students to build their own knowledge. One of the goals of mathematics instruction in school is to develop mathematical communication ability. Mathematical representation is regarded as a part of mathematical communication. It is a description, expression, symbolization, or modeling of mathematical ideas/concepts as an attempt of clarifying meanings or seeking for solutions to the problems encountered by students. The research aims to develop a learning model and teaching materials by applying the principles of brain-based learning aided by GeoGebra to improve junior high school students' mathematical representation ability. It adopted a quasi-experimental method with the non-randomized control group pretest-posttest design and the 2x3 factorial model. Based on analysis of the data, it is found that the increase in the mathematical representation ability of students who were treated with mathematics instruction applying the brain-based learning principles aided by GeoGebra was greater than the increase of the students given conventional instruction, both as a whole and based on the categories of students' initial mathematical ability.

Pre-Service Elementary Mathematics Teachers' Metaphors on Scientific Research and Foundations of Their Perceptions

ERIC Educational Resources Information Center

Bas, Fatih

2016-01-01

In this study, it is aimed to investigate pre-service elementary mathematics teachers' perceptions about scientific research with metaphor analysis and determine the foundations of these perceptions. This phenomenological study was conducted with 182 participants. The data were collected with two open-ended survey forms formed for investigating…

Gender-Based Differential Item Performance in Mathematics Achievement Items.

ERIC Educational Resources Information Center

Doolittle, Allen E.; Cleary, T. Anne

1987-01-01

Eight randomly equivalent samples of high school seniors were each given a unique form of the ACT Assessment Mathematics Usage Test (ACTM). Signed measures of differential item performance (DIP) were obtained for each item in the eight ACTM forms. DIP estimates were analyzed and a significant item category effect was found. (Author/LMO)

Mathematics in Chemistry: Indeterminate Forms and Their Meaning

ERIC Educational Resources Information Center

Segurado, Manuel A. P.; Silva, Margarida F. B.; Castro, Rita

2011-01-01

The mathematical language and its tools are complementary to the formalism in chemistry, in particular at an advanced level. It is thus crucial, for its understanding, that students acquire a solid knowledge in Calculus and that they know how to apply it. The frequent occurrence of indeterminate forms in multiple areas, particularly in Physical…

Teaching Mathematical Induction: An Alternative Approach.

ERIC Educational Resources Information Center

Allen, Lucas G.

2001-01-01

Describes experience using a new approach to teaching induction that was developed by the Mathematical Methods in High School Project. The basic idea behind the new approach is to use induction to prove that two formulas, one in recursive form and the other in a closed or explicit form, will always agree for whole numbers. (KHR)

The analysis of mathematics literacy on PMRI learning with media schoology of junior high school students

NASA Astrophysics Data System (ADS)

Wardono; Mariani, S.

2018-03-01

Indonesia as a developing country in the future will have high competitiveness if its students have high mathematics literacy ability. The current reality from year to year rankings of PISA mathematics literacy Indonesian students are still not good. This research is motivated by the importance and low ability of the mathematics literacy. The purpose of this study is to: (1) analyze the effectiveness of PMRI learning with media Schoology, (2) describe the ability of students' mathematics literacy on PMRI learning with media Schoology which is reviewed based on seven components of mathematics literacy, namely communication, mathematizing, representation, reasoning, devising strategies, using symbols, and using mathematics tool. The method used in this research is the method of sequential design method mix. Techniques of data collection using observation, interviews, tests, and documentation. Data analysis techniques use proportion test, appellate test, and use descriptive analysis. Based on the data analysis, it can be concluded; (1) PMRI learning with media Schoology effectively improve the ability of mathematics literacy because of the achievement of classical completeness, students' mathematics literacy ability in PMRI learning with media Schoology is higher than expository learning, and there is increasing ability of mathematics literacy in PMRI learning with media Schoology of 30%. (2) Highly capable students attain excellent mathematics literacy skills, can work using broad thinking with appropriate resolution strategies. Students who are capable of achieving good mathematics literacy skills can summarize information, present problem-solving processes, and interpret solutions. low-ability students have reached the level of ability of mathematics literacy good enough that can solve the problem in a simple way.

The Evolvement of Numeracy and Mathematical Literacy Curricula and the Construction of Hierarchies of Numerate or Mathematically Literate Subjects

ERIC Educational Resources Information Center

Jablonka, Eva

2015-01-01

This contribution briefly sketches the evolvement of numeracy or mathematical literacy as models for mathematics curricula, which will be described as driven by a weakening of the insulation between discourses, that is, as a process of "declassification". The question then arises as to whether and how coherence of new forms of initially…

An Exploration of the Common Content Knowledge of High School Mathematics Teachers

ERIC Educational Resources Information Center

Bansilal, Sarah; Brijlall, Deonarain; Mkhwanazi, Thokozani

2014-01-01

Many studies point to the problem of poor mathematics content knowledge of mathematics teachers in South Africa. The purpose of this study was to investigate teachers' knowledge of the mathematics they are themselves teaching. Data was generated from the teachers' (n = 253) written responses to test that was a shortened form of a previous Grade 12…

A Guided Tour of Mathematical Methods - 2nd Edition

NASA Astrophysics Data System (ADS)

Snieder, Roel

2004-09-01

Mathematical methods are essential tools for all physical scientists. This second edition provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students in this area. In contrast to more traditional textbooks, all the material is presented in the form of problems. Within these problems the basic mathematical theory and its physical applications are well integrated. The mathematical insights that the student acquires are therefore driven by their physical insight. Topics that are covered include vector calculus, linear algebra, Fourier analysis, scale analysis, complex integration, Green's functions, normal modes, tensor calculus, and perturbation theory. The second edition contains new chapters on dimensional analysis, variational calculus, and the asymptotic evaluation of integrals. This book can be used by undergraduates, and lower-level graduate students in the physical sciences. It can serve as a stand-alone text, or as a source of problems and examples to complement other textbooks. All the material is presented in the form of problems Mathematical insights are gained by getting the reader to develop answers themselves Many applications of the mathematics are given

Mathematical sense-making in quantum mechanics: An initial peek

NASA Astrophysics Data System (ADS)

Dreyfus, Benjamin W.; Elby, Andrew; Gupta, Ayush; Sohr, Erin Ronayne

2017-12-01

Mathematical sense-making—looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world—is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and "science studies" have explored how expert physicists engage in it. What is largely missing, with a few exceptions, is theoretical and empirical work at the intermediate level—upper division physics students—especially when they are learning difficult new mathematical formalism. In this paper, we present analysis of a segment of video-recorded discussion between two students grappling with a quantum mechanics question to illustrate what mathematical sense-making can look like in quantum mechanics. We claim that mathematical sense-making is possible and productive for learning and problem solving in quantum mechanics. Mathematical sense-making in quantum mechanics is continuous in many ways with mathematical sense-making in introductory physics. However, in the context of quantum mechanics, the connections between formalism, intuitive conceptual schema, and the physical world become more compound (nested) and indirect. We illustrate these similarities and differences in part by proposing a new symbolic form, eigenvector eigenvalue, which is composed of multiple primitive symbolic forms.

Mathematics Used in Occupations: An Interrelated Guide.

ERIC Educational Resources Information Center

Minneapolis Public Schools, Minn. Dept. of Vocational Technical Education.

Intended for use by counselors and mathematics teachers, this guide brings together mathematical and occupational skills to form an interrelated curriculum. Eight occupational clusters are included as follow: (1) business and office, (2) communications, (3) construction, (4) hospitality, (5) manufacturing, (6) marketing and distribution, (7)…

Mathematics Laboratories--More than Fun

ERIC Educational Resources Information Center

Vance, James H.; Kieren, Thomas E.

1972-01-01

The study assessed the effectiveness of methematical laboratories as compared with the regular mathematics teaching program. A control group, mathematical laboratory group, and a third group called a Class Discovery Group were formed for making comparisons. Gains were higher on cumulative achievement, transfer, and divergent thinking measures for…

Children's Mathematical Reasoning: Opportunities for Developing Understanding and Creative Thinking

ERIC Educational Resources Information Center

Vale, Colleen; Bragg, Leicha A.; Widjaja, Wanty; Herbert, Sandra; Loong, Esther Yook-Kin

2017-01-01

Reasoning underpins students' mathematical understanding and promotes creative thinking. It is regarded as a key mathematical proficiency. This article discusses the reasoning actions that primary children employed and teachers noticed for the "What else belongs?" task focused on forming and testing conjectures.

On the mathematical modeling of the Reynolds stress's equations

NASA Technical Reports Server (NTRS)

Lin, Avi

1990-01-01

By considering the Reynolds stress equations as a possible descriptor of complex turbulent fields, pressure-velocity interaction and turbulence dissipation are studied as two of the main physical contributions to Reynolds stress balancing in turbulent flow fields. It is proven that the pressure interaction term contains turbulence generation elements. However, the usual 'return to isotropy' element appears more weakly than in the standard models. In addition, convection-like elements are discovered mathematically, but there is no mathematical evidence that the pressure fluctuations contribute to the turbulent transport mechanism. Calculations of some simple one-dimensional fields indicate that this extra convection, rather than the turbulent transport, is needed mathematically. Similarly, an expression for the turbulence dissipation is developed. The end result is a dynamic equation for the dissipation tensor which is based on the tensorial length scales.

RF tumour ablation: computer simulation and mathematical modelling of the effects of electrical and thermal conductivity.

PubMed

Lobo, S M; Liu, Z-J; Yu, N C; Humphries, S; Ahmed, M; Cosman, E R; Lenkinski, R E; Goldberg, W; Goldberg, S N

2005-05-01

This study determined the effects of thermal conductivity on RF ablation tissue heating using mathematical modelling and computer simulations of RF heating coupled to thermal transport. Computer simulation of the Bio-Heat equation coupled with temperature-dependent solutions for RF electric fields (ETherm) was used to generate temperature profiles 2 cm away from a 3 cm internally-cooled electrode. Multiple conditions of clinically relevant electrical conductivities (0.07-12 S m-1) and 'tumour' radius (5-30 mm) at a given background electrical conductivity (0.12 S m-1) were studied. Temperature response surfaces were plotted for six thermal conductivities, ranging from 0.3-2 W m-1 degrees C (the range of anticipated clinical and experimental systems). A temperature response surface was obtained for each thermal conductivity at 25 electrical conductivities and 17 radii (n=425 temperature data points). The simulated temperature response was fit to a mathematical model derived from prior phantom data. This mathematical model is of the form (T=a+bRc exp(dR) s(f) exp(g)(s)) for RF generator-energy dependent situations and (T=h+k exp(mR)+n?exp(p)(s)) for RF generator-current limited situations, where T is the temperature (degrees C) 2 cm from the electrode and a, b, c, d, f, g, h, k, m, n and p are fitting parameters. For each of the thermal conductivity temperature profiles generated, the mathematical model fit the response surface to an r2 of 0.97-0.99. Parameters a, b, c, d, f, k and m were highly correlated to thermal conductivity (r2=0.96-0.99). The monotonic progression of fitting parameters permitted their mathematical expression using simple functions. Additionally, the effect of thermal conductivity simplified the above equation to the extent that g, h, n and p were found to be invariant. Thus, representation of the temperature response surface could be accurately expressed as a function of electrical conductivity, radius and thermal conductivity. As a result, the non-linear temperature response of RF induced heating can be adequately expressed mathematically as a function of electrical conductivity, radius and thermal conductivity. Hence, thermal conductivity accounts for some of the previously unexplained variance. Furthermore, the addition of this variable into the mathematical model substantially simplifies the equations and, as such, it is expected that this will permit improved prediction of RF ablation induced temperatures in clinical practice.

Mathematical methods for protein science

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

Hart, W.; Istrail, S.; Atkins, J.

1997-12-31

Understanding the structure and function of proteins is a fundamental endeavor in molecular biology. Currently, over 100,000 protein sequences have been determined by experimental methods. The three dimensional structure of the protein determines its function, but there are currently less than 4,000 structures known to atomic resolution. Accordingly, techniques to predict protein structure from sequence have an important role in aiding the understanding of the Genome and the effects of mutations in genetic disease. The authors describe current efforts at Sandia to better understand the structure of proteins through rigorous mathematical analyses of simple lattice models. The efforts have focusedmore » on two aspects of protein science: mathematical structure prediction, and inverse protein folding.« less

A new adaptive estimation method of spacecraft thermal mathematical model with an ensemble Kalman filter

NASA Astrophysics Data System (ADS)

Akita, T.; Takaki, R.; Shima, E.

2012-04-01

An adaptive estimation method of spacecraft thermal mathematical model is presented. The method is based on the ensemble Kalman filter, which can effectively handle the nonlinearities contained in the thermal model. The state space equations of the thermal mathematical model is derived, where both temperature and uncertain thermal characteristic parameters are considered as the state variables. In the method, the thermal characteristic parameters are automatically estimated as the outputs of the filtered state variables, whereas, in the usual thermal model correlation, they are manually identified by experienced engineers using trial-and-error approach. A numerical experiment of a simple small satellite is provided to verify the effectiveness of the presented method.

Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.

Global stability and periodic solution of the viral dynamics

NASA Astrophysics Data System (ADS)

Song, Xinyu; Neumann, Avidan U.

2007-05-01

It is well known that the mathematical models provide very important information for the research of human immunodeficiency virus-type 1 and hepatitis C virus (HCV). However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T cells and the viral particles. In this paper, we consider the classical mathematical model with saturation response of the infection rate. By stability analysis we obtain sufficient conditions on the parameters for the global stability of the infected steady state and the infection-free steady state. We also obtain the conditions for the existence of an orbitally asymptotically stable periodic solution. Numerical simulations are presented to illustrate the results.

Modelling Mathematical Argumentation: The Importance of Qualification

ERIC Educational Resources Information Center

Inglis, Matthew; Mejia-Ramos, Juan; Simpson, Adrian

2007-01-01

In recent years several mathematics education researchers have attempted to analyse students' arguments using a restricted form of Toulmina's ["The Uses of Argument," Cambridge University Press, UK, 1958] argumentation scheme. In this paper we report data from task-based interviews conducted with highly talented postgraduate mathematics students,…

Investigating Preservice Mathematics Teachers' Manipulative Material Design Processes

ERIC Educational Resources Information Center

Sandir, Hakan

2016-01-01

Students use concrete manipulatives to form an imperative affiliation between conceptual and procedural knowledge (Balka, 1993). Hence, it is necessary to design specific mathematics manipulatives that focus on different mathematical concepts. Preservice teachers need to know how to make and use manipulatives that stimulate students' thinking as…

Transformative Learning: Personal Empowerment in Learning Mathematics

ERIC Educational Resources Information Center

Hassi, Marja-Liisa; Laursen, Sandra L.

2015-01-01

This article introduces the concept of personal empowerment as a form of transformative learning. It focuses on commonly ignored but enhancing elements of mathematics learning and argues that crucial personal resources can be essentially promoted by high engagement in mathematical problem solving, inquiry, and collaboration. This personal…

Victorian Certificate of Education: Mathematics, Science and Gender

ERIC Educational Resources Information Center

Cox, Peter J.; Leder, Gilah C.; Forgasz, Helen J.

2004-01-01

Gender differences in participation and performance at "high stakes" examinations have received much public attention, which has often focused on mathematics and science subjects. This paper describes the innovative forms of assessment introduced into mathematics and science subjects within the Victorian Certificate of Education (VCE)…

Mechanics of train collision

DOT National Transportation Integrated Search

1976-04-30

A simple and a more detailed mathematical model for the simulation of train collisions are presented. The study presents considerable insight as to the causes and consequences of train motions on impact. Comparison of model predictions with two full ...

A causal framework for integrating contemporary and Vedic holism.

PubMed

Kineman, John J

2017-12-01

Whereas the last Century of science was characterized by epistemological uncertainty; the current Century will likely be characterized by ontological complexity (Gorban and Yablonsky, 2013). Advances in Systems Theory by mathematical biologist Robert Rosen suggest an elegant way forward (Rosen, 2013). "R-theory" (Kineman, 2012) is a synthesis of Rosen's theories explaining complexity and life in terms of a meta-model for 'whole' systems (and their fractions) in terms of "5 th -order holons". Such holons are Rosen "modeling relations" relating system-dependent processes with their formative contexts via closed cycles of four archetypal (Aristotelian) causes. This approach has post-predicted the three most basic taxa of life, plus a quasi-organismic form that may describe proto, component, and ecosystemic life. R-theory thus suggests a fundamentally complex ontology of existence inverting the current view that complexity arises from simple mechanisms. This model of cyclical causality corresponds to the ancient meta-model described in the Vedas and Upanishads of India. Part I of this discussion (Kineman, 2016a) presented a case for associating Vedic philosophy with Harappan civilization, allowing interpretation of ancient concepts of "cosmic order" (Rta) in the Rig Veda, nonduality (advaita), seven-fold beingness (saptanna) and other forms of holism appearing later in the Upanishads. By deciphering the model of wholeness that was applied and tested in ancient times, it is possible to compare, test, and confirm the holon model as a mathematical definition of life, systemic wholeness, and sustainability that may be applied today in modern terms, even as a foundation for holistic science. Copyright © 2017 Elsevier Ltd. All rights reserved.

Disentangling the effects of working memory, language, parental education, and non-verbal intelligence on children’s mathematical abilities

PubMed Central

Pina, Violeta; Fuentes, Luis J.; Castillo, Alejandro; Diamantopoulou, Sofia

2014-01-01

It is assumed that children’s performance in mathematical abilities is influenced by several factors such as working memory (WM), verbal ability, intelligence, and socioeconomic status. The present study explored the contribution of those factors to mathematical performance taking a componential view of both WM and mathematics. We explored the existing relationship between different WM components (verbal and spatial) with tasks that make differential recruitment of the central executive, and simple and complex mathematical skills in a sample of 102 children in grades 4–6. The main findings point to a relationship between the verbal WM component and complex word arithmetic problems, whereas language and non-verbal intelligence were associated with knowledge of quantitative concepts and arithmetic ability. The spatial WM component was associated with the subtest Series, whereas the verbal component was with the subtest Concepts. The results also suggest a positive relationship between parental educational level and children’s performance on Quantitative Concepts. These findings suggest that specific cognitive skills might be trained in order to improve different aspects of mathematical ability. PMID:24847306

Mathematical Metaphors: Problem Reformulation and Analysis Strategies

NASA Technical Reports Server (NTRS)

Thompson, David E.

2005-01-01

This paper addresses the critical need for the development of intelligent or assisting software tools for the scientist who is working in the initial problem formulation and mathematical model representation stage of research. In particular, examples of that representation in fluid dynamics and instability theory are discussed. The creation of a mathematical model that is ready for application of certain solution strategies requires extensive symbolic manipulation of the original mathematical model. These manipulations can be as simple as term reordering or as complicated as discovery of various symmetry groups embodied in the equations, whereby Backlund-type transformations create new determining equations and integrability conditions or create differential Grobner bases that are then solved in place of the original nonlinear PDEs. Several examples are presented of the kinds of problem formulations and transforms that can be frequently encountered in model representation for fluids problems. The capability of intelligently automating these types of transforms, available prior to actual mathematical solution, is advocated. Physical meaning and assumption-understanding can then be propagated through the mathematical transformations, allowing for explicit strategy development.

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

NASA Astrophysics Data System (ADS)

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

2008-02-01

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

Pyroelectric effect in tryglicyne sulphate single crystals - Differential measurement method

NASA Astrophysics Data System (ADS)

Trybus, M.

2018-06-01

A simple mathematical model of the pyroelectric phenomenon was used to explain the electric response of the TGS (triglycine sulphate) samples in the linear heating process in ferroelectric and paraelectric phases. Experimental verification of mathematical model was realized. TGS single crystals were grown and four electrode samples were fabricated. Differential measurements of the pyroelectric response of two different regions of the samples were performed and the results were compared with data obtained from the model. Experimental results are in good agreement with model calculations.

On symmetries, conservation laws and exact solutions of the nonlinear Schrödinger-Hirota equation

NASA Astrophysics Data System (ADS)

Akbulut, Arzu; Taşcan, Filiz

2018-04-01

In this paper, conservation laws and exact solution are found for nonlinear Schrödinger-Hirota equation. Conservation theorem is used for finding conservation laws. We get modified conservation laws for given equation. Modified simple equation method is used to obtain the exact solutions of the nonlinear Schrödinger-Hirota equation. It is shown that the suggested method provides a powerful mathematical instrument for solving nonlinear equations in mathematical physics and engineering.

Gravitational orientation of the orbital complex, Salyut-6--Soyuz

NASA Technical Reports Server (NTRS)

Grecho, G. M.; Sarychev, V. A.; Legostayev, V. P.; Sazonov, V. V.; Gansvind, I. N.

1983-01-01

A simple mathematical model is proposed for the Salyut-6-Soyuz orbital complex motion with respect to the center of mass under the one-axis gravity-gradient orientation regime. This model was used for processing the measurements of the orbital complex motion parameters when the above orientation region was implemented. Some actual satellite motions are simulated and the satellite's aerodynamic parameters are determined. Estimates are obtained for the accuracy of measurements as well as that of the mathematical model.

Understanding the persistence of measles: reconciling theory, simulation and observation.

PubMed Central

Keeling, Matt J; Grenfell, Bryan T

2002-01-01

Ever since the pattern of localized extinction associated with measles was discovered by Bartlett in 1957, many models have been developed in an attempt to reproduce this phenomenon. Recently, the use of constant infectious and incubation periods, rather than the more convenient exponential forms, has been presented as a simple means of obtaining realistic persistence levels. However, this result appears at odds with rigorous mathematical theory; here we reconcile these differences. Using a deterministic approach, we parameterize a variety of models to fit the observed biennial attractor, thus determining the level of seasonality by the choice of model. We can then compare fairly the persistence of the stochastic versions of these models, using the 'best-fit' parameters. Finally, we consider the differences between the observed fade-out pattern and the more theoretically appealing 'first passage time'. PMID:11886620

On Solving "Problems"

NASA Astrophysics Data System (ADS)

Ghez, Richard

2006-04-01

Counting and estimating are no doubt ancient survival skills. And yet, present educational methods tend to downplay these very skills. This breeds senseless innumeracy and social disruption. Jumbling inches with centimeters, for example, can cause a Mars mission to fail. With minor distortion, elementary and high schools (and beyond) teach that all fractions are simple, that all square roots are rational, and that trigonometric functions need be evaluated only for 30, 45, and 60 degrees. We thus inflict threefold damage on our children and students. First, they come to believe that numbers beyond 10 (except for current account deficits) are intuitively inaccessible; second, that answers to all mathematical questions are "formulas"; and third, that the art of estimation merely requires punching keys on a calculator—a dismal sort of black magic. These beliefs I wish to expose in the form of eight short numerical tales.

The problem of exact interior solutions for rotating rigid bodies in general relativity

NASA Technical Reports Server (NTRS)

Wahlquist, H. D.

1993-01-01

The (3 + 1) dyadic formalism for timelike congruences is applied to derive interior solutions for stationary, axisymmetric, rigidly rotating bodies. In this approach the mathematics is formulated in terms of three-space-covariant, first-order, vector-dyadic, differential equations for a and Omega, the acceleration and angular velocity three-vectors of the rigid body; for T, the stress dyadic of the matter; and for A and B, the 'electric' and 'magnetic' Weyl curvature dyadics which describe the gravitational field. It is shown how an appropriate ansatz for the forms of these dyadics can be used to discover exact rotating interior solutions such as the perfect fluid solution first published in 1968. By incorporating anisotropic stresses, a generalization is found of that previous solution and, in addition, a very simple new solution that can only exist in toroidal configurations.

A simple approach to nonlinear estimation of physical systems

USGS Publications Warehouse

Christakos, G.

1988-01-01

Recursive algorithms for estimating the states of nonlinear physical systems are developed. This requires some key hypotheses regarding the structure of the underlying processes. Members of this class of random processes have several desirable properties for the nonlinear estimation of random signals. An assumption is made about the form of the estimator, which may then take account of a wide range of applications. Under the above assumption, the estimation algorithm is mathematically suboptimal but effective and computationally attractive. It may be compared favorably to Taylor series-type filters, nonlinear filters which approximate the probability density by Edgeworth or Gram-Charlier series, as well as to conventional statistical linearization-type estimators. To link theory with practice, some numerical results for a simulated system are presented, in which the responses from the proposed and the extended Kalman algorithms are compared. ?? 1988.

Random walk, diffusion and mixing in simulations of scalar transport in fluid flows

NASA Astrophysics Data System (ADS)

Klimenko, A. Y.

2008-12-01

Physical similarity and mathematical equivalence of continuous diffusion and particle random walk form one of the cornerstones of modern physics and the theory of stochastic processes. In many applied models used in simulation of turbulent transport and turbulent combustion, mixing between particles is used to reflect the influence of the continuous diffusion terms in the transport equations. We show that the continuous scalar transport and diffusion can be accurately specified by means of mixing between randomly walking Lagrangian particles with scalar properties and assess errors associated with this scheme. This gives an alternative formulation for the stochastic process which is selected to represent the continuous diffusion. This paper focuses on statistical errors and deals with relatively simple cases, where one-particle distributions are sufficient for a complete description of the problem.

Verification of floating-point software

NASA Technical Reports Server (NTRS)

Hoover, Doug N.

1990-01-01

Floating point computation presents a number of problems for formal verification. Should one treat the actual details of floating point operations, or accept them as imprecisely defined, or should one ignore round-off error altogether and behave as if floating point operations are perfectly accurate. There is the further problem that a numerical algorithm usually only approximately computes some mathematical function, and we often do not know just how good the approximation is, even in the absence of round-off error. ORA has developed a theory of asymptotic correctness which allows one to verify floating point software with a minimum entanglement in these problems. This theory and its implementation in the Ariel C verification system are described. The theory is illustrated using a simple program which finds a zero of a given function by bisection. This paper is presented in viewgraph form.

Evaluation of generalized degrees of freedom for sparse estimation by replica method

NASA Astrophysics Data System (ADS)

Sakata, A.

2016-12-01

We develop a method to evaluate the generalized degrees of freedom (GDF) for linear regression with sparse regularization. The GDF is a key factor in model selection, and thus its evaluation is useful in many modelling applications. An analytical expression for the GDF is derived using the replica method in the large-system-size limit with random Gaussian predictors. The resulting formula has a universal form that is independent of the type of regularization, providing us with a simple interpretation. Within the framework of replica symmetric (RS) analysis, GDF has a physical meaning as the effective fraction of non-zero components. The validity of our method in the RS phase is supported by the consistency of our results with previous mathematical results. The analytical results in the RS phase are calculated numerically using the belief propagation algorithm.

Measurement uncertainty of liquid chromatographic analyses visualized by Ishikawa diagrams.

PubMed

Meyer, Veronika R

2003-09-01

Ishikawa, or cause-and-effect diagrams, help to visualize the parameters that influence a chromatographic analysis. Therefore, they facilitate the set up of the uncertainty budget of the analysis, which can then be expressed in mathematical form. If the uncertainty is calculated as the Gaussian sum of all uncertainty parameters, it is necessary to quantitate them all, a task that is usually not practical. The other possible approach is to use the intermediate precision as a base for the uncertainty calculation. In this case, it is at least necessary to consider the uncertainty of the purity of the reference material in addition to the precision data. The Ishikawa diagram is then very simple, and so is the uncertainty calculation. This advantage is given by the loss of information about the parameters that influence the measurement uncertainty.

Structure theorems and the dynamics of nitrogen catabolite repression in yeast

PubMed Central

Boczko, Erik M.; Cooper, Terrance G.; Gedeon, Tomas; Mischaikow, Konstantin; Murdock, Deborah G.; Pratap, Siddharth; Wells, K. Sam

2005-01-01

By using current biological understanding, a conceptually simple, but mathematically complex, model is proposed for the dynamics of the gene circuit responsible for regulating nitrogen catabolite repression (NCR) in yeast. A variety of mathematical “structure” theorems are described that allow one to determine the asymptotic dynamics of complicated systems under very weak hypotheses. It is shown that these theorems apply to several subcircuits of the full NCR circuit, most importantly to the URE2–GLN3 subcircuit that is independent of the other constituents but governs the switching behavior of the full NCR circuit under changes in nitrogen source. Under hypotheses that are fully consistent with biological data, it is proven that the dynamics of this subcircuit is simple periodic behavior in synchrony with the cell cycle. Although the current mathematical structure theorems do not apply to the full NCR circuit, extensive simulations suggest that the dynamics is constrained in much the same way as that of the URE2–GLN3 subcircuit. This finding leads to the proposal that mathematicians study genetic circuits to find new geometries for which structure theorems may exist. PMID:15814615

Using Graphing Software to Teach about Algebraic Forms: A Study of Technology-Supported Practice in Secondary-School Mathematics

ERIC Educational Resources Information Center

Ruthven, Kenneth; Deaney, Rosemary; Hennessy, Sara

2009-01-01

From preliminary analysis of teacher-nominated examples of successful technology-supported practice in secondary-school mathematics, the use of graphing software to teach about algebraic forms was identified as being an important archetype. Employing evidence from lesson observation and teacher interview, such practice was investigated in greater…

Using Menelaus' Theorem and Dynamic Mathematics Software to Convey the Meanings of Indeterminate Forms to Students

ERIC Educational Resources Information Center

Çekmez, Erdem

2016-01-01

This study investigates the effectiveness of a teaching activity that aimed to convey the meaning of indeterminate forms to a group of undergraduate students who were enrolled in an elementary mathematics education programme. The study reports the implementation sequence of the activity and students' experiences in the classroom. To assess the…

Children's Construction of Mathematical Knowledge in Solving Novel Isomorphic Problems in Concrete and Written Form.

ERIC Educational Resources Information Center

English, Lyn D.

1996-01-01

Presents case study data of low- and high-achieving nine-year olds focusing on construction and analogical transfer of mathematical knowledge during novel problem solving, as reflected in strategies for dealing with isomorphic combinatorial problems presented in hands-on and written form. Results showed that achievement level does not predict…

A simple model of circadian rhythms based on dimerization and proteolysis of PER and TIM

PubMed Central

Tyson, JJ; Hong, CI; Thron, CD; Novak, B

1999-01-01

Many organisms display rhythms of physiology and behavior that are entrained to the 24-h cycle of light and darkness prevailing on Earth. Under constant conditions of illumination and temperature, these internal biological rhythms persist with a period close to 1 day ("circadian"), but it is usually not exactly 24 h. Recent discoveries have uncovered stunning similarities among the molecular circuitries of circadian clocks in mice, fruit flies, and bread molds. A consensus picture is coming into focus around two proteins (called PER and TIM in fruit flies), which dimerize and then inhibit transcription of their own genes. Although this picture seems to confirm a venerable model of circadian rhythms based on time-delayed negative feedback, we suggest that just as crucial to the circadian oscillator is a positive feedback loop based on stabilization of PER upon dimerization. These ideas can be expressed in simple mathematical form (phase plane portraits), and the model accounts naturally for several hallmarks of circadian rhythms, including temperature compensation and the per(L) mutant phenotype. In addition, the model suggests how an endogenous circadian oscillator could have evolved from a more primitive, light-activated switch. PMID:20540926

NMR signals within the generalized Langevin model for fractional Brownian motion

NASA Astrophysics Data System (ADS)

Lisý, Vladimír; Tóthová, Jana

2018-03-01

The methods of Nuclear Magnetic Resonance belong to the best developed and often used tools for studying random motion of particles in different systems, including soft biological tissues. In the long-time limit the current mathematical description of the experiments allows proper interpretation of measurements of normal and anomalous diffusion. The shorter-time dynamics is however correctly considered only in a few works that do not go beyond the standard memoryless Langevin description of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spin-bearing particles in a magnetic-field gradient, expressed in a form applicable for any kind of stationary stochastic dynamics of spins with or without a memory, is calculated in the frame of the model of fractional BM. The solution of the model for particles trapped in a harmonic potential is obtained in an exceedingly simple way and used for the calculation of S (t). In the limit of free particles coupled to a fractal heat bath, the results compare favorably with experiments acquired in human neuronal tissues. The effect of the trap is demonstrated by introducing a simple model for the generalized diffusion coefficient of the particle.

Approximate analytical solution for induction heating of solid cylinders

DOE PAGES

Jankowski, Todd Andrew; Pawley, Norma Helen; Gonzales, Lindsey Michal; ...

2015-10-20

An approximate solution to the mathematical model for induction heating of a solid cylinder in a cylindrical induction coil is presented here. The coupled multiphysics model includes equations describing the electromagnetic field in the heated object, a heat transfer simulation to determine temperature of the heated object, and an AC circuit simulation of the induction heating power supply. A multiple-scale perturbation method is used to solve the multiphysics model. The approximate analytical solution yields simple closed-form expressions for the electromagnetic field and heat generation rate in the solid cylinder, for the equivalent impedance of the associated tank circuit, and formore » the frequency response of a variable frequency power supply driving the tank circuit. The solution developed here is validated by comparing predicted power supply frequency to both experimental measurements and calculated values from finite element analysis for heating of graphite cylinders in an induction furnace. The simple expressions from the analytical solution clearly show the functional dependence of the power supply frequency on the material properties of the load and the geometrical characteristics of the furnace installation. In conclusion, the expressions developed here provide physical insight into observations made during load signature analysis of induction heating.« less

Role of community tolerance level (CTL) in predicting the prevalence of the annoyance of road and rail noise.

PubMed

Schomer, Paul; Mestre, Vincent; Fidell, Sanford; Berry, Bernard; Gjestland, Truls; Vallet, Michel; Reid, Timothy

2012-04-01

Fidell et al. [(2011), J. Acoust. Soc. Am. 130(2), 791-806] have shown (1) that the rate of growth of annoyance with noise exposure reported in attitudinal surveys of the annoyance of aircraft noise closely resembles the exponential rate of change of loudness with sound level, and (2) that the proportion of a community highly annoyed and the variability in annoyance prevalence rates in communities are well accounted for by a simple model with a single free parameter: a community tolerance level (abbreviated CTL, and represented symbolically in mathematical expressions as L(ct)), expressed in units of DNL. The current study applies the same modeling approach to predicting the prevalence of annoyance of road traffic and rail noise. The prevalence of noise-induced annoyance of all forms of transportation noise is well accounted for by a simple, loudness-like exponential function with community-specific offsets. The model fits all of the road traffic findings well, but the prevalence of annoyance due to rail noise is more accurately predicted separately for interviewing sites with and without high levels of vibration and/or rattle.

The transition to formal thinking in mathematics

NASA Astrophysics Data System (ADS)

Tall, David

2008-09-01

This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts towards a formal framework of axiomatic systems and mathematical proof. In this paper, the transition in thinking is formulated within a framework of `three worlds of mathematics'- the `conceptual-embodied' world based on perception, action and thought experiment, the `proceptual-symbolic' world of calculation and algebraic manipulation compressing processes such as counting into concepts such as number, and the `axiomatic-formal' world of set-theoretic concept definitions and mathematical proof. Each `world' has its own sequence of development and its own forms of proof that may be blended together to give a rich variety of ways of thinking mathematically. This reveals mathematical thinking as a blend of differing knowledge structures; for instance, the real numbers blend together the embodied number line, symbolic decimal arithmetic and the formal theory of a complete ordered field. Theoretical constructs are introduced to describe how genetic structures set before birth enable the development of mathematical thinking, and how experiences that the individual has met before affect their personal growth. These constructs are used to consider how students negotiate the transition from school to university mathematics as embodiment and symbolism are blended with formalism. At a higher level, structure theorems proved in axiomatic theories link back to more sophisticated forms of embodiment and symbolism, revealing the intimate relationship between the three worlds.

Blessing of dimensionality: mathematical foundations of the statistical physics of data.

PubMed

Gorban, A N; Tyukin, I Y

2018-04-28

The concentrations of measure phenomena were discovered as the mathematical background to statistical mechanics at the end of the nineteenth/beginning of the twentieth century and have been explored in mathematics ever since. At the beginning of the twenty-first century, it became clear that the proper utilization of these phenomena in machine learning might transform the curse of dimensionality into the blessing of dimensionality This paper summarizes recently discovered phenomena of measure concentration which drastically simplify some machine learning problems in high dimension, and allow us to correct legacy artificial intelligence systems. The classical concentration of measure theorems state that i.i.d. random points are concentrated in a thin layer near a surface (a sphere or equators of a sphere, an average or median-level set of energy or another Lipschitz function, etc.). The new stochastic separation theorems describe the thin structure of these thin layers: the random points are not only concentrated in a thin layer but are all linearly separable from the rest of the set, even for exponentially large random sets. The linear functionals for separation of points can be selected in the form of the linear Fisher's discriminant. All artificial intelligence systems make errors. Non-destructive correction requires separation of the situations (samples) with errors from the samples corresponding to correct behaviour by a simple and robust classifier. The stochastic separation theorems provide us with such classifiers and determine a non-iterative (one-shot) procedure for their construction.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

Blessing of dimensionality: mathematical foundations of the statistical physics of data

NASA Astrophysics Data System (ADS)

Gorban, A. N.; Tyukin, I. Y.

2018-04-01

The concentrations of measure phenomena were discovered as the mathematical background to statistical mechanics at the end of the nineteenth/beginning of the twentieth century and have been explored in mathematics ever since. At the beginning of the twenty-first century, it became clear that the proper utilization of these phenomena in machine learning might transform the curse of dimensionality into the blessing of dimensionality. This paper summarizes recently discovered phenomena of measure concentration which drastically simplify some machine learning problems in high dimension, and allow us to correct legacy artificial intelligence systems. The classical concentration of measure theorems state that i.i.d. random points are concentrated in a thin layer near a surface (a sphere or equators of a sphere, an average or median-level set of energy or another Lipschitz function, etc.). The new stochastic separation theorems describe the thin structure of these thin layers: the random points are not only concentrated in a thin layer but are all linearly separable from the rest of the set, even for exponentially large random sets. The linear functionals for separation of points can be selected in the form of the linear Fisher's discriminant. All artificial intelligence systems make errors. Non-destructive correction requires separation of the situations (samples) with errors from the samples corresponding to correct behaviour by a simple and robust classifier. The stochastic separation theorems provide us with such classifiers and determine a non-iterative (one-shot) procedure for their construction. This article is part of the theme issue `Hilbert's sixth problem'.

Mathematical Ability Relies on Knowledge, Too

ERIC Educational Resources Information Center

Sweller, John; Clark, Richard E.; Kirschner, Paul A.

2011-01-01

Recent "reform" curricula both ignore the absence of supporting data and completely misunderstand the role of problem solving in cognition. If, the argument goes, teachers are not really teaching people mathematics but rather are teaching them some form of general problem solving, then mathematical content can be reduced in importance. According…

Investigating Student Use of Electronic Support Tools and Mathematical Reasoning

ERIC Educational Resources Information Center

Higgins, Kristina N.; Crawford, Lindy; Huscroft-D'Angelo, Jacqueline; Horney, Mark

2016-01-01

Mathematical reasoning involves comprehending mathematical information and concepts in a logical way and forming conclusions and generalizations based on this comprehension. Computer-based learning has been incorporated into classrooms across the country, and specific aspects of technology need to be studied to determine how programs are…

The Object Metaphor and Synecdoche in Mathematics Classroom Discourse

ERIC Educational Resources Information Center

Font, Vicenc; Godino, Juan D.; Planas, Nuria; Acevedo, Jorge I.

2010-01-01

This article describes aspects of classroom discourse, illustrated through vignettes, that reveal the complex relationship between the forms in which mathematical objects exist and their ostensive representations. We illustrate various aspects of the process through which students come to consider the reality of mathematical objects that are…

A Tree at Bedtime Investigation: Connecting Mathematics, Science, and Literature

ERIC Educational Resources Information Center

Kieff, Judith

2006-01-01

Activities that promote "active thinking" help children learn mathematics and science by allowing them to work at forming relationships, making connections, and integrating concepts and procedures. Dynamic and exciting children's books invite and motivate children to learn mathematics and science by responding to stories, characters, and their…

Mathematical Description and Mechanistic Reasoning: A Pathway toward STEM Integration

ERIC Educational Resources Information Center

Weinberg, Paul J.

2017-01-01

Because reasoning about mechanism is critical to disciplined inquiry in science, technology, engineering, and mathematics (STEM) domains, this study focuses on ways to support the development of this form of reasoning. This study attends to how mechanistic reasoning is constituted through mathematical description. This study draws upon Smith's…

Circles, Materiality and Movement

ERIC Educational Resources Information Center

Chorney, Sean

2017-01-01

This paper approaches the concept of the circle through the framework of mathematics-as-becoming. This paper focuses specifically on how a concept can be thought of as a process, and on the implications that this might have for mathematics learning. Contrary to long-standing assumptions about mathematical concepts as ideal, inert, Platonic forms,…

The Representational Value of Hats

ERIC Educational Resources Information Center

Watson, Jane M.; Fitzallen, Noleine E.; Wilson, Karen G.; Creed, Julie F.

2008-01-01

The literature that is available on the topic of representations in mathematics is vast. One commonly discussed item is graphical representations. From the history of mathematics to modern uses of technology, a variety of graphical forms are available for middle school students to use to represent mathematical ideas. The ideas range from algebraic…

Classroom Strategies to Make Sense and Persevere

ERIC Educational Resources Information Center

Wilburne, Jane M.; Wildmann, Tara; Morret, Michael; Stipanovic, Julie

2014-01-01

Three mid-level mathematics teachers (grades 7 and 8) and a university mathematics educator formed a year-long professional learning community. The objective was to collectively look at how they were promoting the Standards for Mathematical Practice (SMP) (CCSSI 2010) in their classes. The monthly discussions followed an iterative cycle in which…

A Framework for Understanding Whiteness in Mathematics Education

ERIC Educational Resources Information Center

Battey, Dan; Leyva, Luis A.

2016-01-01

In this article, the authors provide a framework for understanding whiteness in mathematics education. While whiteness is receiving more attention in the broader education literature, only a handful of scholars address whiteness in mathematics education in any form. This lack of attention to whiteness leaves it invisible and neutral in documenting…

Mathematics and Martial Arts as Connected Art Forms

ERIC Educational Resources Information Center

Hekimoglu, Serkan

2010-01-01

Parallels between martial arts and mathematics are explored. Misguided public perception of both disciplines, students' misconceptions, and the similarities between proofs and katas are among the striking commonalities between martial arts and mathematics. The author also reflects on what he has learned in his martial arts training, and how this…

Defining, Developing, and Measuring "Proclivities for Teaching Mathematics"

ERIC Educational Resources Information Center

Lewis, Jennifer M.; Fischman, Davida; Riggs, Matt

2015-01-01

This article presents a form of teacher reasoning that we call "proclivities for teaching mathematics." We define proclivities for teaching mathematics as the beliefs, knowledge, and dispositions that are actionable in the flow of instruction, and we argue that growth in this area contributes to positive change in mathematics…

Mathematical Communication in State Standards before the Common Core

ERIC Educational Resources Information Center

Kosko, Karl Wesley; Gao, Yang

2017-01-01

Mathematical communication has been an important feature of standards documents since National Council of Teachers of Mathematics' (NCTM) (1989) "Curriculum and Evaluation Standards." Such an emphasis has influenced content standards of states from then to present. This study examined how effective the prevalence of various forms of…

Modeling Translation in Protein Synthesis with TASEP: A Tutorial and Recent Developments

NASA Astrophysics Data System (ADS)

Zia, R. K. P.; Dong, J. J.; Schmittmann, B.

2011-07-01

The phenomenon of protein synthesis has been modeled in terms of totally asymmetric simple exclusion processes (TASEP) since 1968. In this article, we provide a tutorial of the biological and mathematical aspects of this approach. We also summarize several new results, concerned with limited resources in the cell and simple estimates for the current (protein production rate) of a TASEP with inhomogeneous hopping rates, reflecting the characteristics of real genes.

Analytical determination of space station response to crew motion and design of suspension system for microgravity experiments

NASA Technical Reports Server (NTRS)

Liu, F. C.

1986-01-01

The objective of this investigation is to make analytical determination of the acceleration produced by crew motion in an orbiting space station and define design parameters for the suspension system of microgravity experiments. A simple structural model for simulation of the IOC space station is proposed. Mathematical formulation of this model provides the engineers a simple and direct tool for designing an effective suspension system.

Simple Examples of the Interpretation of Changes in Kinetic and Potential Energy Under Galilean Transformations

NASA Astrophysics Data System (ADS)

Ginsberg, Edw. S.

2018-02-01

The compatibility of the Newtonian formulation of mechanical energy and the transformation equations of Galilean relativity is demonstrated for three simple examples of motion treated in most introductory physics courses (free fall, a frictionless inclined plane, and a mass/spring system). Only elementary concepts and mathematics, accessible to students at that level, are used. Emphasis is on pedagogy and concepts related to the transformation properties of potential energy.

Design Of Feedforward Controllers For Multivariable Plants

NASA Technical Reports Server (NTRS)

Seraji, Homayoun

1989-01-01

Controllers based on simple low-order transfer functions. Mathematical criteria derived for design of feedforward controllers for class of multiple-input/multiple-output linear plants. Represented by simple low-order transfer functions, obtained without reconstruction of states of commands and disturbances. Enables plant to track command while remaining unresponsive to disturbance in steady state. Feedback controller added independently to stabilize plant or to make control system less susceptible to variations in parameters of plant.

Including Thermal Fluctuations in Actomyosin Stable States Increases the Predicted Force per Motor and Macroscopic Efficiency in Muscle Modelling

PubMed Central

2016-01-01

Muscle contractions are generated by cyclical interactions of myosin heads with actin filaments to form the actomyosin complex. To simulate actomyosin complex stable states, mathematical models usually define an energy landscape with a corresponding number of wells. The jumps between these wells are defined through rate constants. Almost all previous models assign these wells an infinite sharpness by imposing a relatively simple expression for the detailed balance, i.e., the ratio of the rate constants depends exponentially on the sole myosin elastic energy. Physically, this assumption corresponds to neglecting thermal fluctuations in the actomyosin complex stable states. By comparing three mathematical models, we examine the extent to which this hypothesis affects muscle model predictions at the single cross-bridge, single fiber, and organ levels in a ceteris paribus analysis. We show that including fluctuations in stable states allows the lever arm of the myosin to easily and dynamically explore all possible minima in the energy landscape, generating several backward and forward jumps between states during the lifetime of the actomyosin complex, whereas the infinitely sharp minima case is characterized by fewer jumps between states. Moreover, the analysis predicts that thermal fluctuations enable a more efficient contraction mechanism, in which a higher force is sustained by fewer attached cross-bridges. PMID:27626630

Annual cycle of Scots pine photosynthesis

NASA Astrophysics Data System (ADS)

Hari, Pertti; Kerminen, Veli-Matti; Kulmala, Liisa; Kulmala, Markku; Noe, Steffen; Petäjä, Tuukka; Vanhatalo, Anni; Bäck, Jaana

2017-12-01

Photosynthesis, i.e. the assimilation of atmospheric carbon to organic molecules with the help of solar energy, is a fundamental and well-understood process. Here, we connect theoretically the fundamental concepts affecting C3 photosynthesis with the main environmental drivers (ambient temperature and solar light intensity), using six axioms based on physiological and physical knowledge, and yield straightforward and simple mathematical equations. The light and carbon reactions in photosynthesis are based on the coherent operation of the photosynthetic machinery, which is formed of a complicated chain of enzymes, membrane pumps and pigments. A powerful biochemical regulation system has emerged through evolution to match photosynthesis with the annual cycle of solar light and temperature. The action of the biochemical regulation system generates the annual cycle of photosynthesis and emergent properties, the state of the photosynthetic machinery and the efficiency of photosynthesis. The state and the efficiency of the photosynthetic machinery is dynamically changing due to biosynthesis and decomposition of the molecules. The mathematical analysis of the system, defined by the very fundamental concepts and axioms, resulted in exact predictions of the behaviour of daily and annual patterns in photosynthesis. We tested the predictions with extensive field measurements of Scots pine (Pinus sylvestris L.) photosynthesis on a branch scale in northern Finland. Our theory gained strong support through rigorous testing.

Regulatory design governing progression of population growth phases in bacteria.

PubMed

Martínez-Antonio, Agustino; Lomnitz, Jason G; Sandoval, Santiago; Aldana, Maximino; Savageau, Michael A

2012-01-01

It has long been noted that batch cultures inoculated with resting bacteria exhibit a progression of growth phases traditionally labeled lag, exponential, pre-stationary and stationary. However, a detailed molecular description of the mechanisms controlling the transitions between these phases is lacking. A core circuit, formed by a subset of regulatory interactions involving five global transcription factors (FIS, HNS, IHF, RpoS and GadX), has been identified by correlating information from the well- established transcriptional regulatory network of Escherichia coli and genome-wide expression data from cultures in these different growth phases. We propose a functional role for this circuit in controlling progression through these phases. Two alternative hypotheses for controlling the transition between the growth phases are first, a continuous graded adjustment to changing environmental conditions, and second, a discontinuous hysteretic switch at critical thresholds between growth phases. We formulate a simple mathematical model of the core circuit, consisting of differential equations based on the power-law formalism, and show by mathematical and computer-assisted analysis that there are critical conditions among the parameters of the model that can lead to hysteretic switch behavior, which--if validated experimentally--would suggest that the transitions between different growth phases might be analogous to cellular differentiation. Based on these provocative results, we propose experiments to test the alternative hypotheses.

ABSIM. Simulation of Absorption Systems in Flexible and Modular Form

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

Grossman, G.

1994-06-01

The computer code has been developed for simulation of absorption systems at steady-state in a flexible and modular form, making it possible to investigate various cycle configurations with different working fluids. The code is based on unit subroutines containing the governing equations for the system`s components. When all the equations have been established, a mathematical solver routine is employed to solve them simultaneously. Property subroutines contained in a separate data base serve to provide thermodynamic properties of the working fluids. The code is user-oriented and requires a relatively simple input containing the given operating conditions and the working fluid atmore » each state point. the user conveys to the computer an image of the cycle by specifying the different components and their interconnections. Based on this information, the program calculates the temperature, flowrate, concentration, pressure and vapor fraction at each state point in the system and the heat duty at each unit, from which the coefficient of performance may be determined. A graphical user-interface is provided to facilitate interactive input and study of the output.« less

ABSIM. Simulation of Absorption Systems in Flexible and Modular Form

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

Grossman, G.

1994-06-01

The computer code has been developed for simulation of absorption systems at steady-state in a flexible and modular form, making it possible to investigate various cycle configurations with different working fluids. The code is based on unit subroutines containing the governing equations for the system's components. When all the equations have been established, a mathematical solver routine is employed to solve them simultaneously. Property subroutines contained in a separate data base serve to provide thermodynamic properties of the working fluids. The code is user-oriented and requires a relatively simple input containing the given operating conditions and the working fluid atmore » each state point. the user conveys to the computer an imagev of the cycle by specifying the different components and their interconnections. Based on this information, the program calculates the temperature, flowrate, concentration, pressure and vapor fraction at each state point in the system and the heat duty at each unit, from which the coefficient of performance may be determined. A graphical user-interface is provided to fcilitate interactive input and study of the output.« less

A Simple Method to Determine the Refractive Index of Glass.

ERIC Educational Resources Information Center

Mak, Se-yuen

1988-01-01

Describes an experiment for determining the refractive index. Discusses the experiment procedure and mathematical expression for calculating the index. Provides two geometrical diagrams and a graph for determining the index with a typical data. (YP)

Power and Efficiency.

ERIC Educational Resources Information Center

Boyd, James N.

1991-01-01

Presents a mathematical problem that, when examined and generalized, develops the relationships between power and efficiency in energy transfer. Offers four examples of simple electrical and mechanical systems to illustrate the principle that maximum power occurs at 50 percent efficiency. (MDH)

A study of stiffness, residual strength and fatigue life relationships for composite laminates

NASA Technical Reports Server (NTRS)

Ryder, J. T.; Crossman, F. W.

1983-01-01

Qualitative and quantitative exploration of the relationship between stiffness, strength, fatigue life, residual strength, and damage of unnotched, graphite/epoxy laminates subjected to tension loading. Clarification of the mechanics of the tension loading is intended to explain previous contradictory observations and hypotheses; to develop a simple procedure to anticipate strength, fatigue life, and stiffness changes; and to provide reasons for the study of more complex cases of compression, notches, and spectrum fatigue loading. Mathematical models are developed based upon analysis of the damage states. Mathematical models were based on laminate analysis, free body type modeling or a strain energy release rate. Enough understanding of the tension loaded case is developed to allow development of a proposed, simple procedure for calculating strain to failure, stiffness, strength, data scatter, and shape of the stress-life curve for unnotched laminates subjected to tension load.

Data-driven outbreak forecasting with a simple nonlinear growth model.

PubMed

Lega, Joceline; Brown, Heidi E

2016-12-01

Recent events have thrown the spotlight on infectious disease outbreak response. We developed a data-driven method, EpiGro, which can be applied to cumulative case reports to estimate the order of magnitude of the duration, peak and ultimate size of an ongoing outbreak. It is based on a surprisingly simple mathematical property of many epidemiological data sets, does not require knowledge or estimation of disease transmission parameters, is robust to noise and to small data sets, and runs quickly due to its mathematical simplicity. Using data from historic and ongoing epidemics, we present the model. We also provide modeling considerations that justify this approach and discuss its limitations. In the absence of other information or in conjunction with other models, EpiGro may be useful to public health responders. Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.

The Mathematics of Dispatchability, Revisited

NASA Technical Reports Server (NTRS)

Morris, Paul

2016-01-01

Dispatchability is an important property for the efficient execution of temporal plans where the temporal constraints are represented as a Simple Temporal Network (STN). It has been shown that every STN may be reformulated as a dispatchable STN, and dispatchability ensures that the temporal constraints need only be satisfied locally during execution. Recently, it has also been shown that Simple Temporal Networks with Uncertainty, augmented with wait edges, are Dynamically Controllable provided every projection is dispatchable. Thus, dispatchability has considerable theoretical as well as practical significance. One thing that hampers further work in this area is the underdeveloped theory. Moreover, the existing foundation is inadequate in certain respects. In this paper, we develop a new mathematical theory of dispatchability and its relationship to execution. We also provide several characterizations of dispatchability, including characterizations in terms of the structural properties of the STN graph. This facilitates the potential application of the theory to other areas.

The Mathematics of Dispatchability Revisited

NASA Technical Reports Server (NTRS)

Morris, Paul

2016-01-01

Dispatchability is an important property for the efficient execution of temporal plans where the temporal constraints are represented as a Simple Temporal Network (STN). It has been shown that every STN may be reformulated as a dispatchable STN, and dispatchability ensures that the temporal constraints need only be satisfied locally during execution. Recently it has also been shown that Simple Temporal Networks with Uncertainty, augmented with wait edges, are Dynamically Controllable provided every projection is dispatchable. Thus, the dispatchability property has both theoretical and practical interest. One thing that hampers further work in this area is the underdeveloped theory. The existing definitions are expressed in terms of algorithms, and are less suitable for mathematical proofs. In this paper, we develop a new formal theory of dispatchability in terms of execution sequences. We exploit this to prove a characterization of dispatchability involving the structural properties of the STN graph. This facilitates the potential application of the theory to uncertainty reasoning.

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.

Defining Computational Thinking for Mathematics and Science Classrooms

NASA Astrophysics Data System (ADS)

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

2016-02-01

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

Correlation of spacecraft thermal mathematical models to reference data

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

The mass-luminosity relation in an introductory astronomy lab

NASA Astrophysics Data System (ADS)

LoPresto, Michael C.

2016-11-01

Exposing students in general education science courses of lower mathematical levels to experiments that make use of quantitative skills such as collecting and analyzing data is very important because they provide examples of how science is actually done. Experiments with relatively simple procedures that are also interesting and engaging which serve this purpose can be hard to find. This can especially be true for introductory college astronomy courses; however, courses of this type often do still have a laboratory component because most students, regardless of major, are required to take at least one laboratory science course. When required to work with data in a quantitative fashion, the difficulty students with lower mathematical skills often have is that any actual physical meaning of an experiment can become completely lost in a procedure that, to them, seems to be purely an exercise in complex mathematics and for which they have resorted to simply following by rote, from which, perhaps needless to say, they are likely to learn little or nothing. I have seen this happen numerous times and it has inspired me to focus on attempting to develop meaningful laboratory experiences for students of lower mathematical level courses, such as introductory astronomy and conceptual physics, that involve both the gathering and analysis of numerical data. What follows is a simple experiment of this type on the mass-luminosity relation for stars on the main sequence of the Hertzsprung-Russell diagram that has proven useful for an introductory astronomy laboratory course.

Transformations of Mathematical and Stimulus Functions

PubMed Central

Ninness, Chris; Barnes-Holmes, Dermot; Rumph, Robin; McCuller, Glen; Ford, Angela M; Payne, Robert; Ninness, Sharon K; Smith, Ronald J; Ward, Todd A; Elliott, Marc P

2006-01-01

Following a pretest, 8 participants who were unfamiliar with algebraic and trigonometric functions received a brief presentation on the rectangular coordinate system. Next, they participated in a computer-interactive matching-to-sample procedure that trained formula-to-formula and formula-to-graph relations. Then, they were exposed to 40 novel formula-to-graph tests and 10 novel graph-to-formula tests. Seven of the 8 participants showed substantial improvement in identifying formula-to-graph relations; however, in the test of novel graph-to-formula relations, participants tended to select equations in their factored form. Next, we manipulated contextual cues in the form of rules regarding mathematical preferences. First, we informed participants that standard forms of equations were preferred over factored forms. In a subsequent test of 10 additional novel graph-to-formula relations, participants shifted their selections to favor equations in their standard form. This preference reversed during 10 more tests when financial reward was made contingent on correct identification of formulas in factored form. Formula preferences and transformation of novel mathematical and stimulus functions are discussed. PMID:17020211

Mathematical Modeling for Scrub Typhus and Its Implications for Disease Control.

PubMed

Min, Kyung Duk; Cho, Sung Il

2018-03-19

The incidence rate of scrub typhus has been increasing in the Republic of Korea. Previous studies have suggested that this trend may have resulted from the effects of climate change on the transmission dynamics among vectors and hosts, but a clear explanation of the process is still lacking. In this study, we applied mathematical models to explore the potential factors that influence the epidemiology of tsutsugamushi disease. We developed mathematical models of ordinary differential equations including human, rodent and mite groups. Two models, including simple and complex models, were developed, and all parameters employed in the models were adopted from previous articles that represent epidemiological situations in the Republic of Korea. The simulation results showed that the force of infection at the equilibrium state under the simple model was 0.236 (per 100,000 person-months), and that in the complex model was 26.796 (per 100,000 person-months). Sensitivity analyses indicated that the most influential parameters were rodent and mite populations and contact rate between them for the simple model, and trans-ovarian transmission for the complex model. In both models, contact rate between humans and mites is more influential than morality rate of rodent and mite group. The results indicate that the effect of controlling either rodents or mites could be limited, and reducing the contact rate between humans and mites is more practical and effective strategy. However, the current level of control would be insufficient relative to the growing mite population. © 2018 The Korean Academy of Medical Sciences.

Teaching Secondary Mathematics with ICT. Learning & Teaching with ICT

ERIC Educational Resources Information Center

Johnston-Wilder, Sue; Pimm, David

2004-01-01

This book shows the reader how to use Information and Communication Technology (ICT) effectively to enhance the teaching of mathematics in the secondary school. It explains which forms of technology can be used to improve mathematics teaching and learning, how to get started and where to go for further information. The book includes practical…

Do Pre-Service Elementary School Teachers Still Have Mathematics Anxiety? Some Factors and Correlates

ERIC Educational Resources Information Center

Çatlioglu, Hakan; Gürbüz, Ramazan; Birgin, Osman

2014-01-01

This study aims to provide new evidence from Turkish pre-service elementary school (PES) teachers and to identify some correlations and factors associated with mathematics anxiety (MA). 480 Turkish PES teachers participated in this study. Data was collected using a "Personal Information Form," "Mathematics Anxiety Scale," and…

Conceptualizing Mathematics as Discourse in Different Educational Settings

ERIC Educational Resources Information Center

Güçler, Beste; Wang, Sasha; Kim, Dong-Joong

2015-01-01

In this work, we focus on a relatively new theory in mathematics education research, which views thinking as communication and characterizes mathematics as a form of discourse. We discuss how this framework can be utilized in different educational settings by giving examples from our own research to highlight the insights it provides in the…

Putting It into Perspective: Mathematics in the Undergraduate Science Curriculum

ERIC Educational Resources Information Center

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

2009-01-01

Mathematics and science are tightly interwoven, yet they are often treated as distinct disciplines in the educational context. This study details the development, implementation and outcomes of a teaching intervention that highlights the links between mathematics and science, in the form of a first-year interdisciplinary course. A mixed method…

Parental Cultural Capital and Student School Performance in Mathematics and Science across Nations

ERIC Educational Resources Information Center

Huang, Haigen; Liang, Guodong

2016-01-01

The authors' purpose was to examine the relationship between three forms of cultural capital--the embodied, the objectified, and the institutionalized--and student performance in mathematics and science. Their analysis of Trends in International Mathematics and Science Study 2011 data from 32 countries and regions revealed that parental…

Family Involvement in Children's Mathematics Education Experiences: Voices of Immigrant Chinese American Students and Their Parents

ERIC Educational Resources Information Center

Liang, Senfeng

2013-01-01

This study examines ways in which Chinese immigrant families are involved in their children's mathematics education, particularly focusing on how different types of families utilize different forms of capital to support their children's mathematics education. The theoretical framework defines four types of Chinese immigrant families--working…

Didactics and History of Mathematics: Knowledge and Self-Knowledge

ERIC Educational Resources Information Center

Fried, Michael N.

2007-01-01

The basic assumption of this paper is that mathematics and history of mathematics are both forms of knowledge and, therefore, represent different ways of knowing. This was also the basic assumption of Fried (2001) who maintained that these ways of knowing imply different conceptual and methodological commitments, which, in turn, lead to a conflict…

Cognitive Activities in Solving Mathematical Tasks: The Role of a Cognitive Obstacle

ERIC Educational Resources Information Center

Antonijevic, Radovan

2016-01-01

In the process of learning mathematics, students practice various forms of thinking activities aimed to substantially contribute to the development of their different cognitive structures. In this paper, the subject matter is a "cognitive obstacle", a phenomenon that occurs in the procedures of solving mathematical tasks. Each task in…

Developing and Piloting the Planning for Facilitating Mathematical Processes and Strategies for Preschool Learners

ERIC Educational Resources Information Center

Botha, M.; Maree, J. G.; de Witt, M. W.

2005-01-01

From an early age young children actively engage informally in acquiring fundamental concepts and process skills that form a basis for mathematical understanding. Quite logically, questions will arise during planning when young children first encounter a more formal learning environment: what strategy should one use to develop mathematical …

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

ERIC Educational Resources Information Center

Treacy, Páraic; O'Donoghue, John

2014-01-01

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

Infographics and Mathematics: A Mechanism for Effective Learning in the Classroom

ERIC Educational Resources Information Center

Sudakov, Ivan; Bellsky, Thomas; Usenyuk, Svetlana; Polyakova, Victoria V.

2016-01-01

This work discusses the creation and use of infographics in an undergraduate mathematics course. Infographics are a visualization of information that combines data, formulas, and images. This article discusses how to form an infographic and uses infographics on topics within mathematics and climate as examples. It concludes with survey data from…

Cognitive and Mathematical Profiles for Different Forms of Learning Difficulties

PubMed Central

Cirino, Paul T.; Fuchs, Lynn S.; Elias, John T.; Powell, Sarah R.; Schumacher, Robin F.

2014-01-01

The purpose of this study was to compare subgroups of students with various forms of learning difficulties (< 25th percentile) on cognitive and mathematics characteristics. Students with mathematics difficulty (MD, n = 105), reading difficulty (RD, n = 65), both (MDRD, n = 87), or neither (NoLD, n = 403) were evaluated on an array of cognitive measures (e.g., working memory and language) and on mathematics measures of foundational numerical competencies, computation, and problem solving. Results revealed expected level differences among groups in both domains: NoLD outperformed RD, and MD outperformed MDRD. Profile differences were noted among pairs of subgroups on cognitive measures. On mathematics measures, profile differences were noted between RD and other subgroups, but not between MD and MDRD subgroups. The most discriminating cognitive measures were processing speed and language; the most discriminating mathematics measures depended on the subgroups being compared. Results were further evaluated according to more severe (< 10th percentile) criteria for MD and RD, which generally affected level differences more than the profile patterns. Results have implications for understanding comorbid MD and RD and for conceptualizing core deficits in MD. PMID:23851137

An Evolutionary Perspective on Learning Disability in Mathematics

PubMed Central

Geary, David C.

2015-01-01

A distinction between potentially evolved, or biologically-primary forms of cognition, and the culturally-specific, or biologically-secondary forms of cognition that are built from primary systems is used to explore mathematical learning disability (MLD). Using this model, MLD could result from deficits in the brain and cognitive systems that support biologically-primary mathematical competencies, or from the brain and cognitive systems that support the modification of primary systems for the creation of secondary knowledge and secondary cognitive competencies. The former include visuospatial long-term and working memory and the intraparietal sulcus, whereas the latter include the central executive component of working memory and the anterior cingulate cortex and lateral prefrontal cortex. Different forms of MLD are discussed as related to each of the cognitive and brain systems. PMID:17650991

Simulated Three-Point Problems.

ERIC Educational Resources Information Center

Leyden, Michael B.

1979-01-01

The concept of sloping bedrock strata is portrayed by simple construction of a cardboard model. By use of wires and graph paper, students simulate the drilling of wells and use standard mathematical operations to determine strike and dip of the model stratum. (RE)

Foxes and Rabbits - and a Spreadsheet.

ERIC Educational Resources Information Center

Carson, S. R.

1996-01-01

Presents a numerical simulation of a simple food chain together with a set of mathematical rules generalizing the model to a food web of any complexity. Discusses some of the model's interesting features and its use by students. (Author/JRH)

Mastery of Simple Probability Ideas Among G.C.E. Ordinary Level Mathematics Candidates

ERIC Educational Resources Information Center

Wood, R.; Brown, M.

1976-01-01

Questions concerning probability which appeared on the General Certificate of Education test are analyzed in terms of the processes required to answer them. The relationships between these processes and cognitive development are discussed. (SD)

Science, Technology, Engineering, Mathematics Poster

NASA Technical Reports Server (NTRS)

Kozusko, Timothy J.

2016-01-01

This is a simple poster for Community Day at the Visitor Center. It describes, as an overview, an example of the use of GPS and LiDAR data to determine the loss of scrubjay habitat due to a change in water table.

Using Simple Quadratic Equations to Estimate Equilibrium Concentrations of an Acid

ERIC Educational Resources Information Center

Brilleslyper, Michael A.

2004-01-01

Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.

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

Bastian, Mark; Trigueros, Jose V.

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

Concentrator optical characterization using computer mathematical modelling and point source testing

NASA Technical Reports Server (NTRS)

Dennison, E. W.; John, S. L.; Trentelman, G. F.

1984-01-01

The optical characteristics of a paraboloidal solar concentrator are analyzed using the intercept factor curve (a format for image data) to describe the results of a mathematical model and to represent reduced data from experimental testing. This procedure makes it possible not only to test an assembled concentrator, but also to evaluate single optical panels or to conduct non-solar tests of an assembled concentrator. The use of three-dimensional ray tracing computer programs to calculate the mathematical model is described. These ray tracing programs can include any type of optical configuration from simple paraboloids to array of spherical facets and can be adapted to microcomputers or larger computers, which can graphically display real-time comparison of calculated and measured data.

Classification of quantum groups and Belavin–Drinfeld cohomologies for orthogonal and symplectic Lie algebras

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

Kadets, Boris; Karolinsky, Eugene; Pop, Iulia

2016-05-15

In this paper we continue to study Belavin–Drinfeld cohomology introduced in Kadets et al., Commun. Math. Phys. 344(1), 1-24 (2016) and related to the classification of quantum groups whose quasi-classical limit is a given simple complex Lie algebra #Mathematical Fraktur Small G#. Here we compute Belavin–Drinfeld cohomology for all non-skewsymmetric r-matrices on the Belavin–Drinfeld list for simple Lie algebras of type B, C, and D.

Mathematical prediction of core body temperature from environment, activity, and clothing: The heat strain decision aid (HSDA).

PubMed

Potter, Adam W; Blanchard, Laurie A; Friedl, Karl E; Cadarette, Bruce S; Hoyt, Reed W

2017-02-01

Physiological models provide useful summaries of complex interrelated regulatory functions. These can often be reduced to simple input requirements and simple predictions for pragmatic applications. This paper demonstrates this modeling efficiency by tracing the development of one such simple model, the Heat Strain Decision Aid (HSDA), originally developed to address Army needs. The HSDA, which derives from the Givoni-Goldman equilibrium body core temperature prediction model, uses 16 inputs from four elements: individual characteristics, physical activity, clothing biophysics, and environmental conditions. These inputs are used to mathematically predict core temperature (T c ) rise over time and can estimate water turnover from sweat loss. Based on a history of military applications such as derivation of training and mission planning tools, we conclude that the HSDA model is a robust integration of physiological rules that can guide a variety of useful predictions. The HSDA model is limited to generalized predictions of thermal strain and does not provide individualized predictions that could be obtained from physiological sensor data-driven predictive models. This fully transparent physiological model should be improved and extended with new findings and new challenging scenarios. Published by Elsevier Ltd.

Can gender priming eliminate the effects of stereotype threat? The case of simple dynamic systems.

PubMed

Lungwitz, Vivien; Sedlmeier, Peter; Schwarz, Marcus

2018-05-31

Mathematics and mental rotation are classic fields where it has been shown that priming women with their gender identity impedes performance. Whereas past research focused mainly on stereotype threat effects in women in a narrowly defined context, this study broadened the research focus: We primed 264 women and men equally with a male, a neutral, or a female prime before they had to solve a simple dynamic system task. As expected, female-primed women subsequently performed worst of all six groups. Solution rates were almost 14% higher for the women in the male-primed condition. Men performed better than women in all three priming conditions. However, this difference was reduced in the male-primed condition as women's performance had increased as anticipated. Unexpected was a decline in the male performance in the same condition. The study showed that gender priming had a significant effect on women in tasks involving simple dynamic systems. However, mathematical knowledge and area of occupation clearly were stronger predictors for both men and women. Priming alone cannot eliminate the effects of stereotype threat. Copyright © 2018. Published by Elsevier B.V.

Experiment and mathematical model for the heat transfer in water around 4 °C

NASA Astrophysics Data System (ADS)

Ogawa, Naohisa; Kaneko, Fumitoshi

2017-03-01

Water, which is the habitat for a variety of living creatures, has a maximum density at 4.0 °C. This crucial property is considered to play a very important role in the biology of a lake and also has a close relationship with the areas of environmentology and geoscience. It would be desirable for students to confirm this important property of water themselves by carrying out simple experiments. However, it is not easy to detect the maximum density at 4.0 °C because the temperature dependence of the water density is very small close to its freezing point. For example, the density of water is 0.999 975 g cm-3 at 4.0 °C and 0.999 850 g cm-3 at 0.1 °C. The aim in this manuscript is to demonstrate a simple experiment to detect 4.0 °C as the temperature of maximum density, in which the time dependence of the water temperature is measured at several different depths by chilling the water surface. This is a simple experiment that can also be performed by high school students. We also present a mathematical model that can explain the results of this experiment.

Mathematical modelling of risk reduction in reinsurance

NASA Astrophysics Data System (ADS)

Balashov, R. B.; Kryanev, A. V.; Sliva, D. E.

2017-01-01

The paper presents a mathematical model of efficient portfolio formation in the reinsurance markets. The presented approach provides the optimal ratio between the expected value of return and the risk of yield values below a certain level. The uncertainty in the return values is conditioned by use of expert evaluations and preliminary calculations, which result in expected return values and the corresponding risk levels. The proposed method allows for implementation of computationally simple schemes and algorithms for numerical calculation of the numerical structure of the efficient portfolios of reinsurance contracts of a given insurance company.

On laminar and turbulent friction

NASA Technical Reports Server (NTRS)

Von Karman, TH

1946-01-01

Report deals, first with the theory of the laminar friction flow, where the basic concepts of Prandtl's boundary layer theory are represented from mathematical and physical points of view, and a method is indicated by means of which even more complicated cases can be treated with simple mathematical means, at least approximately. An attempt is also made to secure a basis for the computation of the turbulent friction by means of formulas through which the empirical laws of the turbulent pipe resistance can be applied to other problems on friction drag. (author)

Theoretical Foundations of Study of Cartography

NASA Astrophysics Data System (ADS)

Talhofer, Václav; Hošková-Mayerová, Šárka

2018-05-01

Cartography and geoinformatics are technical-based fields which deal with modelling and visualization of landscape in the form of a map. The theoretical foundation is necessary to obtain during study of cartography and geoinformatics based mainly on mathematics. For the given subjects, mathematics is necessary for understanding of many procedures that are connected to modelling of the Earth as a celestial body, to ways of its projection into a plane, to methods and procedures of modelling of landscape and phenomena in society and visualization of these models in the form of electronic as well as classic paper maps. Not only general mathematics, but also its extension of differential geometry of curves and surfaces, ways of approximation of lines and surfaces of functional surfaces, mathematical statistics and multi-criterial analyses seem to be suitable and necessary. Underestimation of the significance of mathematical education in cartography and geoinformatics is inappropriate and lowers competence of cartographers and professionals in geographic information science and technology to solve problems.

Typology of engineering mathematics learners in a Singapore polytechnic: a socio-psychological perspective

NASA Astrophysics Data System (ADS)

Khiat, Henry

2012-03-01

This study aims to understand how engineering mathematics students form intentions in mathematics learning from a socio-psychological perspective. A grounded theory approach was adopted and 21 engineering students and six tutors participated in the study. The main findings in this study show that a student's intention in engineering mathematics learning is made up of a number of sequential components - their critical trigger, internalized significance, aim and perceived intention-related consequences in engineering mathematics learning. Accordingly, the participants may be broadly classified into five types of learners: idealistic learners, competitive learners, pragmatic learners, fatalistic learners and dissonant learners according to their intentions in engineering mathematics learning.

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

PubMed

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

2014-08-28

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

Software Template for Instruction in Mathematics

NASA Technical Reports Server (NTRS)

Shelton, Robert O.; Moebes, Travis A.; Beall, Anna

2005-01-01

Intelligent Math Tutor (IMT) is a software system that serves as a template for creating software for teaching mathematics. IMT can be easily connected to artificial-intelligence software and other analysis software through input and output of files. IMT provides an easy-to-use interface for generating courses that include tests that contain both multiple-choice and fill-in-the-blank questions, and enables tracking of test scores. IMT makes it easy to generate software for Web-based courses or to manufacture compact disks containing executable course software. IMT also can function as a Web-based application program, with features that run quickly on the Web, while retaining the intelligence of a high-level language application program with many graphics. IMT can be used to write application programs in text, graphics, and/or sound, so that the programs can be tailored to the needs of most handicapped persons. The course software generated by IMT follows a "back to basics" approach of teaching mathematics by inducing the student to apply creative mathematical techniques in the process of learning. Students are thereby made to discover mathematical fundamentals and thereby come to understand mathematics more deeply than they could through simple memorization.

Analysis of creative mathematic thinking ability in problem based learning model based on self-regulation learning

NASA Astrophysics Data System (ADS)

Munahefi, D. N.; Waluya, S. B.; Rochmad

2018-03-01

The purpose of this research identified the effectiveness of Problem Based Learning (PBL) models based on Self Regulation Leaning (SRL) on the ability of mathematical creative thinking and analyzed the ability of mathematical creative thinking of high school students in solving mathematical problems. The population of this study was students of grade X SMA N 3 Klaten. The research method used in this research was sequential explanatory. Quantitative stages with simple random sampling technique, where two classes were selected randomly as experimental class was taught with the PBL model based on SRL and control class was taught with expository model. The selection of samples at the qualitative stage was non-probability sampling technique in which each selected 3 students were high, medium, and low academic levels. PBL model with SRL approach effectived to students’ mathematical creative thinking ability. The ability of mathematical creative thinking of low academic level students with PBL model approach of SRL were achieving the aspect of fluency and flexibility. Students of academic level were achieving fluency and flexibility aspects well. But the originality of students at the academic level was not yet well structured. Students of high academic level could reach the aspect of originality.

The Art of Mathematics: Bedding Down for a New Era

ERIC Educational Resources Information Center

Brown, Tony

2007-01-01

Comparisons made between art and mathematics so often centre on the beauty of mathematics and how its forms might be seen as aesthetically pleasing. Yet the prominence of beauty as an attribute is less prevalent in contemporary art. Rather, art has a much broader scope of concern, perhaps with a greater emphasis on providing apparatus through…

Model-Eliciting Activities (MEAs) as a Bridge between Engineering Education Research and Mathematics Education Research

ERIC Educational Resources Information Center

Hamilton, Eric; Lesh, Richard; Lester, Frank; Brilleslyper, Michael

2008-01-01

This article introduces Model-Eliciting Activities (MEAs) as a form of case study team problem-solving. MEA design focuses on eliciting from students conceptual models that they iteratively revise in problem-solving. Though developed by mathematics education researchers to study the evolution of mathematical problem-solving expertise in middle…

Attributes of Instances of Student Mathematical Thinking That Are Worth Building on in Whole-Class Discussion

ERIC Educational Resources Information Center

Van Zoest, Laura R.; Stockero, Shari L.; Leatham, Keith R.; Peterson, Blake E.; Atanga, Napthalin A.; Ochieng, Mary A.

2017-01-01

This study investigated attributes of 278 instances of student mathematical thinking during whole-class interactions that were identified as having high potential, if made the object of discussion, to foster learners' understanding of important mathematical ideas. Attributes included the form of the thinking (e.g., question vs. declarative…

A Comparison of Authoring Software for Developing Mathematics Self-Learning Software Packages.

ERIC Educational Resources Information Center

Suen, Che-yin; Pok, Yang-ming

Four years ago, the authors started to develop a self-paced mathematics learning software called NPMaths by using an authoring package called Tencore. However, NPMaths had some weak points. A development team was hence formed to develop similar software called Mathematics On Line. This time the team used another development language called…

Mathematical Induction and Recursive Definition in Teaching Training

ERIC Educational Resources Information Center

Vármonostory, Endre

2009-01-01

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

Secondary School Students' Attitudes towards Mathematics Computer--Assisted Instruction Environment in Kenya

ERIC Educational Resources Information Center

Mwei, Philip K.; Wando, Dave; Too, Jackson K.

2012-01-01

This paper reports the results of research conducted in six classes (Form IV) with 205 students with a sample of 94 respondents. Data represent students' statements that describe (a) the role of Mathematics teachers in a computer-assisted instruction (CAI) environment and (b) effectiveness of CAI in Mathematics instruction. The results indicated…

A Cross-Cultural Investigation into How Tasks Influence Seatwork Activities in Mathematics Lessons

ERIC Educational Resources Information Center

Serrano, Ana M.

2012-01-01

This study examined how types of tasks influenced student activities/thinking and defined the role of Seatwork in mathematics lessons. It used 60 lessons from the TIMSS videotaped Study. These data indicated that practice was the most prevalent form of tasks in the U.S. In Germany, students completed mathematical calculations after a complex…

Mathematics Anxiety: What Have We Learned in 60 Years?

PubMed

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

2016-01-01

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

Lemon-Lime Science Time.

ERIC Educational Resources Information Center

Brown, Helen

1995-01-01

Presents a unit to investigate lemons and experience the real taste of a lemon that includes simple, enjoyable, and inexpensive activities that develop students' observation, prediction, measurement, and inference skills. Students also developed creative arts projects, explored mathematical concepts, and wrote stories about fruit. (NB)

Colour by Numbers

ERIC Educational Resources Information Center

Wetherell, Chris

2017-01-01

This is an edited extract from the keynote address given by Dr. Chris Wetherell at the 26th Biennial Conference of the Australian Association of Mathematics Teachers Inc. The author investigates the surprisingly rich structure that exists within a simple arrangement of numbers: the times tables.

Exploring simple, transparent, interpretable and predictive QSAR models for classification and quantitative prediction of rat toxicity of ionic liquids using OECD recommended guidelines.

PubMed

Das, Rudra Narayan; Roy, Kunal; Popelier, Paul L A

2015-11-01

The present study explores the chemical attributes of diverse ionic liquids responsible for their cytotoxicity in a rat leukemia cell line (IPC-81) by developing predictive classification as well as regression-based mathematical models. Simple and interpretable descriptors derived from a two-dimensional representation of the chemical structures along with quantum topological molecular similarity indices have been used for model development, employing unambiguous modeling strategies that strictly obey the guidelines of the Organization for Economic Co-operation and Development (OECD) for quantitative structure-activity relationship (QSAR) analysis. The structure-toxicity relationships that emerged from both classification and regression-based models were in accordance with the findings of some previous studies. The models suggested that the cytotoxicity of ionic liquids is dependent on the cationic surfactant action, long alkyl side chains, cationic lipophilicity as well as aromaticity, the presence of a dialkylamino substituent at the 4-position of the pyridinium nucleus and a bulky anionic moiety. The models have been transparently presented in the form of equations, thus allowing their easy transferability in accordance with the OECD guidelines. The models have also been subjected to rigorous validation tests proving their predictive potential and can hence be used for designing novel and "greener" ionic liquids. The major strength of the present study lies in the use of a diverse and large dataset, use of simple reproducible descriptors and compliance with the OECD norms. Copyright © 2015 Elsevier Ltd. All rights reserved.

Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches.

PubMed

Wiratsudakul, Anuwat; Suparit, Parinya; Modchang, Charin

2018-01-01

The Zika virus was first discovered in 1947. It was neglected until a major outbreak occurred on Yap Island, Micronesia, in 2007. Teratogenic effects resulting in microcephaly in newborn infants is the greatest public health threat. In 2016, the Zika virus epidemic was declared as a Public Health Emergency of International Concern (PHEIC). Consequently, mathematical models were constructed to explicitly elucidate related transmission dynamics. In this review article, two steps of journal article searching were performed. First, we attempted to identify mathematical models previously applied to the study of vector-borne diseases using the search terms "dynamics," "mathematical model," "modeling," and "vector-borne" together with the names of vector-borne diseases including chikungunya, dengue, malaria, West Nile, and Zika. Then the identified types of model were further investigated. Second, we narrowed down our survey to focus on only Zika virus research. The terms we searched for were "compartmental," "spatial," "metapopulation," "network," "individual-based," "agent-based" AND "Zika." All relevant studies were included regardless of the year of publication. We have collected research articles that were published before August 2017 based on our search criteria. In this publication survey, we explored the Google Scholar and PubMed databases. We found five basic model architectures previously applied to vector-borne virus studies, particularly in Zika virus simulations. These include compartmental, spatial, metapopulation, network, and individual-based models. We found that Zika models carried out for early epidemics were mostly fit into compartmental structures and were less complicated compared to the more recent ones. Simple models are still commonly used for the timely assessment of epidemics. Nevertheless, due to the availability of large-scale real-world data and computational power, recently there has been growing interest in more complex modeling frameworks. Mathematical models are employed to explore and predict how an infectious disease spreads in the real world, evaluate the disease importation risk, and assess the effectiveness of intervention strategies. As the trends in modeling of infectious diseases have been shifting towards data-driven approaches, simple and complex models should be exploited differently. Simple models can be produced in a timely fashion to provide an estimation of the possible impacts. In contrast, complex models integrating real-world data require more time to develop but are far more realistic. The preparation of complicated modeling frameworks prior to the outbreaks is recommended, including the case of future Zika epidemic preparation.

Reactant conversion in homogeneous turbulence: Mathematical modeling, computational validations and practical applications

NASA Technical Reports Server (NTRS)

Madnia, C. K.; Frankel, S. H.; Givi, P.

1992-01-01

Closed form analytical expressions are obtained for predicting the limited rate of reactant conversion in a binary reaction of the type F + rO yields (1 + r) Product in unpremixed homogeneous turbulence. These relations are obtained by means of a single point Probability Density Function (PDF) method based on the Amplitude Mapping Closure. It is demonstrated that with this model, the maximum rate of the reactants' decay can be conveniently expressed in terms of definite integrals of the Parabolic Cylinder Functions. For the cases with complete initial segregation, it is shown that the results agree very closely with those predicted by employing a Beta density of the first kind for an appropriately defined Shvab-Zeldovich scalar variable. With this assumption, the final results can also be expressed in terms of closed form analytical expressions which are based on the Incomplete Beta Functions. With both models, the dependence of the results on the stoichiometric coefficient and the equivalence ratio can be expressed in an explicit manner. For a stoichiometric mixture, the analytical results simplify significantly. In the mapping closure, these results are expressed in terms of simple trigonometric functions. For the Beta density model, they are in the form of Gamma Functions. In all the cases considered, the results are shown to agree well with data generated by Direct Numerical Simulations (DNS). Due to the simplicity of these expressions and because of nice mathematical features of the Parabolic Cylinder and the Incomplete Beta Functions, these models are recommended for estimating the limiting rate of reactant conversion in homogeneous reacting flows. These results also provide useful insights in assessing the extent of validity of turbulence closures in the modeling of unpremixed reacting flows. Some discussions are provided on the extension of the model for treating more complicated reacting systems including realistic kinetics schemes and multi-scalar mixing with finite rate chemical reactions in more complex configurations.

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.

CSMP (Continuous System Modeling Program) modeling of brushless DC motors

NASA Astrophysics Data System (ADS)

Thomas, S. M.

1984-09-01

Recent improvements in rare earth magnets have made it possible to construct strong, lightweight, high horsepower DC motors. This has occasioned a reassessment of electromechanical actuators as alternatives to comparable pneumatic and hydraulic systems for use in flight control actuators for tactical missiles. This thesis develops a low-order mathematical model for the simulation and analysis of brushless DC motor performance. This model is implemented in CSMP language. It is used to predict such motor performance curves as speed, current and power versus torque. Electronic commutation based on Hall effect sensor positional feedback is simulated. Steady state motor behavior is studied under both constant and variable air gap flux conditions. The variable flux takes two different forms. In the first case, the flux is varied as a simple sinusoid. In the second case, the flux is varied as the sum of a sinusoid and one of its harmonics.

A numerical algorithm of tooth profile of non-circular cylindrical gear

NASA Astrophysics Data System (ADS)

Wang, Xuan

2017-08-01

Non-circular cylindrical gear (NCCG) is a common form of non-circular gear. Different from the circular gear, the tooth profile equation of NCCG cannot be obtained. So it is necessary to use a numerical algorithm to calculate the tooth profile of NCCG. For this reason, this paper presents a simple and highly efficient numerical algorithm to obtain the tooth profile of NCCG. Firstly, the mathematical model of tooth profile envelope of NCCG is established based on the principle of gear shaping, and the tooth profile envelope of NCCG is obtained. Secondly, the polar radius and polar angle of shaper cutter tooth profile are chosen as the criterions, by which the points of NCCG tooth cogging can be screened out. Finally, the boundary of tooth cogging points is extracted by a distance criterion and correspondingly the tooth profile of NCCG is obtained.

Impact of the Equation of State in Models for Surfactant Spreading Experiments

NASA Astrophysics Data System (ADS)

Levy, Rachel

2014-11-01

Pulmonary surfactant spreading models often rely on an equation of state relating surfactant concentration to surface tension. Mathematically, these models have been analyzed with simple functional relationships. However, to model an experiment with a given fluid and surfactant, a physically meaningful equation of state can be derived from experimentally obtained isotherms. We discuss the comparison between model and experiment for NBD-PC lipid (surfactant) spreading on glycerol for an empirically-determined equation of state, and compare those results to simulations with traditionally employed functional forms. In particular we compare the timescales by tracking the leading edge of surfactant, the central fluid height and dynamics of the Marangoni ridge. We consider both outward spreading of a disk-shaped region of surfactant and the hole-closure problem in which a disk-shaped surfactant-free region self-heals. Support from NSF-DMS-FRG 0968154, RCSA-CCS-19788, and HHMI.

Identification and simulation evaluation of an AH-64 helicopter hover math model

NASA Technical Reports Server (NTRS)

Schroeder, J. A.; Watson, D. C.; Tischler, M. B.; Eshow, M. M.

1991-01-01

Frequency-domain parameter-identification techniques were used to develop a hover mathematical model of the AH-64 Apache helicopter from flight data. The unstable AH-64 bare-airframe characteristics without a stability-augmentation system were parameterized in the convectional stability-derivative form. To improve the model's vertical response, a simple transfer-function model approximating the effects of dynamic inflow was developed. Additional subcomponents of the vehicle were also modeled and simulated, such as a basic engine response for hover and the vehicle stick dynamic characteristics. The model, with and without stability augmentation, was then evaluated by AH-64 pilots in a moving-base simulation. It was the opinion of the pilots that the simulation was a satisfactory representation of the aircraft for the tasks of interest. The principal negative comment was that height control was more difficult in the simulation than in the aircraft.

Nonlinear Thermoelastic Model for SMAs and SMA Hybrid Composites

NASA Technical Reports Server (NTRS)

Turner, Travis L.

2004-01-01

A constitutive mathematical model has been developed that predicts the nonlinear thermomechanical behaviors of shape-memory-alloys (SMAs) and of shape-memory-alloy hybrid composite (SMAHC) structures, which are composite-material structures that contain embedded SMA actuators. SMAHC structures have been investigated for their potential utility in a variety of applications in which there are requirements for static or dynamic control of the shapes of structures, control of the thermoelastic responses of structures, or control of noise and vibrations. The present model overcomes deficiencies of prior, overly simplistic or qualitative models that have proven ineffective or intractable for engineering of SMAHC structures. The model is sophisticated enough to capture the essential features of the mechanics of SMAHC structures yet simple enough to accommodate input from fundamental engineering measurements and is in a form that is amenable to implementation in general-purpose structural analysis environments.

Constructing a polynomial whose nodal set is the three-twist knot 52

NASA Astrophysics Data System (ADS)

Dennis, Mark R.; Bode, Benjamin

2017-06-01

We describe a procedure that creates an explicit complex-valued polynomial function of three-dimensional space, whose nodal lines are the three-twist knot 52. The construction generalizes a similar approach for lemniscate knots: a braid representation is engineered from finite Fourier series and then considered as the nodal set of a certain complex polynomial which depends on an additional parameter. For sufficiently small values of this parameter, the nodal lines form the three-twist knot. Further mathematical properties of this map are explored, including the relationship of the phase critical points with the Morse-Novikov number, which is nonzero as this knot is not fibred. We also find analogous functions for other simple knots and links. The particular function we find, and the general procedure, should be useful for designing knotted fields of particular knot types in various physical systems.

A comparative study of Conroy and Monte Carlo methods applied to multiple quadratures and multiple scattering

NASA Technical Reports Server (NTRS)

Deepak, A.; Fluellen, A.

1978-01-01

An efficient numerical method of multiple quadratures, the Conroy method, is applied to the problem of computing multiple scattering contributions in the radiative transfer through realistic planetary atmospheres. A brief error analysis of the method is given and comparisons are drawn with the more familiar Monte Carlo method. Both methods are stochastic problem-solving models of a physical or mathematical process and utilize the sampling scheme for points distributed over a definite region. In the Monte Carlo scheme the sample points are distributed randomly over the integration region. In the Conroy method, the sample points are distributed systematically, such that the point distribution forms a unique, closed, symmetrical pattern which effectively fills the region of the multidimensional integration. The methods are illustrated by two simple examples: one, of multidimensional integration involving two independent variables, and the other, of computing the second order scattering contribution to the sky radiance.

A Local-Realistic Model of Quantum Mechanics Based on a Discrete Spacetime

NASA Astrophysics Data System (ADS)

Sciarretta, Antonio

2018-01-01

This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on probabilities, in particular assuming a discrete spacetime under the form of a Euclidean lattice. Individual (spinless) particle trajectories are described as random walks. Transition probabilities are simple functions of a few quantities that are either randomly associated to the particles during their preparation, or stored in the lattice nodes they visit during the walk. QM predictions are retrieved as probability distributions of similarly-prepared ensembles of particles. The scenarios considered to assess the model comprise of free particle, constant external force, harmonic oscillator, particle in a box, the Delta potential, particle on a ring, particle on a sphere and include quantization of energy levels and angular momentum, as well as momentum entanglement.

Random blebbing motion: A simple model linking cell structural properties to migration characteristics.

PubMed

Woolley, Thomas E; Gaffney, Eamonn A; Goriely, Alain

2017-07-01

If the plasma membrane of a cell is able to delaminate locally from its actin cortex, a cellular bleb can be produced. Blebs are pressure-driven protrusions, which are noteworthy for their ability to produce cellular motion. Starting from a general continuum mechanics description, we restrict ourselves to considering cell and bleb shapes that maintain approximately spherical forms. From this assumption, we obtain a tractable algebraic system for bleb formation. By including cell-substrate adhesions, we can model blebbing cell motility. Further, by considering mechanically isolated blebbing events, which are randomly distributed over the cell, we can derive equations linking the macroscopic migration characteristics to the microscopic structural parameters of the cell. This multiscale modeling framework is then used to provide parameter estimates, which are in agreement with current experimental data. In summary, the construction of the mathematical model provides testable relationships between the bleb size and cell motility.

Image based method for aberration measurement of lithographic tools

NASA Astrophysics Data System (ADS)

Xu, Shuang; Tao, Bo; Guo, Yongxing; Li, Gongfa

2018-01-01

Information of lens aberration of lithographic tools is important as it directly affects the intensity distribution in the image plane. Zernike polynomials are commonly used for a mathematical description of lens aberrations. Due to the advantage of lower cost and easier implementation of tools, image based measurement techniques have been widely used. Lithographic tools are typically partially coherent systems that can be described by a bilinear model, which entails time consuming calculations and does not lend a simple and intuitive relationship between lens aberrations and the resulted images. Previous methods for retrieving lens aberrations in such partially coherent systems involve through-focus image measurements and time-consuming iterative algorithms. In this work, we propose a method for aberration measurement in lithographic tools, which only requires measuring two images of intensity distribution. Two linear formulations are derived in matrix forms that directly relate the measured images to the unknown Zernike coefficients. Consequently, an efficient non-iterative solution is obtained.

Market penetration of energy supply technologies

NASA Astrophysics Data System (ADS)

Condap, R. J.

1980-03-01

Techniques to incorporate the concepts of profit-induced growth and risk aversion into policy-oriented optimization models of the domestic energy sector are examined. After reviewing the pertinent market penetration literature, simple mathematical programs in which the introduction of new energy technologies is constrained primarily by the reinvestment of profits are formulated. The main results involve the convergence behavior of technology production levels under various assumptions about the form of the energy demand function. Next, profitability growth constraints are embedded in a full-scale model of U.S. energy-economy interactions. A rapidly convergent algorithm is developed to utilize optimal shadow prices in the computation of profitability for individual technologies. Allowance is made for additional policy variables such as government funding and taxation. The result is an optimal deployment schedule for current and future energy technologies which is consistent with the sector's ability to finance capacity expansion.

Zipf's word frequency law in natural language: a critical review and future directions.

PubMed

Piantadosi, Steven T

2014-10-01

The frequency distribution of words has been a key object of study in statistical linguistics for the past 70 years. This distribution approximately follows a simple mathematical form known as Zipf's law. This article first shows that human language has a highly complex, reliable structure in the frequency distribution over and above this classic law, although prior data visualization methods have obscured this fact. A number of empirical phenomena related to word frequencies are then reviewed. These facts are chosen to be informative about the mechanisms giving rise to Zipf's law and are then used to evaluate many of the theoretical explanations of Zipf's law in language. No prior account straightforwardly explains all the basic facts or is supported with independent evaluation of its underlying assumptions. To make progress at understanding why language obeys Zipf's law, studies must seek evidence beyond the law itself, testing assumptions and evaluating novel predictions with new, independent data.

Three different methods for determination of binary mixture of Amlodipine and Atorvastatin using dual wavelength spectrophotometry

NASA Astrophysics Data System (ADS)

Darwish, Hany W.; Hassan, Said A.; Salem, Maissa Y.; El-Zeany, Badr A.

2013-03-01

Three simple, specific, accurate and precise spectrophotometric methods depending on the proper selection of two wavelengths are developed for the simultaneous determination of Amlodipine besylate (AML) and Atorvastatin calcium (ATV) in tablet dosage forms. The first method is the new Ratio Difference method, the second method is the Bivariate method and the third one is the Absorbance Ratio method. The calibration curve is linear over the concentration range of 4-40 and 8-32 μg/mL for AML and ATV, respectively. These methods are tested by analyzing synthetic mixtures of the above drugs and they are applied to commercial pharmaceutical preparation of the subjected drugs. Methods are validated according to the ICH guidelines and accuracy, precision, repeatability and robustness are found to be within the acceptable limit. The mathematical explanation of the procedures is illustrated.

Hitchin functionals are related to measures of entanglement

NASA Astrophysics Data System (ADS)

Lévay, Péter; Sárosi, Gábor

2012-11-01

According to the black hole/qubit correspondence (BHQC) certain black hole entropy formulas in supergravity can be related to multipartite entanglement measures of quantum information. Here we show that the origin of this correspondence is a connection between Hitchin functionals used as action functionals for form theories of gravity related to topological strings and entanglement measures for systems with a small number of constituents. The basic idea acting as a unifying agent in these seemingly unrelated fields is stability connected to the mathematical notion of special prehomogeneous vector spaces associated to Freudenthal systems coming from simple Jordan algebras. It is shown that the nonlinear function featuring these functionals and defining Calabi-Yau and generalized Calabi-Yau structures is the Freudenthal dual, a concept introduced recently in connection with the BHQC. We propose to use the Hitchin invariant for three-forms in seven dimensions as an entanglement measure playing a basic role in classifying three-fermion systems with seven modes. The representative of the class of maximal tripartite entanglement is the three-form used as a calibration for compactification on manifolds with G2 holonomy. The idea that entanglement measures are related to action functionals from which the usual correspondence of the BHQC follows at the tree level suggests that one can use the BHQC in a more general context.

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.

Analyzing the dynamics of cell cycle processes from fixed samples through ergodic principles

PubMed Central

Wheeler, Richard John

2015-01-01

Tools to analyze cyclical cellular processes, particularly the cell cycle, are of broad value for cell biology. Cell cycle synchronization and live-cell time-lapse observation are widely used to analyze these processes but are not available for many systems. Simple mathematical methods built on the ergodic principle are a well-established, widely applicable, and powerful alternative analysis approach, although they are less widely used. These methods extract data about the dynamics of a cyclical process from a single time-point “snapshot” of a population of cells progressing through the cycle asynchronously. Here, I demonstrate application of these simple mathematical methods to analysis of basic cyclical processes—cycles including a division event, cell populations undergoing unicellular aging, and cell cycles with multiple fission (schizogony)—as well as recent advances that allow detailed mapping of the cell cycle from continuously changing properties of the cell such as size and DNA content. This includes examples using existing data from mammalian, yeast, and unicellular eukaryotic parasite cell biology. Through the ongoing advances in high-throughput cell analysis by light microscopy, electron microscopy, and flow cytometry, these mathematical methods are becoming ever more important and are a powerful complementary method to traditional synchronization and time-lapse cell cycle analysis methods. PMID:26543196

A Simple Mathematical Model for Standard Model of Elementary Particles and Extension Thereof

NASA Astrophysics Data System (ADS)

Sinha, Ashok

2016-03-01

An algebraically (and geometrically) simple model representing the masses of the elementary particles in terms of the interaction (strong, weak, electromagnetic) constants is developed, including the Higgs bosons. The predicted Higgs boson mass is identical to that discovered by LHC experimental programs; while possibility of additional Higgs bosons (and their masses) is indicated. The model can be analyzed to explain and resolve many puzzles of particle physics and cosmology including the neutrino masses and mixing; origin of the proton mass and the mass-difference between the proton and the neutron; the big bang and cosmological Inflation; the Hubble expansion; etc. A novel interpretation of the model in terms of quaternion and rotation in the six-dimensional space of the elementary particle interaction-space - or, equivalently, in six-dimensional spacetime - is presented. Interrelations among particle masses are derived theoretically. A new approach for defining the interaction parameters leading to an elegant and symmetrical diagram is delineated. Generalization of the model to include supersymmetry is illustrated without recourse to complex mathematical formulation and free from any ambiguity. This Abstract represents some results of the Author's Independent Theoretical Research in Particle Physics, with possible connection to the Superstring Theory. However, only very elementary mathematics and physics is used in my presentation.

A mathematical model of the pancreatic duct cell generating high bicarbonate concentrations in pancreatic juice.

PubMed

Whitcomb, David C; Ermentrout, G Bard

2004-08-01

To develop a simple, physiologically based mathematical model of pancreatic duct cell secretion using experimentally derived parameters that generates pancreatic fluid bicarbonate concentrations of >140 mM after CFTR activation. A new mathematical model was developed simulating a duct cell within a proximal pancreatic duct and included a sodium-2-bicarbonate cotransporter (NBC) and sodium-potassium pump (NaK pump) on a chloride-impermeable basolateral membrane, CFTR on the luminal membrane with 0.2 to 1 bicarbonate to chloride permeability ratio. Chloride-bicarbonate antiporters (Cl/HCO3 AP) were added or subtracted from the basolateral (APb) and luminal (APl) membranes. The model was integrated over time using XPPAUT. This model predicts robust, NaK pump-dependent bicarbonate secretion with opening of the CFTR, generates and maintains pancreatic fluid secretion with bicarbonate concentrations >140 mM, and returns to basal levels with CFTR closure. Limiting CFTR permeability to bicarbonate, as seen in some CFTR mutations, markedly inhibited pancreatic bicarbonate and fluid secretion. A simple CFTR-dependent duct cell model can explain active, high-volume, high-concentration bicarbonate secretion in pancreatic juice that reproduces the experimental findings. This model may also provide insight into why CFTR mutations that predominantly affect bicarbonate permeability predispose to pancreatic dysfunction in humans.

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

PubMed

Polak, Justyna; Bartoszek, Mariola; Chorążewski, Mirosław

2015-07-22

A new method of determining antioxidant capacity based on a mathematical model is presented in this paper. The model was fitted to 1000 data points of electron paramagnetic resonance (EPR) spectroscopy measurements of various food product samples such as tea, wine, juice, and herbs with Trolox equivalent antioxidant capacity (TEAC) values from 20 to 2000 μmol TE/100 mL. The proposed mathematical equation allows for a determination of TEAC of food products based on a single EPR spectroscopy measurement. The model was tested on the basis of 80 EPR spectroscopy measurements of herbs, tea, coffee, and juice samples. The proposed model works for both strong and weak antioxidants (TEAC values from 21 to 2347 μmol TE/100 mL). The determination coefficient between TEAC values obtained experimentally and TEAC values calculated with proposed mathematical equation was found to be R(2) = 0.98. Therefore, the proposed new method of TEAC determination based on a mathematical model is a good alternative to the standard EPR method due to its being fast, accurate, inexpensive, and simple to perform.

Evolutionary game theory using agent-based methods.

PubMed

Adami, Christoph; Schossau, Jory; Hintze, Arend

2016-12-01

Evolutionary game theory is a successful mathematical framework geared towards understanding the selective pressures that affect the evolution of the strategies of agents engaged in interactions with potential conflicts. While a mathematical treatment of the costs and benefits of decisions can predict the optimal strategy in simple settings, more realistic settings such as finite populations, non-vanishing mutations rates, stochastic decisions, communication between agents, and spatial interactions, require agent-based methods where each agent is modeled as an individual, carries its own genes that determine its decisions, and where the evolutionary outcome can only be ascertained by evolving the population of agents forward in time. While highlighting standard mathematical results, we compare those to agent-based methods that can go beyond the limitations of equations and simulate the complexity of heterogeneous populations and an ever-changing set of interactors. We conclude that agent-based methods can predict evolutionary outcomes where purely mathematical treatments cannot tread (for example in the weak selection-strong mutation limit), but that mathematics is crucial to validate the computational simulations. Copyright © 2016 Elsevier B.V. All rights reserved.

Divergence thrust loss calculations for convergent-divergent nozzles: Extensions to the classical case

NASA Technical Reports Server (NTRS)

Berton, Jeffrey J.

1991-01-01

The analytical derivations of the non-axial thrust divergence losses for convergent-divergent nozzles are described as well as how these calculations are embodied in the Navy/NASA engine computer program. The convergent-divergent geometries considered are simple classic axisymmetric nozzles, two dimensional rectangular nozzles, and axisymmetric and two dimensional plug nozzles. A simple, traditional, inviscid mathematical approach is used to deduce the influence of the ineffectual non-axial thrust as a function of the nozzle exit divergence angle.

Mathematics and the Internet: A Source of Enormous Confusion and Great Potential

DTIC Science & Technology

2009-05-01

free Internet Myth The story recounted below of the scale-free nature of the Internet seems convincing, sound, and al- most too good to be true ...models. In fact, much of the initial excitement in the nascent field of network science can be attributed to an ear- ly and appealingly simple class...this new class of networks, com- monly referred to as scale-free networks. The term scale-free derives from the simple observation that power-law node

Procedures for Scaling the 1990 Edition of the Nevada Proficiency Examinations in Reading and Mathematics.

ERIC Educational Resources Information Center

Klein, Thomas W.

Steps involved in the item analysis and scaling of the 1990 edition of Forms A and B of the Nevada High School Proficiency Examinations (NHSPEs) are described. Pilot tests of Forms A and B of the 47-item reading and 45-item mathematics tests were each administered to random samples of more than 600 eleventh-grade students. A computer program was…

The intrinsic combinatorial organization and information theoretic content of a sequence are correlated to the DNA encoded nucleosome organization of eukaryotic genomes.

PubMed

Utro, Filippo; Di Benedetto, Valeria; Corona, Davide F V; Giancarlo, Raffaele

2016-03-15

Thanks to research spanning nearly 30 years, two major models have emerged that account for nucleosome organization in chromatin: statistical and sequence specific. The first is based on elegant, easy to compute, closed-form mathematical formulas that make no assumptions of the physical and chemical properties of the underlying DNA sequence. Moreover, they need no training on the data for their computation. The latter is based on some sequence regularities but, as opposed to the statistical model, it lacks the same type of closed-form formulas that, in this case, should be based on the DNA sequence only. We contribute to close this important methodological gap between the two models by providing three very simple formulas for the sequence specific one. They are all based on well-known formulas in Computer Science and Bioinformatics, and they give different quantifications of how complex a sequence is. In view of how remarkably well they perform, it is very surprising that measures of sequence complexity have not even been considered as candidates to close the mentioned gap. We provide experimental evidence that the intrinsic level of combinatorial organization and information-theoretic content of subsequences within a genome are strongly correlated to the level of DNA encoded nucleosome organization discovered by Kaplan et al Our results establish an important connection between the intrinsic complexity of subsequences in a genome and the intrinsic, i.e. DNA encoded, nucleosome organization of eukaryotic genomes. It is a first step towards a mathematical characterization of this latter 'encoding'. Supplementary data are available at Bioinformatics online. futro@us.ibm.com. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Formulation and Testing of a Novel River Nitrification Model

EPA Science Inventory

The nitrification process in many riverwater quality models has been approximated by a simple first order dependency on the water column ammonia concentration, while the benthic contribution has routinely been neglected. In this study a mathematical framework was developed for se...

Calculator Cryptography.

ERIC Educational Resources Information Center

Hall, Matthew

2003-01-01

Uses cryptography to demonstrate the importance of algebra and the use of technology as an effective real application of mathematics. Explains simple encoding and decoding of messages for student learning of modular arithmetic. This elementary encounter with cryptography along with its historical and modern background serves to motivate student…

Computer Simulation of Human Service Program Evaluations.

ERIC Educational Resources Information Center

Trochim, William M. K.; Davis, James E.

1985-01-01

Describes uses of computer simulations for the context of human service program evaluation. Presents simple mathematical models for most commonly used human service outcome evaluation designs (pretest-posttest randomized experiment, pretest-posttest nonequivalent groups design, and regression-discontinuity design). Translates models into single…

Search and Rescue!

ERIC Educational Resources Information Center

Sharland, Hannah

2011-01-01

The author believes that to truly engage children in learning, an imaginative approach with purposeful activities is very important. One way that this can be implemented is through simple "engineering projects" where science, design and technology (D&T), mathematics and information and communication technology (ICT) are combined,…

Turn customer input into innovation.

PubMed

Ulwick, Anthony W

2002-01-01

It's difficult to find a company these days that doesn't strive to be customer-driven. Too bad, then, that most companies go about the process of listening to customers all wrong--so wrong, in fact, that they undermine innovation and, ultimately, the bottom line. What usually happens is this: Companies ask their customers what they want. Customers offer solutions in the form of products or services. Companies then deliver these tangibles, and customers just don't buy. The reason is simple--customers aren't expert or informed enough to come up with solutions. That's what your R&D team is for. Rather, customers should be asked only for outcomes--what they want a new product or service to do for them. The form the solutions take should be up to you, and you alone. Using Cordis Corporation as an example, this article describes, in fine detail, a series of effective steps for capturing, analyzing, and utilizing customer input. First come indepth interviews, in which a moderator works with customers to deconstruct a process or activity in order to unearth "desired outcomes." Addressing participants' comments one at a time, the moderator rephrases them to be both unambiguous and measurable. Once the interviews are complete, researchers then compile a comprehensive list of outcomes that participants rank in order of importance and degree to which they are satisfied by existing products. Finally, using a simple mathematical formula called the "opportunity calculation," researchers can learn the relative attractiveness of key opportunity areas. These data can be used to uncover opportunities for product development, to properly segment markets, and to conduct competitive analysis.

Working memory and language: skill-specific or domain-general relations to mathematics?

PubMed

Purpura, David J; Ganley, Colleen M

2014-06-01

Children's early mathematics skills develop in a cumulative fashion; foundational skills form a basis for the acquisition of later skills. However, non-mathematical factors such as working memory and language skills have also been linked to mathematical development at a broad level. Unfortunately, little research has been conducted to evaluate the specific relations of these two non-mathematical factors to individual aspects of early mathematics. Thus, the focus of this study was to determine whether working memory and language were related to only individual aspects of early mathematics or related to many components of early mathematics skills. A total of 199 4- to 6-year-old preschool and kindergarten children were assessed on a battery of early mathematics tasks as well as measures of working memory and language. Results indicated that working memory has a specific relation to only a few-but critically important-early mathematics skills and language has a broad relation to nearly all early mathematics skills. Copyright © 2014 Elsevier Inc. All rights reserved.

Multiscale Materials Science - A Mathematical Approach to the Role of Defects and Uncertainty

DTIC Science & Technology

2016-10-28

AFRL-AFOSR-UK-TR-2016-0034 Multiscale materials science - a mathematical approach to the role of defects and uncertainty Claude Le Bris ECOLE...science - a mathematical approach to the role of defects and uncertainty 5a.  CONTRACT NUMBER 5b.  GRANT NUMBER FA8655-13-1-3061 5c.  PROGRAM ELEMENT...1FORM SF 298 10/31/2016https://livelink.ebs.afrl.af.mil/livelink/llisapi.dll Contract FA 8655-13-1-3061 Multiscale materials science: a mathematical

Examining the Interactions between Mathematical Content and Pedagogical Form: Notes on the Structure of the Lesson

ERIC Educational Resources Information Center

Karp, Alexander

2004-01-01

Research conducted during the Trends in International Mathematics and Science Study (TIMSS) and later (Stigler et al. 1999; Stigler and Hiebert 1999) undertook a thorough analysis of lessons in the United States, Japan, and Germany. This article focuses on certain aspects of mathematics lessons in Russia. Specifically, the attempt is made to…

Adapting Sources of Middle School Mathematics Self-Efficacy Scale to Turkish Culture

ERIC Educational Resources Information Center

Kontas, Hakki; Özcan, Bahadir

2017-01-01

The purpose of this study was to adapt the Sources of Middle School Mathematics Self-Efficacy Scale developed by Usher and Pajares to Turkish culture. This scale assesses Bandura's theorized sources of self-efficacy among mathematics students in middle school. After the Turkish version of the scale was formed, it was applied 6th, 7th and 8th…

Developing Mathematical Knowledge and Skills through the Awareness Approach of Teaching and Learning

ERIC Educational Resources Information Center

Cherif, Abour H.; Gialamas, Stefanos; Stamati, Angeliki

2017-01-01

Every object we think of or encounter, whether a natural or human-made, has a regular or irregular shape. In its own intrinsic conceptual design, it has elements of mathematics, science, engineering, and arts, etc., which are part of the object's geometric shape, form and structure. Geometry is not only an important part of mathematics, but it is…

Equating TIMSS Mathematics Subtests with Nonlinear Equating Methods Using NEAT Design: Circle-Arc Equating Approaches

ERIC Educational Resources Information Center

Ozdemir, Burhanettin

2017-01-01

The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test…

Spoon-Feeding to Tongue-Biting and Beyond: Factors That Contributed to Changes in Irish Primary School Teachers' Mathematics Practice

ERIC Educational Resources Information Center

Treacy, Mia

2017-01-01

Research that aimed to examine teachers' experiences whilst implementing a reform approach to mathematics teaching in an Irish primary school forms the basis of this paper. In particular, factors that contributed to changing mathematics practice in this case study school are outlined. The school engaged in professional development (PD) that…

Teaching Problem Solving to Students Receiving Tiered Interventions Using the Concrete-Representational-Abstract Sequence and Schema-Based Instruction

ERIC Educational Resources Information Center

Flores, Margaret M.; Hinton, Vanessa M.; Burton, Megan E.

2016-01-01

Mathematical word problems are the most common form of mathematics problem solving implemented in K-12 schools. Identifying key words is a frequent strategy taught in classrooms in which students struggle with problem solving and show low success rates in mathematics. Researchers show that using the concrete-representational-abstract (CRA)…

Generating a Networked Improvement Community to Improve Secondary Mathematics Teacher Preparation: Network Leadership, Organization, and Operation

ERIC Educational Resources Information Center

Martin, W. Gary; Gobstein, Howard

2015-01-01

The Mathematics Teacher Education Partnership (MTE-Partnership) was formed to address the undersupply of new secondary mathematics teachers who are well prepared to help their students attain the goals of the Common Core State Standards and other college- and career-ready standards. This national consortium of more than 90 universities and 100…

Using a Sequence of Number Pairs as an Example in Teaching Mathematics

ERIC Educational Resources Information Center

Mauch, Elizabeth; Shi, Yixun

2005-01-01

A sequence of number pairs can be used to generate many interesting examples in teaching mathematics subjects at various levels. It is often used in elementary or middle school mathematics classes to illustrate the concept of "patterns." In this paper the authors present a few interesting ways of using this sequence to form examples for high…

Cognitive and mathematical profiles for different forms of learning difficulties.

PubMed

Cirino, Paul T; Fuchs, Lynn S; Elias, John T; Powell, Sarah R; Schumacher, Robin F

2015-01-01

The purpose of this study was to compare subgroups of students with various forms of learning difficulties (< 25th percentile) on cognitive and mathematics characteristics. Students with mathematics difficulty (MD, n = 105), reading difficulty (RD, n = 65), both (MDRD, n = 87), or neither (NoLD, n = 403) were evaluated on an array of cognitive measures (e.g., working memory and language) and on mathematics measures of foundational numerical competencies, computation, and problem solving. Results revealed expected level differences among groups in both domains: NoLD outperformed RD, and MD outperformed MDRD. Profile differences were noted among pairs of subgroups on cognitive measures. On mathematics measures, profile differences were noted between RD and other subgroups, but not between MD and MDRD subgroups. The most discriminating cognitive measures were processing speed and language; the most discriminating mathematics measures depended on the subgroups being compared. Results were further evaluated according to more severe (< 10th percentile) criteria for MD and RD, which generally affected level differences more than the profile patterns. Results have implications for understanding comorbid MD and RD and for conceptualizing core deficits in MD. © Hammill Institute on Disabilities 2013.

On the botanic model of plant growth with intermediate vegetative-reproductive stage.

PubMed

Ioslovich, Ilya; Gutman, Per-Olof

2005-11-01

The application of dynamic optimization to mathematical models of ontogenic biological growth has been the subject of much research [see e.g. . J. Theor. Biol. 33, 299-307]. Kozłowsky and Ziółko [1988. Thor. Popul. Biol. 34, 118-129] and Ziółko and Kozłowski [1995. IEEE Trans. Automat. Contr. 40(10), 1779-1783] presented a model with gradual transition from vegetative to reproductive growth. The central point of their model is a mixed state-control constraint on the rate of reproductive growth, which leads to a mixed vegetative-reproductive growth period. Their model is modified here in order to take into account the difference of photosynthesis use efficiency when energy is accumulated in the vegetative and in the reproductive organs of a plant, respectively. The simple assumption on correlation between photosynthesis and temperature permits us to modify the model in a form that is useful for changing climate. Unfortunately, the mathematical solution of the optimal control problem in Kozłowsky and Ziółko (1988) and Ziółko and Kozłowski (1995) is incorrect. The strict mathematical solution is presented here, the numerical example from is solved, and the results are compared. The influence of the length of the season and the relative photosynthesis use efficiency, as well as of the potential sink demand of the reproductive organs, on the location and duration of the mixed vegetative-reproduction period of growth is investigated numerically. The results show that the mixed growth period is increased and shifted toward the end of the season when the lengths of the season is increased. Additional details of the sensitivity analysis are also presented.

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

NASA Astrophysics Data System (ADS)

Abdullah, Mohd Faizal Nizam Lee; Vimalanandan, Lena

2017-05-01

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

Mathematics Anxiety: What Have We Learned in 60 Years?

PubMed Central

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

2016-01-01

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

Engineering physics and mathematics division

NASA Astrophysics Data System (ADS)

Sincovec, R. F.

1995-07-01

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

Role of cognitive theory in the study of learning disability in mathematics.

PubMed

Geary, David C

2005-01-01

Gersten, Jordan, and Flojo (in this issue) provide the beginnings of an essential bridge between basic research on mathematical disabilities (MD) in young children and the application of this research for the early identification and remediation of these forms of learning disability. As they acknowledge, the field of MD is in the early stages of development, and thus recommendations regarding identification measures and remedial techniques must be considered preliminary. I discuss the importance of maintaining a tight link between theoretical and empirical research on children's developing numerical, arithmetical, and mathematical competencies and future research on learning disabilities in mathematics. This link will provide the foundation for transforming experimental procedures into assessment measures, understanding the cognitive strengths and weaknesses of children with these forms of learning disability, and developing remedial approaches based on the pattern of cognitive strengths and weaknesses for individual children.