On some stochastic formulations and related statistical moments of pharmacokinetic models.

PubMed

Matis, J H; Wehrly, T E; Metzler, C M

1983-02-01

This paper presents the deterministic and stochastic model for a linear compartment system with constant coefficients, and it develops expressions for the mean residence times (MRT) and the variances of the residence times (VRT) for the stochastic model. The expressions are relatively simple computationally, involving primarily matrix inversion, and they are elegant mathematically, in avoiding eigenvalue analysis and the complex domain. The MRT and VRT provide a set of new meaningful response measures for pharmacokinetic analysis and they give added insight into the system kinetics. The new analysis is illustrated with an example involving the cholesterol turnover in rats.

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.

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.

Implementation of density functional theory method on object-oriented programming (C++) to calculate energy band structure using the projector augmented wave (PAW)

NASA Astrophysics Data System (ADS)

Alfianto, E.; Rusydi, F.; Aisyah, N. D.; Fadilla, R. N.; Dipojono, H. K.; Martoprawiro, M. A.

2017-05-01

This study implemented DFT method into the C++ programming language with object-oriented programming rules (expressive software). The use of expressive software results in getting a simple programming structure, which is similar to mathematical formula. This will facilitate the scientific community to develop the software. We validate our software by calculating the energy band structure of Silica, Carbon, and Germanium with FCC structure using the Projector Augmented Wave (PAW) method then compare the results to Quantum Espresso calculation’s results. This study shows that the accuracy of the software is 85% compared to Quantum Espresso.

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.

Robot Control Based On Spatial-Operator Algebra

NASA Technical Reports Server (NTRS)

Rodriguez, Guillermo; Kreutz, Kenneth K.; Jain, Abhinandan

1992-01-01

Method for mathematical modeling and control of robotic manipulators based on spatial-operator algebra providing concise representation and simple, high-level theoretical frame-work for solution of kinematical and dynamical problems involving complicated temporal and spatial relationships. Recursive algorithms derived immediately from abstract spatial-operator expressions by inspection. Transition from abstract formulation through abstract solution to detailed implementation of specific algorithms to compute solution greatly simplified. Complicated dynamical problems like two cooperating robot arms solved more easily.

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.

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…

Do medical students with A-level mathematics have a better understanding of the principles behind evidence-based medicine?

PubMed

Ben-Shlomo, Y; Fallon, U; Sterne, J; Brookes, S

2004-12-01

With the advent of evidence-based medicine, medical students, doctors and other healthcare professionals are required to be more skilled in the interpretation and manipulation of numerical data. The authors observed that undergraduate students without A-level mathematics expressed concern as to their ability to cope with an epidemiology and biostatistics course. It was hypothesized that these anxieties reflected differences in attitudes to numerical manipulation rather than any real lack of competence. Mean exam performance scores were compared for 498 first-year medical students between 2000 and 2002 depending on whether the students did or did not have A-level mathematics. The data revealed no difference in performance. Students without mathematics A-level scored marginally worse (-1.1%, 95% CI -3.1% to 0.8%, p=0.20) but were no more likely to fail the exam (odds ratio=0.98, 95% CI 0.40 to 2.6, p=0.9). It is concluded that some students experience 'numerophobia'-- a perceived and, it is thought, disproportionate fear of numbers and simple mathematical manipulation. This may act as a psychological barrier for future evidence-based practitioners.

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)

Expected Shannon Entropy and Shannon Differentiation between Subpopulations for Neutral Genes under the Finite Island Model.

PubMed

Chao, Anne; Jost, Lou; Hsieh, T C; Ma, K H; Sherwin, William B; Rollins, Lee Ann

2015-01-01

Shannon entropy H and related measures are increasingly used in molecular ecology and population genetics because (1) unlike measures based on heterozygosity or allele number, these measures weigh alleles in proportion to their population fraction, thus capturing a previously-ignored aspect of allele frequency distributions that may be important in many applications; (2) these measures connect directly to the rich predictive mathematics of information theory; (3) Shannon entropy is completely additive and has an explicitly hierarchical nature; and (4) Shannon entropy-based differentiation measures obey strong monotonicity properties that heterozygosity-based measures lack. We derive simple new expressions for the expected values of the Shannon entropy of the equilibrium allele distribution at a neutral locus in a single isolated population under two models of mutation: the infinite allele model and the stepwise mutation model. Surprisingly, this complex stochastic system for each model has an entropy expressable as a simple combination of well-known mathematical functions. Moreover, entropy- and heterozygosity-based measures for each model are linked by simple relationships that are shown by simulations to be approximately valid even far from equilibrium. We also identify a bridge between the two models of mutation. We apply our approach to subdivided populations which follow the finite island model, obtaining the Shannon entropy of the equilibrium allele distributions of the subpopulations and of the total population. We also derive the expected mutual information and normalized mutual information ("Shannon differentiation") between subpopulations at equilibrium, and identify the model parameters that determine them. We apply our measures to data from the common starling (Sturnus vulgaris) in Australia. Our measures provide a test for neutrality that is robust to violations of equilibrium assumptions, as verified on real world data from starlings.

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.

Atmospheric refraction effects on baseline error in satellite laser ranging systems

NASA Technical Reports Server (NTRS)

Im, K. E.; Gardner, C. S.

1982-01-01

Because of the mathematical complexities involved in exact analyses of baseline errors, it is not easy to isolate atmospheric refraction effects; however, by making certain simplifying assumptions about the ranging system geometry, relatively simple expressions can be derived which relate the baseline errors directly to the refraction errors. The results indicate that even in the absence of other errors, the baseline error for intercontinental baselines can be more than an order of magnitude larger than the refraction error.

Summing up the noise in gene networks

NASA Astrophysics Data System (ADS)

Paulsson, Johan

2004-01-01

Random fluctuations in genetic networks are inevitable as chemical reactions are probabilistic and many genes, RNAs and proteins are present in low numbers per cell. Such `noise' affects all life processes and has recently been measured using green fluorescent protein (GFP). Two studies show that negative feedback suppresses noise, and three others identify the sources of noise in gene expression. Here I critically analyse these studies and present a simple equation that unifies and extends both the mathematical and biological perspectives.

An Introduction to Turbulent Flow

NASA Astrophysics Data System (ADS)

Mathieu, Jean; Scott, Julian

2000-06-01

In recent years, turbulence has become a very lively area of scientific research and application, attracting many newcomers who need a basic introduction to the subject. Turbulent Flows ably meets this need, developing both physical insight and the mathematical framework needed to express the theory. The authors present basic theory and illustrate it with examples of simple turbulent flows and classical models of jets, wakes, and boundary layers. A deeper understanding of turbulence dynamics is provided by their treatment of spectral analysis and its applications.

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.

REVIEW ARTICLE: Oscillations and temporal signalling in cells

NASA Astrophysics Data System (ADS)

Tiana, G.; Krishna, S.; Pigolotti, S.; Jensen, M. H.; Sneppen, K.

2007-06-01

The development of new techniques to quantitatively measure gene expression in cells has shed light on a number of systems that display oscillations in protein concentration. Here we review the different mechanisms which can produce oscillations in gene expression or protein concentration using a framework of simple mathematical models. We focus on three eukaryotic genetic regulatory networks which show 'ultradian' oscillations, with a time period of the order of hours, and involve, respectively, proteins important for development (Hes1), apoptosis (p53) and immune response (NF-κB). We argue that underlying all three is a common design consisting of a negative feedback loop with time delay which is responsible for the oscillatory behaviour.

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.

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

Induced Eddy Currents in Simple Conductive Geometries: Mathematical Formalism Describes the Excitation of Electrical Eddy Currents in a Time-Varying Magnetic Field

DOE PAGES

Nagel, James R.

2017-12-22

In this paper, a complete mathematical formalism is introduced to describe the excitation of electrical eddy currents due to a time-varying magnetic field. The process works by applying a quasistatic approximation to Ampere's law and then segregating the magnetic field into impressed and induced terms. The result is a nonhomogeneous vector Helmholtz equation that can be analytically solved for many practical geometries. Four demonstration cases are then solved under a constant excitation field over all space—an infinite slab in one dimension, a longitudinal cylinder in two dimensions, a transverse cylinder in two dimensions, and a sphere in three dimensions. Numericalmore » simulations are also performed in parallel with analytic computations, all of which verify the accuracy of the derived expressions.« less

Induced Eddy Currents in Simple Conductive Geometries: Mathematical Formalism Describes the Excitation of Electrical Eddy Currents in a Time-Varying Magnetic Field

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

Nagel, James R.

In this paper, a complete mathematical formalism is introduced to describe the excitation of electrical eddy currents due to a time-varying magnetic field. The process works by applying a quasistatic approximation to Ampere's law and then segregating the magnetic field into impressed and induced terms. The result is a nonhomogeneous vector Helmholtz equation that can be analytically solved for many practical geometries. Four demonstration cases are then solved under a constant excitation field over all space—an infinite slab in one dimension, a longitudinal cylinder in two dimensions, a transverse cylinder in two dimensions, and a sphere in three dimensions. Numericalmore » simulations are also performed in parallel with analytic computations, all of which verify the accuracy of the derived expressions.« less

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.

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.

Travelling and splitting of a wave of hedgehog expression involved in spider-head segmentation.

PubMed

Kanayama, Masaki; Akiyama-Oda, Yasuko; Nishimura, Osamu; Tarui, Hiroshi; Agata, Kiyokazu; Oda, Hiroki

2011-10-11

During development segmentation is a process that generates a spatial periodic pattern. Peak splitting of waves of gene expression is a mathematically predicted, simple strategy accounting for this type of process, but it has not been well characterized biologically. Here we show temporally repeated splitting of gene expression into stripes that is associated with head axis growth in the spider Achaearanea embryo. Preceding segmentation, a wave of hedgehog homologue gene expression is observed to travel posteriorly during development stage 6. This stripe, co-expressing an orthodenticle homologue, undergoes two cycles of splitting and shifting accompanied by convergent extension, serving as a generative zone for the head segments. The two orthodenticle and odd-paired homologues are identified as targets of Hedgehog signalling, and evidence suggests that their activities mediate feedback to maintain the head generative zone and to promote stripe splitting in this zone. We propose that the 'stripe-splitting' strategy employs genetic components shared with Drosophila blastoderm subdivision, which are required for participation in an autoregulatory signalling network.

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…

A common base method for analysis of qPCR data and the application of simple blocking in qPCR experiments.

PubMed

Ganger, Michael T; Dietz, Geoffrey D; Ewing, Sarah J

2017-12-01

qPCR has established itself as the technique of choice for the quantification of gene expression. Procedures for conducting qPCR have received significant attention; however, more rigorous approaches to the statistical analysis of qPCR data are needed. Here we develop a mathematical model, termed the Common Base Method, for analysis of qPCR data based on threshold cycle values (C q ) and efficiencies of reactions (E). The Common Base Method keeps all calculations in the logscale as long as possible by working with log 10 (E) ∙ C q , which we call the efficiency-weighted C q value; subsequent statistical analyses are then applied in the logscale. We show how efficiency-weighted C q values may be analyzed using a simple paired or unpaired experimental design and develop blocking methods to help reduce unexplained variation. The Common Base Method has several advantages. It allows for the incorporation of well-specific efficiencies and multiple reference genes. The method does not necessitate the pairing of samples that must be performed using traditional analysis methods in order to calculate relative expression ratios. Our method is also simple enough to be implemented in any spreadsheet or statistical software without additional scripts or proprietary components.

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

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.

Analysis of Mathematical Modelling on Potentiometric Biosensors

PubMed Central

Mehala, N.; Rajendran, L.

2014-01-01

A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories. PMID:25969765

Analysis of mathematical modelling on potentiometric biosensors.

PubMed

Mehala, N; Rajendran, L

2014-01-01

A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.

Superradiant effects on pulse propagation in resonant media. [atomic excitations/coherent radiation - operators (mathematics)/matrices (mathematics)

NASA Technical Reports Server (NTRS)

Lee, C.

1975-01-01

Adopting the so-called genealogical construction, the eigenstates of collective operators can be expressed corresponding to a specified mode for an N-atom system in terms of those for an (N-1)-atom system. Matrix element of a collective operator of an arbitrary mode is presented which can be written as the product of an m-dependent factor and an m-independent reduced matrix element (RME). A set of recursion formulas for the RME was obtained. A graphical representation of the RME on the branching diagram for binary irreducible representations of permutation groups was then introduced. This gave a simple and systematic way of calculating the RME. Results show explicitly the geometry dependence of superradiance and the relative importance of r-conserving and r-nonconserving processes and clears up the chief difficulty encounted in the problem of N two-level atoms, spread over large regions, interacting with a multimode radiation field.

Cell-Free Optogenetic Gene Expression System.

PubMed

Jayaraman, Premkumar; Yeoh, Jing Wui; Jayaraman, Sudhaghar; Teh, Ai Ying; Zhang, Jingyun; Poh, Chueh Loo

2018-04-20

Optogenetic tools provide a new and efficient way to dynamically program gene expression with unmatched spatiotemporal precision. To date, their vast potential remains untapped in the field of cell-free synthetic biology, largely due to the lack of simple and efficient light-switchable systems. Here, to bridge the gap between cell-free systems and optogenetics, we studied our previously engineered one component-based blue light-inducible Escherichia coli promoter in a cell-free environment through experimental characterization and mathematical modeling. We achieved >10-fold dynamic expression and demonstrated rapid and reversible activation of the target gene to generate oscillatory response. The deterministic model developed was able to recapitulate the system behavior and helped to provide quantitative insights to optimize dynamic response. This in vitro optogenetic approach could be a powerful new high-throughput screening technology for rapid prototyping of complex biological networks in both space and time without the need for chemical induction.

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…

How Do Kindergarteners Express Their Mathematics Understanding?

ERIC Educational Resources Information Center

Johns, Kyoko

2015-01-01

This article describes how kindergarten students represent their understanding of mathematical knowledge. The study examines the students' use of oral expressions, drawings, written language, and gestures when communicating mathematically with their classmates and teacher.

Simple, accurate formula for the average bit error probability of multiple-input multiple-output free-space optical links over negative exponential turbulence channels.

PubMed

Peppas, Kostas P; Lazarakis, Fotis; Alexandridis, Antonis; Dangakis, Kostas

2012-08-01

In this Letter we investigate the error performance of multiple-input multiple-output free-space optical communication systems employing intensity modulation/direct detection and operating over strong atmospheric turbulence channels. Atmospheric-induced strong turbulence fading is modeled using the negative exponential distribution. For the considered system, an approximate yet accurate analytical expression for the average bit error probability is derived and an efficient method for its numerical evaluation is proposed. Numerically evaluated and computer simulation results are further provided to demonstrate the validity of the proposed mathematical analysis.

Fundamental formulae for wave-energy conversion

PubMed Central

Falnes, Johannes; Kurniawan, Adi

2015-01-01

The time-average wave power that is absorbed from an incident wave by means of a wave-energy conversion (WEC) unit, or by an array of WEC units—i.e. oscillating immersed bodies and/or oscillating water columns (OWCs)—may be mathematically expressed in terms of the WEC units' complex oscillation amplitudes, or in terms of the generated outgoing (diffracted plus radiated) waves, or alternatively, in terms of the radiated waves alone. Following recent controversy, the corresponding three optional expressions are derived, compared and discussed in this paper. They all provide the correct time-average absorbed power. However, only the first-mentioned expression is applicable to quantify the instantaneous absorbed wave power and the associated reactive power. In this connection, new formulae are derived that relate the ‘added-mass’ matrix, as well as a couple of additional reactive radiation-parameter matrices, to the difference between kinetic energy and potential energy in the water surrounding the immersed oscillating WEC array. Further, a complex collective oscillation amplitude is introduced, which makes it possible to derive, by a very simple algebraic method, various simple expressions for the maximum time-average wave power that may be absorbed by the WEC array. The real-valued time-average absorbed power is illustrated as an axisymmetric paraboloid defined on the complex collective-amplitude plane. This is a simple illustration of the so-called ‘fundamental theorem for wave power’. Finally, the paper also presents a new derivation that extends a recently published result on the direction-average maximum absorbed wave power to cases where the WEC array's radiation damping matrix may be singular and where the WEC array may contain OWCs in addition to oscillating bodies. PMID:26064612

Fundamental formulae for wave-energy conversion.

PubMed

Falnes, Johannes; Kurniawan, Adi

2015-03-01

The time-average wave power that is absorbed from an incident wave by means of a wave-energy conversion (WEC) unit, or by an array of WEC units-i.e. oscillating immersed bodies and/or oscillating water columns (OWCs)-may be mathematically expressed in terms of the WEC units' complex oscillation amplitudes, or in terms of the generated outgoing (diffracted plus radiated) waves, or alternatively, in terms of the radiated waves alone. Following recent controversy, the corresponding three optional expressions are derived, compared and discussed in this paper. They all provide the correct time-average absorbed power. However, only the first-mentioned expression is applicable to quantify the instantaneous absorbed wave power and the associated reactive power. In this connection, new formulae are derived that relate the 'added-mass' matrix, as well as a couple of additional reactive radiation-parameter matrices, to the difference between kinetic energy and potential energy in the water surrounding the immersed oscillating WEC array. Further, a complex collective oscillation amplitude is introduced, which makes it possible to derive, by a very simple algebraic method, various simple expressions for the maximum time-average wave power that may be absorbed by the WEC array. The real-valued time-average absorbed power is illustrated as an axisymmetric paraboloid defined on the complex collective-amplitude plane. This is a simple illustration of the so-called 'fundamental theorem for wave power'. Finally, the paper also presents a new derivation that extends a recently published result on the direction-average maximum absorbed wave power to cases where the WEC array's radiation damping matrix may be singular and where the WEC array may contain OWCs in addition to oscillating bodies.

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 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.

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.

Robust Combining of Disparate Classifiers Through Order Statistics

NASA Technical Reports Server (NTRS)

Tumer, Kagan; Ghosh, Joydeep

2001-01-01

Integrating the outputs of multiple classifiers via combiners or meta-learners has led to substantial improvements in several difficult pattern recognition problems. In this article we investigate a family of combiners based on order statistics, for robust handling of situations where there are large discrepancies in performance of individual classifiers. Based on a mathematical modeling of how the decision boundaries are affected by order statistic combiners, we derive expressions for the reductions in error expected when simple output combination methods based on the the median, the maximum and in general, the ith order statistic, are used. Furthermore, we analyze the trim and spread combiners, both based on linear combinations of the ordered classifier outputs, and show that in the presence of uneven classifier performance, they often provide substantial gains over both linear and simple order statistics combiners. Experimental results on both real world data and standard public domain data sets corroborate these findings.

Segmentation-based wavelet transform for still-image compression

NASA Astrophysics Data System (ADS)

Mozelle, Gerard; Seghier, Abdellatif; Preteux, Francoise J.

1996-10-01

In order to address simultaneously the two functionalities, content-based scalability required by MPEG-4, we introduce a segmentation-based wavelet transform (SBWT). SBWT takes into account both the mathematical properties of multiresolution analysis and the flexibility of region-based approaches for image compression. The associated methodology has two stages: 1) image segmentation into convex and polygonal regions; 2) 2D-wavelet transform of the signal corresponding to each region. In this paper, we have mathematically studied a method for constructing a multiresolution analysis (VjOmega)j (epsilon) N adapted to a polygonal region which provides an adaptive region-based filtering. The explicit construction of scaling functions, pre-wavelets and orthonormal wavelets bases defined on a polygon is carried out by using scaling functions is established by using the theory of Toeplitz operators. The corresponding expression can be interpreted as a location property which allow defining interior and boundary scaling functions. Concerning orthonormal wavelets and pre-wavelets, a similar expansion is obtained by taking advantage of the properties of the orthogonal projector P(V(j(Omega )) perpendicular from the space Vj(Omega ) + 1 onto the space (Vj(Omega )) perpendicular. Finally the mathematical results provide a simple and fast algorithm adapted to polygonal regions.

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

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)

Mathematical toy model inspired by the problem of the adaptive origins of the sexual orientation continuum

NASA Astrophysics Data System (ADS)

Skinner, Brian

2016-09-01

Same-sex sexual behaviour is ubiquitous in the animal kingdom, but its adaptive origins remain a prominent puzzle. Here, I suggest the possibility that same-sex sexual behaviour arises as a consequence of the competition between an evolutionary drive for a wide diversity in traits, which improves the adaptability of a population, and a drive for sexual dichotomization of traits, which promotes opposite-sex attraction and increases the rate of reproduction. This trade-off is explored via a simple mathematical `toy model'. The model exhibits a number of interesting features and suggests a simple mathematical form for describing the sexual orientation continuum.

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.

Mathematical toy model inspired by the problem of the adaptive origins of the sexual orientation continuum.

PubMed

Skinner, Brian

2016-09-01

Same-sex sexual behaviour is ubiquitous in the animal kingdom, but its adaptive origins remain a prominent puzzle. Here, I suggest the possibility that same-sex sexual behaviour arises as a consequence of the competition between an evolutionary drive for a wide diversity in traits, which improves the adaptability of a population, and a drive for sexual dichotomization of traits, which promotes opposite-sex attraction and increases the rate of reproduction. This trade-off is explored via a simple mathematical 'toy model'. The model exhibits a number of interesting features and suggests a simple mathematical form for describing the sexual orientation continuum.

A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence: An analytical theory

NASA Technical Reports Server (NTRS)

Ristorcelli, J. R.

1995-01-01

The mathematical consequences of a few simple scaling assumptions about the effects of compressibility are explored using a simple singular perturbation idea and the methods of statistical fluid mechanics. Representations for the pressure-dilation and dilatational dissipation covariances appearing in single-point moment closures for compressible turbulence are obtained. While the results are expressed in the context of a second-order statistical closure they provide some interesting and very clear physical metaphors for the effects of compressibility that have not been seen using more traditional linear stability methods. In the limit of homogeneous turbulence with quasi-normal large-scales the expressions derived are - in the low turbulent Mach number limit - asymptotically exact. The expressions obtained are functions of the rate of change of the turbulence energy, its correlation length scale, and the relative time scale of the cascade rate. The expressions for the dilatational covariances contain constants which have a precise and definite physical significance; they are related to various integrals of the longitudinal velocity correlation. The pressure-dilation covariance is found to be a nonequilibrium phenomena related to the time rate of change of the internal energy and the kinetic energy of the turbulence. Also of interest is the fact that the representation for the dilatational dissipation in turbulence, with or without shear, features a dependence on the Reynolds number. This article is a documentation of an analytical investigation of the implications of a pseudo-sound theory for the effects of compressibility.

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.

Adiabatic dynamics of one-dimensional classical Hamiltonian dissipative systems

NASA Astrophysics Data System (ADS)

Pritula, G. M.; Petrenko, E. V.; Usatenko, O. V.

2018-02-01

A linearized plane pendulum with the slowly varying mass and length of string and the suspension point moving at a slowly varying speed is presented as an example of a simple 1D mechanical system described by the generalized harmonic oscillator equation, which is a basic model in discussion of the adiabatic dynamics and geometric phase. The expression for the pendulum geometric phase is obtained by three different methods. The pendulum is shown to be canonically equivalent to the damped harmonic oscillator. This supports the mathematical conclusion, not widely accepted in physical community, of no difference between the dissipative and Hamiltonian 1D systems.

Boundary assessment under uncertainty: A case study

USGS Publications Warehouse

Pawlowsky, V.; Olea, R.A.; Davis, J.C.

1993-01-01

Estimating certain attributes within a geological body whose exact boundary is not known presents problems because of the lack of information. Estimation may result in values that are inadmissible from a geological point of view, especially with attributes which necessarily must be zero outside the boundary, such as the thickness of the oil column outside a reservoir. A simple but effective way to define the boundary is to use indicator kriging in two steps, the first for the purpose of extrapolating control points outside the body, the second to obtain a weighting function which expresses the uncertainty attached to estimations obtained in the boundary region. ?? 1993 International Association for Mathematical Geology.

Artificially Constructed Quorum-Sensing Circuits Are Used for Subtle Control of Bacterial Population Density

PubMed Central

Wang, Zhaoshou; Wu, Xin; Peng, Jianghai; Hu, Yidan; Fang, Baishan; Huang, Shiyang

2014-01-01

Vibrio fischeri is a typical quorum-sensing bacterium for which lux box, luxR, and luxI have been identified as the key elements involved in quorum sensing. To decode the quorum-sensing mechanism, an artificially constructed cell–cell communication system has been built. In brief, the system expresses several programmed cell-death BioBricks and quorum-sensing genes driven by the promoters lux pR and PlacO-1 in Escherichia coli cells. Their transformation and expression was confirmed by gel electrophoresis and sequencing. To evaluate its performance, viable cell numbers at various time periods were investigated. Our results showed that bacteria expressing killer proteins corresponding to ribosome binding site efficiency of 0.07, 0.3, 0.6, or 1.0 successfully sensed each other in a population-dependent manner and communicated with each other to subtly control their population density. This was also validated using a proposed simple mathematical model. PMID:25119347

Sub-cellular mRNA localization modulates the regulation of gene expression by small RNAs in bacteria

NASA Astrophysics Data System (ADS)

Teimouri, Hamid; Korkmazhan, Elgin; Stavans, Joel; Levine, Erel

2017-10-01

Small non-coding RNAs can exert significant regulatory activity on gene expression in bacteria. In recent years, substantial progress has been made in understanding bacterial gene expression by sRNAs. However, recent findings that demonstrate that families of mRNAs show non-trivial sub-cellular distributions raise the question of how localization may affect the regulatory activity of sRNAs. Here we address this question within a simple mathematical model. We show that the non-uniform spatial distributions of mRNA can alter the threshold-linear response that characterizes sRNAs that act stoichiometrically, and modulate the hierarchy among targets co-regulated by the same sRNA. We also identify conditions where the sub-cellular organization of cofactors in the sRNA pathway can induce spatial heterogeneity on sRNA targets. Our results suggest that under certain conditions, interpretation and modeling of natural and synthetic gene regulatory circuits need to take into account the spatial organization of the transcripts of participating genes.

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.

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

ERIC Educational Resources Information Center

Chang, Lawrence A.; And Others

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

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.

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…

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

PubMed

Nilsen, Vegard; Wyller, John

2016-01-01

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

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.

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.

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)

A Conversion Tool for Mathematical Expressions in Web XML Files.

ERIC Educational Resources Information Center

Ohtake, Nobuyuki; Kanahori, Toshihiro

2003-01-01

This article discusses the conversion of mathematical equations into Extensible Markup Language (XML) on the World Wide Web for individuals with visual impairments. A program is described that converts the presentation markup style to the content markup style in MathML to allow browsers to render mathematical expressions without other programs.…

Online handwritten mathematical expression recognition

NASA Astrophysics Data System (ADS)

Büyükbayrak, Hakan; Yanikoglu, Berrin; Erçil, Aytül

2007-01-01

We describe a system for recognizing online, handwritten mathematical expressions. The system is designed with a user-interface for writing scientific articles, supporting the recognition of basic mathematical expressions as well as integrals, summations, matrices etc. A feed-forward neural network recognizes symbols which are assumed to be single-stroke and a recursive algorithm parses the expression by combining neural network output and the structure of the expression. Preliminary results show that writer-dependent recognition rates are very high (99.8%) while writer-independent symbol recognition rates are lower (75%). The interface associated with the proposed system integrates the built-in recognition capabilities of the Microsoft's Tablet PC API for recognizing textual input and supports conversion of hand-drawn figures into PNG format. This enables the user to enter text, mathematics and draw figures in a single interface. After recognition, all output is combined into one LATEX code and compiled into a PDF file.

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 +…

Random walk study of electron motion in helium in crossed electromagnetic fields

NASA Technical Reports Server (NTRS)

Englert, G. W.

1972-01-01

Random walk theory, previously adapted to electron motion in the presence of an electric field, is extended to include a transverse magnetic field. In principle, the random walk approach avoids mathematical complexity and concomitant simplifying assumptions and permits determination of energy distributions and transport coefficients within the accuracy of available collisional cross section data. Application is made to a weakly ionized helium gas. Time of relaxation of electron energy distribution, determined by the random walk, is described by simple expressions based on energy exchange between the electron and an effective electric field. The restrictive effect of the magnetic field on electron motion, which increases the required number of collisions per walk to reach a terminal steady state condition, as well as the effect of the magnetic field on electron transport coefficients and mean energy can be quite adequately described by expressions involving only the Hall parameter.

Quantify spatial relations to discover handwritten graphical symbols

NASA Astrophysics Data System (ADS)

Li, Jinpeng; Mouchère, Harold; Viard-Gaudin, Christian

2012-01-01

To model a handwritten graphical language, spatial relations describe how the strokes are positioned in the 2-dimensional space. Most of existing handwriting recognition systems make use of some predefined spatial relations. However, considering a complex graphical language, it is hard to express manually all the spatial relations. Another possibility would be to use a clustering technique to discover the spatial relations. In this paper, we discuss how to create a relational graph between strokes (nodes) labeled with graphemes in a graphical language. Then we vectorize spatial relations (edges) for clustering and quantization. As the targeted application, we extract the repetitive sub-graphs (graphical symbols) composed of graphemes and learned spatial relations. On two handwriting databases, a simple mathematical expression database and a complex flowchart database, the unsupervised spatial relations outperform the predefined spatial relations. In addition, we visualize the frequent patterns on two text-lines containing Chinese characters.

Exceptional point in a simple textbook example

NASA Astrophysics Data System (ADS)

Fernández, Francisco M.

2018-07-01

We propose to introduce the concept of exceptional points in intermediate courses on mathematics and classical mechanics by means of simple textbook examples. The first one is an ordinary second-order differential equation with constant coefficients. The second one is the well-known damped harmonic oscillator. From a strict mathematical viewpoint both are the same problem that enables one to connect the occurrence of linearly dependent exponential solutions with a defective matrix which cannot be diagonalized but can be transformed into a Jordan canonical form.

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.

Prediction of inspired oxygen fraction for targeted arterial oxygen tension following open heart surgery in non-smoking and smoking patients.

PubMed

Bou-Khalil, Pierre; Zeineldine, Salah; Chatburn, Robert; Ayyoub, Chakib; Elkhatib, Farouk; Bou-Akl, Imad; El-Khatib, Mohamad

2017-10-01

Simple and accurate expressions describing the P a O 2 -F i O 2 relationship in mechanically ventilated patients are lacking. The current study aims to validate a novel mathematical expression for accurate prediction of the fraction of inspired oxygen that will result in a targeted arterial oxygen tension in non-smoking and smoking patients receiving mechanical ventilation following open heart surgeries. One hundred P a O 2 -F i O 2 data pairs were obtained from 25 non-smoking patients mechanically ventilated following open heart surgeries. One data pair was collected at each of F i O 2 of 40, 60, 80, and 100% while maintaining same mechanical ventilation support settings. Similarly, another 100 hundred P a O 2 -F i O 2 data pairs were obtained from 25 smoking patients mechanically ventilated following open heart surgeries. The utility of the new mathematical expression in accurately describing the P a O 2 -F i O 2 relationship in these patients was assessed by the regression and Bland-Altman analyses. Significant correlations were seen between the true and estimated F i O 2 values in non-smoking (r 2  = 0.9424; p < 0.05) and smoking (r 2  = 0.9466; p < 0.05) patients. Tight biases between the true and estimated F i O 2 values for non-smoking (3.1%) and smoking (4.1%) patients were observed. Also, significant correlations were seen between the true and estimated P a O 2 /F i O 2 ratios in non-smoking (r 2  = 0.9530; p < 0.05) and smoking (r 2  = 0.9675; p < 0.05) patients. Tight biases between the true and estimated P a O 2 /F i O 2 ratios for non-smoking (-18 mmHg) and smoking (-16 mmHg) patients were also observed. The new mathematical expression for the description of the P a O 2 -F i O 2 relationship is valid and accurate in non-smoking and smoking patients who are receiving mechanical ventilation for post cardiac surgery.

Middle-School Mathematics Teachers' Beliefs in NCTM's Vision

ERIC Educational Resources Information Center

Perrin, John Robert

2012-01-01

This study examined the extent to which seventh- and eighth-grade mathematics teachers are aware of National Council of Teachers of Mathematics (NCTM) standards documents, Curriculum and Evaluation Standards for School Mathematics and Principles and Standards for School Mathematics and agree with NCTM's vision of school mathematics as expressed in…

Biodiversity patterns along ecological gradients: unifying β-diversity indices.

PubMed

Szava-Kovats, Robert C; Pärtel, Meelis

2014-01-01

Ecologists have developed an abundance of conceptions and mathematical expressions to define β-diversity, the link between local (α) and regional-scale (γ) richness, in order to characterize patterns of biodiversity along ecological (i.e., spatial and environmental) gradients. These patterns are often realized by regression of β-diversity indices against one or more ecological gradients. This practice, however, is subject to two shortcomings that can undermine the validity of the biodiversity patterns. First, many β-diversity indices are constrained to range between fixed lower and upper limits. As such, regression analysis of β-diversity indices against ecological gradients can result in regression curves that extend beyond these mathematical constraints, thus creating an interpretational dilemma. Second, despite being a function of the same measured α- and γ-diversity, the resultant biodiversity pattern depends on the choice of β-diversity index. We propose a simple logistic transformation that rids beta-diversity indices of their mathematical constraints, thus eliminating the possibility of an uninterpretable regression curve. Moreover, this transformation results in identical biodiversity patterns for three commonly used classical beta-diversity indices. As a result, this transformation eliminates the difficulties of both shortcomings, while allowing the researcher to use whichever beta-diversity index deemed most appropriate. We believe this method can help unify the study of biodiversity patterns along ecological gradients.

Biodiversity Patterns along Ecological Gradients: Unifying β-Diversity Indices

PubMed Central

Szava-Kovats, Robert C.; Pärtel, Meelis

2014-01-01

Ecologists have developed an abundance of conceptions and mathematical expressions to define β-diversity, the link between local (α) and regional-scale (γ) richness, in order to characterize patterns of biodiversity along ecological (i.e., spatial and environmental) gradients. These patterns are often realized by regression of β-diversity indices against one or more ecological gradients. This practice, however, is subject to two shortcomings that can undermine the validity of the biodiversity patterns. First, many β-diversity indices are constrained to range between fixed lower and upper limits. As such, regression analysis of β-diversity indices against ecological gradients can result in regression curves that extend beyond these mathematical constraints, thus creating an interpretational dilemma. Second, despite being a function of the same measured α- and γ-diversity, the resultant biodiversity pattern depends on the choice of β-diversity index. We propose a simple logistic transformation that rids beta-diversity indices of their mathematical constraints, thus eliminating the possibility of an uninterpretable regression curve. Moreover, this transformation results in identical biodiversity patterns for three commonly used classical beta-diversity indices. As a result, this transformation eliminates the difficulties of both shortcomings, while allowing the researcher to use whichever beta-diversity index deemed most appropriate. We believe this method can help unify the study of biodiversity patterns along ecological gradients. PMID:25330181

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…

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.

The Effects of Expressive Writing on General and Mathematics Anxiety for a Sample of High School Students

ERIC Educational Resources Information Center

Hines, Claudia L.; Brown, Nina W.; Myran, Steve

2016-01-01

Ninety-three (n = 93) students in grades 9-12 who failed the Virginia Standards of Learning mathematics test were placed into experimental and control groups. Pre and posttest measures for general and mathematics anxiety, and physical symptoms of stress were administered. The Expressive Writing intervention was used with both groups where the…

Mathematical Modeling Of Life-Support Systems

NASA Technical Reports Server (NTRS)

Seshan, Panchalam K.; Ganapathi, Balasubramanian; Jan, Darrell L.; Ferrall, Joseph F.; Rohatgi, Naresh K.

1994-01-01

Generic hierarchical model of life-support system developed to facilitate comparisons of options in design of system. Model represents combinations of interdependent subsystems supporting microbes, plants, fish, and land animals (including humans). Generic model enables rapid configuration of variety of specific life support component models for tradeoff studies culminating in single system design. Enables rapid evaluation of effects of substituting alternate technologies and even entire groups of technologies and subsystems. Used to synthesize and analyze life-support systems ranging from relatively simple, nonregenerative units like aquariums to complex closed-loop systems aboard submarines or spacecraft. Model, called Generic Modular Flow Schematic (GMFS), coded in such chemical-process-simulation languages as Aspen Plus and expressed as three-dimensional spreadsheet.

Statistical methods for astronomical data with upper limits. I - Univariate distributions

NASA Technical Reports Server (NTRS)

Feigelson, E. D.; Nelson, P. I.

1985-01-01

The statistical treatment of univariate censored data is discussed. A heuristic derivation of the Kaplan-Meier maximum-likelihood estimator from first principles is presented which results in an expression amenable to analytic error analysis. Methods for comparing two or more censored samples are given along with simple computational examples, stressing the fact that most astronomical problems involve upper limits while the standard mathematical methods require lower limits. The application of univariate survival analysis to six data sets in the recent astrophysical literature is described, and various aspects of the use of survival analysis in astronomy, such as the limitations of various two-sample tests and the role of parametric modelling, are discussed.

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)

Light-Stimulated Synaptic Devices Utilizing Interfacial Effect of Organic Field-Effect Transistors.

PubMed

Dai, Shilei; Wu, Xiaohan; Liu, Dapeng; Chu, Yingli; Wang, Kai; Yang, Ben; Huang, Jia

2018-06-14

Synaptic transistors stimulated by light waves or photons may offer advantages to the devices, such as wide bandwidth, ultrafast signal transmission, and robustness. However, previously reported light-stimulated synaptic devices generally require special photoelectric properties from the semiconductors and sophisticated device's architectures. In this work, a simple and effective strategy for fabricating light-stimulated synaptic transistors is provided by utilizing interface charge trapping effect of organic field-effect transistors (OFETs). Significantly, our devices exhibited highly synapselike behaviors, such as excitatory postsynaptic current (EPSC) and pair-pulse facilitation (PPF), and presented memory and learning ability. The EPSC decay, PPF curves, and forgetting behavior can be well expressed by mathematical equations for synaptic devices, indicating that interfacial charge trapping effect of OFETs can be utilized as a reliable strategy to realize organic light-stimulated synapses. Therefore, this work provides a simple and effective strategy for fabricating light-stimulated synaptic transistors with both memory and learning ability, which enlightens a new direction for developing neuromorphic devices.

Students' Understanding of Mathematical Expressions in Physical Chemistry Contexts: An Analysis Using Sherin's Symbolic Forms

ERIC Educational Resources Information Center

Becker, Nicole; Towns, Marcy

2012-01-01

Undergraduate physical chemistry courses require students to be proficient in calculus in order to develop an understanding of thermodynamics concepts. Here we present the findings of a study that examines student understanding of mathematical expressions, including partial derivative expressions, in two undergraduate physical chemistry courses.…

Quantifying shapes of volcanoes on Venus

NASA Technical Reports Server (NTRS)

Garvin, J. B.

1994-01-01

A large population of discrete volcanic edifices on Venus has been identified and cataloged by means of Magellan SAR images, and an extensive database describing thousands of such features is in final preparation. Those volcanoes categorized as Intermediate to Large in scale, while relatively small in number (approx. 400), nonetheless constitute a significant volumetric component (approx. 13 x 10(exp 6) cu km) of the total apparent crustal volume of Venus. For this reason, we have focused attention on the morphometry of a representative suite of the larger edifices on Venus and, in particular, on ways of constraining the eruptive histories of these possibly geologically youthful landforms. Our approach has been to determine a series of reproducible morphometric parameters for as many of the discrete volcanoes on Venus that have an obvious expression within the global altimetry data acquired by Magellan. In addition, we have attempted to objectively and systematically define the mathematical essence of the shapes of these larger volcanoes using a polynomial cross-section approximation involving only parameters easily measured from digital topography, as well as with simple surface cylindrical harmonic expansions. The goal is to reduce the topological complexities of the larger edifices to a few simple parameters which can then be related to similar expressions for well-studied terrestrial and martian features.

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.

Analysis and modelling of septic shock microarray data using Singular Value Decomposition.

PubMed

Allanki, Srinivas; Dixit, Madhulika; Thangaraj, Paul; Sinha, Nandan Kumar

2017-06-01

Being a high throughput technique, enormous amounts of microarray data has been generated and there arises a need for more efficient techniques of analysis, in terms of speed and accuracy. Finding the differentially expressed genes based on just fold change and p-value might not extract all the vital biological signals that occur at a lower gene expression level. Besides this, numerous mathematical models have been generated to predict the clinical outcome from microarray data, while very few, if not none, aim at predicting the vital genes that are important in a disease progression. Such models help a basic researcher narrow down and concentrate on a promising set of genes which leads to the discovery of gene-based therapies. In this article, as a first objective, we have used the lesser known and used Singular Value Decomposition (SVD) technique to build a microarray data analysis tool that works with gene expression patterns and intrinsic structure of the data in an unsupervised manner. We have re-analysed a microarray data over the clinical course of Septic shock from Cazalis et al. (2014) and have shown that our proposed analysis provides additional information compared to the conventional method. As a second objective, we developed a novel mathematical model that predicts a set of vital genes in the disease progression that works by generating samples in the continuum between health and disease, using a simple normal-distribution-based random number generator. We also verify that most of the predicted genes are indeed related to septic shock. Copyright © 2017 Elsevier Inc. All rights reserved.

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.

Mathematical Modeling and Pure Mathematics

ERIC Educational Resources Information Center

Usiskin, Zalman

2015-01-01

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

Mathematical estimation of melt depth in conduction mode of laser spot remelting process

NASA Astrophysics Data System (ADS)

Hadi, Iraj

2012-12-01

A one-dimensional mathematical model based on the front tracking method was developed to predict the melt depth as a function of internal and external parameters of laser spot remelting process in conduction mode. Power density, pulse duration, and thermophysical properties of material including thermal diffusivity, melting point, latent heat, and absorption coefficient have been taken into account in the model of this article. By comparing the theoretical results and experimental welding data of commercial pure nickel and titanium plates, the validity of the developed model was examined. Comparison shows a reasonably good agreement between the theory and experiment. For the sake of simplicity, a graphical technique was presented to obtain the melt depth of various materials at any arbitrary amount of power density and pulse duration. In the graphical technique, two dimensionless constants including the Stefan number (Ste) and an introduced constant named laser power factor (LPF) are used. Indeed, all of the internal and external parameters have been gathered in LPF. The effect of power density and pulse duration on the variation of melt depth for different materials such as aluminum, copper, and stainless steel were investigated. Additionally, appropriate expressions were extracted to describe the minimum power density and time to reach melting point in terms of process parameters. A simple expression is also extracted to estimate the thickness of mushy zone for alloys.

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)

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

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)

A Solution to the Cosmic Conundrum including Cosmological Constant and Dark Energy Problems

NASA Astrophysics Data System (ADS)

Singh, A.

2009-12-01

A comprehensive solution to the cosmic conundrum is presented that also resolves key paradoxes of quantum mechanics and relativity. A simple mathematical model, the Gravity Nullification model (GNM), is proposed that integrates the missing physics of the spontaneous relativistic conversion of mass to energy into the existing physics theories, specifically a simplified general theory of relativity. Mechanistic mathematical expressions are derived for a relativistic universe expansion, which predict both the observed linear Hubble expansion in the nearby universe and the accelerating expansion exhibited by the supernova observations. The integrated model addresses the key questions haunting physics and Big Bang cosmology. It also provides a fresh perspective on the misconceived birth and evolution of the universe, especially the creation and dissolution of matter. The proposed model eliminates singularities from existing models and the need for the incredible and unverifiable assumptions including the superluminous inflation scenario, multiple universes, multiple dimensions, Anthropic principle, and quantum gravity. GNM predicts the observed features of the universe without any explicit consideration of time as a governing parameter.

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.

Tailoring Mathematical Models to Stem-Cell Derived Cardiomyocyte Lines Can Improve Predictions of Drug-Induced Changes to Their Electrophysiology.

PubMed

Lei, Chon Lok; Wang, Ken; Clerx, Michael; Johnstone, Ross H; Hortigon-Vinagre, Maria P; Zamora, Victor; Allan, Andrew; Smith, Godfrey L; Gavaghan, David J; Mirams, Gary R; Polonchuk, Liudmila

2017-01-01

Human induced pluripotent stem cell derived cardiomyocytes (iPSC-CMs) have applications in disease modeling, cell therapy, drug screening and personalized medicine. Computational models can be used to interpret experimental findings in iPSC-CMs, provide mechanistic insights, and translate these findings to adult cardiomyocyte (CM) electrophysiology. However, different cell lines display different expression of ion channels, pumps and receptors, and show differences in electrophysiology. In this exploratory study, we use a mathematical model based on iPSC-CMs from Cellular Dynamic International (CDI, iCell), and compare its predictions to novel experimental recordings made with the Axiogenesis Cor.4U line. We show that tailoring this model to the specific cell line, even using limited data and a relatively simple approach, leads to improved predictions of baseline behavior and response to drugs. This demonstrates the need and the feasibility to tailor models to individual cell lines, although a more refined approach will be needed to characterize individual currents, address differences in ion current kinetics, and further improve these results.

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…

Technical Report for Contract N00039-82-C-0235, 15 November 1981-30 September 1983

DTIC Science & Technology

1983-09-30

Management of Data, Ann Arbor, Rich., June 1982. -. 2 ’’.’ , . .. ’,, .* ,° • ,"%,.° % °%" ° %- " "%" . . ." " -.. . . ,.%. Interactive Mathematical ...developed and implemented a hierachical representation for mathematical expres- sioms that includes display position, expression dimensions, font...etc) in internal forms are accepted and converted to box frames which can be displayed. 2. Strophe’s representation of mathematical expressions is

Active output state of the Synechococcus Kai circadian oscillator

PubMed Central

Paddock, Mark L.; Boyd, Joseph S.; Adin, Dawn M.; Golden, Susan S.

2013-01-01

The mechanisms by which cellular oscillators keep time and transmit temporal information are poorly understood. In cyanobacteria, the timekeeping aspect of the circadian oscillator, composed of the KaiA, KaiB, and KaiC proteins, involves a cyclic progression of phosphorylation states at Ser431 and Thr432 of KaiC. Elucidating the mechanism that uses this temporal information to modulate gene expression is complicated by unknowns regarding the number, structure, and regulatory effects of output components. To identify oscillator signaling states without a complete description of the output machinery, we defined a simple metric, Kai-complex output activity (KOA), that represents the difference in expression of reporter genes between strains that carry specific variants of KaiC and baseline strains that lack KaiC. In the absence of the oscillator, expression of the class 1 paradigm promoter PkaiBC was locked at its usual peak level; conversely, that of the class 2 paradigm promoter PpurF was locked at its trough level. However, for both classes of promoters, peak KOA in wild-type strains coincided late in the circadian cycle near subjective dawn, when KaiC-pST becomes most prevalent (Ser431 is phosphorylated and Thr432 is not). Analogously, peak KOA was detected specifically for the phosphomimetic of KaiC-pST (KaiC-ET). Notably, peak KOA required KaiB, indicating that a KaiBC complex is involved in the output activity. We also found evidence that phosphorylated RpaA (regulator of phycobilisome associated) represses an RpaA-independent output of KOA. A simple mathematical expression successfully simulated two key features of the oscillator—the time of peak KOA and the peak-to-trough amplitude changes. PMID:24043774

Active output state of the Synechococcus Kai circadian oscillator.

PubMed

Paddock, Mark L; Boyd, Joseph S; Adin, Dawn M; Golden, Susan S

2013-10-01

The mechanisms by which cellular oscillators keep time and transmit temporal information are poorly understood. In cyanobacteria, the timekeeping aspect of the circadian oscillator, composed of the KaiA, KaiB, and KaiC proteins, involves a cyclic progression of phosphorylation states at Ser431 and Thr432 of KaiC. Elucidating the mechanism that uses this temporal information to modulate gene expression is complicated by unknowns regarding the number, structure, and regulatory effects of output components. To identify oscillator signaling states without a complete description of the output machinery, we defined a simple metric, Kai-complex output activity (KOA), that represents the difference in expression of reporter genes between strains that carry specific variants of KaiC and baseline strains that lack KaiC. In the absence of the oscillator, expression of the class 1 paradigm promoter P(kaiBC) was locked at its usual peak level; conversely, that of the class 2 paradigm promoter P(purF) was locked at its trough level. However, for both classes of promoters, peak KOA in wild-type strains coincided late in the circadian cycle near subjective dawn, when KaiC-pST becomes most prevalent (Ser431 is phosphorylated and Thr432 is not). Analogously, peak KOA was detected specifically for the phosphomimetic of KaiC-pST (KaiC-ET). Notably, peak KOA required KaiB, indicating that a KaiBC complex is involved in the output activity. We also found evidence that phosphorylated RpaA (regulator of phycobilisome associated) represses an RpaA-independent output of KOA. A simple mathematical expression successfully simulated two key features of the oscillator-the time of peak KOA and the peak-to-trough amplitude changes.

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.

Determination of the direction to a source of antineutrinos via inverse beta decay in Double Chooz

NASA Astrophysics Data System (ADS)

Nikitenko, Ya.

2016-11-01

To determine the direction to a source of neutrinos (and antineutrinos) is an important problem for the physics of supernovae and of the Earth. The direction to a source of antineutrinos can be estimated through the reaction of inverse beta decay. We show that the reactor neutrino experiment Double Chooz has unique capabilities to study antineutrino signal from point-like sources. Contemporary experimental data on antineutrino directionality is given. A rigorous mathematical approach for neutrino direction studies has been developed. Exact expressions for the precision of the simple mean estimator of neutrinos' direction for normal and exponential distributions for a finite sample and for the limiting case of many events have been obtained.

Design, development and validation of software for modelling dietary exposure to food chemicals and nutrients.

PubMed

McNamara, C; Naddy, B; Rohan, D; Sexton, J

2003-10-01

The Monte Carlo computational system for stochastic modelling of dietary exposure to food chemicals and nutrients is presented. This system was developed through a European Commission-funded research project. It is accessible as a Web-based application service. The system allows and supports very significant complexity in the data sets used as the model input, but provides a simple, general purpose, linear kernel for model evaluation. Specific features of the system include the ability to enter (arbitrarily) complex mathematical or probabilistic expressions at each and every input data field, automatic bootstrapping on subjects and on subject food intake diaries, and custom kernels to apply brand information such as market share and loyalty to the calculation of food and chemical intake.

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.

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...

Designing Mathematical Learning Environments for Teachers

ERIC Educational Resources Information Center

Madden, Sandra R.

2010-01-01

Technology use in mathematics often involves either exploratory or expressive modeling. When using exploratory models, students use technology to investigate a premade expert model of some phenomena. When creating expressive models, students have greater flexibility for constructing their own model for investigation using objects and mechanisms…

An Analysis of Pre-Service Mathematics Teachers' Performance in Modelling Tasks in Terms of Spatial Visualisation Ability

ERIC Educational Resources Information Center

Tasova, Halil Ibrahim; Delice, Ali

2012-01-01

Mathematical modelling involves mathematical constructions chosen to represent some real world situations and the relationships among them; it is the process of expressing a real world situation mathematically. Visualisation can play a significant role in the development of thinking or understanding mathematical concepts, and also makes abstract…

Early Mathematics Fluency with CCSSM

ERIC Educational Resources Information Center

Matney, Gabriel T.

2014-01-01

To develop second-grade students' confidence and ease, this author presents examples of learning tasks (Number of the Day, Word Problem Solving, and Modeling New Mathematical Ideas) that align with Common Core State Standards for Mathematics and that build mathematical fluency to promote students' creative expression of mathematical…

Expanding Audio Access to Mathematics Expressions by Students with Visual Impairments via MathML. Research Report. ETS RR-17-13

ERIC Educational Resources Information Center

Frankel, Lois; Brownstein, Beth; Soiffer, Neil

2017-01-01

This report describes the pilot conducted in the final phase of a project, Expanding Audio Access to Mathematics Expressions by Students With Visual Impairments via MathML, to provide easy-to-use tools for authoring and rendering secondary-school algebra-level math expressions in synthesized speech that is useful for students with blindness or low…

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.

Optimization and analysis of large chemical kinetic mechanisms using the solution mapping method - Combustion of methane

NASA Technical Reports Server (NTRS)

Frenklach, Michael; Wang, Hai; Rabinowitz, Martin J.

1992-01-01

A method of systematic optimization, solution mapping, as applied to a large-scale dynamic model is presented. The basis of the technique is parameterization of model responses in terms of model parameters by simple algebraic expressions. These expressions are obtained by computer experiments arranged in a factorial design. The developed parameterized responses are then used in a joint multiparameter multidata-set optimization. A brief review of the mathematical background of the technique is given. The concept of active parameters is discussed. The technique is applied to determine an optimum set of parameters for a methane combustion mechanism. Five independent responses - comprising ignition delay times, pre-ignition methyl radical concentration profiles, and laminar premixed flame velocities - were optimized with respect to thirteen reaction rate parameters. The numerical predictions of the optimized model are compared to those computed with several recent literature mechanisms. The utility of the solution mapping technique in situations where the optimum is not unique is also demonstrated.

A time-dependent model to determine the thermal conductivity of a nanofluid

NASA Astrophysics Data System (ADS)

Myers, T. G.; MacDevette, M. M.; Ribera, H.

2013-07-01

In this paper, we analyse the time-dependent heat equations over a finite domain to determine expressions for the thermal diffusivity and conductivity of a nanofluid (where a nanofluid is a fluid containing nanoparticles with average size below 100 nm). Due to the complexity of the standard mathematical analysis of this problem, we employ a well-known approximate solution technique known as the heat balance integral method. This allows us to derive simple analytical expressions for the thermal properties, which appear to depend primarily on the volume fraction and liquid properties. The model is shown to compare well with experimental data taken from the literature even up to relatively high concentrations and predicts significantly higher values than the Maxwell model for volume fractions approximately >1 %. The results suggest that the difficulty in reproducing the high values of conductivity observed experimentally may stem from the use of a static heat flow model applied over an infinite domain rather than applying a dynamic model over a finite domain.

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...

Mother and Child Emotions during Mathematics Homework

ERIC Educational Resources Information Center

Else-Quest, Nicole M.; Hyde, Janet S.; Hejmadi, Ahalya

2008-01-01

Mathematics is often thought of as a purely intellectual and unemotional activity. Recently, researchers have begun to question the validity of this approach, arguing that emotions and cognition are intertwined. The emotions expressed during mathematics work may be linked to mathematics achievement. We used behavioral measures to identify the…

Automatic Semantic Generation and Arabic Translation of Mathematical Expressions on the Web

ERIC Educational Resources Information Center

Doush, Iyad Abu; Al-Bdarneh, Sondos

2013-01-01

Automatic processing of mathematical information on the web imposes some difficulties. This paper presents a novel technique for automatic generation of mathematical equations semantic and Arabic translation on the web. The proposed system facilitates unambiguous representation of mathematical equations by correlating equations to their known…

Setting the Tempo in Development: An Investigation of the Zebrafish Somite Clock Mechanism

PubMed Central

Giudicelli, François; Özbudak, Ertuğrul M; Wright, Gavin J; Lewis, Julian

2007-01-01

The somites of the vertebrate embryo are clocked out sequentially from the presomitic mesoderm (PSM) at the tail end of the embryo. Formation of each somite corresponds to one cycle of oscillation of the somite segmentation clock—a system of genes whose expression switches on and off periodically in the cells of the PSM. We have previously proposed a simple mathematical model explaining how the oscillations, in zebrafish at least, may be generated by a delayed negative feedback loop in which the products of two Notch target genes, her1 and her7, directly inhibit their own transcription, as well as that of the gene for the Notch ligand DeltaC; Notch signalling via DeltaC keeps the oscillations of neighbouring cells in synchrony. Here we subject the model to quantitative tests. We show how to read temporal information from the spatial pattern of stripes of gene expression in the anterior PSM and in this way obtain values for the biosynthetic delays and molecular lifetimes on which the model critically depends. Using transgenic lines of zebrafish expressing her1 or her7 under heat-shock control, we confirm the regulatory relationships postulated by the model. From the timing of somite segmentation disturbances following a pulse of her7 misexpression, we deduce that although her7 continues to oscillate in the anterior half of the PSM, it governs the future somite segmentation behaviour of the cells only while they are in the posterior half. In general, the findings strongly support the mathematical model of how the somite clock works, but they do not exclude the possibility that other oscillator mechanisms may operate upstream from the her7/her1 oscillator or in parallel with it. PMID:17535112

Staircase Methods of Sensitivity Testing,

DTIC Science & Technology

1946-03-21

Mathematical Preliminaries ............. 32 b. Outline of the Investigation ..... .......... 35 8. The Possible Adjustments ...... ............... .. 36 9...bh Ar’Lied MathematIcs Pa-nel. ZCC, uU, -. for one decermntation !f tie per centtage point and the average nmber ee exp-li.-n. required far one such...accuracy per explosion. 32. II. TECOI4ICPJJ 7. Introduction. a. Some Mathematical Preliminaries. Expressed mathematically , the problem of sensitivity

The Negative Sign and Exponential Expressions: Unveiling Students' Persistent Errors and Misconceptions

ERIC Educational Resources Information Center

Cangelosi, Richard; Madrid, Silvia; Cooper, Sandra; Olson, Jo; Hartter, Beverly

2013-01-01

The purpose of this study was to determine whether or not certain errors made when simplifying exponential expressions persist as students progress through their mathematical studies. College students enrolled in college algebra, pre-calculus, and first- and second-semester calculus mathematics courses were asked to simplify exponential…

University of Chicago School Mathematics Project (UCSMP) Algebra. WWC Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2009

2009-01-01

University of Chicago School Mathematics Project (UCSMP) Algebra is a one-year course covering three primary topics: (1) linear and quadratic expressions, sentences, and functions; (2) exponential expressions and functions; and (3) linear systems. Topics from geometry, probability, and statistics are integrated with the appropriate algebra.…

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.

Statical longitudinal stability of airplanes

NASA Technical Reports Server (NTRS)

Warner, Edward P

1921-01-01

This report, which is a continuation of the "Preliminary report on free flight testing" (report no. NACA-TR-70), presents a detailed theoretical analysis of statical stability with free and locked controls and also the results of many free flight test on several types of airplanes. In developing the theory of stability with locked controls an expression for pitching moment is derived in simple terms by considering the total moment as the sum of the moments due to wings and tail surface. This expression, when differentiated with respect to angle of incidence, enables an analysis to be made of the factors contributing to the pitching moment. The effects of slipstream and down wash are also considered and it is concluded that the C. G. Location has but slight effect or stability, and that stability is much improved by increasing the efficiency of the tail surfaces, which may be done by using an "inverted" tail plane. The results of free flight tests with locked controls are discussed at length and it is shown that the agreement between the experimental results and theory is very satisfactory. The theory of stability with free controls is not amendable to the simple mathematical treatment used in the case of locked controls, but a clear statement of the conditions enables several conclusions to be drawn, one of which is that the fixed tail surfaces should be much larger than the movable surfaces.

Characteristic time scales for diffusion processes through layers and across interfaces

NASA Astrophysics Data System (ADS)

Carr, Elliot J.

2018-04-01

This paper presents a simple tool for characterizing the time scale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in composite materials, flow in layered aquifers, and drug diffusion through the layers of the skin. In such processes, the physical properties of the medium vary across layers and internal boundary conditions apply at the interfaces between adjacent layers. To characterize the time scale, we use the concept of mean action time, which provides the mean time scale at each position in the medium by utilizing the fact that the transition of the transient solution of the underlying partial differential equation model, from initial state to steady state, can be represented as a cumulative distribution function of time. Using this concept, we define the characteristic time scale for a multilayer diffusion process as the maximum value of the mean action time across the layered medium. For given initial conditions and internal and external boundary conditions, this approach leads to simple algebraic expressions for characterizing the time scale that depend on the physical and geometrical properties of the medium, such as the diffusivities and lengths of the layers. Numerical examples demonstrate that these expressions provide useful insight into explaining how the parameters in the model affect the time it takes for a multilayer diffusion process to reach steady state.

Characteristic time scales for diffusion processes through layers and across interfaces.

PubMed

Carr, Elliot J

2018-04-01

This paper presents a simple tool for characterizing the time scale for continuum diffusion processes through layered heterogeneous media. This mathematical problem is motivated by several practical applications such as heat transport in composite materials, flow in layered aquifers, and drug diffusion through the layers of the skin. In such processes, the physical properties of the medium vary across layers and internal boundary conditions apply at the interfaces between adjacent layers. To characterize the time scale, we use the concept of mean action time, which provides the mean time scale at each position in the medium by utilizing the fact that the transition of the transient solution of the underlying partial differential equation model, from initial state to steady state, can be represented as a cumulative distribution function of time. Using this concept, we define the characteristic time scale for a multilayer diffusion process as the maximum value of the mean action time across the layered medium. For given initial conditions and internal and external boundary conditions, this approach leads to simple algebraic expressions for characterizing the time scale that depend on the physical and geometrical properties of the medium, such as the diffusivities and lengths of the layers. Numerical examples demonstrate that these expressions provide useful insight into explaining how the parameters in the model affect the time it takes for a multilayer diffusion process to reach steady state.

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.

Quantification of human responses

NASA Technical Reports Server (NTRS)

Steinlage, R. C.; Gantner, T. E.; Lim, P. Y. W.

1992-01-01

Human perception is a complex phenomenon which is difficult to quantify with instruments. For this reason, large panels of people are often used to elicit and aggregate subjective judgments. Print quality, taste, smell, sound quality of a stereo system, softness, and grading Olympic divers and skaters are some examples of situations where subjective measurements or judgments are paramount. We usually express what is in our mind through language as a medium but languages are limited in available choices of vocabularies, and as a result, our verbalizations are only approximate expressions of what we really have in mind. For lack of better methods to quantify subjective judgments, it is customary to set up a numerical scale such as 1, 2, 3, 4, 5 or 1, 2, 3, ..., 9, 10 for characterizing human responses and subjective judgments with no valid justification except that these scales are easy to understand and convenient to use. But these numerical scales are arbitrary simplifications of the complex human mind; the human mind is not restricted to such simple numerical variations. In fact, human responses and subjective judgments are psychophysical phenomena that are fuzzy entities and therefore difficult to handle by conventional mathematics and probability theory. The fuzzy mathematical approach provides a more realistic insight into understanding and quantifying human responses. This paper presents a method for quantifying human responses and subjective judgments without assuming a pattern of linear or numerical variation for human responses. In particular, quantification and evaluation of linguistic judgments was investigated.

[Differences of vegetation phenology monitoring by remote sensing based on different spectral vegetation indices.

PubMed

Zuo, Lu; Wang, Huan Jiong; Liu, Rong Gao; Liu, Yang; Shang, Rong

2018-02-01

Vegetation phenology is a comprehensive indictor for the responses of terrestrial ecosystem to climatic and environmental changes. Remote sensing spectrum has been widely used in the extraction of vegetation phenology information. However, there are many differences between phenology extracted by remote sensing and site observations, with their physical meaning remaining unclear. We selected one tile of MODIS data in northeastern China (2000-2014) to examine the SOS and EOS differences derived from the normalized difference vegetation index (NDVI) and the simple ratio vegetation index (SR) based on both the red and near-infrared bands. The results showed that there were significant differences between NDVI-phenology and SR-phenology. SOS derived from NDVI averaged 18.9 days earlier than that from SR. EOS derived from NDVI averaged 19.0 days later than from SR. NDVI-phenology had a longer growing season. There were significant differences in the inter-annual variation of phenology from NDVI and SR. More than 20% of the pixel SOS and EOS derived from NDVI and SR showed the opposite temporal trend. These results caused by the seasonal curve characteristics and noise resistance differences of NDVI and SR. The observed data source of NDVI and SR were completely consistent, only the mathematical expressions were different, but phenology results were significantly different. Our results indicated that vegetation phenology monitoring by remote sensing is highly dependent on the mathematical expression of vegetation index. How to establish a reliable method for extracting vegetation phenology by remote sensing needs further research.

E-Coli and Other Problems

ERIC Educational Resources Information Center

Scott, Paul

2009-01-01

In applied mathematics particularly, one is interested in modeling real life situations; that is why, one tries to express some actual phenomenon mathematically, and then uses mathematics to determine future outcomes. It may be that one actually wishes to change the future outcome. Mathematics will not do this, but at least it tells one what to…

The Construction of Deductive Warrant Derived from Inductive Warrant in Preservice-Teacher Mathematical Argumentations

ERIC Educational Resources Information Center

Tristanti, Lia Budi; Sutawidjaja, Akbar; As'ari, Abdur Rahman; Muskar, Makbul

2016-01-01

This study discusses the construction of deductive warrant derived from inductive warrant in mathematical argumentations expressed by pre-service teacher. In completing a mathematics task, a problem solver needs argumentation to determine, reveal, and support a reasonable solution. A mathematical argumentation can be analyzed by Toulmin scheme…

Mathematics Teacher-Candidates' Performance in Solving Problems with Different Representation Styles: The Trigonometry Example

ERIC Educational Resources Information Center

Dündar, Sefa

2015-01-01

Using multiple representations of a problem can reveal the relationship between complex concepts by expressing the same mathematical condition differently and can contribute to the meaningful learning of mathematical concepts. The purpose of this study is to assess the performances of mathematics teacher-candidates on trigonometry problems…

Steady-state groundwater recharge in trapezoidal-shaped aquifers: A semi-analytical approach based on variational calculus

NASA Astrophysics Data System (ADS)

Mahdavi, Ali; Seyyedian, Hamid

2014-05-01

This study presents a semi-analytical solution for steady groundwater flow in trapezoidal-shaped aquifers in response to an areal diffusive recharge. The aquifer is homogeneous, anisotropic and interacts with four surrounding streams of constant-head. Flow field in this laterally bounded aquifer-system is efficiently constructed by means of variational calculus. This is accomplished by minimizing a properly defined penalty function for the associated boundary value problem. Simple yet demonstrative scenarios are defined to investigate anisotropy effects on the water table variation. Qualitative examination of the resulting equipotential contour maps and velocity vector field illustrates the validity of the method, especially in the vicinity of boundary lines. Extension to the case of triangular-shaped aquifer with or without an impervious boundary line is also demonstrated through a hypothetical example problem. The present solution benefits from an extremely simple mathematical expression and exhibits strictly close agreement with the numerical results obtained from Modflow. Overall, the solution may be used to conduct sensitivity analysis on various hydrogeological parameters that affect water table variation in aquifers defined in trapezoidal or triangular-shaped domains.

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.

24 CFR 51.103 - Criteria and standards.

Code of Federal Regulations, 2010 CFR

2010-04-01

... decibels to sound levels in the night from 10 p.m. to 7 a.m. Mathematical expressions for average sound..., as indicated in § 51.106(a)(3). Methods for assessing the contribution of loud impulsive sounds to day-night average sound level at a site and mathematical expressions for determining whether a sound...

Researching Race in Mathematics Education

ERIC Educational Resources Information Center

Martin, Danny Bernard

2009-01-01

Background: Within mathematics education research, policy, and practice, race remains undertheorized in relation to mathematics learning and participation. Although race is characterized in the sociological and critical theory literatures as socially and politically constructed with structural expressions, most studies of differential outcomes in…

Missing Dimensions of Mathematics Instruction.

ERIC Educational Resources Information Center

Meyer, Walter

1995-01-01

Emphasizes how to express the breadth of mathematics itself. Addresses other missing dimensions which make mathematics attractive to a larger number of students by making it appear less isolated and more tied to thoughts and experiences that students find familiar and congenial. (ASK)

A simple expression for quantifying bacterial chemotaxis using capillary assay data: application to the analysis of enhanced chemotactic responses from growth-limited cultures.

PubMed

Ford, R M; Lauffenburger, D A

1992-05-01

An individual cell-based mathematical model of Rivero et al. provides a framework for determining values of the chemotactic sensitivity coefficient chi 0, an intrinsic cell population parameter that characterizes the chemotactic response of bacterial populations. This coefficient can theoretically relate the swimming behavior of individual cells to the resulting migration of a bacterial population. When this model is applied to the commonly used capillary assay, an approximate solution can be obtained for a particular range of chemotactic strengths yielding a very simple analytical expression for estimating the value of chi 0, [formula: see text] from measurements of cell accumulation in the capillary, N, when attractant uptake is negligible. A0 and A infinity are the dimensionless attractant concentrations initially present at the mouth of the capillary and far into the capillary, respectively, which are scaled by Kd, the effective dissociation constant for receptor-attractant binding. D is the attractant diffusivity, and mu is the cell random motility coefficient. NRM is the cell accumulation in the capillary in the absence of an attractant gradient, from which mu can be determined independently as mu = (pi/4t)(NRM/pi r2bc)2, with r the capillary tube radius and bc the bacterial density initially in the chamber. When attractant uptake is significant, a slightly more involved procedure requiring a simple numerical integration becomes necessary. As an example, we apply this approach to quantitatively characterize, in terms of the chemotactic sensitivity coefficient chi 0, data from Terracciano indicating enhanced chemotactic responses of Escherichia coli to galactose when cultured under growth-limiting galactose levels in a chemostat.

A formulation of the foundations of genetics and evolution.

PubMed

Bahr, Brian Edward

2016-05-01

This paper proposes a formulation of theories of the foundations of genetics and evolution that can be used to mathematically simulate phenotype expression, reproduction, mutation, and natural selection. It will be shown that Mendelian inheritance can be mathematically simulated with expressions involving matrices and that these expressions can also simulate phenomena that are modifications to Mendel's basic principles, like alleles that give rise to quantitative effects and traits that are the expression of multiple alleles and/or multiple genetic loci. Copyright © 2016 Elsevier Inc. All rights reserved.

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…

Loving and Hating Mathematics: Challenging the Myths of Mathematical Life

ERIC Educational Resources Information Center

Hersh, Reuben; John-Steiner, Vera

2010-01-01

Mathematics is often thought of as the coldest expression of pure reason. But few subjects provoke hotter emotions--and inspire more love and hatred--than mathematics. And although math is frequently idealized as floating above the messiness of human life, its story is nothing if not human; often, it is all too human. "Loving and Hating…

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…

On the origin of Hawking mini black-holes and the cold early universe

NASA Technical Reports Server (NTRS)

Canuto, V.

1978-01-01

A simple argument is outlined leading to the result that the mass of mini black holes exploding today is 10 to the 15th power g. A mathematical model is discussed which indicates that the equation of state is greatly softened in the high-density regime and a phase transition may exist, such that any length (particularly very small sizes) will grow with time irrespective of its relation to the size of the particle horizon. It is shown that the effect of spin-2 mesons with respect to the equation of state is to soften the pressure and make it negative. An analytical expression is given for the probability that any particular region in a hot early universe will evolve into a black hole.

Defect of the well-known (classical) expression for the ionization rate in gas-discharge plasma and its modification

NASA Astrophysics Data System (ADS)

Litvinov, I. I.

2015-11-01

A critical analysis is given of the well-known expression for the electron-impact ionization rate constant α i of neutral atoms and ions, derived by linearization of the ionization cross section σ i (ɛ) as a function of the electron energy near the threshold I and containing the characteristic factor ( I + 2 kT). Using the classical Thomson expression for the ionization cross section, it is shown that in addition to the linear slope of σ i (ɛ), it is also necessary to take into account the large negative curvature of this function near the threshold. In this case, the second term in parentheses changes its sign, which means that the commonly used expression for α i (˜4 kT/I) already at moderate values of the temperature ( kT/I ˜ 0.1). The source of this error lies in a mathematical mistake in the original approach and is related to the incorrect choice of the sequential orders of terms small in the parameter kT/I. On the basis of a large amount of experimental data and considerations similar to the Gryzinski theory, a universal two-parameter modification of the Thomson formula (as well as the Bethe—Born formula) is proposed and a new simple expression for the ionization rate constant for arbitrary values of kT/I is derived.

Error propagation in eigenimage filtering.

PubMed

Soltanian-Zadeh, H; Windham, J P; Jenkins, J M

1990-01-01

Mathematical derivation of error (noise) propagation in eigenimage filtering is presented. Based on the mathematical expressions, a method for decreasing the propagated noise given a sequence of images is suggested. The signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) of the final composite image are compared to the SNRs and CNRs of the images in the sequence. The consistency of the assumptions and accuracy of the mathematical expressions are investigated using sequences of simulated and real magnetic resonance (MR) images of an agarose phantom and a human brain.

Disease-induced resource constraints can trigger explosive epidemics

NASA Astrophysics Data System (ADS)

Böttcher, L.; Woolley-Meza, O.; Araújo, N. A. M.; Herrmann, H. J.; Helbing, D.

2015-11-01

Advances in mathematical epidemiology have led to a better understanding of the risks posed by epidemic spreading and informed strategies to contain disease spread. However, a challenge that has been overlooked is that, as a disease becomes more prevalent, it can limit the availability of the capital needed to effectively treat those who have fallen ill. Here we use a simple mathematical model to gain insight into the dynamics of an epidemic when the recovery of sick individuals depends on the availability of healing resources that are generated by the healthy population. We find that epidemics spiral out of control into “explosive” spread if the cost of recovery is above a critical cost. This can occur even when the disease would die out without the resource constraint. The onset of explosive epidemics is very sudden, exhibiting a discontinuous transition under very general assumptions. We find analytical expressions for the critical cost and the size of the explosive jump in infection levels in terms of the parameters that characterize the spreading process. Our model and results apply beyond epidemics to contagion dynamics that self-induce constraints on recovery, thereby amplifying the spreading process.

Disease-induced resource constraints can trigger explosive epidemics.

PubMed

Böttcher, L; Woolley-Meza, O; Araújo, N A M; Herrmann, H J; Helbing, D

2015-11-16

Advances in mathematical epidemiology have led to a better understanding of the risks posed by epidemic spreading and informed strategies to contain disease spread. However, a challenge that has been overlooked is that, as a disease becomes more prevalent, it can limit the availability of the capital needed to effectively treat those who have fallen ill. Here we use a simple mathematical model to gain insight into the dynamics of an epidemic when the recovery of sick individuals depends on the availability of healing resources that are generated by the healthy population. We find that epidemics spiral out of control into "explosive" spread if the cost of recovery is above a critical cost. This can occur even when the disease would die out without the resource constraint. The onset of explosive epidemics is very sudden, exhibiting a discontinuous transition under very general assumptions. We find analytical expressions for the critical cost and the size of the explosive jump in infection levels in terms of the parameters that characterize the spreading process. Our model and results apply beyond epidemics to contagion dynamics that self-induce constraints on recovery, thereby amplifying the spreading process.

Disease-induced resource constraints can trigger explosive epidemics

PubMed Central

Böttcher, L.; Woolley-Meza, O.; Araújo, N. A. M.; Herrmann, H. J.; Helbing, D.

2015-01-01

Advances in mathematical epidemiology have led to a better understanding of the risks posed by epidemic spreading and informed strategies to contain disease spread. However, a challenge that has been overlooked is that, as a disease becomes more prevalent, it can limit the availability of the capital needed to effectively treat those who have fallen ill. Here we use a simple mathematical model to gain insight into the dynamics of an epidemic when the recovery of sick individuals depends on the availability of healing resources that are generated by the healthy population. We find that epidemics spiral out of control into “explosive” spread if the cost of recovery is above a critical cost. This can occur even when the disease would die out without the resource constraint. The onset of explosive epidemics is very sudden, exhibiting a discontinuous transition under very general assumptions. We find analytical expressions for the critical cost and the size of the explosive jump in infection levels in terms of the parameters that characterize the spreading process. Our model and results apply beyond epidemics to contagion dynamics that self-induce constraints on recovery, thereby amplifying the spreading process. PMID:26568377

Development of an ultralow-light-level luminescence image analysis system for dynamic measurements of transcriptional activity in living and migrating cells.

PubMed

Maire, E; Lelièvre, E; Brau, D; Lyons, A; Woodward, M; Fafeur, V; Vandenbunder, B

2000-04-10

We have developed an approach to study in single living epithelial cells both cell migration and transcriptional activation, which was evidenced by the detection of luminescence emission from cells transfected with luciferase reporter vectors. The image acquisition chain consists of an epifluorescence inverted microscope, connected to an ultralow-light-level photon-counting camera and an image-acquisition card associated to specialized image analysis software running on a PC computer. Using a simple method based on a thin calibrated light source, the image acquisition chain has been optimized following comparisons of the performance of microscopy objectives and photon-counting cameras designed to observe luminescence. This setup allows us to measure by image analysis the luminescent light emitted by individual cells stably expressing a luciferase reporter vector. The sensitivity of the camera was adjusted to a high value, which required the use of a segmentation algorithm to eliminate the background noise. Following mathematical morphology treatments, kinetic changes of luminescent sources were analyzed and then correlated with the distance and speed of migration. Our results highlight the usefulness of our image acquisition chain and mathematical morphology software to quantify the kinetics of luminescence changes in migrating cells.

Theoretical ecology without species

NASA Astrophysics Data System (ADS)

Tikhonov, Mikhail

The sequencing-driven revolution in microbial ecology demonstrated that discrete ``species'' are an inadequate description of the vast majority of life on our planet. Developing a novel theoretical language that, unlike classical ecology, would not require postulating the existence of species, is a challenge of tremendous medical and environmental significance, and an exciting direction for theoretical physics. Here, it is proposed that community dynamics can be described in a naturally hierarchical way in terms of population fluctuation eigenmodes. The approach is applied to a simple model of division of labor in a multi-species community. In one regime, effective species with a core and accessory genome are shown to naturally appear as emergent concepts. However, the same model allows a transition into a regime where the species formalism becomes inadequate, but the eigenmode description remains well-defined. Treating a community as a black box that expresses enzymes in response to resources reveals mathematically exact parallels between a community and a single coherent organism with its own fitness function. This coherence is a generic consequence of division of labor, requires no cooperative interactions, and can be expected to be widespread in microbial ecosystems. Harvard Center of Mathematical Sciences and Applications;John A. Paulson School of Engineering and Applied Sciences.

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.

WISC-IV Intellectual Profiles in Italian Children with Specific Learning Disorder and Related Impairments in Reading, Written Expression, and Mathematics

ERIC Educational Resources Information Center

Poletti, Michele

2016-01-01

The fifth edition of the "Diagnostic and Statistical Manual of Mental Disorders" grouped specific learning disabilities in the single diagnostic category of specific learning disorder (SLD), with specifiers for impairments in reading, written expression, and mathematics. This study aimed at investigating the intellectual profile,…

Prediction of Layer Thickness in Molten Borax Bath with Genetic Evolutionary Programming

NASA Astrophysics Data System (ADS)

Taylan, Fatih

2011-04-01

In this study, the vanadium carbide coating in molten borax bath process is modeled by evolutionary genetic programming (GEP) with bath composition (borax percentage, ferro vanadium (Fe-V) percentage, boric acid percentage), bath temperature, immersion time, and layer thickness data. Five inputs and one output data exist in the model. The percentage of borax, Fe-V, and boric acid, temperature, and immersion time parameters are used as input data and the layer thickness value is used as output data. For selected bath components, immersion time, and temperature variables, the layer thicknesses are derived from the mathematical expression. The results of the mathematical expressions are compared to that of experimental data; it is determined that the derived mathematical expression has an accuracy of 89%.

Exploring grade 3 teachers' resistance to `take up' progressive mathematics teaching roles

NASA Astrophysics Data System (ADS)

Westaway, Lise; Graven, Mellony

2018-03-01

This article addresses the question: Why teachers of mathematics have yet to `take up' progressive roles? Drawing on the philosophy of critical realism and its methodological equivalent, social realism, we analyse interview and observation data of four grade 3 teachers, with the view to identifying the mechanisms conditioning the expression of teachers' identities. In so doing, we show how post-apartheid changes in systemic roles of teachers create contradictory tensions for teachers as these bring their own mathematical learning and teaching experiences into contradiction with the new post-apartheid roles they are mandated to enact. We examine how this contradiction, together with beliefs about mathematics, pedagogy and learners, is expressed in the teaching of grade 3 mathematics. We maintain that the complementarity between teachers' beliefs and old systemic roles provides an explanation for why teachers of grade 3 mathematics have yet to `take-up' progressive roles. The implications point to the need for teacher development that creates enablers that lead to changes in classroom practices that align with policy-designated, progressive roles in teaching 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.

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.

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…

The Great Mathematician Project

ERIC Educational Resources Information Center

Goldberg, Sabrina R.

2013-01-01

The Great Mathematician Project (GMP) introduces both mathematically sophisticated and struggling students to the history of mathematics. The rationale for the GMP is twofold: first, mathematics is a uniquely people-centered discipline that is used to make sense of the world; and second, students often express curiosity about the history of…

Structural analysis of online handwritten mathematical symbols based on support vector machines

NASA Astrophysics Data System (ADS)

Simistira, Foteini; Papavassiliou, Vassilis; Katsouros, Vassilis; Carayannis, George

2013-01-01

Mathematical expression recognition is still a very challenging task for the research community mainly because of the two-dimensional (2d) structure of mathematical expressions (MEs). In this paper, we present a novel approach for the structural analysis between two on-line handwritten mathematical symbols of a ME, based on spatial features of the symbols. We introduce six features to represent the spatial affinity of the symbols and compare two multi-class classification methods that employ support vector machines (SVMs): one based on the "one-against-one" technique and one based on the "one-against-all", in identifying the relation between a pair of symbols (i.e. subscript, numerator, etc). A dataset containing 1906 spatial relations derived from the Competition on Recognition of Online Handwritten Mathematical Expressions (CROHME) 2012 training dataset is constructed to evaluate the classifiers and compare them with the rule-based classifier of the ILSP-1 system participated in the contest. The experimental results give an overall mean error rate of 2.61% for the "one-against-one" SVM approach, 6.57% for the "one-against-all" SVM technique and 12.31% error rate for the ILSP-1 classifier.

Type Specialization in Aldor

NASA Astrophysics Data System (ADS)

Dragan, Laurentiu; Watt, Stephen M.

Computer algebra in scientific computation squarely faces the dilemma of natural mathematical expression versus efficiency. While higher-order programming constructs and parametric polymorphism provide a natural and expressive language for mathematical abstractions, they can come at a considerable cost. We investigate how deeply nested type constructions may be optimized to achieve performance similar to that of hand-tuned code written in lower-level languages.

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.

MONTO: A Machine-Readable Ontology for Teaching Word Problems in Mathematics

ERIC Educational Resources Information Center

Lalingkar, Aparna; Ramnathan, Chandrashekar; Ramani, Srinivasan

2015-01-01

The Indian National Curriculum Framework has as one of its objectives the development of mathematical thinking and problem solving ability. However, recent studies conducted in Indian metros have expressed concern about students' mathematics learning. Except in some private coaching academies, regular classroom teaching does not include problem…

Mathematics Diagnostic Testing in Engineering: An International Comparison between Ireland and Portugal

ERIC Educational Resources Information Center

Carr, M.; Fidalgo, C.; Bigotte de Almeida, M. E.; Branco, J. R.; Santos, V.; Murphy, E.; Ní Fhloinn, E.

2015-01-01

Concern has been expressed throughout Europe about the significant deficiencies in the basic mathematical skills of many engineering undergraduates. Mathematics diagnostic tests in the UK, Ireland and Portugal have shown these shortcomings, which provide a challenge to those striving to introduce more innovative educational practices into…

Maths Games: A Universal Design Approach to Mathematical Reasoning

ERIC Educational Resources Information Center

Buchheister, Kelley; Jackson, Christa; Taylor, Cynthia E.

2017-01-01

Providing students with an opportunity to explore mathematical content through games allows teachers to include tasks that: (1) present alternative representations of the content; (2) welcome various expressions of mathematical reasoning; and (3) incorporate variations that empower all students to engage in the problem solving process. Games not…

Mathematical Abilities in Elementary School Children with Autism Spectrum Disorder

ERIC Educational Resources Information Center

Titeca, Daisy; Roeyers, Herbert; Loeys, Tom; Ceulemans, Annelies; Desoete, Annemie

2015-01-01

Although clinical practitioners often express concerns about the mathematical functioning of children with autism spectrum disorder (ASD), the field of mathematics remains a relatively unexplored topic in individuals with ASD. Moreover, research findings are fragmentary and hold inconclusive results. The present study aimed to examine whether…

Emotion and Disaffection with School Mathematics

ERIC Educational Resources Information Center

Lewis, Gareth

2013-01-01

This paper reports some initial findings from research designed to understand more deeply the motivational and emotional landscape of disaffection with school mathematics. A context is described in which there has been significant concern expressed about a number of aspects of mathematics education, but where affect is seen as salient to these…

A group matrix representation relevant to scales of measurement of clinical disease states via stratified vectors.

PubMed

Sawamura, Jitsuki; Morishita, Shigeru; Ishigooka, Jun

2016-02-09

Previously, we applied basic group theory and related concepts to scales of measurement of clinical disease states and clinical findings (including laboratory data). To gain a more concrete comprehension, we here apply the concept of matrix representation, which was not explicitly exploited in our previous work. Starting with a set of orthonormal vectors, called the basis, an operator Rj (an N-tuple patient disease state at the j-th session) was expressed as a set of stratified vectors representing plural operations on individual components, so as to satisfy the group matrix representation. The stratified vectors containing individual unit operations were combined into one-dimensional square matrices [Rj]s. The [Rj]s meet the matrix representation of a group (ring) as a K-algebra. Using the same-sized matrix of stratified vectors, we can also express changes in the plural set of [Rj]s. The method is demonstrated on simple examples. Despite the incompleteness of our model, the group matrix representation of stratified vectors offers a formal mathematical approach to clinical medicine, aligning it with other branches of natural science.

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…

RF multicoupler design techniques to minimize problems of corona, multipaction, and stability

NASA Technical Reports Server (NTRS)

Hurley, H. S.; Kozakoff, D. J.

1971-01-01

A mathematical expression was derived describing multipacting and corona effects in a coaxial cavity. Both mechanical and electrical design techniques were investigated to minimize the susceptibility of coaxial cavity to corona and multipacting-type breakdown. To assist in the design of a multicoupler free from corona and multipactor breakdown, a flow chart obtained from the derived mathematical expression is included.

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.

Analysis of bacterial migration. 2: Studies with multiple attractant gradients

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

Strauss, I.; Frymier, P.D.; Hahn, C.M.

1995-02-01

Many motile bacteria exhibit chemotaxis, the ability to bias their random motion toward or away from increasing concentrations of chemical substances which benefit or inhibit their survival, respectively. Since bacteria encounter numerous chemical concentration gradients simultaneously in natural surroundings, it is necessary to know quantitatively how a bacterial population responds in the presence of more than one chemical stimulus to develop predictive mathematical models describing bacterial migration in natural systems. This work evaluates three hypothetical models describing the integration of chemical signals from multiple stimuli: high sensitivity, maximum signal, and simple additivity. An expression for the tumbling probability for individualmore » stimuli is modified according to the proposed models and incorporated into the cell balance equation for a 1-D attractant gradient. Random motility and chemotactic sensitivity coefficients, required input parameters for the model, are measured for single stimulus responses. Theoretical predictions with the three signal integration models are compared to the net chemotactic response of Escherichia coli to co- and antidirectional gradients of D-fucose and [alpha]-methylaspartate in the stopped-flow diffusion chamber assay. Results eliminate the high-sensitivity model and favor the simple additivity over the maximum signal. None of the simple models, however, accurately predict the observed behavior, suggesting a more complex model with more steps in the signal processing mechanism is required to predict responses to multiple stimuli.« less

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…

Reciprocal Sliding Friction Model for an Electro-Deposited Coating and Its Parameter Estimation Using Markov Chain Monte Carlo Method

PubMed Central

Kim, Kyungmok; Lee, Jaewook

2016-01-01

This paper describes a sliding friction model for an electro-deposited coating. Reciprocating sliding tests using ball-on-flat plate test apparatus are performed to determine an evolution of the kinetic friction coefficient. The evolution of the friction coefficient is classified into the initial running-in period, steady-state sliding, and transition to higher friction. The friction coefficient during the initial running-in period and steady-state sliding is expressed as a simple linear function. The friction coefficient in the transition to higher friction is described with a mathematical model derived from Kachanov-type damage law. The model parameters are then estimated using the Markov Chain Monte Carlo (MCMC) approach. It is identified that estimated friction coefficients obtained by MCMC approach are in good agreement with measured ones. PMID:28773359

Temperature extrapolation of multicomponent grand canonical free energy landscapes

NASA Astrophysics Data System (ADS)

Mahynski, Nathan A.; Errington, Jeffrey R.; Shen, Vincent K.

2017-08-01

We derive a method for extrapolating the grand canonical free energy landscape of a multicomponent fluid system from one temperature to another. Previously, we introduced this statistical mechanical framework for the case where kinetic energy contributions to the classical partition function were neglected for simplicity [N. A. Mahynski et al., J. Chem. Phys. 146, 074101 (2017)]. Here, we generalize the derivation to admit these contributions in order to explicitly illustrate the differences that result. Specifically, we show how factoring out kinetic energy effects a priori, in order to consider only the configurational partition function, leads to simpler mathematical expressions that tend to produce more accurate extrapolations than when these effects are included. We demonstrate this by comparing and contrasting these two approaches for the simple cases of an ideal gas and a non-ideal, square-well fluid.

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.

Measurement of the configuration of a concave surface by the interference of reflected light

NASA Technical Reports Server (NTRS)

Kumazawa, T.; Sakamoto, T.; Shida, S.

1985-01-01

A method whereby a concave surface is irradiated with coherent light and the resulting interference fringes yield information on the concave surface is described. This method can be applied to a surface which satisfies the following conditions: (1) the concave face has a mirror surface; (2) the profile of the face is expressed by a mathematical function with a point of inflection. In this interferometry, multilight waves reflected from the concave surface interfere and make fringes wherever the reflected light propagates. Interference fringe orders. Photographs of the fringe patterns for a uniformly loaded thin silicon plate clamped at the edge are shown experimentally. The experimental and the theoretical values of the maximum optical path difference show good agreement. This simple method can be applied to obtain accurate information on concave surfaces.

A survey of functional programming language principles

NASA Technical Reports Server (NTRS)

Holloway, C. M.

1986-01-01

Research in the area of functional programming languages has intensified in the 8 years since John Backus' Turing Award Lecture on the topic was published. The purpose of this paper is to present a survey of the ideas of functional programming languages. The paper assumes the reader is comfortable with mathematics and has knowledge of the basic principles of traditional programming languages, but does not assume any prior knowledge of the ideas of functional languages. A simple functional language is defined and used to illustrate the basic ideas. Topics discussed include the reasons for developing functional languages, methods of expressing concurrency, the algebra of functional programming languages, program transformation techniques, and implementations of functional languages. Existing functional languages are also mentioned. The paper concludes with the author's opinions as to the future of functional languages. An annotated bibliography on the subject is also included.

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.

Science Education - Deja Vu Revised.

ERIC Educational Resources Information Center

Walsh, John

1982-01-01

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

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.

Note-Taking in a Mathematics Classroom

ERIC Educational Resources Information Center

Hoong, Leong Yew; Guan, Tay Eng; Seng, Quek Khiok; Fwe, Yap Sook; Luen, Tong Cherng; Toh, Wei Yeng Karen; Chia, Alexander; Teck, Ong Yao

2014-01-01

The authors are a team of teachers and teacher educators who are deeply interested in helping mathematically-challenged students improve in their learning of mathematics. In Singapore, depending on their performance at the end of a nationwide Year 6 examination, students are channelled into three ability streams for Years 7 to 10: Express (60%),…

A Snowflake Project: Calculating, Analyzing, and Optimizing with the Koch Snowflake.

ERIC Educational Resources Information Center

Bolte, Linda A.

2002-01-01

Presents a project that addresses several components of the Algebra and Communication Standards for Grades 9-12 presented in Principles and Standards for School Mathematics (NCTM, 2000). Describes doing mathematical modeling and using the language of mathematics to express a recursive relationship in the perimeter and area of the Koch snowflake.…

Building Conceptual Understanding in a Remedial College Mathematics Classroom: A Study of Effectiveness

ERIC Educational Resources Information Center

Bachman, Rachel Marie

2013-01-01

This study investigated the effectiveness of two remedial mathematics courses that aimed to (a) present topics conceptually, (b) construct adequate schemata, and (c) introduce students to the culture of mathematics. The topics covered during the two courses were word problems, equivalence, variables and expressions, equations and inequalities, and…

Promoting the Understanding of Mathematics in Physics at Secondary Level

ERIC Educational Resources Information Center

Thompson, Alaric

2016-01-01

This article explores some of the common mathematical difficulties that 11- to 16-year-old students experience with respect to their learning of physics. The definition of "understanding" expressed in the article is in the sense of transferability of mathematical skills from topic to topic within physics as well as between the separate…

Fifty Years of A-Level Mathematics: Have Standards Changed?

ERIC Educational Resources Information Center

Jones, Ian; Wheadon, Chris; Humphries, Sara; Inglis, Matthew

2016-01-01

Advanced-level (A-level) mathematics is a high-profile qualification taken by many school leavers in England, Wales, Northern Ireland and around the world as preparation for university study. Concern has been expressed in these countries that standards in A-level mathematics have declined over time, and that school leavers enter university or the…

Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics

NASA Astrophysics Data System (ADS)

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-07-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit-reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science.

Simplification of Markov chains with infinite state space and the mathematical theory of random gene expression bursts.

PubMed

Jia, Chen

2017-09-01

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths. Furthermore, we apply our simplification approach to the standard Markov model of single-cell stochastic gene expression and provide a mathematical theory of random gene expression bursts. We give the precise mathematical conditions for the bursting kinetics of both mRNAs and proteins. It turns out that random bursts exactly correspond to the fast transition paths of the Markov model. This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the fundamental multiscale biochemical reaction kinetics of stochastic gene expression.

Simplification of Markov chains with infinite state space and the mathematical theory of random gene expression bursts

NASA Astrophysics Data System (ADS)

Jia, Chen

2017-09-01

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths. Furthermore, we apply our simplification approach to the standard Markov model of single-cell stochastic gene expression and provide a mathematical theory of random gene expression bursts. We give the precise mathematical conditions for the bursting kinetics of both mRNAs and proteins. It turns out that random bursts exactly correspond to the fast transition paths of the Markov model. This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the fundamental multiscale biochemical reaction kinetics of stochastic gene expression.

Predicting earthquakes by analyzing accelerating precursory seismic activity

USGS Publications Warehouse

Varnes, D.J.

1989-01-01

During 11 sequences of earthquakes that in retrospect can be classed as foreshocks, the accelerating rate at which seismic moment is released follows, at least in part, a simple equation. This equation (1) is {Mathematical expression},where {Mathematical expression} is the cumulative sum until time, t, of the square roots of seismic moments of individual foreshocks computed from reported magnitudes;C and n are constants; and tfis a limiting time at which the rate of seismic moment accumulation becomes infinite. The possible time of a major foreshock or main shock, tf,is found by the best fit of equation (1), or its integral, to step-like plots of {Mathematical expression} versus time using successive estimates of tfin linearized regressions until the maximum coefficient of determination, r2,is obtained. Analyzed examples include sequences preceding earthquakes at Cremasta, Greece, 2/5/66; Haicheng, China 2/4/75; Oaxaca, Mexico, 11/29/78; Petatlan, Mexico, 3/14/79; and Central Chile, 3/3/85. In 29 estimates of main-shock time, made as the sequences developed, the errors in 20 were less than one-half and in 9 less than one tenth the time remaining between the time of the last data used and the main shock. Some precursory sequences, or parts of them, yield no solution. Two sequences appear to include in their first parts the aftershocks of a previous event; plots using the integral of equation (1) show that the sequences are easily separable into aftershock and foreshock segments. Synthetic seismic sequences of shocks at equal time intervals were constructed to follow equation (1), using four values of n. In each series the resulting distributions of magnitudes closely follow the linear Gutenberg-Richter relation log N=a-bM, and the product n times b for each series is the same constant. In various forms and for decades, equation (1) has been used successfully to predict failure times of stressed metals and ceramics, landslides in soil and rock slopes, and volcanic eruptions. Results of more recent experiments and theoretical studies on crack propagation, fault mechanics, and acoustic emission can be closely reproduced by equation (1). Rate-process theory and continuum damage mechanics offer leads toward understanding the physical processes. ?? 1989 Birkha??user Verlag.

Diderot: a Domain-Specific Language for Portable Parallel Scientific Visualization and Image Analysis.

PubMed

Kindlmann, Gordon; Chiw, Charisee; Seltzer, Nicholas; Samuels, Lamont; Reppy, John

2016-01-01

Many algorithms for scientific visualization and image analysis are rooted in the world of continuous scalar, vector, and tensor fields, but are programmed in low-level languages and libraries that obscure their mathematical foundations. Diderot is a parallel domain-specific language that is designed to bridge this semantic gap by providing the programmer with a high-level, mathematical programming notation that allows direct expression of mathematical concepts in code. Furthermore, Diderot provides parallel performance that takes advantage of modern multicore processors and GPUs. The high-level notation allows a concise and natural expression of the algorithms and the parallelism allows efficient execution on real-world datasets.

Mathematical Astronomy in India

NASA Astrophysics Data System (ADS)

Plofker, Kim

Astronomy in South Asia's Sanskrit tradition, apparently originating in simple calendric computations regulating the timing of ancient ritual practices, expanded over the course of two or three millennia to include detailed spherical models, an endless variety of astrological systems, and academic mathematics in general. Assimilating various technical models, methods, and genres from the astronomy of neighboring cultures, Indian astronomers created new forms that were in turn borrowed by their foreign counterparts. Always recognizably related to the main themes of Eurasian geocentric mathematical astronomy, Indian astral science nonetheless maintained its culturally distinct character until Keplerian heliocentrism and Newtonian mechanics replaced it in colonial South Asia's academic mainstream.

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.

A simple, mass balance model of carbon flow in a controlled ecological life support system

NASA Technical Reports Server (NTRS)

Garland, Jay L.

1989-01-01

Internal cycling of chemical elements is a fundamental aspect of a Controlled Ecological Life Support System (CELSS). Mathematical models are useful tools for evaluating fluxes and reservoirs of elements associated with potential CELSS configurations. A simple mass balance model of carbon flow in CELSS was developed based on data from the CELSS Breadboard project at Kennedy Space Center. All carbon reservoirs and fluxes were calculated based on steady state conditions and modelled using linear, donor-controlled transfer coefficients. The linear expression of photosynthetic flux was replaced with Michaelis-Menten kinetics based on dynamical analysis of the model which found that the latter produced more adequate model output. Sensitivity analysis of the model indicated that accurate determination of the maximum rate of gross primary production is critical to the development of an accurate model of carbon flow. Atmospheric carbon dioxide was particularly sensitive to changes in photosynthetic rate. The small reservoir of CO2 relative to large CO2 fluxes increases the potential for volatility in CO2 concentration. Feedback control mechanisms regulating CO2 concentration will probably be necessary in a CELSS to reduce this system instability.

Characteristics of Viscoelastic Crustal Deformation Following a Megathrust Earthquake: Discrepancy Between the Apparent and Intrinsic Relaxation Time Constants

NASA Astrophysics Data System (ADS)

Fukahata, Yukitoshi; Matsu'ura, Mitsuhiro

2018-02-01

The viscoelastic deformation of an elastic-viscoelastic composite system is significantly different from that of a simple viscoelastic medium. Here, we show that complicated transient deformation due to viscoelastic stress relaxation after a megathrust earthquake can occur even in a very simple situation, in which an elastic surface layer (lithosphere) is underlain by a viscoelastic substratum (asthenosphere) under gravity. Although the overall decay rate of the system is controlled by the intrinsic relaxation time constant of the asthenosphere, the apparent decay time constant at each observation point is significantly different from place to place and generally much longer than the intrinsic relaxation time constant of the asthenosphere. It is also not rare that the sense of displacement rate is reversed during the viscoelastic relaxation. If we do not bear these points in mind, we may draw false conclusions from observed deformation data. Such complicated transient behavior can be explained mathematically from the characteristics of viscoelastic solution: for an elastic-viscoelastic layered half-space, the viscoelastic solution is expressed as superposition of three decaying components with different relaxation time constants that depend on wavelength.

A Primary Care Workload Production Model for Estimating Relative Value Unit Output

DTIC Science & Technology

2011-03-01

for Medicare and Medicaid Services, Office of the Actuary , National Health Statistics Group; and U.S. Department of Commerce, Bureau of Economic...The systematic variation in a relationship can be represented by a mathematical expression, whereas stochastic variation cannot. Further, stochastic...expressed mathematically as an equation, whereby a response variable Y is fitted to a function of “regressor variables and parameters” (SAS©, 2010). A

Mathematical formula recognition using graph grammar

NASA Astrophysics Data System (ADS)

Lavirotte, Stephane; Pottier, Loic

1998-04-01

This paper describes current results of Ofr, a system for extracting and understanding mathematical expressions in documents. Such a tool could be really useful to be able to re-use knowledge in scientific books which are not available in electronic form. We currently also study use of this system for direct input of formulas with a graphical tablet for computer algebra system softwares. Existing solutions for mathematical recognition have problems to analyze 2D expressions like vectors and matrices. This is because they often try to use extended classical grammar to analyze formulas, relatively to baseline. But a lot of mathematical notations do not respect rules for such a parsing and that is the reason why they fail to extend text parsing technic. We investigate graph grammar and graph rewriting as a solution to recognize 2D mathematical notations. Graph grammar provide a powerful formalism to describe structural manipulations of multi-dimensional data. The main two problems to solve are ambiguities between rules of grammar and construction of graph.

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.

"A Bad Head for Maths"? Constructions of Educability and Mathematics in Adult Students' Narrative Life Histories

ERIC Educational Resources Information Center

Siivonen, Päivi

2013-01-01

The article focuses on the social differences of educability constructed in Finnish general upper secondary school adult graduates' narratives on mathematics. Social class, gender, and age intertwine in the narratives that express the adult students' worries about their ability and competence to study and learn mathematics. Social differences of…

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).

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.

Advances and Computational Tools towards Predictable Design in Biological Engineering

PubMed Central

2014-01-01

The design process of complex systems in all the fields of engineering requires a set of quantitatively characterized components and a method to predict the output of systems composed by such elements. This strategy relies on the modularity of the used components or the prediction of their context-dependent behaviour, when parts functioning depends on the specific context. Mathematical models usually support the whole process by guiding the selection of parts and by predicting the output of interconnected systems. Such bottom-up design process cannot be trivially adopted for biological systems engineering, since parts function is hard to predict when components are reused in different contexts. This issue and the intrinsic complexity of living systems limit the capability of synthetic biologists to predict the quantitative behaviour of biological systems. The high potential of synthetic biology strongly depends on the capability of mastering this issue. This review discusses the predictability issues of basic biological parts (promoters, ribosome binding sites, coding sequences, transcriptional terminators, and plasmids) when used to engineer simple and complex gene expression systems in Escherichia coli. A comparison between bottom-up and trial-and-error approaches is performed for all the discussed elements and mathematical models supporting the prediction of parts behaviour are illustrated. PMID:25161694

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

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.

Exploring international gender differences in mathematics self-concept

PubMed Central

Goldman, Amy D.; Penner, Andrew M.

2013-01-01

This study provides an international perspective on mathematics by examnnng mathematics self-concept, achievement, and the desire to enter a career involving mathematics among eighth graders in 49 countries. Using data from the Trends in International Mathematics and Science Study, this study shows that self-concept in mathematics is more closely related to the desire to enter a career using mathematics than achievement is. Further, while gender differences in mathematics self-concept are smaller in more egalitarian countries, both girls and boys have lower mathematics self-concepts and less interest in mathematics careers in these countries. These findings reveal a policy paradox: policies aimed at training the next generation of STEM professionals often highlight the need to close the gender gap, but countries with smaller gender gaps have fewer boys and girls interested in mathematics-intensive careers. We conclude by highlighting the importance of disentangling instrumental and expressive aspects of gender inequality in STEM fields. PMID:27840545

Methods for Quantum Circuit Design and Simulation

DTIC Science & Technology

2010-03-01

cannot be deter- mined given the one output. Reversible gates, expressed mathematically, are unitary matrices. 16 3.3.1 PAULI Gates/Matrices Three...common single-qubit gates are expressed mathematically as Pauli matrices, which are 2x2 matrices. A 2x2 quantum gate can be applied to a single quantum...bit (a 2x1 column vector). The Pauli matrices are expressed as follows: X =   0 1 1 0   Y =   0 −i i 0   Z =   1 0 0 −1   (3.10) where i

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)

Dynamic Characteristics of Simple Cylindrical Hydraulic Engine Mount Utilizing Air Compressibility

NASA Astrophysics Data System (ADS)

Nakahara, Kazunari; Nakagawa, Noritoshi; Ohta, Katsutoshi

A cylindrical hydraulic engine mount with simple construction has been developed. This engine mount has a sub chamber formed by utilizing air compressibility without a diaphragm. A mathematical model of the mount is presented to predict non-linear dynamic characteristics in consideration of the effect of the excitation amplitude on the storage stiffness and loss factor. The mathematical model predicts experimental results well for the frequency responses of the storage stiffness and loss factor over the frequency range of 5 Hz to 60Hz. The effect of air volume and internal pressure on the dynamic characteristics is clarified by the analysis and dynamic characterization testing. The effectiveness of the cylindrical hydraulic engine mount on the reduction of engine shake is demonstrated for riding comfort through on-vehicle testing with a chassis dynamometer.

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.

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.

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.

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.

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 reality of Mathematics

NASA Astrophysics Data System (ADS)

Ligomenides, Panos A.

2009-05-01

The power of mathematics is discussed as a way of expressing reasoning, aesthetics and insight in symbolic non-verbal communication. The human culture of discovering mathematical ways of thinking in the enterprise of exploring the understanding of the nature and the evolution of our world through hypotheses, theories and experimental affirmation of the scientific notion of algorithmic and non-algorithmic [`]computation', is examined and commended upon.

A Cognitive Analysis of Developmental Mathematics Students' Errors and Misconceptions in Real Number Computations and Evaluating Algebraic Expressions

ERIC Educational Resources Information Center

Titus, Freddie

2010-01-01

Fifty percent of college-bound students graduate from high school underprepared for mathematics at the post-secondary level. As a result, thirty-five percent of college students take developmental mathematics courses. What is even more shocking is the high failure rate (ranging from 35 to 42 percent) of students enrolled in developmental…

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…

Interaction of Antiinflammatory Drugs with EPC Liposomes: Calorimetric Study in a Broad Concentration Range

PubMed Central

Matos, Carla; Lima, José L. C.; Reis, Salette; Lopes, António; Bastos, Margarida

2004-01-01

Isothermal titration calorimetry was used to characterize and quantify the partition of indomethacin and acemetacin between the bulk aqueous phase and the membrane of egg phosphatidylcholine vesicles. Significant electrostatic effects were observed due to binding of the charged drugs to the membrane, which implied the use of the Gouy-Chapman theory to calculate the interfacial concentrations. The binding/partition phenomenon was quantified in terms of the partition coefficient (Kp), and/or the equilibrium constant (Kb). Mathematical expressions were developed, either to encompass the electrostatic effects in the partition model, or to numerically relate partition coefficients and binding constants. Calorimetric titrations conducted under a lipid/drug ratio >100:1 lead to a constant heat release and were used to directly calculate the enthalpy of the process, ΔH, and indirectly, ΔG and ΔS. As the lipid/drug ratio decreased, the constancy of reaction enthalpy was tested in the fitting process. Under low lipid/drug ratio conditions simple partition was no longer valid and the interaction phenomenon was interpreted in terms of binding isotherms. A mathematical expression was deduced for quantification of the binding constants and the number of lipid molecules associated with one drug molecule. The broad range of concentrations used stressed the biphasic nature of the interaction under study. As the lipid/drug ratio was varied, the results showed that the interaction of both drugs does not present a unique behavior in all studied regimes: the extent of the interaction, as well as the binding stoichiometry, is affected by the lipid/drug ratio. The change in these parameters reflects the biphasic behavior of the interaction—possibly the consequence of a modification of the membrane's physical properties as it becomes saturated with the drug. PMID:14747330

Theoretical model of hardness anisotropy in brittle materials

NASA Astrophysics Data System (ADS)

Gao, Faming

2012-07-01

Anisotropy is prominent in the hardness test of single crystals. However, the anisotropic nature is not demonstrated quantitatively in previous hardness model. In this work, it is found that the electron transition energy per unit volume in the glide region and the orientation of glide region play critical roles in determining hardness value and hardness anisotropy for a single crystal material. We express the mathematical definition of hardness anisotropy through simple algebraic relations. The calculated Knoop hardnesses of the single crystals are in good agreement with observations. This theory, extended to polycrystalline materials by including hall-petch effect and quantum size effect, predicts that the polycrystalline diamond with low angle grain boundaries can be harder than single-crystal bulk diamond. Combining first-principles technique and the formula of hardness anisotropy the hardness of monoclinic M-carbon, orthorhombic W-carbon, Z-carbon, and T-carbon are predicted.

Use of the truncated shifted Pareto distribution in assessing size distribution of oil and gas fields

USGS Publications Warehouse

Houghton, J.C.

1988-01-01

The truncated shifted Pareto (TSP) distribution, a variant of the two-parameter Pareto distribution, in which one parameter is added to shift the distribution right and left and the right-hand side is truncated, is used to model size distributions of oil and gas fields for resource assessment. Assumptions about limits to the left-hand and right-hand side reduce the number of parameters to two. The TSP distribution has advantages over the more customary lognormal distribution because it has a simple analytic expression, allowing exact computation of several statistics of interest, has a "J-shape," and has more flexibility in the thickness of the right-hand tail. Oil field sizes from the Minnelusa play in the Powder River Basin, Wyoming and Montana, are used as a case study. Probability plotting procedures allow easy visualization of the fit and help the assessment. ?? 1988 International Association for Mathematical Geology.

Performance analysis of the lineal model for estimating the maximum power of a HCPV module in different climate conditions

NASA Astrophysics Data System (ADS)

Fernández, Eduardo F.; Almonacid, Florencia; Sarmah, Nabin; Mallick, Tapas; Sanchez, Iñigo; Cuadra, Juan M.; Soria-Moya, Alberto; Pérez-Higueras, Pedro

2014-09-01

A model based on easily obtained atmospheric parameters and on a simple lineal mathematical expression has been developed at the Centre of Advanced Studies in Energy and Environment in southern Spain. The model predicts the maximum power of a HCPV module as a function of direct normal irradiance, air temperature and air mass. Presently, the proposed model has only been validated in southern Spain and its performance in locations with different atmospheric conditions still remains unknown. In order to address this issue, several HCPV modules have been measured in two different locations with different climate conditions than the south of Spain: the Environment and Sustainability Institute in southern UK and the National Renewable Energy Center in northern Spain. Results show that the model has an adequate match between actual and estimated data with a RMSE lower than 3.9% at locations with different climate conditions.

Population modeling and its role in toxicological studies

USGS Publications Warehouse

Sauer, John R.; Pendleton, Grey W.; Hoffman, David J.; Rattner, Barnett A.; Burton, G. Allen; Cairns, John

1995-01-01

A model could be defined as any abstraction from reality that is used to provide some insight into the real system. In this discussion, we will use a more specific definition that a model is a set of rules or assumptions, expressed as mathematical equations, that describe how animals survive and reproduce, including the external factors that affect these characteristics. A model simplifies a system, retaining essential components while eliminating parts that are not of interest. ecology has a rich history of using models to gain insight into populations, often borrowing both model structures and analysis methods from demographers and engineers. Much of the development of the models has been a consequence of mathematicians and physicists seeing simple analogies between their models and patterns in natural systems. Consequently, one major application of ecological modeling has been to emphasize the analysis of dynamics of often complex models to provide insight into theoretical aspects of ecology.1

New method for calculating a mathematical expression for streamflow recession

USGS Publications Warehouse

Rutledge, Albert T.

1991-01-01

An empirical method has been devised to calculate the master recession curve, which is a mathematical expression for streamflow recession during times of negligible direct runoff. The method is based on the assumption that the storage-delay factor, which is the time per log cycle of streamflow recession, varies linearly with the logarithm of streamflow. The resulting master recession curve can be nonlinear. The method can be executed by a computer program that reads a data file of daily mean streamflow, then allows the user to select several near-linear segments of streamflow recession. The storage-delay factor for each segment is one of the coefficients of the equation that results from linear least-squares regression. Using results for each recession segment, a mathematical expression of the storage-delay factor as a function of the log of streamflow is determined by linear least-squares regression. The master recession curve, which is a second-order polynomial expression for time as a function of log of streamflow, is then derived using the coefficients of this function.

Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth

PubMed Central

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

2014-01-01

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

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

PubMed

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

2014-08-01

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

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)

Mathematical Model of Bubble Sloshing Dynamics for Cryogenic Liquid Helium in Orbital Spacecraft Dewar Container

NASA Technical Reports Server (NTRS)

Hung, R. J.; Pan, H. L.

1995-01-01

A generalized mathematical model is investigated of sloshing dynamics for dewar containers, partially filled with a liquid of cryogenic superfluid helium 2, driven by both gravity gradient and jitter accelerations applicable to two types of scientific spacecrafts, which are eligible to carry out spinning motion and/or slew motion to perform scientific observations during normal spacecraft operation. Two examples are given for the Gravity Probe-B (GP-B) with spinning motion, and the Advanced X-Ray Astrophysics Facility-Spectroscopy (AXAF-S) with slew motion, which are responsible for the sloshing dynamics. Explicit mathematical expressions for the modelling of sloshing dynamics to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics will be based on the noninertial frame spacecraft bound coordinate, and we will solve the time-dependent three-dimensional formulations of partial differential equations subject to initial and boundary conditions. Explicit mathematical expressions of boundary conditions lo cover capillary force effects on the liquid-vapor interface in microgravity environments are also derived. Results of the simulations of the mathematical model are illustrated.

Signs of In/Equality: A History of Representation and Reform in Elementary School Mathematics from the 1950s to the Present

ERIC Educational Resources Information Center

Diaz, Jennifer DeNet

2014-01-01

This study begins with the assumption that the equal sign (=) in elementary school mathematics is not merely a symbol of mathematical logic. Rather, as the equal sign (=) appears in the school math curriculum, it orders children's thinking about equality by assigning identities to things of the world--as expressions of equivalences and…

Interactions between Mathematics and Physics: The History of the Concept of Function--Teaching with and about Nature of Mathematics

ERIC Educational Resources Information Center

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-01-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another…

Implementing digital holograms to create and measure complex-plane optical fields

NASA Astrophysics Data System (ADS)

Dudley, Angela; Majola, Nombuso; Chetty, Naven; Forbes, Andrew

2016-02-01

The coherent superposition of a Gaussian beam with an optical vortex can be mathematically described to occupy the complex plane. We provide a simple analogy between the mathematics, in the form of the complex plane, and the visual representation of these two superimposed optical fields. We provide detailed instructions as to how one can experimentally produce, measure, and control these fields with the use of digital holograms encoded on a spatial light modulator.

Mathematics beliefs and achievement of a national sample of Native American students: results from the Trends in International Mathematics and Science Study (TIMSS) 2003 United States assessment.

PubMed

House, J Daniel

2009-04-01

Recent mathematics assessment findings indicate that Native American students tend to score below students of the ethnic majority. Findings suggest that students' beliefs about mathematics are significantly related to achievement outcomes. This study examined relations between self-beliefs and mathematics achievement for a national sample of 130 Grade 8 Native American students from the Trends in International Mathematics and Science Study (TIMSS) 2003 United States sample of (M age = 14.2 yr., SD = 0.5). Multiple regression indicated several significant relations of mathematics beliefs with achievement and accounted for 26.7% of the variance in test scores. Students who earned high test scores tended to hold more positive beliefs about their ability to learn mathematics quickly, while students who earned low scores expressed negative beliefs about their ability to learn new mathematics topics.

Mathematics is always invisible, Professor Dowling

NASA Astrophysics Data System (ADS)

Cable, John

2015-09-01

This article provides a critical evaluation of a technique of analysis, the Social Activity Method, recently offered by Dowling (2013) as a `gift' to mathematics education. The method is found to be inadequate, firstly, because it employs a dichotomy (between `expression' and `content') instead of a finer analysis (into symbols, concepts and setting or phenomena), and, secondly, because the distinction between `public' and `esoteric' mathematics, although interesting, is allowed to obscure the structure of the mathematics itself. There is also criticism of what Dowling calls the `myth of participation', which denies the intimate links between mathematics and the rest of the universe that lie at the heart of mathematical pedagogy. Behind all this lies Dowling's `essentially linguistic' conception of mathematics, which is criticised on the dual ground that it ignores the chastening experience of formalism in mathematical philosophy and that linguistics itself has taken a wrong turn and ignores lessons that might be learnt from mathematics education.

Introducing Seismic Tomography with Computational Modeling

NASA Astrophysics Data System (ADS)

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

2011-12-01

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

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.

The research of statistical properties of colorimetric features of screens with a three-component color formation principle

NASA Astrophysics Data System (ADS)

Zharinov, I. O.; Zharinov, O. O.

2017-12-01

The problem of the research is concerned with quantitative analysis of influence of technological variation of the screen color profile parameters on chromaticity coordinates of the displayed image. Some mathematical expressions which approximate the two-dimensional distribution of chromaticity coordinates of an image, which is displayed on the screen with a three-component color formation principle were proposed. Proposed mathematical expressions show the way to development of correction techniques to improve reproducibility of the colorimetric features of displays.

Using online handwriting and audio streams for mathematical expressions recognition: a bimodal approach

NASA Astrophysics Data System (ADS)

Medjkoune, Sofiane; Mouchère, Harold; Petitrenaud, Simon; Viard-Gaudin, Christian

2013-01-01

The work reported in this paper concerns the problem of mathematical expressions recognition. This task is known to be a very hard one. We propose to alleviate the difficulties by taking into account two complementary modalities. The modalities referred to are handwriting and audio ones. To combine the signals coming from both modalities, various fusion methods are explored. Performances evaluated on the HAMEX dataset show a significant improvement compared to a single modality (handwriting) based system.

Projecting 2D gene expression data into 3D and 4D space.

PubMed

Gerth, Victor E; Katsuyama, Kaori; Snyder, Kevin A; Bowes, Jeff B; Kitayama, Atsushi; Ueno, Naoto; Vize, Peter D

2007-04-01

Video games typically generate virtual 3D objects by texture mapping an image onto a 3D polygonal frame. The feeling of movement is then achieved by mathematically simulating camera movement relative to the polygonal frame. We have built customized scripts that adapt video game authoring software to texture mapping images of gene expression data onto b-spline based embryo models. This approach, known as UV mapping, associates two-dimensional (U and V) coordinates within images to the three dimensions (X, Y, and Z) of a b-spline model. B-spline model frameworks were built either from confocal data or de novo extracted from 2D images, once again using video game authoring approaches. This system was then used to build 3D models of 182 genes expressed in developing Xenopus embryos and to implement these in a web-accessible database. Models can be viewed via simple Internet browsers and utilize openGL hardware acceleration via a Shockwave plugin. Not only does this database display static data in a dynamic and scalable manner, the UV mapping system also serves as a method to align different images to a common framework, an approach that may make high-throughput automated comparisons of gene expression patterns possible. Finally, video game systems also have elegant methods for handling movement, allowing biomechanical algorithms to drive the animation of models. With further development, these biomechanical techniques offer practical methods for generating virtual embryos that recapitulate morphogenesis.

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.

Post-transcriptional bursting in genes regulated by small RNA molecules

NASA Astrophysics Data System (ADS)

Rodrigo, Guillermo

2018-03-01

Gene expression programs in living cells are highly dynamic due to spatiotemporal molecular signaling and inherent biochemical stochasticity. Here we study a mechanism based on molecule-to-molecule variability at the RNA level for the generation of bursts of protein production, which can lead to heterogeneity in a cell population. We develop a mathematical framework to show numerically and analytically that genes regulated post transcriptionally by small RNA molecules can exhibit such bursts due to different states of translation activity (on or off), mostly revealed in a regime of few molecules. We exploit this framework to compare transcriptional and post-transcriptional bursting and also to illustrate how to tune the resulting protein distribution with additional post-transcriptional regulations. Moreover, because RNA-RNA interactions are predictable with an energy model, we define the kinetic constants of on-off switching as functions of the two characteristic free-energy differences of the system, activation and formation, with a nonequilibrium scheme. Overall, post-transcriptional bursting represents a distinctive principle linking gene regulation to gene expression noise, which highlights the importance of the RNA layer beyond the simple information transfer paradigm and significantly contributes to the understanding of the intracellular processes from a first-principles perspective.

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

NASA Astrophysics Data System (ADS)

Bartley, Sarah R.; Ingram, Naomi

2017-12-01

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

Mathematics and engineering in real life through mathematical competitions

NASA Astrophysics Data System (ADS)

More, M.

2018-02-01

We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build curiosity and give an understanding of mathematical applications in real life. Participation in the competition has been classified under four broad categories. Student can showcase their findings in various forms of expression like model, poster, soft presentation, animation, live performance, art and poetry. The basic focus of the competition is on using open source computation tools and modern technology, to emphasize the relationship of mathematical concepts with engineering applications in real life.

Generalization across Domains: The Relating-Forming-Extending Generalization Framework

ERIC Educational Resources Information Center

Ellis, Amy; Tillema, Erik; Lockwood, Elise; Moore, Kevin

2017-01-01

Generalization is a critical aspect of doing mathematics, with policy makers recommending that it be a central component of mathematics instruction at all levels. This recommendation poses serious challenges, however, given researchers consistently identifying students' difficulties in creating and expressing normative mathematical…

The mathematical research for the Kuramoto model of the describing neuronal synchrony in the brain

NASA Astrophysics Data System (ADS)

Lin, Chang; Lin, Mai-mai

2009-08-01

The Kuramoto model of the describing neuronal synchrony is mathematically investigated in the brain. A general analytical solutions (the most sententious description) for the Kuramoto model, incorporating the inclusion of a Ki,j (t) term to represent time-varying coupling strengths, have been obtained by using the precise mathematical approach. We derive an exact analytical expression, opening out the connotative and latent linear relation, for the mathematical character of the phase configurations in the Kuramoto model of the describing neuronal synchrony in the brain.

The Written Expression Abilities of Adolescents with Attention-Deficit/Hyperactivity Disorder

PubMed Central

Molitor, Stephen J.; Langberg, Joshua M.; Evans, Steve W.

2016-01-01

Students with Attention-Deficit/Hyperactivity Disorder (ADHD) often experience deficits in academic achievement. Written expression abilities in this population have not been extensively studied but existing prevalence estimates suggest that rates of comorbid writing underachievement may be substantially higher than rates of comorbid reading and mathematics underachievement. The current study examined written expression abilities in a school-based sample of 326 middle school age students with ADHD. The prevalence of written expression impairment, the associations between written expression and academic outcomes, and specific patterns of written expression were investigated. Students with ADHD in this sample experienced written expression impairment (17.2% – 22.4%) at a similar rate to reading impairment (17.0% – 24.3%) and at a slightly lower rate than mathematics impairment (24.7% – 36.3%). Students’ written expression abilities were significantly associated with school grades and parent ratings of academic functioning, above and beyond the influence of intelligence. Analyses of patterns suggest that students with ADHD exhibit greater deficits in written expression tasks requiring organization and attention to detail, especially in the context of a complex task. PMID:26802631

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.

What is rate? Does context or representation matter?

NASA Astrophysics Data System (ADS)

Herbert, Sandra; Pierce, Robyn

2011-12-01

Rate is an important, but difficult, mathematical concept. Despite more than 20 years of research, especially with calculus students, difficulties are reported with this concept. This paper reports the results from analysis of data from 20 Australian Grade 10 students. Interviews targeted students' conceptions of rate, focussing on the influence of representation and context on their expression of their understanding of rate. This analysis shows that different representations of functions provide varying levels of rate-related information for individual students. Understandings of rate in one representation or context are not necessarily transferred to another representation or context. Rate is an important, but commonly misunderstood, mathematical concept with many everyday applications (Swedosh, Dowsey, Caruso, Flynn, & Tynan, 2007). It is a complicated concept comprising many interwoven ideas such as the ratio of two numeric, measurable quantities but in a context where both quantities are changing. In mathematics classes, this is commonly expressed as change in the dependent variable resulting from a unit change in the independent variable, and variously described as constant or variable rate; average or instantaneous rate. In addition, rate may be seen as a purely abstract mathematical notion or embedded in the understanding of real-world applications. This paper explores the research question: Are students' expressions of their conceptions of rate affected by either context or mathematical representation? This question was part of a larger study (Herbert, 2010) conducted with Grade 10 students from the Australian state of Victoria.

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 ...

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.

Exponential growth kinetics for Polyporus versicolor and Pleurotus ostreatus in submerged culture

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

Carroad, P.A.; Wilke, C.R.

1977-04-01

Simple mathematical models for a batch culture of pellet-forming fungi in submerged culture were tested on growth data for Polyporus versicolor (ATCC 12679) and Pleurotus ostreatus (ATCC 9415). A kinetic model based on a growth rate proportional to the two-thirds power of the cell mass was shown to be satisfactory. A model based on a growth rate directly proportional to the cell mass fitted the data equally well, however, and may be preferable because of mathematical simplicity.

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.

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

Rethinking the connection between working memory and language impairment.

PubMed

Archibald, Lisa M D; Harder Griebeling, Katherine

2016-05-01

Working memory deficits have been found for children with specific language impairment (SLI) on tasks imposing increasing short-term memory load with or without additional, consistent (and simple) processing load. To examine the processing function of working memory in children with low language (LL) by employing tasks imposing increasing processing loads with constant storage demands individually adjusted based on each participant's short-term memory capacity. School-age groups with LL (n = 17) and typical language with either average (n = 28) or above-average nonverbal intelligence (n = 15) completed complex working memory-span tasks varying processing load while keeping storage demands constant, varying storage demands while keeping processing load constant, simple storage-span tasks, and measures of language and nonverbal intelligence. Teachers completed questionnaires about cognition and learning. Significantly lower scores were found for the LL than either matched group on storage-based tasks, but no group differences were found on the tasks varying processing load. Teachers' ratings of oral expression and mathematics abilities discriminated those who did or did not complete the most challenging cognitive tasks. The results implicate a deficit in the phonological storage but not in the central executive component of working memory for children with LL. Teacher ratings may reveal personality traits related to perseverance of effort in cognitive research. © 2015 Royal College of Speech and Language Therapists.

Analytic derivation of bacterial growth laws from a simple model of intracellular chemical dynamics.

PubMed

Pandey, Parth Pratim; Jain, Sanjay

2016-09-01

Experiments have found that the growth rate and certain other macroscopic properties of bacterial cells in steady-state cultures depend upon the medium in a surprisingly simple manner; these dependencies are referred to as 'growth laws'. Here we construct a dynamical model of interacting intracellular populations to understand some of the growth laws. The model has only three population variables: an amino acid pool, a pool of enzymes that transport an external nutrient and produce the amino acids, and ribosomes that catalyze their own and the enzymes' production from the amino acids. We assume that the cell allocates its resources between the enzyme sector and the ribosomal sector to maximize its growth rate. We show that the empirical growth laws follow from this assumption and derive analytic expressions for the phenomenological parameters in terms of the more basic model parameters. Interestingly, the maximization of the growth rate of the cell as a whole implies that the cell allocates resources to the enzyme and ribosomal sectors in inverse proportion to their respective 'efficiencies'. The work introduces a mathematical scheme in which the cellular growth rate can be explicitly determined and shows that two large parameters, the number of amino acid residues per enzyme and per ribosome, are useful for making approximations.

Validation of DNA-based identification software by computation of pedigree likelihood ratios.

PubMed

Slooten, K

2011-08-01

Disaster victim identification (DVI) can be aided by DNA-evidence, by comparing the DNA-profiles of unidentified individuals with those of surviving relatives. The DNA-evidence is used optimally when such a comparison is done by calculating the appropriate likelihood ratios. Though conceptually simple, the calculations can be quite involved, especially with large pedigrees, precise mutation models etc. In this article we describe a series of test cases designed to check if software designed to calculate such likelihood ratios computes them correctly. The cases include both simple and more complicated pedigrees, among which inbred ones. We show how to calculate the likelihood ratio numerically and algebraically, including a general mutation model and possibility of allelic dropout. In Appendix A we show how to derive such algebraic expressions mathematically. We have set up these cases to validate new software, called Bonaparte, which performs pedigree likelihood ratio calculations in a DVI context. Bonaparte has been developed by SNN Nijmegen (The Netherlands) for the Netherlands Forensic Institute (NFI). It is available free of charge for non-commercial purposes (see www.dnadvi.nl for details). Commercial licenses can also be obtained. The software uses Bayesian networks and the junction tree algorithm to perform its calculations. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.

A simple method to evaluate the number of bradyrhizobia on soybean seeds and its implication on inoculant quality control

PubMed Central

2011-01-01

Soybean seeds are non-sterile and their bacterial population interferes with the enumeration of beneficial bacteria, making it difficult to assess survival under different conditions. Within this context, the principal aims of this work were: (1) to improve a selective media for the enumeration of B. japonicum recovered from inoculated soybean seeds; (2) to establish the most representative mathematical function for B. japonicum mortality on soybean seeds after inoculation; (3) to evaluate if environmental or physiological conditions modify B. japonicum mortality on soybean seeds; and (4) to create a new protocol for quality control of soybean inoculants. We successfully evaluated the combination of pentachloronitrobenzene and vancomycin added to the yeast-mannitol medium to inhibit most fungi and Gram-positive soybean microbiota, thus producing reliable counts of B. japonicum from inoculated soybean seeds. Percentages of recovery and survival factors were obtained and used to construct a two-phase exponential decay non-linear regression function. High temperature and desiccation decreased these parameters, while the optimization of temperature and the use of osmoprotective compounds with inoculants increased them. The use of this protocol minimized heterogeneity between experiments and may be considered more reliable than the simple expression of direct colony count of bacteria recovered from seeds. PMID:21906377

A bio-physical basis of mathematics in synaptic function of the nervous system: a theory.

PubMed

Dempsher, J

1980-01-01

The purpose of this paper is to present a bio-physical basis of mathematics. The essence of the theory is that function in the nervous system is mathematical. The mathematics arises as a result of the interaction of energy (a wave with a precise curvature in space and time) and matter (a molecular or ionic structure with a precise form in space and time). In this interaction, both energy and matter play an active role. That is, the interaction results in a change in form of both energy and matter. There are at least six mathematical operations in a simple synaptic region. It is believed the form of both energy and matter are specific, and their interaction is specific, that is, function in most of the 'mind' and placed where it belongs - in nature and the synaptic regions of the nervous system; it results in both places from a precise interaction between energy (in a precise form) and matter ( in a precise structure).

Analytical drafting curves provide exact equations for plotted data

NASA Technical Reports Server (NTRS)

Stewart, R. B.

1967-01-01

Analytical drafting curves provide explicit mathematical expressions for any numerical data that appears in the form of graphical plots. The curves each have a reference coordinate axis system indicated on the curve as well as the mathematical equation from which the curve was generated.

An Out-of-Math Experience: Einstein, Relativity, and the Developmental Mathematics Student.

ERIC Educational Resources Information Center

Fiore, Greg

2000-01-01

Discusses Einstein's special relativity theory and some of the developmental mathematics involved. Presents motivational classroom materials used in discussing relative-motion problems, evaluating a radical expression, graphing with asymptotes, interpreting a graph, studying variation, and solving literal and radical equations. (KHR)

Variables in Elementary Mathematics Education

ERIC Educational Resources Information Center

Brizuela, Bárbara M.

2016-01-01

In this article, I analyze episodes from two third-grade classrooms drawn from a larger classroom teaching experiment to explore how these students began to incorporate nonnumerical symbols in their mathematical expressions when asked to represent indeterminate quantities. The article addresses two research questions: What understandings did these…

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.

Organizing principles as tools for bridging the gap between system theory and biological experimentation.

PubMed

Mekios, Constantinos

2016-04-01

Twentieth-century theoretical efforts towards the articulation of general system properties came short of having the significant impact on biological practice that their proponents envisioned. Although the latter did arrive at preliminary mathematical formulations of such properties, they had little success in showing how these could be productively incorporated into the research agenda of biologists. Consequently, the gap that kept system-theoretic principles cut-off from biological experimentation persisted. More recently, however, simple theoretical tools have proved readily applicable within the context of systems biology. In particular, examples reviewed in this paper suggest that rigorous mathematical expressions of design principles, imported primarily from engineering, could produce experimentally confirmable predictions of the regulatory properties of small biological networks. But this is not enough for contemporary systems biologists who adopt the holistic aspirations of early systemologists, seeking high-level organizing principles that could provide insights into problems of biological complexity at the whole-system level. While the presented evidence is not conclusive about whether this strategy could lead to the realization of the lofty goal of a comprehensive explanatory integration, it suggests that the ongoing quest for organizing principles is pragmatically advantageous for systems biologists. The formalisms postulated in the course of this process can serve as bridges between system-theoretic concepts and the results of molecular experimentation: they constitute theoretical tools for generalizing molecular data, thus producing increasingly accurate explanations of system-wide phenomena.

An innovative method for coordinate measuring machine one-dimensional self-calibration with simplified experimental process.

PubMed

Fang, Cheng; Butler, David Lee

2013-05-01

In this paper, an innovative method for CMM (Coordinate Measuring Machine) self-calibration is proposed. In contrast to conventional CMM calibration that relies heavily on a high precision reference standard such as a laser interferometer, the proposed calibration method is based on a low-cost artefact which is fabricated with commercially available precision ball bearings. By optimizing the mathematical model and rearranging the data sampling positions, the experimental process and data analysis can be simplified. In mathematical expression, the samples can be minimized by eliminating the redundant equations among those configured by the experimental data array. The section lengths of the artefact are measured at arranged positions, with which an equation set can be configured to determine the measurement errors at the corresponding positions. With the proposed method, the equation set is short of one equation, which can be supplemented by either measuring the total length of the artefact with a higher-precision CMM or calibrating the single point error at the extreme position with a laser interferometer. In this paper, the latter is selected. With spline interpolation, the error compensation curve can be determined. To verify the proposed method, a simple calibration system was set up on a commercial CMM. Experimental results showed that with the error compensation curve uncertainty of the measurement can be reduced to 50%.

Application of simple mathematical expressions to relate the half-lives of xenobiotics in rats to values in humans.

PubMed

Ward, Keith W; Erhardt, Paul; Bachmann, Kenneth

2005-01-01

Previous publications from GlaxoSmithKline and University of Toledo laboratories convey our independent attempts to predict the half-lives of xenobiotics in humans using data obtained from rats. The present investigation was conducted to compare the performance of our published models against a common dataset obtained by merging the two sets of rat versus human half-life (hHL) data previously used by each laboratory. After combining data, mathematical analyses were undertaken by deploying both of our previous models, namely the use of an empirical algorithm based on a best-fit model and the use of rat-to-human liver blood flow ratios as a half-life correction factor. Both qualitative and quantitative analyses were performed, as well as evaluation of the impact of molecular properties on predictability. The merged dataset was remarkably diverse with respect to physiochemical and pharmacokinetic (PK) properties. Application of both models revealed similar predictability, depending upon the measure of stipulated accuracy. Certain molecular features, particularly rotatable bond count and pK(a), appeared to influence the accuracy of prediction. This collaborative effort has resulted in an improved understanding and appreciation of the value of rats to serve as a surrogate for the prediction of xenobiotic half-lives in humans when clinical pharmacokinetic studies are not possible or practicable.

Qualitative-Modeling-Based Silicon Neurons and Their Networks

PubMed Central

Kohno, Takashi; Sekikawa, Munehisa; Li, Jing; Nanami, Takuya; Aihara, Kazuyuki

2016-01-01

The ionic conductance models of neuronal cells can finely reproduce a wide variety of complex neuronal activities. However, the complexity of these models has prompted the development of qualitative neuron models. They are described by differential equations with a reduced number of variables and their low-dimensional polynomials, which retain the core mathematical structures. Such simple models form the foundation of a bottom-up approach in computational and theoretical neuroscience. We proposed a qualitative-modeling-based approach for designing silicon neuron circuits, in which the mathematical structures in the polynomial-based qualitative models are reproduced by differential equations with silicon-native expressions. This approach can realize low-power-consuming circuits that can be configured to realize various classes of neuronal cells. In this article, our qualitative-modeling-based silicon neuron circuits for analog and digital implementations are quickly reviewed. One of our CMOS analog silicon neuron circuits can realize a variety of neuronal activities with a power consumption less than 72 nW. The square-wave bursting mode of this circuit is explained. Another circuit can realize Class I and II neuronal activities with about 3 nW. Our digital silicon neuron circuit can also realize these classes. An auto-associative memory realized on an all-to-all connected network of these silicon neurons is also reviewed, in which the neuron class plays important roles in its performance. PMID:27378842

Development of Energy Concepts in Introductory Physics Courses.

ERIC Educational Resources Information Center

Arons, Arnold B.

1999-01-01

Believes that a student's understanding of energy concepts can be enhanced by introducing and using the concept of internal energy by articulating the first law of thermodynamics in a simple, phenomenological form without mathematical encumbrances. (Author/CCM)

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.

[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)

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.

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.

Development of an algorithm for improving quality and information processing capacity of MathSpeak synthetic speech renderings.

PubMed

Isaacson, M D; Srinivasan, S; Lloyd, L L

2010-01-01

MathSpeak is a set of rules for non speaking of mathematical expressions. These rules have been incorporated into a computerised module that translates printed mathematics into the non-ambiguous MathSpeak form for synthetic speech rendering. Differences between individual utterances produced with the translator module are difficult to discern because of insufficient pausing between utterances; hence, the purpose of this study was to develop an algorithm for improving the synthetic speech rendering of MathSpeak. To improve synthetic speech renderings, an algorithm for inserting pauses was developed based upon recordings of middle and high school math teachers speaking mathematic expressions. Efficacy testing of this algorithm was conducted with college students without disabilities and high school/college students with visual impairments. Parameters measured included reception accuracy, short-term memory retention, MathSpeak processing capacity and various rankings concerning the quality of synthetic speech renderings. All parameters measured showed statistically significant improvements when the algorithm was used. The algorithm improves the quality and information processing capacity of synthetic speech renderings of MathSpeak. This increases the capacity of individuals with print disabilities to perform mathematical activities and to successfully fulfill science, technology, engineering and mathematics academic and career objectives.

A Cognitive Analysis of Students’ Mathematical Communication Ability on Geometry

NASA Astrophysics Data System (ADS)

Sari, D. S.; Kusnandi, K.; Suhendra, S.

2017-09-01

This study aims to analyze the difficulties of mathematical communication ability of students in one of secondary school on “three-dimensional space” topic. This research conducted by using quantitative approach with descriptive method. The population in this research was all students of that school and the sample was thirty students that was chosen by purposive sampling technique. Data of mathematical communication were collected through essay test. Furthermore, the data were analyzed with a descriptive way. The results of this study indicate that the percentage of achievement of student mathematical communication indicators as follows 1) Stating a situation, ideas, and mathematic correlation into images, graphics, or algebraic expressions is 35%; 2) Stating daily experience into a mathematic language / symbol, or a mathematic model is 35%; and 3) Associating images or diagrams into mathematical ideas is 53.3%. Based on the percentage of achievement on each indicator, it can be concluded that the level of achievement of students’ mathematical communication ability is still low. It can be caused the students were not used to convey or write their mathematical ideas systematically. Therefore students’ mathematical communication ability need to be improved.

An Objectivist Critique of Relativism in Mathematics Education

NASA Astrophysics Data System (ADS)

Rowlands, Stuart; Graham, Ted; Berry, John

Many constructivists tag as `absolutist' references to mathematics as an abstract body of knowledge, and stake-out the moral high-ground with the argument that mathematics is not only utilised oppressively but that mathematics is, in-itself, oppressive. With much reference to Ernest's (1991) Philosophy of Mathematics Education this tag has been justified on the grounds that if mathematics is a social-cultural creation that is mutable and fallible then it must be social acceptance that confers the objectivity of mathematics. This paper argues that mathematics, albeit a social-cultural creation that is mutable and fallible, is a body of knowledge the objectivity of which is independent of origin or social acceptance. Recently, Ernest (1998) has attempted to express social constructivism as a philosophy of mathematics and has included the category of logical necessity in his elaboration of the objectivity of mathematics. We argue that this inclusion of logical necessity not only represents a U-turn, but that the way in which Ernest has included this category is an attempt to maintain his earlier position that it is social acceptance that confers the objectivity of mathematics.

An analysis of primary school students’ representational ability in mathematics based on gender perspective

NASA Astrophysics Data System (ADS)

Kowiyah; Mulyawati, I.

2018-01-01

Mathematic representation is one of the basic mathematic skills that allows students to communicate their mathematic ideas through visual realities such as pictures, tables, mathematic expressions and mathematic equities. The present research aims at: 1) analysing students’ mathematic representation ability in solving mathematic problems and 2) examining the difference of students’ mathematic ability based on their gender. A total of sixty primary school students participated in this study comprising of thirty males and thirty females. Data required in this study were collected through mathematic representation tests, interviews and test evaluation rubric. Findings of this study showed that students’ mathematic representation of visual realities (image and tables) was reported higher at 62.3% than at in the form of description (or statement) at 8.6%. From gender perspective, male students performed better than the females at action planning stage. The percentage of males was reported at 68% (the highest), 33% (medium) and 21.3% (the lowest) while the females were at 36% (the highest), 37.7% (medium) and 32.6% (the lowest).

Insights into Fourier Synthesis and Analysis: Part 2--A Simplified Mathematics.

ERIC Educational Resources Information Center

Moore, Guy S. M.

1988-01-01

Introduced is an analysis of a waveform into its Fourier components. Topics included are simplified analysis of a square waveform, a triangular waveform, half-wave rectified alternating current (AC), and impulses. Provides the mathematical expression and simplified analysis diagram of each waveform. (YP)

Instructional Gaming: Using Technology to Support Early Mathematical Proficiency

ERIC Educational Resources Information Center

Nelson-Walker, Nancy J.; Doabler, Christian T.; Fien, Hank; Gause, Marshall; Baker, Scott K.; Clarke, Ben

2013-01-01

Widespread concern has been expressed about the persistent low mathematics achievement of students in the US, particularly for students from low-income and minority backgrounds and students with disabilities. Instructional gaming technology, when designed and fictionalized well, has the potential to improve the motivation and mathematics…

How to Teach Verbal Problems

ERIC Educational Resources Information Center

Dahmus, Maurice E.

1970-01-01

Presents a technique for teaching the lower ninety percent in mathematics. Concentrates on converting English statements, both expressed and implied, into one or many mathematical statements. Emphasis on translating in a direct, piecemeal, pure, and complete manner (DPPC). This method differs from others in that it is concrete rather than…

Assessment of Student Memo Assignments in Management Science

ERIC Educational Resources Information Center

Williams, Julie Ann Stuart; Stanny, Claudia J.; Reid, Randall C.; Hill, Christopher J.; Rosa, Katie Martin

2015-01-01

Frequently in Management Science courses, instructors focus primarily on teaching students the mathematics of linear programming models. However, the ability to discuss mathematical expressions in business terms is an important professional skill. The authors present an analysis of student abilities to discuss management science concepts through…

Narrative assessment: making mathematics learning visible in early childhood settings

NASA Astrophysics Data System (ADS)

Anthony, Glenda; McLachlan, Claire; Lim Fock Poh, Rachel

2015-09-01

Narratives that capture children's learning as they go about their day-to-day activities are promoted as a powerful assessment tool within early childhood settings. However, in the New Zealand context, there is increasing concern that learning stories—the preferred form of narrative assessment—currently downplay domain knowledge. In this paper, we draw on data from 13 teacher interviews and samples of 18 children's learning stories to examine how mathematics is made visible within learning stories. Despite appreciating that mathematics is embedded in a range of everyday activities within the centres, we found that the nature of a particular activity appeared to influence `how' and `what' the teachers chose to document as mathematics learning. Many of the teachers expressed a preference to document and analyse mathematics learning that occurred within explicit mathematics activities rather than within play that involves mathematics. Our concern is that this restricted documentation of mathematical activity could potentially limit opportunities for mathematics learning both in the centre and home settings.

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.

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.

Historical mathematics in the French eighteenth century.

PubMed

Richards, Joan L

2006-12-01

At least since the seventeenth century, the strange combination of epistemological certainty and ontological power that characterizes mathematics has made it a major focus of philosophical, social, and cultural negotiation. In the eighteenth century, all of these factors were at play as mathematical thinkers struggled to assimilate and extend the analysis they had inherited from the seventeenth century. A combination of educational convictions and historical assumptions supported a humanistic mathematics essentially defined by its flexibility and breadth. This mathematics was an expression of l'esprit humain, which was unfolding in a progressive historical narrative. The French Revolution dramatically altered the historical and educational landscapes that had supported this eighteenth-century approach, and within thirty years Augustin Louis Cauchy had radically reconceptualized and restructured mathematics to be rigorous rather than narrative.

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.

Undergraduate Mathematics Students' Understanding of the Concept of Function

ERIC Educational Resources Information Center

Bardini, Caroline; Pierce, Robyn; Vincent, Jill; King, Deborah

2014-01-01

Concern has been expressed that many commencing undergraduate mathematics students have mastered skills without conceptual understanding. A pilot study carried out at a leading Australian university indicates that a significant number of students, with high tertiary entrance ranks, have very limited understanding of the concept of function,…

Confidence and Competence with Mathematical Procedures

ERIC Educational Resources Information Center

Foster, Colin

2016-01-01

Confidence assessment (CA), in which students state alongside each of their answers a confidence level expressing how certain they are, has been employed successfully within higher education. However, it has not been widely explored with school pupils. This study examined how school mathematics pupils (N?=?345) in five different secondary schools…

The Root of the Problem

ERIC Educational Resources Information Center

Grosser-Clarkson, Dana L.

2015-01-01

The Common Core State Standards for Mathematics expect students to build on their knowledge of the number system, expressions and equations, and functions throughout school mathematics. For example, students learn that they can add something to both sides of an equation and that doing so will not affect the equivalency; however, squaring both…

Ethical Concerns: Negotiating Truth and Trust

ERIC Educational Resources Information Center

McGarvey, Lynn M.; Sterenberg, Gladys

2009-01-01

Few studies in mathematics education explicitly address ethical issues arising from student interactions. The ethical concerns held by students are expressed in their words, actions, and interactions. The purpose of this article is to explore the ethical nature of copying as it arises in a mathematics classroom. We investigate the basis for…

A note on misunderstandings of Piron's axioms for quantum mechanics

NASA Astrophysics Data System (ADS)

Foulis, D. J.; Randall, C. H.

1984-01-01

Piron's axioms for a realistically interpreted quantum mechanics are analyzed in detail within the context of a formal mathematical structure expressed in the conventional set-theoretic idiom of mathematics. As a result, some of the serious misconceptions that have encouraged recent criticisms of Piron's axioms are exposed.

Physics Teaching: Mathematics as an Epistemological Tool

ERIC Educational Resources Information Center

Kneubil, Fabiana B.; Robilotta, Manoel R.

2015-01-01

We study the interconnection between Physics and Mathematics in concrete instances, departing from the usual expression for the Coulomb electric field, produced by a point-like charge. It is scrutinized by means of six epistemology-intensive questions and radical answers are proposed, intended to widen one's understanding of the subject. Our…

Mathematical model of a smoldering log.

Treesearch

Fernando de Souza Costa; David Sandberg

2004-01-01

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

Developing Students' Mathematical Skills Involving Order of Operations

ERIC Educational Resources Information Center

Ali Rahman, Ernna Sukinnah; Shahrill, Masitah; Abbas, Nor Arifahwati; Tan, Abby

2017-01-01

This small-scale action research study examines the students' ability in using their mathematical skills when performing order of operations in numerical expressions. In this study, the "hierarchy-of-operators triangle" by Ameis (2011) was introduced as an alternative BODMAS approach to help students in gaining a better understanding…

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)

Implementing the "Curriculum and Evaluation Standards."

ERIC Educational Resources Information Center

Pacyga, Robert

1994-01-01

Describes two activities to analyze unit-cell structures from a geometric viewpoint and invite students to apply their mathematical understanding to scientific phenomena. Students form models of the simple cube, a building block of crystalline structures, and a methane molecule. (MDH)

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.

Approximate method for calculating convective heat flux on the surface of bodies of simple geometric shapes

NASA Astrophysics Data System (ADS)

Kuzenov, V. V.; Ryzhkov, S. V.

2017-02-01

The paper formulated engineering and physical mathematical model for aerothermodynamics hypersonic flight vehicle (HFV) in laminar and turbulent boundary layers (model designed for an approximate estimate of the convective heat flow in the range of speeds M = 6-28, and height H = 20-80 km). 2D versions of calculations of convective heat flows for bodies of simple geometric forms (individual elements of the design HFV) are presented.

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.

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

Farfour, Mohammed; Yoon, Wang Jung; Yoon-Geun

Defining and understanding hydrocarbon expressions in seismic expression is main concern of geoscientists in oil and gas exploration and production. Over the last decades several mathematical approaches have been developed in this regard. Most of approaches have addressed information in amplitude of seismic data. Recently, more attention has been drawn towards frequency related information in order to extract frequency behaviors of hydrocarbons bearing sediments. Spectrally decomposing seismic data into individual frequencies found to be an excellent tool for investigating geological formations and their pore fluids. To accomplish this, several mathematical approaches have been invoked. Continuous wavelet transform and Short Timemore » Window Fourier transform are widely used techniques for this purpose. This paper gives an overview of some widely used mathematical technique in hydrocarbon reservoir detection and mapping. This is followed by an application on real data from Boonsville field.« less

Clinical Application of Prognostic Gene Expression Signature in Fusion Gene-Negative Rhabdomyosarcoma: A Report from the Children's Oncology Group.

PubMed

Hingorani, Pooja; Missiaglia, Edoardo; Shipley, Janet; Anderson, James R; Triche, Timothy J; Delorenzi, Mauro; Gastier-Foster, Julie; Wing, Michele; Hawkins, Douglas S; Skapek, Stephen X

2015-10-15

Pediatric rhabdomyosarcoma (RMS) has two common histologic subtypes: embryonal (ERMS) and alveolar (ARMS). PAX-FOXO1 fusion gene status is a more reliable prognostic marker than alveolar histology, whereas fusion gene-negative (FN) ARMS patients are clinically similar to ERMS patients. A five-gene expression signature (MG5) previously identified two diverse risk groups within the fusion gene-negative RMS (FN-RMS) patients, but this has not been independently validated. The goal of this study was to test whether expression of the MG5 metagene, measured using a technical platform that can be applied to routine pathology material, would correlate with outcome in a new cohort of patients with FN-RMS. Cases were taken from the Children's Oncology Group (COG) D9803 study of children with intermediate-risk RMS, and gene expression profiling for the MG5 genes was performed using the nCounter assay. The MG5 score was correlated with clinical and pathologic characteristics as well as overall and event-free survival. MG5 standardized score showed no significant association with any of the available clinicopathologic variables. The MG5 signature score showed a significant correlation with overall (N = 57; HR, 7.3; 95% CI, 1.9-27.0; P = 0.003) and failure-free survival (N = 57; HR, 6.1; 95% CI, 1.9-19.7; P = 0.002). This represents the first, validated molecular prognostic signature for children with FN-RMS who otherwise have intermediate-risk disease. The capacity to measure the expression of a small number of genes in routine pathology material and apply a simple mathematical formula to calculate the MG5 metagene score provides a clear path toward better risk stratification in future prospective clinical trials. ©2015 American Association for Cancer Research.

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)

Kinetic models of gene expression including non-coding RNAs

NASA Astrophysics Data System (ADS)

Zhdanov, Vladimir P.

2011-03-01

In cells, genes are transcribed into mRNAs, and the latter are translated into proteins. Due to the feedbacks between these processes, the kinetics of gene expression may be complex even in the simplest genetic networks. The corresponding models have already been reviewed in the literature. A new avenue in this field is related to the recognition that the conventional scenario of gene expression is fully applicable only to prokaryotes whose genomes consist of tightly packed protein-coding sequences. In eukaryotic cells, in contrast, such sequences are relatively rare, and the rest of the genome includes numerous transcript units representing non-coding RNAs (ncRNAs). During the past decade, it has become clear that such RNAs play a crucial role in gene expression and accordingly influence a multitude of cellular processes both in the normal state and during diseases. The numerous biological functions of ncRNAs are based primarily on their abilities to silence genes via pairing with a target mRNA and subsequently preventing its translation or facilitating degradation of the mRNA-ncRNA complex. Many other abilities of ncRNAs have been discovered as well. Our review is focused on the available kinetic models describing the mRNA, ncRNA and protein interplay. In particular, we systematically present the simplest models without kinetic feedbacks, models containing feedbacks and predicting bistability and oscillations in simple genetic networks, and models describing the effect of ncRNAs on complex genetic networks. Mathematically, the presentation is based primarily on temporal mean-field kinetic equations. The stochastic and spatio-temporal effects are also briefly discussed.

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.

Making Connections by Using Molecular Models in Geometry.

ERIC Educational Resources Information Center

Pacyga, Robert

1995-01-01

Describes two activities to analyze unit-cell structures from a geometric viewpoint and invites students to apply their mathematical understanding to scientific phenomena. Students form models of the simple cube, a building block of crystalline structures, and a methane molecule. (MKR)

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.

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.

Mathematics beliefs and achievement of adolescent students in Japan: results from the TIMSS 1999 assessment.

PubMed

House, J Daniel

2005-12-01

A recent study (1) of undergraduate students in a precalculus course indicated that they expressed slightly positive attitudes toward mathematics. It is important, however, to examine relationships between students' initial attitudes and achievement outcomes. The present purpose was to assess the relationship between self-beliefs and mathematics achievement for a large national sample of students from the TIMSS 1999 international sample (eighth graders) from Japan. Several significant relationships between mathematics beliefs and test scores were noted. In addition, the overall multiple regression equation that assessed the joint significance of the complete set of self-belief variables was significant (F7.65 = 159.48, p < .001) and explained 20.6% of the variance in mathematics achievement test scores.

Profile of mathematical reasoning ability of 8th grade students seen from communicational ability, basic skills, connection, and logical thinking

NASA Astrophysics Data System (ADS)

Sumarsih; Budiyono; Indriati, D.

2018-04-01

This research aims to understand the students’ weaknesses in mathematical reasoning ability in junior secondary school. A set of multiple choice tests were used to measure this ability involve components mathematical communication, basic skills, connection, and logical thinking. A total of 259 respondents were determined by stratified cluster random sampling. Data were analyzed using one-way Anova test with Fobs = 109.5760 and F = 3.0000. The results show that students’ ability from schools with high National Exam in mathematics category was the best and followed by medium and low category. Mathematical connection is the most difficult component performed by students. In addition, most students also have difficulty in expressing ideas and developing logical arguments.

Spectral Analysis: From Additive Perspective to Multiplicative Perspective

NASA Astrophysics Data System (ADS)

Wu, Z.

2017-12-01

The early usage of trigonometric functions can be traced back to at least 17th century BC. It was Bhaskara II of the 12th century CE who first proved the mathematical equivalence between the sum of two trigonometric functions of any given angles and the product of two trigonometric functions of related angles, which has been taught these days in middle school classroom. The additive perspective of trigonometric functions led to the development of the Fourier transform that is used to express any functions as the sum of a set of trigonometric functions and opened a new mathematical field called harmonic analysis. Unfortunately, Fourier's sum cannot directly express nonlinear interactions between trigonometric components of different periods, and thereby lacking the capability of quantifying nonlinear interactions in dynamical systems. In this talk, the speaker will introduce the Huang transform and Holo-spectrum which were pioneered by Norden Huang and emphasizes the multiplicative perspective of trigonometric functions in expressing any function. Holo-spectrum is a multi-dimensional spectral expression of a time series that explicitly identifies the interactions among different scales and quantifies nonlinear interactions hidden in a time series. Along with this introduction, the developing concepts of physical, rather than mathematical, analysis of data will be explained. Various enlightening applications of Holo-spectrum analysis in atmospheric and climate studies will also be presented.

Belgian and Turkish Pre-Service Primary School Teachers' Metaphoric Expressions about Mathematics

ERIC Educational Resources Information Center

Kiliç, Çigdem; Yanpar Yelken, Tugba

2013-01-01

Problem Statement: Recent studies in education have focused on how to handle metaphors as research and evaluation tools. Metaphors have many advantages for researchers, educators and learners with the most important being that they can help educators understand pre-service teachers' thinking and belief systems of mathematics. A study of previous…

Increasing Communication in Geometry by Using a Personal Math Concept Chart

ERIC Educational Resources Information Center

Friedman, Rhonda; Kazerouni, Gety; Lax, Stacey; Weisdorf, Elli

2011-01-01

The action research team developed a "Personal Math Concept Chart". This chart required students to describe the mathematical concepts that they were studying in the Geometry strand of Mathematics using their own images and words. In this study, students were encouraged to express their own understanding of geometric concepts in order to…

Host - HIF- 1alpha Pathway And Hypoxia: In Vitro Studies And Mathematical Model

DTIC Science & Technology

2016-08-30

TERMS mathematical model, signaling pathways, hypoxia, immunohistochemistry, ELISA , inhalation chamber 16. SECURITY CLASSIFICATION OF: U 17...B. HIF-1α ELISA Procedure ........................................................................................27 Appendix C. HIF-1α Model...Quantifying Induction of HIF-1α Expression using ELISA .........................................15 Figure 10. Simulation Outputs from HIF-1α Kinetic

Associations of Students' Beliefs with Self-Regulated Problem Solving in College Algebra

ERIC Educational Resources Information Center

Cifarelli, Victor; Goodson-Espy, Tracy; Chae, Jeong-Lim

2010-01-01

This paper reports results from a study of self-regulated problem solving actions of students enrolled in College Algebra (N = 139). The study examined the associations between the expressed mathematical beliefs of students and the students' self-regulated actions in solving mathematics problems. The research questions are: (a) What are some…

Translating a "Relevance Imperative" into Junior Secondary Mathematics and Science Pedagogy

ERIC Educational Resources Information Center

Darby, Linda

2009-01-01

Inquiries into the state of mathematics and science education in Australia express the need to make curriculum and teaching practices more relevant and meaningful to students' lives. This vision requires that teachers understand how relevance can enter the classroom in meaningful, appropriate, and subject-specific ways. In this paper I use…

Mathematics Education in Rural Communities: A Mathematician's View. Working Paper Series.

ERIC Educational Resources Information Center

Mahoney, Carolyn R.

Elizabeth City State University (ECSU) serves the 21 counties of rural northeastern North Carolina. In Fall 2000 ECSU administrators met with educators in area school districts to discuss their professional development needs. This paper reports on those expressed needs relevant to mathematics education and discusses ways to help achieve excellence…

Focus in High School Mathematics: Reasoning and Sense Making in Algebra

ERIC Educational Resources Information Center

Graham, Karen; Cuoco, Albert; Zimmermann, Gwendolyn

2010-01-01

This book examines the five key elements (meaningful use of symbols, mindful manipulation, reasoned solving, connection algebra with geometry, and linking expressions and functions) identified in "Focus in High School Mathematics: Reasoning and Sense Making" in more detail and elaborates on the associated reasoning habits. This volume is one of a…

Defining Levels on the 1990 Mathematics Composite.

ERIC Educational Resources Information Center

Johnson, Eugene G.

Procedures used to map the achievement levels, expressed as total expected scores on the full set of items presented to a grade, onto the Mathematics Composite of the 1990 National Assessment of Educational Progress (NAEP) are described. The Composite, defined as a weighted average of subdomain scores, provides a global measure of mathematics…

Scoring Points: Goals for Real World Problem Solving

ERIC Educational Resources Information Center

Galbraith, Peter

2012-01-01

This paper is presented in two parts. Through an example the first part takes up the issue of applying mathematics to situations that form part of the life context of students--the priority expressed in three curriculum statements presented. Then, noting the particular point in time--development of a National Curriculum for Mathematics--the second…

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.

Nonlinear mathematical modeling and sensitivity analysis of hydraulic drive unit

NASA Astrophysics Data System (ADS)

Kong, Xiangdong; Yu, Bin; Quan, Lingxiao; Ba, Kaixian; Wu, Liujie

2015-09-01

The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity indexes values of four measurable parameters, such as supply pressure, proportional gain, initial position of servo cylinder piston and load force, are verified experimentally on test platform of hydraulic drive unit, and the experimental research shows that the sensitivity analysis results obtained through simulation are approximate to the test results. This research indicates each parameter sensitivity characteristics of hydraulic drive unit, the performance-affected main parameters and secondary parameters are got under different working conditions, which will provide the theoretical foundation for the control compensation and structure optimization of hydraulic drive unit.

On the stochastic dissemination of faults in an admissible network

NASA Technical Reports Server (NTRS)

Kyrala, A.

1987-01-01

The dynamic distribution of faults in a general type network is discussed. The starting point is a uniquely branched network in which each pair of nodes is connected by a single branch. Mathematical expressions for the uniquely branched network transition matrix are derived to show that sufficient stationarity exists to ensure the validity of the use of the Markov Chain model to analyze networks. In addition the conditions for the use of Semi-Markov models are discussed. General mathematical expressions are derived in an examination of branch redundancy techniques commonly used to increase reliability.

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.

Difficulties in initial algebra learning in Indonesia

NASA Astrophysics Data System (ADS)

Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja

2014-12-01

Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was significantly below the average student performance in other Southeast Asian countries such as Thailand, Malaysia, and Singapore. This fact gave rise to this study which aims to investigate Indonesian students' difficulties in algebra. In order to do so, a literature study was carried out on students' difficulties in initial algebra. Next, an individual written test on algebra tasks was administered, followed by interviews. A sample of 51 grade VII Indonesian students worked the written test, and 37 of them were interviewed afterwards. Data analysis revealed that mathematization, i.e., the ability to translate back and forth between the world of the problem situation and the world of mathematics and to reorganize the mathematical system itself, constituted the most frequently observed difficulty in both the written test and the interview data. Other observed difficulties concerned understanding algebraic expressions, applying arithmetic operations in numerical and algebraic expressions, understanding the different meanings of the equal sign, and understanding variables. The consequences of these findings on both task design and further research in algebra education are discussed.

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.

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

A comparative mathematical analysis of RL and RC electrical circuits via Atangana-Baleanu and Caputo-Fabrizio fractional derivatives

NASA Astrophysics Data System (ADS)

Abro, Kashif Ali; Memon, Anwar Ahmed; Uqaili, Muhammad Aslam

2018-03-01

This research article is analyzed for the comparative study of RL and RC electrical circuits by employing newly presented Atangana-Baleanu and Caputo-Fabrizio fractional derivatives. The governing ordinary differential equations of RL and RC electrical circuits have been fractionalized in terms of fractional operators in the range of 0 ≤ ξ ≤ 1 and 0 ≤ η ≤ 1. The analytic solutions of fractional differential equations for RL and RC electrical circuits have been solved by using the Laplace transform with its inversions. General solutions have been investigated for periodic and exponential sources by implementing the Atangana-Baleanu and Caputo-Fabrizio fractional operators separately. The investigated solutions have been expressed in terms of simple elementary functions with convolution product. On the basis of newly fractional derivatives with and without singular kernel, the voltage and current have interesting behavior with several similarities and differences for the periodic and exponential sources.

A comparative study of some mathematical models of the mean wind structure and aerodynamic drag of plant canopies

NASA Technical Reports Server (NTRS)

Massman, William

1987-01-01

A semianalytical method for describing the mean wind profile and shear stress within plant canopies and for estimating the roughness length and the displacement height is presented. This method incorporates density and vertical structure of the canopy and includes simple parameterizations of the roughness sublayer and shelter factor. Some of the wind profiles examined are consistent with first-order closure techniques while others are consistent with second-order closure techniques. Some profiles show a shearless region near the base of the canopy; however, none displays a secondary maximum there. Comparing several different analytical expressions for the canopy wind profile against observations suggests that one particular type of profile (an Airy function which is associated with the triangular foliage surface area density distribution) is superior to the others. Because of the numerical simplicity of the methods outlined, it is suggested that they may be profitably used in large-scale models of plant-atmosphere exchanges.

Low-order modelling of a drop on a highly-hydrophobic substrate: statics and dynamics

NASA Astrophysics Data System (ADS)

Wray, Alexander W.; Matar, Omar K.; Davis, Stephen H.

2017-11-01

We analyse the behaviour of droplets resting on highly-hydrophobic substrates. This problem is of practical interest due to its appearance in many physical contexts involving the spreading, wetting, and dewetting of fluids on solid substrates. In mathematical terms, it exhibits an interesting challenge as the interface is multi-valued as a function of the natural Cartesian co-ordinates, presenting a stumbling block to typical low-order modelling techniques. Nonetheless, we show that in the static case, the interfacial shape is governed by the Young-Laplace equation, which may be solved explicitly in terms of elliptic functions. We present simple low-order expressions that faithfully reproduce the shapes. We then consider the dynamic case, showing that the predictions of our low-order model compare favourably with those obtained from direct numerical simulations. We also examine the characteristic flow regimes of interest. EPSRC, UK, MEMPHIS program Grant (EP/K003976/1), RAEng Research Chair (OKM).

A Log Logistic Survival Model Applied to Hypobaric Decompression Sickness

NASA Technical Reports Server (NTRS)

Conkin, Johnny

2001-01-01

Decompression sickness (DCS) is a complex, multivariable problem. A mathematical description or model of the likelihood of DCS requires a large amount of quality research data, ideas on how to define a decompression dose using physical and physiological variables, and an appropriate analytical approach. It also requires a high-performance computer with specialized software. I have used published DCS data to develop my decompression doses, which are variants of equilibrium expressions for evolved gas plus other explanatory variables. My analytical approach is survival analysis, where the time of DCS occurrence is modeled. My conclusions can be applied to simple hypobaric decompressions - ascents lasting from 5 to 30 minutes - and, after minutes to hours, to denitrogenation (prebreathing). They are also applicable to long or short exposures, and can be used whether the sufferer of DCS is at rest or exercising at altitude. Ultimately I would like my models to be applied to astronauts to reduce the risk of DCS during spacewalks, as well as to future spaceflight crews on the Moon and Mars.

Comment on ``Correlated noise in a logistic growth model''

NASA Astrophysics Data System (ADS)

Behera, Anita; O'Rourke, S. Francesca C.

2008-01-01

We argue that the results published by Ai [Phys. Rev. E 67, 022903 (2003)] on “correlated noise in logistic growth” are not correct. Their conclusion that, for larger values of the correlation parameter λ , the cell population is peaked at x=0 , which denotes a high extinction rate, is also incorrect. We find the reverse behavior to their results, that increasing λ promotes the stable growth of tumor cells. In particular, their results for the steady-state probability, as a function of cell number, at different correlation strengths, presented in Figs. 1 and 2 of their paper show different behavior than one would expect from the simple mathematical expression for the steady-state probability. Additionally, their interpretation that at small values of cell number the steady-state probability increases as the correlation parameter is increased is also questionable. Another striking feature in their Figs. 1 and 3 is that, for the same values of the parameters λ and α , their simulation produces two different curves, both qualitatively and quantitatively.

An analytical model for transient deformation of viscoelastically coated beams: Applications to static-mode microcantilever chemical sensors

NASA Astrophysics Data System (ADS)

Heinrich, S. M.; Wenzel, M. J.; Josse, F.; Dufour, I.

2009-06-01

The problem governing the transient deformation of an elastic cantilever beam with viscoelastic coating, subjected to a time-dependent coating eigenstrain, is mathematically formulated. An analytical solution for an exponential eigenstrain history, exact within the context of beam theory, is obtained in terms of the coating and base layer thicknesses, the elastic modulus of the base material, the initial coating modulus, the coating relaxation percentage (0%-100%), and the time constants of the coating's relaxation process and its eigenstrain history. Approximate formulas, valid for thin coatings, are derived as special cases to provide insight into system behavior. Main results include (1) the time histories of the beam curvature and the coating stresses, (2) a criterion governing the response type (monotonic or "overshoot" response), and (3) simple expressions for the overshoot ratio, defined as the peak response scaled by the steady-state response, and the time at which the peak response occurs. Applications to polymer-coated microcantilever-based chemical sensors operating in the static mode are discussed.

Small RNA biology is systems biology.

PubMed

Jost, Daniel; Nowojewski, Andrzej; Levine, Erel

2011-01-01

During the last decade small regulatory RNA (srRNA) emerged as central players in the regulation of gene expression in all kingdoms of life. Multiple pathways for srRNA biogenesis and diverse mechanisms of gene regulation may indicate that srRNA regulation evolved independently multiple times. However, small RNA pathways share numerous properties, including the ability of a single srRNA to regulate multiple targets. Some of the mechanisms of gene regulation by srRNAs have significant effect on the abundance of free srRNAs that are ready to interact with new targets. This results in indirect interactions among seemingly unrelated genes, as well as in a crosstalk between different srRNA pathways. Here we briefly review and compare the major srRNA pathways, and argue that the impact of srRNA is always at the system level. We demonstrate how a simple mathematical model can ease the discussion of governing principles. To demonstrate these points we review a few examples from bacteria and animals.

Are there laws of genome evolution?

PubMed

Koonin, Eugene V

2011-08-01

Research in quantitative evolutionary genomics and systems biology led to the discovery of several universal regularities connecting genomic and molecular phenomic variables. These universals include the log-normal distribution of the evolutionary rates of orthologous genes; the power law-like distributions of paralogous family size and node degree in various biological networks; the negative correlation between a gene's sequence evolution rate and expression level; and differential scaling of functional classes of genes with genome size. The universals of genome evolution can be accounted for by simple mathematical models similar to those used in statistical physics, such as the birth-death-innovation model. These models do not explicitly incorporate selection; therefore, the observed universal regularities do not appear to be shaped by selection but rather are emergent properties of gene ensembles. Although a complete physical theory of evolutionary biology is inconceivable, the universals of genome evolution might qualify as "laws of evolutionary genomics" in the same sense "law" is understood in modern physics.

Mathematical models of the fate of lymphoma B cells after antigen receptor ligation with specific antibodies.

PubMed

Alarcón, Tomás; Marches, Radu; Page, Karen M

2006-05-07

We formulate models of the mechanism(s) by which B cell lymphoma cells stimulated with an antibody specific to the B cell receptor (IgM) become quiescent or apoptotic. In particular, we aim to reproduce experimental results by Marches et al. according to which the fate of the targeted cells (Daudi) depends on the levels of expression of p21(Waf1) (p21) cell-cycle inhibitor. A simple model is formulated in which the basic ingredients are p21 and caspase activity, and their mutual inhibition. We show that this model does not reproduce the experimental results and that further refinement is needed. A second model successfully reproduces the experimental observations, for a given set of parameter values, indicating a critical role for Myc in the fate decision process. We use bifurcation analysis and objective sensitivity analysis to assess the robustness of our results. Importantly, this analysis yields experimentally testable predictions on the role of Myc, which could have therapeutic implications.

Fractional Langevin Equation Model for Characterization of Anomalous Brownian Motion from NMR Signals

NASA Astrophysics Data System (ADS)

Lisý, Vladimír; Tóthová, Jana

2018-02-01

Nuclear magnetic resonance is often used to study random motion of spins in different systems. 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 Langevin theory of the Brownian motion (BM). In the present work, the attenuation function S (t) for an ensemble of spins 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 a 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.

Rad4 recognition-at-a-distance: Physical basis of conformation-specific anomalous diffusion of DNA repair proteins.

PubMed

Kong, Muwen; Van Houten, Bennett

2017-08-01

Since Robert Brown's first observations of random walks by pollen particles suspended in solution, the concept of diffusion has been subject to countless theoretical and experimental studies in diverse fields from finance and social sciences, to physics and biology. Diffusive transport of macromolecules in cells is intimately linked to essential cellular functions including nutrient uptake, signal transduction, gene expression, as well as DNA replication and repair. Advancement in experimental techniques has allowed precise measurements of these diffusion processes. Mathematical and physical descriptions and computer simulations have been applied to model complicated biological systems in which anomalous diffusion, in addition to simple Brownian motion, was observed. The purpose of this review is to provide an overview of the major physical models of anomalous diffusion and corresponding experimental evidence on the target search problem faced by DNA-binding proteins, with an emphasis on DNA repair proteins and the role of anomalous diffusion in DNA target recognition. Copyright © 2016 Elsevier Ltd. All rights reserved.

Apparent Strength Conceals Instability in a Model for the Collapse of Historical States

PubMed Central

Lawson, Daniel John; Oak, Neeraj

2014-01-01

An explanation for the political processes leading to the sudden collapse of empires and states would be useful for understanding both historical and contemporary political events. We examine political disintegration across eras, cultures and geographical scale to form a simple hypothesis that can be expressed verbally yet formulated mathematically. Factions within a state make choices described by game-theory about whether to accept the political status quo, or to attempt to better their circumstances through costly rebellion. In lieu of precise data we verify our model using sensitivity analysis. We find that a small amount of dissatisfaction is typically harmless to the state, but can trigger sudden collapse when there is a sufficient buildup of political inequality. Contrary to intuition, a state is predicted to be least stable when its leadership is at the height of its political power and thus most able to exert its influence through external warfare, lavish expense or autocratic decree. PMID:24810228

Evolution in time of an N-atom system. I. A physical basis set for the projection of the master equation

NASA Astrophysics Data System (ADS)

Freedhoff, Helen

2004-01-01

We study an aggregate of N identical two-level atoms (TLA’s) coupled by the retarded interatomic interaction, using the Lehmberg-Agarwal master equation. First, we calculate the entangled eigenstates of the system; then, we use these eigenstates as a basis set for the projection of the master equation. We demonstrate that in this basis the equations of motion for the level populations, as well as the expressions for the emission and absorption spectra, assume a simple mathematical structure and allow for a transparent physical interpretation. To illustrate the use of the general theory in emission processes, we study an isosceles triangle of atoms, and present in the long wavelength limit the (cascade) emission spectrum for a hexagon of atoms fully excited at t=0. To illustrate its use for absorption processes, we tabulate (in the same limit) the biexciton absorption frequencies, linewidths, and relative intensities for polygons consisting of N=2,…,9 TLA’s.

Approximate Expressions for the Period of a Simple Pendulum Using a Taylor Series Expansion

ERIC Educational Resources Information Center

Belendez, Augusto; Arribas, Enrique; Marquez, Andres; Ortuno, Manuel; Gallego, Sergi

2011-01-01

An approximate scheme for obtaining the period of a simple pendulum for large-amplitude oscillations is analysed and discussed. When students express the exact frequency or the period of a simple pendulum as a function of the oscillation amplitude, and they are told to expand this function in a Taylor series, they always do so using the…

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,…

Decoding of the light changes in eclipsing Wolf-Rayet binaries. I. A non-classical approach to the solution of light curves

NASA Astrophysics Data System (ADS)

Perrier, C.; Breysacher, J.; Rauw, G.

2009-09-01

Aims: We present a technique to determine the orbital and physical parameters of eclipsing eccentric Wolf-Rayet + O-star binaries, where one eclipse is produced by the absorption of the O-star light by the stellar wind of the W-R star. Methods: Our method is based on the use of the empirical moments of the light curve that are integral transforms evaluated from the observed light curves. The optical depth along the line of sight and the limb darkening of the W-R star are modelled by simple mathematical functions, and we derive analytical expressions for the moments of the light curve as a function of the orbital parameters and the key parameters of the transparency and limb-darkening functions. These analytical expressions are then inverted in order to derive the values of the orbital inclination, the stellar radii, the fractional luminosities, and the parameters of the wind transparency and limb-darkening laws. Results: The method is applied to the SMC W-R eclipsing binary HD 5980, a remarkable object that underwent an LBV-like event in August 1994. The analysis refers to the pre-outburst observational data. A synthetic light curve based on the elements derived for the system allows a quality assessment of the results obtained.

Finite element meshing approached as a global minimization process

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

WITKOWSKI,WALTER R.; JUNG,JOSEPH; DOHRMANN,CLARK R.

2000-03-01

The ability to generate a suitable finite element mesh in an automatic fashion is becoming the key to being able to automate the entire engineering analysis process. However, placing an all-hexahedron mesh in a general three-dimensional body continues to be an elusive goal. The approach investigated in this research is fundamentally different from any other that is known of by the authors. A physical analogy viewpoint is used to formulate the actual meshing problem which constructs a global mathematical description of the problem. The analogy used was that of minimizing the electrical potential of a system charged particles within amore » charged domain. The particles in the presented analogy represent duals to mesh elements (i.e., quads or hexes). Particle movement is governed by a mathematical functional which accounts for inter-particles repulsive, attractive and alignment forces. This functional is minimized to find the optimal location and orientation of each particle. After the particles are connected a mesh can be easily resolved. The mathematical description for this problem is as easy to formulate in three-dimensions as it is in two- or one-dimensions. The meshing algorithm was developed within CoMeT. It can solve the two-dimensional meshing problem for convex and concave geometries in a purely automated fashion. Investigation of the robustness of the technique has shown a success rate of approximately 99% for the two-dimensional geometries tested. Run times to mesh a 100 element complex geometry were typically in the 10 minute range. Efficiency of the technique is still an issue that needs to be addressed. Performance is an issue that is critical for most engineers generating meshes. It was not for this project. The primary focus of this work was to investigate and evaluate a meshing algorithm/philosophy with efficiency issues being secondary. The algorithm was also extended to mesh three-dimensional geometries. Unfortunately, only simple geometries were tested before this project ended. The primary complexity in the extension was in the connectivity problem formulation. Defining all of the interparticle interactions that occur in three-dimensions and expressing them in mathematical relationships is very difficult.« less

The soil water characteristic as new class of closed-form parametric expressions for the flow duration curve

NASA Astrophysics Data System (ADS)

Sadegh, M.; Vrugt, J. A.; Gupta, H. V.; Xu, C.

2016-04-01

The flow duration curve is a signature catchment characteristic that depicts graphically the relationship between the exceedance probability of streamflow and its magnitude. This curve is relatively easy to create and interpret, and is used widely for hydrologic analysis, water quality management, and the design of hydroelectric power plants (among others). Several mathematical expressions have been proposed to mimic the FDC. Yet, these efforts have not been particularly successful, in large part because available functions are not flexible enough to portray accurately the functional shape of the FDC for a large range of catchments and contrasting hydrologic behaviors. Here, we extend the work of Vrugt and Sadegh (2013) and introduce several commonly used models of the soil water characteristic as new class of closed-form parametric expressions for the flow duration curve. These soil water retention functions are relatively simple to use, contain between two to three parameters, and mimic closely the empirical FDCs of 430 catchments of the MOPEX data set. We then relate the calibrated parameter values of these models to physical and climatological characteristics of the watershed using multivariate linear regression analysis, and evaluate the regionalization potential of our proposed models against those of the literature. If quality of fit is of main importance then the 3-parameter van Genuchten model is preferred, whereas the 2-parameter lognormal, 3-parameter GEV and generalized Pareto models show greater promise for regionalization.

Advanced statistics: linear regression, part I: simple linear regression.

PubMed

Marill, Keith A

2004-01-01

Simple linear regression is a mathematical technique used to model the relationship between a single independent predictor variable and a single dependent outcome variable. In this, the first of a two-part series exploring concepts in linear regression analysis, the four fundamental assumptions and the mechanics of simple linear regression are reviewed. The most common technique used to derive the regression line, the method of least squares, is described. The reader will be acquainted with other important concepts in simple linear regression, including: variable transformations, dummy variables, relationship to inference testing, and leverage. Simplified clinical examples with small datasets and graphic models are used to illustrate the points. This will provide a foundation for the second article in this series: a discussion of multiple linear regression, in which there are multiple predictor variables.

What's an Adult Numeracy Teacher to Teach? Negotiating the Complexity of Adult Numeracy Instruction

ERIC Educational Resources Information Center

Ginsburg, Lynda

2017-01-01

In this Forum article, the author addresses how to assist adults in improving mathematics and numeracy literacy. Ginsburg observes educators who strive to address their learners' educational gaps and needs are finding themselves in an environment of competing priorities and expectations that can be expressed as mathematics numeracy education. What…

Visualization of Problem Solving Related to the Quantitative Composition of Solutions in the Dynamic "GeoGebra" Environment

ERIC Educational Resources Information Center

Kostic, V. Dj.; Jovanovic, V. P. Stankov; Sekulic, T. M.; Takaci, Dj. B.

2016-01-01

Problem solving in the field of quantitative composition of solutions (QCS), expressed as mass share and molar concentration, is essential for chemistry students. Since successful chemistry education is based on different mathematical contents, it is important to be proficient in both mathematical and chemistry concepts as well as interconnections…

Using a Framework for Three Levels of Sense Making in a Mathematics Classroom

ERIC Educational Resources Information Center

Moss, Diana L.; Lamberg, Teruni

2016-01-01

This discussion-based lesson is designed to support Year 6 students in their initial understanding of using letters to represent numbers, expressions, and equations in algebra. The three level framework is designed for: (1) making thinking explicit, (2) exploring each other's solutions, and (3) developing new mathematical insights. In each level…

Preliminary Findings from the First Two Waves of a Panel Study of Developing Career Expectations.

ERIC Educational Resources Information Center

Hotchkiss, Lawrence; Chiteji, Lisa

This report is an exploratory application of a dynamic mathematical model to express a theory of changes in youth's career expectations over time. Main content is divided into two focuses: (1) theoretical interpretations of the differential equations which embody the mathematical model and (2) reporting and discussion of the results of preliminary…

Students' Expression of Affect in an Inner-City SimCalc Classroom

ERIC Educational Resources Information Center

Schorr, Roberta Y.; Goldin, Gerald A.

2008-01-01

This research focuses on some of the affordances provided by SimCalc software, suggesting that its use can have important consequences for students' mathematical affect and motivation. We describe an episode in an inner-city SimCalc environment illustrating our approach to the study of affect in the mathematics classroom. We infer students'…

Interdisciplinary Working Practices: Can Creative Dance Improve Math?

ERIC Educational Resources Information Center

Leandro, Cristina Rebelo; Monteiro, Elisabete; Melo, Filipe

2018-01-01

This study is integrated in the field of Dance in Education, focusing on the instrumentalist aspect of art. We focused on creative dance as a catalyst to learn Mathematics' contents. This interdisciplinary work can enhance the learning, as far as the understanding of Mathematics' concepts is achieved through the body and revealed by expressive and…

How to Present It? On the Rhetoric of an Outstanding Lecturer

ERIC Educational Resources Information Center

Movshovitz-Hadar, Nitsa; Hazzan, Orit

2004-01-01

This paper analyses a lecture by an excellent teaching award winner professor of mathematics, given to high school mathematics teachers. The analysis is based upon two sources: (i) the lecture plan, as expressed in a series of 29 transparencies, prepared by the lecturer in advance; (ii) the actual implementation of the lecture, as transcribed from…

A "Great Way to Get On"? The Early Career Destinations of Science, Technology, Engineering and Mathematics Graduates

ERIC Educational Resources Information Center

Smith, Emma; White, Patrick

2017-01-01

Concerns about a shortage of highly skilled workers in the science, technology, engineering and mathematics (STEM) sector have been expressed frequently since the late 1940s. Although these claims have been challenged as being insufficiently grounded in evidence, they have formed the basis of policies directing considerable resources to STEM…

A Comparison of Equality in Computer Algebra and Correctness in Mathematical Pedagogy (II)

ERIC Educational Resources Information Center

Bradford, Russell; Davenport, James H.; Sangwin, Chris

2010-01-01

A perennial problem in computer-aided assessment is that "a right answer", pedagogically speaking, is not the same thing as "a mathematically correct expression", as verified by a computer algebra system, or indeed other techniques such as random evaluation. Paper I in this series considered the difference in cases where there was "the right…

Like Terms: What's in a Name?

ERIC Educational Resources Information Center

de Groot, Cornelis; Boyajian, Meredith

2015-01-01

In introductory algebra and later mathematics courses, students seem to struggle with the concepts of like terms and combining like terms with algebraic expressions. These ideas appear to be unfamiliar to students and do not seem to relate to any mathematics that they have done in the past. In an attempt to link with something that the students do…

Level of Student's Creative Thinking in Classroom Mathematics

ERIC Educational Resources Information Center

Siswono, Tatag Yuli Eko

2011-01-01

It is reasonable to assume that people are creative, but the degree of creativity is different. The Idea of the level of student's creative thinking has been expressed by experts, such as Gotoh (2004), and Krulik and Rudnick (1999). The perspective of the mathematics creative thinking refers to a combination of logical and divergent thinking which…

A Simple Exact Error Rate Analysis for DS-CDMA with Arbitrary Pulse Shape in Flat Nakagami Fading

NASA Astrophysics Data System (ADS)

Rahman, Mohammad Azizur; Sasaki, Shigenobu; Kikuchi, Hisakazu; Harada, Hiroshi; Kato, Shuzo

A simple exact error rate analysis is presented for random binary direct sequence code division multiple access (DS-CDMA) considering a general pulse shape and flat Nakagami fading channel. First of all, a simple model is developed for the multiple access interference (MAI). Based on this, a simple exact expression of the characteristic function (CF) of MAI is developed in a straight forward manner. Finally, an exact expression of error rate is obtained following the CF method of error rate analysis. The exact error rate so obtained can be much easily evaluated as compared to the only reliable approximate error rate expression currently available, which is based on the Improved Gaussian Approximation (IGA).

Wave Propagation in Discontinuous Media by the Scattering Matrix Method

NASA Astrophysics Data System (ADS)

Perino, A.; Orta, R.; Barla, G.

2012-09-01

Propagation of elastic waves in discontinuous media is studied in this paper by the scattering matrix method (SMM). An electromagnetic transmission line analogy is also used to set up the mathematical model. The SMM operates in the frequency domain and allows for all wave polarizations (P, SV and SH). Rock masses are examples of discontinuous media in which the discontinuities (fractures or joints) influence wave propagation. Both elastic and viscoelastic joints are considered and the latter are described by Kelvin-Voigt, Maxwell and Burgers models. Rock joints with Coulomb slip behavior are also analyzed, by applying the averaging principle of Caughy (J Appl Mech 27:640-643, 1960). The evaluation of the effects of periodic discontinuities in a homogeneous medium is presented by introducing the concept of Bloch waves. The dispersion curves of these waves are useful to explain the existence of frequency bands of strong attenuation, also in the case of lossless (perfectly elastic) structures. Simple expressions of transmission and reflection coefficients are obtained. Finally, the SMM results are compared with those computed via the distinct element method (DEM). The comparisons are performed on a medium with joints with Coulomb slip behavior and the agreement is satisfactory, although the SMM must be applied in conjunction with the equivalent linearization technique. Even if the DEM is much more general, the SMM in these simple cases is extremely faster and provides a higher physical insight.

Theory of linear sweep voltammetry with diffuse charge: Unsupported electrolytes, thin films, and leaky membranes

NASA Astrophysics Data System (ADS)

Yan, David; Bazant, Martin Z.; Biesheuvel, P. M.; Pugh, Mary C.; Dawson, Francis P.

2017-03-01

Linear sweep and cyclic voltammetry techniques are important tools for electrochemists and have a variety of applications in engineering. Voltammetry has classically been treated with the Randles-Sevcik equation, which assumes an electroneutral supported electrolyte. In this paper, we provide a comprehensive mathematical theory of voltammetry in electrochemical cells with unsupported electrolytes and for other situations where diffuse charge effects play a role, and present analytical and simulated solutions of the time-dependent Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions for a 1:1 electrolyte and a simple reaction. Using these solutions, we construct theoretical and simulated current-voltage curves for liquid and solid thin films, membranes with fixed background charge, and cells with blocking electrodes. The full range of dimensionless parameters is considered, including the dimensionless Debye screening length (scaled to the electrode separation), Damkohler number (ratio of characteristic diffusion and reaction times), and dimensionless sweep rate (scaled to the thermal voltage per diffusion time). The analysis focuses on the coupling of Faradaic reactions and diffuse charge dynamics, although capacitive charging of the electrical double layers is also studied, for early time transients at reactive electrodes and for nonreactive blocking electrodes. Our work highlights cases where diffuse charge effects are important in the context of voltammetry, and illustrates which regimes can be approximated using simple analytical expressions and which require more careful consideration.

Symmetry Properties of Potentiometric Titration Curves.

ERIC Educational Resources Information Center

Macca, Carlo; Bombi, G. Giorgio

1983-01-01

Demonstrates how the symmetry properties of titration curves can be efficiently and rigorously treated by means of a simple method, assisted by the use of logarithmic diagrams. Discusses the symmetry properties of several typical titration curves, comparing the graphical approach and an explicit mathematical treatment. (Author/JM)

Empirical Studies of Patterning

ERIC Educational Resources Information Center

Pasnak, Robert

2017-01-01

Young children have been taught simple sequences of alternating shapes and colors, referred to as "patterning", for the past half century in the hope that their understanding of pre-algebra and their mathematics achievement would be improved. The evidence that such patterning instruction actually improves children's academic achievement…

Modeling Terminal Velocity

ERIC Educational Resources Information Center

Brand, Neal; Quintanilla, John A.

2013-01-01

Using a simultaneously falling softball as a stopwatch, the terminal velocity of a whiffle ball can be obtained to surprisingly high accuracy with only common household equipment. This classroom activity engages students in an apparently daunting task that nevertheless is tractable, using a simple model and mathematical techniques at their…

Alleviating the Common Confusion Caused by Polarity in Electrochemistry.

ERIC Educational Resources Information Center

Moran, P. J.; Gileadi, E.

1989-01-01

Discussed is some of the confusion encountered in electrochemistry due to misunderstandings of sign conventions and simple mathematical errors. Clarified are issues involving emf series, IUPAC sign conventions, calculation of cell potentials, reference electrodes, the polarity of electrodes in electrochemical devices, and overpotential. (CW)

The Computer Simulation of Liquids by Molecular Dynamics.

ERIC Educational Resources Information Center

Smith, W.

1987-01-01

Proposes a mathematical computer model for the behavior of liquids using the classical dynamic principles of Sir Isaac Newton and the molecular dynamics method invented by other scientists. Concludes that other applications will be successful using supercomputers to go beyond simple Newtonian physics. (CW)

Body Data

ERIC Educational Resources Information Center

Bombaugh, Ruth; Jefferys, Lynn

2006-01-01

In this article, the authors demonstrate how a simple math lab incorporating monthly height measurements can address multiple science and mathematics standards such as collecting, organizing, and describing data in context; drawing conclusions; and making hypotheses from these data. Although the yearlong math lab can be accomplished in either the…

Traffic Flow Estimates.

ERIC Educational Resources Information Center

Hart, Vincent G.

1981-01-01

Two examples are given of ways traffic engineers estimate traffic flow. The first, Floating Car Method, involves some basic ideas and the notion of relative velocity. The second, Maximum Traffic Flow, is viewed to involve simple applications of calculus. The material provides insight into specialized applications of mathematics. (MP)

A VARIABLE REACTIVITY MODEL FOR ION BINDING TO ENVIRONMENTAL SORBENTS

EPA Science Inventory

The conceptual and mathematical basis for a new general-composite modeling approach for ion binding to environmental sorbents is presented. The work extends the Simple Metal Sorption (SiMS) model previously presented for metal and proton binding to humic substances. A surface com...

Sharpen Your Skills: Large Type.

ERIC Educational Resources Information Center

Knisely, Phillis; Wickham, Marian

1984-01-01

Three short articles about large type transcribing are provided for braille transcribers and teachers of the visually handicapped. The first article lists general suggestions for simple typewriter maintenance. The second article reviews the guidelines for typing fractions in large type for mathematics exercises. The third article describes a…

Apparatus for Teaching Physics.

ERIC Educational Resources Information Center

Minnix, Richard B.; Carpenter, D. Rae, Jr.

1983-01-01

Describes a simple apparatus and provides instructions to do relative index of refraction measurements/calculations and to show mathematical relationships betwen indices when light travels from one liquid to another. A listing of a computer program (in BASIC) which will analyze data is available from the author. (JM)

Self-Explanation Training Improves Proof Comprehension

ERIC Educational Resources Information Center

Hodds, Mark; Alcock, Lara; Inglis, Matthew

2014-01-01

In this article we report 3 experiments demonstrating that a simple booklet containing self-explanation training, designed to focus students' attention on logical relationships within a mathematical proof, can significantly improve their proof comprehension. Experiment 1 demonstrated that students who received the training generated higher quality…

Experimenting with Guitar Strings

ERIC Educational Resources Information Center

LoPresto, Michael C.

2006-01-01

What follows is a description of a simple experiment developed in a non-mathematical general education science course on sound and light for fine arts students in which a guitar is used with data collection hardware and software to verify the properties of standing waves on a string.

Special Relativity

NASA Astrophysics Data System (ADS)

Dixon, W. G.

1982-11-01

Preface; 1. The physics of space and time; 2. Affine spaces in mathematics and physics; 3. Foundations of dynamics; 4. Relativistic simple fluids; 5. Electrodynamics of polarisable fluids; Appendix: Vector and dyadic notation in three dimensions; Publications referred to in the text; Summary and index of symbols and conventions; Subject index.

Seasonally forced disease dynamics explored as switching between attractors

NASA Astrophysics Data System (ADS)

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

2001-01-01

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

Exploratory power of the harmony search algorithm: analysis and improvements for global numerical optimization.

PubMed

Das, Swagatam; Mukhopadhyay, Arpan; Roy, Anwit; Abraham, Ajith; Panigrahi, Bijaya K

2011-02-01

The theoretical analysis of evolutionary algorithms is believed to be very important for understanding their internal search mechanism and thus to develop more efficient algorithms. This paper presents a simple mathematical analysis of the explorative search behavior of a recently developed metaheuristic algorithm called harmony search (HS). HS is a derivative-free real parameter optimization algorithm, and it draws inspiration from the musical improvisation process of searching for a perfect state of harmony. This paper analyzes the evolution of the population-variance over successive generations in HS and thereby draws some important conclusions regarding the explorative power of HS. A simple but very useful modification to the classical HS has been proposed in light of the mathematical analysis undertaken here. A comparison with the most recently published variants of HS and four other state-of-the-art optimization algorithms over 15 unconstrained and five constrained benchmark functions reflects the efficiency of the modified HS in terms of final accuracy, convergence speed, and robustness.

A simple mathematical model to predict sea surface temperature over the northwest Indian Ocean

NASA Astrophysics Data System (ADS)

Noori, Roohollah; Abbasi, Mahmud Reza; Adamowski, Jan Franklin; Dehghani, Majid

2017-10-01

A novel and simple mathematical model was developed in this study to enhance the capacity of a reduced-order model based on eigenvectors (RMEV) to predict sea surface temperature (SST) in the northwest portion of the Indian Ocean, including the Persian and Oman Gulfs and Arabian Sea. Developed using only the first two of 12,416 possible modes, the enhanced RMEV closely matched observed daily optimum interpolation SST (DOISST) values. Spatial distribution of the first mode indicated the greatest variations in DOISST occurred in the Persian Gulf. Also, the slightly increasing trend in the temporal component of the first mode observed in the study area over the last 34 years properly reflected the impact of climate change and rising DOISST. Given its simplicity and high level of accuracy, the enhanced RMEV can be applied to forecast DOISST in oceans, which the poor forecasting performance and large computational-time of other numerical models may not allow.

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

The written mathematical communication profile of prospective math teacher in mathematical proving

NASA Astrophysics Data System (ADS)

Pantaleon, K. V.; Juniati, D.; Lukito, A.; Mandur, K.

2018-01-01

Written mathematical communication is the process of expressing mathematical ideas and understanding in writing. It is one of the important aspects that must be mastered by the prospective math teacher as tool of knowledge transfer. This research was a qualitative research that aimed to describe the mathematical communication profile of the prospective mathematics teacher in mathematical proving. This research involved 48 students of Mathematics Education Study Program; one of them with moderate math skills was chosen as the main subject. Data were collected through tests, assignments, and task-based interviews. The results of this study point out that in the proof of geometry, the subject explains what is understood, presents the idea in the form of drawing and symbols, and explains the content/meaning of a representation accurately and clearly, but the subject can not convey the argument systematically and logically. Whereas in the proof of algebra, the subject describes what is understood, explains the method used, and describes the content/meaning of a symbolic representation accurately, systematically, logically, but the argument presented is not clear because it is insufficient detailed and complete.

Essential Mathematics for the Physical Sciences; Volume I: Homogeneous boundary value problems, Fourier methods, and special functions

NASA Astrophysics Data System (ADS)

Borden, Brett; Luscombe, James

2017-10-01

Physics is expressed in the language of mathematics; it is deeply ingrained in how physics is taught and how it's practiced. A study of the mathematics used in science is thus a sound intellectual investment for training as scientists and engineers. This first volume of two is centered on methods of solving partial differential equations and the special functions introduced. This text is based on a course offered at the Naval Postgraduate School (NPS) and while produced for NPS needs, it will serve other universities well.

A Hilbert Space Representation of Generalized Observables and Measurement Processes in the ESR Model

NASA Astrophysics Data System (ADS)

Sozzo, Sandro; Garola, Claudio

2010-12-01

The extended semantic realism ( ESR) model recently worked out by one of the authors embodies the mathematical formalism of standard (Hilbert space) quantum mechanics in a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute. We provide here a Hilbert space representation of the generalized observables introduced by the ESR model that satisfy a simple physical condition, propose a generalization of the projection postulate, and suggest a possible mathematical description of the measurement process in terms of evolution of the compound system made up of the measured system and the measuring apparatus.

REVIEWS OF TOPICAL PROBLEMS: Analytic calculations on digital computers for applications in physics and mathematics

NASA Astrophysics Data System (ADS)

Gerdt, V. P.; Tarasov, O. V.; Shirkov, Dmitrii V.

1980-01-01

The present state of analytic calculations on computers is reviewed. Several programming systems which are used for analytic calculations are discussed: SCHOONSCHIP, CLAM, REDUCE-2, SYMBAL, CAMAL, AVTO-ANALITIK, MACSYMA, etc. It is shown that these systems can be used to solve a wide range of problems in physics and mathematics. Some physical applications are discussed in celestial mechanics, the general theory of relativity, quantum field theory, plasma physics, hydrodynamics, atomic and molecular physics, and quantum chemistry. Some mathematical applications which are discussed are evaluating indefinite integrals, solving differential equations, and analyzing mathematical expressions. This review is addressed to physicists and mathematicians working in a wide range of fields.