The first accurate description of an aurora
NASA Astrophysics Data System (ADS)
Schröder, Wilfried
2006-12-01
As technology has advanced, the scientific study of auroral phenomena has increased by leaps and bounds. A look back at the earliest descriptions of aurorae offers an interesting look into how medieval scholars viewed the subjects that we study.Although there are earlier fragmentary references in the literature, the first accurate description of the aurora borealis appears to be that published by the German Catholic scholar Konrad von Megenberg (1309-1374) in his book Das Buch der Natur (The Book of Nature). The book was written between 1349 and 1350.
NASA Astrophysics Data System (ADS)
Kim, Jibeom; Jeon, Joonhyeon
2015-01-01
Recently, related studies on Equation Of State (EOS) have reported that generalized van der Waals (GvdW) shows poor representations in the near critical region for non-polar and non-sphere molecules. Hence, there are still remains a problem of GvdW parameters to minimize loss in describing saturated vapor densities and vice versa. This paper describes a recursive model GvdW (rGvdW) for an accurate representation of pure fluid materials in the near critical region. For the performance evaluation of rGvdW in the near critical region, other EOS models are also applied together with two pure molecule group: alkane and amine. The comparison results show rGvdW provides much more accurate and reliable predictions of pressure than the others. The calculating model of EOS through this approach gives an additional insight into the physical significance of accurate prediction of pressure in the nearcritical region.
Mathematical Description of Dendrimer Structure
NASA Technical Reports Server (NTRS)
Majoros, Istvan J.; Mehta, Chandan B.; Baker, James R., Jr.
2004-01-01
Characteristics of starburst dendrimers can be easily attributed to the multiplicity of the monomers used to synthesize them. The molecular weight, degree of polymerization, number of terminal groups and branch points for each generation of a dendrimer can be calculated using mathematical formulas incorporating these variables. Mathematical models for the calculation of degree of polymerization, molecular weight, and number of terminal groups and branching groups previously published were revised and elaborated on for poly(amidoamine) (PAMAM) dendrimers, and introduced for poly(propyleneimine) (POPAM) dendrimers and the novel POPAM-PAMAM hybrid, which we call the POMAM dendrimer. Experimental verification of the relationship between theoretical and actual structure for the PAMAM dendrimer was also established.
Accurate Variational Description of Adiabatic Quantum Optimization
NASA Astrophysics Data System (ADS)
Carleo, Giuseppe; Bauer, Bela; Troyer, Matthias
Adiabatic quantum optimization (AQO) is a quantum computing protocol where a system is driven by a time-dependent Hamiltonian. The initial Hamiltonian has an easily prepared ground-state and the final Hamiltonian encodes some desired optimization problem. An adiabatic time evolution then yields a solution to the optimization problem. Several challenges emerge in the theoretical description of this protocol: on one hand, the exact simulation of quantum dynamics is exponentially complex in the size of the optimization problem. On the other hand, approximate approaches such as tensor network states (TNS) are limited to small instances by the amount of entanglement that can be encoded. I will present here an extension of the time-dependent Variational Monte Carlo approach to problems in AQO. This approach is based on a general class of (Jastrow-Feenberg) entangled states, whose parameters are evolved in time according to a stochastic variational principle. We demonstrate this approach for optimization problems of the Ising spin-glass type. A very good accuracy is achieved when compared to exact time-dependent TNS on small instances. We then apply this approach to larger problems, and discuss the efficiency of the quantum annealing scheme in comparison with its classical counterpart.
Towards a Mathematical Description of Biodiversity Evolution
NASA Astrophysics Data System (ADS)
Horvath, Jorge E.
2014-09-01
We outline in this work a mathematical description of biodiversity evolution based on a second-order differential equation (also known as the "inertial/Galilean view"). After discussing the motivations and explicit forms of the simplest "forces", we are lead to an equation analogue to a harmonic oscillator. The known solutions for the homogeneous problem are then tentatively related to the biodiversity curves of Sepkoski and Alroy et al., suggesting mostly an inertial behavior of the time evolution of the number of genera and a quadratic behavior in some long-term evolution after extinction events. We present the Green function for the dynamical system and apply it to the description of the recovery curve after the Permo-Triassic extinction, as recently analyzed by Burgess, Bowring and Shen. Even though the agreement is not satisfactory, we point out direct connections between observed drop times after massive extinctions and mathematical constants and discuss why the failure ensues, suggesting a more complex form of the second-order mathematical description.
A new and accurate continuum description of moving fronts
NASA Astrophysics Data System (ADS)
Johnston, S. T.; Baker, R. E.; Simpson, M. J.
2017-03-01
Processes that involve moving fronts of populations are prevalent in ecology and cell biology. A common approach to describe these processes is a lattice-based random walk model, which can include mechanisms such as crowding, birth, death, movement and agent–agent adhesion. However, these models are generally analytically intractable and it is computationally expensive to perform sufficiently many realisations of the model to obtain an estimate of average behaviour that is not dominated by random fluctuations. To avoid these issues, both mean-field (MF) and corrected mean-field (CMF) continuum descriptions of random walk models have been proposed. However, both continuum descriptions are inaccurate outside of limited parameter regimes, and CMF descriptions cannot be employed to describe moving fronts. Here we present an alternative description in terms of the dynamics of groups of contiguous occupied lattice sites and contiguous vacant lattice sites. Our description provides an accurate prediction of the average random walk behaviour in all parameter regimes. Critically, our description accurately predicts the persistence or extinction of the population in situations where previous continuum descriptions predict the opposite outcome. Furthermore, unlike traditional MF models, our approach provides information about the spatial clustering within the population and, subsequently, the moving front.
Practice; criteria; provisions; mathematical descriptions: Examples
NASA Astrophysics Data System (ADS)
Wijdieks, J.
1983-06-01
Waterhammer is defined as the appearance of pressure changes in closed conduits caused by velocity changes with time of the flow. Therefore waterhammer may occur in all kinds of pipelines in which flow changes occur over time: long or short pipelines for oil, sewage, drinking water, cooling water, slurry, coal slurry, chemicals, and in fresh water or city heating networks. The phenomenon of waterhammer is discussed herein. Specific parameters addressed include: the practical causes of waterhammer, cavitation flow, overpressure, vapor pressures, bulk modulus, continuous and discontinuous flow, and provisions to prevent waterhammer. Calculation of waterhammer is presented along with a mathematical description thereof. Hydraulic equipment (valves, pumps, surge towers) is also discussed.
Secondary Students' Descriptions of "Good" Mathematics Teachers
ERIC Educational Resources Information Center
Murray, Sara
2011-01-01
There are many recent studies which have explored the notion of high quality or effective mathematics teaching but relatively few have sought the views of students. Student perspectives regarding effective teaching are important for many reasons, and are arguably particularly significant in mathematics given the international trends of declining…
Simple Mathematical Models Do Not Accurately Predict Early SIV Dynamics
Noecker, Cecilia; Schaefer, Krista; Zaccheo, Kelly; Yang, Yiding; Day, Judy; Ganusov, Vitaly V.
2015-01-01
Upon infection of a new host, human immunodeficiency virus (HIV) replicates in the mucosal tissues and is generally undetectable in circulation for 1–2 weeks post-infection. Several interventions against HIV including vaccines and antiretroviral prophylaxis target virus replication at this earliest stage of infection. Mathematical models have been used to understand how HIV spreads from mucosal tissues systemically and what impact vaccination and/or antiretroviral prophylaxis has on viral eradication. Because predictions of such models have been rarely compared to experimental data, it remains unclear which processes included in these models are critical for predicting early HIV dynamics. Here we modified the “standard” mathematical model of HIV infection to include two populations of infected cells: cells that are actively producing the virus and cells that are transitioning into virus production mode. We evaluated the effects of several poorly known parameters on infection outcomes in this model and compared model predictions to experimental data on infection of non-human primates with variable doses of simian immunodifficiency virus (SIV). First, we found that the mode of virus production by infected cells (budding vs. bursting) has a minimal impact on the early virus dynamics for a wide range of model parameters, as long as the parameters are constrained to provide the observed rate of SIV load increase in the blood of infected animals. Interestingly and in contrast with previous results, we found that the bursting mode of virus production generally results in a higher probability of viral extinction than the budding mode of virus production. Second, this mathematical model was not able to accurately describe the change in experimentally determined probability of host infection with increasing viral doses. Third and finally, the model was also unable to accurately explain the decline in the time to virus detection with increasing viral dose. These results
Towards a Bernsteinian Language of Description for Mathematics Classroom Discourse
ERIC Educational Resources Information Center
Straehler-Pohl, Hauke; Gellert, Uwe
2013-01-01
This article aims at developing an external language of description to investigate the problem of why particular groups of students are systematically not provided access to school mathematical knowledge. Based on Basil Bernstein's conceptualisation of power in classification, we develop a three-dimensional model that operationalises the…
Connecting Intonation Labels to Mathematical Descriptions of Fundamental Frequency
ERIC Educational Resources Information Center
Grabe, Esther; Kochanski, Greg; Coleman, John
2007-01-01
The mathematical models of intonation used in speech technology are often inaccessible to linguists. By the same token, phonological descriptions of intonation are rarely used by speech technologists, as they cannot be implemented directly in applications. Consequently, these research communities do not benefit much from each other's insights. In…
Santolini, Marc; Mora, Thierry; Hakim, Vincent
2014-01-01
The identification of transcription factor binding sites (TFBSs) on genomic DNA is of crucial importance for understanding and predicting regulatory elements in gene networks. TFBS motifs are commonly described by Position Weight Matrices (PWMs), in which each DNA base pair contributes independently to the transcription factor (TF) binding. However, this description ignores correlations between nucleotides at different positions, and is generally inaccurate: analysing fly and mouse in vivo ChIPseq data, we show that in most cases the PWM model fails to reproduce the observed statistics of TFBSs. To overcome this issue, we introduce the pairwise interaction model (PIM), a generalization of the PWM model. The model is based on the principle of maximum entropy and explicitly describes pairwise correlations between nucleotides at different positions, while being otherwise as unconstrained as possible. It is mathematically equivalent to considering a TF-DNA binding energy that depends additively on each nucleotide identity at all positions in the TFBS, like the PWM model, but also additively on pairs of nucleotides. We find that the PIM significantly improves over the PWM model, and even provides an optimal description of TFBS statistics within statistical noise. The PIM generalizes previous approaches to interdependent positions: it accounts for co-variation of two or more base pairs, and predicts secondary motifs, while outperforming multiple-motif models consisting of mixtures of PWMs. We analyse the structure of pairwise interactions between nucleotides, and find that they are sparse and dominantly located between consecutive base pairs in the flanking region of TFBS. Nonetheless, interactions between pairs of non-consecutive nucleotides are found to play a significant role in the obtained accurate description of TFBS statistics. The PIM is computationally tractable, and provides a general framework that should be useful for describing and predicting TFBSs beyond
THE SHEFFIELD ALCOHOL POLICY MODEL - A MATHEMATICAL DESCRIPTION.
Brennan, Alan; Meier, Petra; Purshouse, Robin; Rafia, Rachid; Meng, Yang; Hill-Macmanus, Daniel; Angus, Colin; Holmes, John
2014-09-30
This methodology paper sets out a mathematical description of the Sheffield Alcohol Policy Model version 2.0, a model to evaluate public health strategies for alcohol harm reduction in the UK. Policies that can be appraised include a minimum price per unit of alcohol, restrictions on price discounting, and broader public health measures. The model estimates the impact on consumers, health services, crime, employers, retailers and government tax revenues. The synthesis of public and commercial data sources to inform the model structure is described. A detailed algebraic description of the model is provided. This involves quantifying baseline levels of alcohol purchasing and consumption by age and gender subgroups, estimating the impact of policies on consumption, for example, using evidence on price elasticities of demand for alcohol, quantification of risk functions relating alcohol consumption to harms including 47 health conditions, crimes, absenteeism and unemployment, and finally monetary valuation of the consequences. The results framework, shown for a minimum price per unit of alcohol, has been used to provide policy appraisals for the UK government policy-makers. In discussion and online appendix, we explore issues around valuation and scope, limitations of evidence/data, how the framework can be adapted to other countries and decisions, and ongoing plans for further development. © 2014 The Authors. Health Economics published by John Wiley & Sons Ltd.
Researchers' Descriptions and the Construction of Mathematical Thinking
ERIC Educational Resources Information Center
Barwell, Richard
2009-01-01
Research in mathematics education is a discursive process: It entails the analysis and production of texts, whether in the analysis of what learners say, the use of transcripts, or the publication of research reports. Much research in mathematics education is concerned with various aspects of mathematical thinking, including mathematical knowing,…
Deadline rush: a time management phenomenon and its mathematical description.
König, Cornelius J; Kleinmann, Martin
2005-01-01
A typical time management phenomenon is the rush before a deadline. Behavioral decision making research can be used to predict how behavior changes before a deadline. People are likely not to work on a project with a deadline in the far future because they generally discount future outcomes. Only when the deadline is close are people likely to work. On the basis of recent intertemporal choice experiments, the authors argue that a hyperbolic function should provide a more accurate description of the deadline rush than an exponential function predicted by an economic model of discounted utility. To show this, the fit of the hyperbolic and the exponential function were compared with data sets that describe when students study for exams. As predicted, the hyperbolic function fit the data significantly better than the exponential function. The implication for time management decisions is that they are most likely to be inconsistent over time (i.e., people make a plan how to use their time but do not follow it).
Accurate description of argon and water adsorption on surfaces of graphene-based carbon allotropes.
Kysilka, Jiří; Rubeš, Miroslav; Grajciar, Lukáš; Nachtigall, Petr; Bludský, Ota
2011-10-20
Accurate interaction energies of nonpolar (argon) and polar (water) adsorbates with graphene-based carbon allotropes were calculated by means of a combined density functional theory (DFT)-ab initio computational scheme. The calculated interaction energy of argon with graphite (-9.7 kJ mol(-1)) is in excellent agreement with the available experimental data. The calculated interaction energy of water with graphene and graphite is -12.8 and -14.6 kJ mol(-1), respectively. The accuracy of combined DFT-ab initio methods is discussed in detail based on a comparison with the highly precise interaction energies of argon and water with coronene obtained at the coupled-cluster CCSD(T) level extrapolated to the complete basis set (CBS) limit. A new strategy for a reliable estimate of the CBS limit is proposed for systems where numerical instabilities occur owing to basis-set near-linear dependence. The most accurate estimate of the argon and water interaction with coronene (-8.1 and -14.0 kJ mol(-1), respectively) is compared with the results of other methods used for the accurate description of weak intermolecular interactions.
Maudlin, P.J.; Stout, M.G.
1996-09-01
Strength and fracture constitutive relationships containing strain rate dependence and thermal softening are important for accurate simulation of metal cutting. The mechanical behavior of a hardened 4340 steel was characterized using the von Mises yield function, the Mechanical Threshold Stress model and the Johnson- Cook fracture model. This constitutive description was implemented into the explicit Lagrangian FEM continuum-mechanics code EPIC, and orthogonal plane-strain metal cutting calculations were performed. Heat conduction and friction at the toolwork-piece interface were included in the simulations. These transient calculations were advanced in time until steady state machining behavior (force) was realized. Experimental cutting force data (cutting and thrust forces) were measured for a planning operation and compared to the calculations. 13 refs., 6 figs.
Accurate electronic-structure description of Mn complexes: a GGA+U approach
NASA Astrophysics Data System (ADS)
Li, Elise Y.; Kulik, Heather; Marzari, Nicola
2008-03-01
Conventional density-functional approach often fail in offering an accurate description of the spin-resolved energetics in transition metals complexes. We will focus here on Mn complexes, where many aspects of the molecular structure and the reaction mechanisms are still unresolved - most notably in the oxygen-evolving complex (OEC) of photosystem II and the manganese catalase (MC). We apply a self-consistent GGA + U approach [1], originally designed within the DFT framework for the treatment of strongly correlated materials, to describe the geometry, the electronic and the magnetic properties of various manganese oxide complexes, finding very good agreement with higher-order ab-initio calculations. In particular, the different oxidation states of dinuclear systems containing the [Mn2O2]^n+ (n= 2, 3, 4) core are investigated, in order to mimic the basic face unit of the OEC complex. [1]. H. J. Kulik, M. Cococcioni, D. A. Scherlis, N. Marzari, Phys. Rev. Lett., 2006, 97, 103001
Descriptions of Free and Freeware Software in the Mathematics Teaching
NASA Astrophysics Data System (ADS)
Antunes de Macedo, Josue; Neves de Almeida, Samara; Voelzke, Marcos Rincon
2016-05-01
This paper presents the analysis and the cataloging of free and freeware mathematical software available on the internet, a brief explanation of them, and types of licenses for use in teaching and learning. The methodology is based on the qualitative research. Among the different types of software found, it stands out in algebra, the Winmat, that works with linear algebra, matrices and linear systems. In geometry, the GeoGebra, which can be used in the study of functions, plan and spatial geometry, algebra and calculus. For graphing, can quote the Graph and Graphequation. With Graphmatica software, it is possible to build various graphs of mathematical equations on the same screen, representing cartesian equations, inequalities, parametric among other functions. The Winplot allows the user to build graphics in two and three dimensions functions and mathematical equations. Thus, this work aims to present the teachers some free math software able to be used in the classroom.
Mathematical Descriptions of Biochemical Networks: Stability, Stochasticity, Evolution
Rosenfeld, Simon
2011-01-01
In this paper, we review some fundamental aspects, as well as some new developments, in the emerging field of network biology. The focus of attention is placed on mathematical approaches to conceptual modeling of biomolecular networks with special emphasis on dynamic stability, stochasticity and evolution. PMID:21419158
Problems of the mathematical description of rocket engines as plants
NASA Astrophysics Data System (ADS)
Kiforenko, B. N.
2012-09-01
Mathematical models of liquid-propellant, nuclear, and electric rocket engines are presented that more fully describe thrust generation than the classical models do. The optimal control of engine thrust is analyzed within the framework of Mayer's general variational problem. It is shown that the control of a rocket engine satisfying the necessary optimality conditions belongs to the boundary arc of the feasible control set between the point of maximum thrust and the point of maximum exhaust velocity
Spear, Jack; Fields, Lanny
2015-12-01
Interpreting and describing complex information shown in graphs are essential skills to be mastered by students in many disciplines; both are skills that are difficult to learn. Thus, interventions that produce these outcomes are of great value. Previous research showed that conditional discrimination training that established stimulus control by some elements of graphs and their printed descriptions produced some improvement in the accuracy of students' written descriptions of graphs. In the present experiment, students wrote nearly perfect descriptions of the information conveyed in interaction-based graphs after the establishment of conditional relations between graphs and their printed descriptions. This outcome was achieved with the use of special conditional discrimination training procedures that required participants to attend to many of the key elements of the graphs and the phrases in the printed descriptions that corresponded to the elements in the graphs. Thus, students learned to write full descriptions of the information represented by complex graphs by an automated training procedure that did not involve the direct training of writing.
Description of a tilt wing mathematical model for piloted simulation
NASA Technical Reports Server (NTRS)
Totah, Joseph J.
1991-01-01
A tilt-wing mathematical model that was used in a piloted six-deg-of-freedom flight simulation application is presented. Two types of control systems developed for the model - a conventional programmed-flap wing-tilt control system and a geared-flap wing-tilt control system - are discussed. The objective of this effort was to develop the capability to study tilt-wing aircraft. Experienced tilt-wing pilots subjectively evaluated the model using programmed-flap control to assess the quality of the simulation. The objective was met and the model was then applied to study geared-flap control to investigate the possibility of eliminating the need for auxiliary pitch control devices. This was performed in the moving-base simulation environment, and the vehicle responses with programmed-flap and geared-flap control were compared.
NASA Technical Reports Server (NTRS)
Lennington, R. K.; Rassbach, M. E.
1979-01-01
Discussed in this report is the clustering algorithm CLASSY, including detailed descriptions of its general structure and mathematical background and of the various major subroutines. The report provides a development of the logic and equations used with specific reference to program variables. Some comments on timing and proposed optimization techniques are included.
Physical and Mathematical Description of Nuclear Weapons Identification System (NWIS) Signatures
Mattingly, J.K.; Mihalczo, J.T.; Mullens, J.A.; Valentine, T.E.
1997-09-26
This report describes all time and frequency analysis parameters measured with the new Nuclear Weapons Identification System (NWIS) processor with three input channels: (1) the 252Cf source ionization chamber (2) a detection channel; and (3) a second detection channel for active measurements. An intuitive and physical description of the various functions is given as well as a brief mathematical description and a brief description of how the data are acquired. If the fill five channel capability is used, the number of functions increases in number but not in type. The parameters provided by this new NWIS processor can be divided into two general classes: time analysis signatures including multiplicities and frequency analysis signatures. Data from measurements with an 18.75 kg highly enriched uranium (93.2 wt 0/0, 235U) metai casting for storage are presented to illustrate the various time and frequency analysis parameters.
Physical and mathematical description of Nuclear Weapons Identification System (NWIS) signatures
Mihalczo, J.T.; Valentine, T.E.; Mullens, J.A.; Mattingly, J.K.
1997-09-26
This report describes all time and frequency analysis parameters measured with the new Nuclear Weapons Identification System (NWIS) processor with three input channels: (1) the {sup 252}Cf source ionization chamber; (2) a detection channel; and (3) a second detection channel for active measurements. An intuitive and physical description of the various functions is given as well as a brief mathematical description and a brief description of how the data are acquired. If the full five channel capability is used, the number of functions increases in number but not in type. The parameters provided by this new NWIS processor can be divided into two general classes: time analysis signatures including multiplicities and frequency analysis signatures. Data from measurements with an 18.75 kg highly enriched uranium (93.2 wt%, {sup 235}U) metal casting for storage are presented to illustrate the various time and frequency analysis parameters.
Towards an accurate description of perovskite ferroelectrics: exchange and correlation effects
Yuk, Simuck F.; Pitike, Krishna Chaitanya; Nakhmanson, Serge M.; Eisenbach, Markus; Li, Ying Wai; Cooper, Valentino R.
2017-01-01
Using the van der Waals density functional with C09 exchange (vdW-DF-C09), which has been applied to describing a wide range of dispersion-bound systems, we explore the physical properties of prototypical ABO3 bulk ferroelectric oxides. Surprisingly, vdW-DF-C09 provides a superior description of experimental values for lattice constants, polarization and bulk moduli, exhibiting similar accuracy to the modified Perdew-Burke-Erzenhoff functional which was designed specifically for bulk solids (PBEsol). The relative performance of vdW-DF-C09 is strongly linked to the form of the exchange enhancement factor which, like PBEsol, tends to behave like the gradient expansion approximation for small reduced gradients. These results suggest the general-purpose nature of the class of vdW-DF functionals, with particular consequences for predicting material functionality across dense and sparse matter regimes. PMID:28256544
Towards an accurate description of perovskite ferroelectrics: exchange and correlation effects.
Yuk, Simuck F; Pitike, Krishna Chaitanya; Nakhmanson, Serge M; Eisenbach, Markus; Li, Ying Wai; Cooper, Valentino R
2017-03-03
Using the van der Waals density functional with C09 exchange (vdW-DF-C09), which has been applied to describing a wide range of dispersion-bound systems, we explore the physical properties of prototypical ABO3 bulk ferroelectric oxides. Surprisingly, vdW-DF-C09 provides a superior description of experimental values for lattice constants, polarization and bulk moduli, exhibiting similar accuracy to the modified Perdew-Burke-Erzenhoff functional which was designed specifically for bulk solids (PBEsol). The relative performance of vdW-DF-C09 is strongly linked to the form of the exchange enhancement factor which, like PBEsol, tends to behave like the gradient expansion approximation for small reduced gradients. These results suggest the general-purpose nature of the class of vdW-DF functionals, with particular consequences for predicting material functionality across dense and sparse matter regimes.
Towards an accurate description of perovskite ferroelectrics: exchange and correlation effects
Yuk, Simuck F.; Pitike, Krishna Chaitanya; Nakhmanson, Serge M.; ...
2017-03-03
Using the van der Waals density functional with C09 exchange (vdW-DF-C09), which has been applied to describing a wide range of dispersion-bound systems, we explore the physical properties of prototypical ABO3 bulk ferroelectric oxides. Surprisingly, vdW-DF-C09 provides a superior description of experimental values for lattice constants, polarization and bulk moduli, exhibiting similar accuracy to the modified Perdew-Burke-Erzenhoff functional which was designed specifically for bulk solids (PBEsol). The relative performance of vdW-DF-C09 is strongly linked to the form of the exchange enhancement factor which, like PBEsol, tends to behave like the gradient expansion approximation for small reduced gradients. These results suggestmore » the general-purpose nature of the class of vdW-DF functionals, with particular consequences for predicting material functionality across dense and sparse matter regimes.« less
Models in biology: ‘accurate descriptions of our pathetic thinking’
2014-01-01
In this essay I will sketch some ideas for how to think about models in biology. I will begin by trying to dispel the myth that quantitative modeling is somehow foreign to biology. I will then point out the distinction between forward and reverse modeling and focus thereafter on the former. Instead of going into mathematical technicalities about different varieties of models, I will focus on their logical structure, in terms of assumptions and conclusions. A model is a logical machine for deducing the latter from the former. If the model is correct, then, if you believe its assumptions, you must, as a matter of logic, also believe its conclusions. This leads to consideration of the assumptions underlying models. If these are based on fundamental physical laws, then it may be reasonable to treat the model as ‘predictive’, in the sense that it is not subject to falsification and we can rely on its conclusions. However, at the molecular level, models are more often derived from phenomenology and guesswork. In this case, the model is a test of its assumptions and must be falsifiable. I will discuss three models from this perspective, each of which yields biological insights, and this will lead to some guidelines for prospective model builders. PMID:24886484
Accurate description of the electronic structure of organic semiconductors by GW methods
NASA Astrophysics Data System (ADS)
Marom, Noa
2017-03-01
Electronic properties associated with charged excitations, such as the ionization potential (IP), the electron affinity (EA), and the energy level alignment at interfaces, are critical parameters for the performance of organic electronic devices. To computationally design organic semiconductors and functional interfaces with tailored properties for target applications it is necessary to accurately predict these properties from first principles. Many-body perturbation theory is often used for this purpose within the GW approximation, where G is the one particle Green’s function and W is the dynamically screened Coulomb interaction. Here, the formalism of GW methods at different levels of self-consistency is briefly introduced and some recent applications to organic semiconductors and interfaces are reviewed.
ERIC Educational Resources Information Center
Petras, Carol-Lynn M.
2010-01-01
This descriptive study was conducted because there is a lack of information regarding the pedagogical orientation associated with Information and Communication Technology, ICT, use in United States mathematics and science classrooms. Eighth grade science and mathematics teachers' pedagogical orientations, their use ICT when teaching and how ICT…
Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth
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
NASA Astrophysics Data System (ADS)
Bianchi, Davide; Chiesa, Matteo; Guzzo, Luigi
2016-10-01
As a step towards a more accurate modelling of redshift-space distortions (RSD) in galaxy surveys, we develop a general description of the probability distribution function of galaxy pairwise velocities within the framework of the so-called streaming model. For a given galaxy separation , such function can be described as a superposition of virtually infinite local distributions. We characterize these in terms of their moments and then consider the specific case in which they are Gaussian functions, each with its own mean μ and variance σ2. Based on physical considerations, we make the further crucial assumption that these two parameters are in turn distributed according to a bivariate Gaussian, with its own mean and covariance matrix. Tests using numerical simulations explicitly show that with this compact description one can correctly model redshift-space distorsions on all scales, fully capturing the overall linear and nonlinear dynamics of the galaxy flow at different separations. In particular, we naturally obtain Gaussian/exponential, skewed/unskewed distribution functions, depending on separation as observed in simulations and data. Also, the recently proposed single-Gaussian description of redshift-space distortions is included in this model as a limiting case, when the bivariate Gaussian is collapsed to a two-dimensional Dirac delta function. More work is needed, but these results indicate a very promising path to make definitive progress in our program to improve RSD estimators.
Lao, Ka Un; Schäffer, Rainer; Jansen, Georg; Herbert, John M
2015-06-09
Three new data sets for intermolecular interactions, AHB21 for anion-neutral dimers, CHB6 for cation-neutral dimers, and IL16 for ion pairs, are assembled here, with complete-basis CCSD(T) results for each. These benchmarks are then used to evaluate the accuracy of the single-exchange approximation that is used for exchange energies in symmetry-adapted perturbation theory (SAPT), and the accuracy of SAPT based on wave function and density-functional descriptions of the monomers is evaluated. High-level SAPT calculations afford poor results for these data sets, and this includes the recently proposed "gold", "silver", and "bronze standards" of SAPT, namely, SAPT2+(3)-δMP2/aug-cc-pVTZ, SAPT2+/aug-cc-pVDZ, and sSAPT0/jun-cc-pVDZ, respectively [ Parker , T. M. , et al. , J. Chem. Phys. 2014 , 140 , 094106 ]. Especially poor results are obtained for symmetric shared-proton systems of the form X(-)···H(+)···X(-), for X = F, Cl, or OH. For the anionic data set, the SAPT2+(CCD)-δMP2/aug-cc-pVTZ method exhibits the best performance, with a mean absolute error (MAE) of 0.3 kcal/mol and a maximum error of 0.7 kcal/mol. For the cationic data set, the highest-level SAPT method, SAPT2+3-δMP2/aug-cc-pVQZ, outperforms the rest of the SAPT methods, with a MAE of 0.2 kcal/mol and a maximum error of 0.4 kcal/mol. For the ion-pair data set, the SAPT2+3-δMP2/aug-cc-pVTZ performs the best among all SAPT methods with a MAE of 0.3 kcal/mol and a maximum error of 0.9 kcal/mol. Overall, SAPT2+3-δMP2/aug-cc-pVTZ affords a small and balanced MAE (<0.5 kcal/mol) for all three data sets, with an overall MAE of 0.4 kcal/mol. Despite the breakdown of perturbation theory for ionic systems at short-range, SAPT can still be saved given two corrections: a "δHF" correction, which requires a supermolecular Hartree-Fock calculation to incorporate polarization effects beyond second order, and a "δMP2" correction, which requires a supermolecular MP2 calculation to account for higher
2011-01-01
Background Data assimilation refers to methods for updating the state vector (initial condition) of a complex spatiotemporal model (such as a numerical weather model) by combining new observations with one or more prior forecasts. We consider the potential feasibility of this approach for making short-term (60-day) forecasts of the growth and spread of a malignant brain cancer (glioblastoma multiforme) in individual patient cases, where the observations are synthetic magnetic resonance images of a hypothetical tumor. Results We apply a modern state estimation algorithm (the Local Ensemble Transform Kalman Filter), previously developed for numerical weather prediction, to two different mathematical models of glioblastoma, taking into account likely errors in model parameters and measurement uncertainties in magnetic resonance imaging. The filter can accurately shadow the growth of a representative synthetic tumor for 360 days (six 60-day forecast/update cycles) in the presence of a moderate degree of systematic model error and measurement noise. Conclusions The mathematical methodology described here may prove useful for other modeling efforts in biology and oncology. An accurate forecast system for glioblastoma may prove useful in clinical settings for treatment planning and patient counseling. Reviewers This article was reviewed by Anthony Almudevar, Tomas Radivoyevitch, and Kristin Swanson (nominated by Georg Luebeck). PMID:22185645
Ballester, Pedro J; Schreyer, Adrian; Blundell, Tom L
2014-03-24
Predicting the binding affinities of large sets of diverse molecules against a range of macromolecular targets is an extremely challenging task. The scoring functions that attempt such computational prediction are essential for exploiting and analyzing the outputs of docking, which is in turn an important tool in problems such as structure-based drug design. Classical scoring functions assume a predetermined theory-inspired functional form for the relationship between the variables that describe an experimentally determined or modeled structure of a protein-ligand complex and its binding affinity. The inherent problem of this approach is in the difficulty of explicitly modeling the various contributions of intermolecular interactions to binding affinity. New scoring functions based on machine-learning regression models, which are able to exploit effectively much larger amounts of experimental data and circumvent the need for a predetermined functional form, have already been shown to outperform a broad range of state-of-the-art scoring functions in a widely used benchmark. Here, we investigate the impact of the chemical description of the complex on the predictive power of the resulting scoring function using a systematic battery of numerical experiments. The latter resulted in the most accurate scoring function to date on the benchmark. Strikingly, we also found that a more precise chemical description of the protein-ligand complex does not generally lead to a more accurate prediction of binding affinity. We discuss four factors that may contribute to this result: modeling assumptions, codependence of representation and regression, data restricted to the bound state, and conformational heterogeneity in data.
NASA Astrophysics Data System (ADS)
Nold, Andreas; Goddard, Ben; Sibley, David; Kalliadasis, Serafim
2014-03-01
Multiscale effects play a predominant role in wetting phenomena such as the moving contact line. An accurate description is of paramount interest for a wide range of industrial applications, yet it is a matter of ongoing research, due to the difficulty of incorporating different physical effects in one model. Important small-scale phenomena are corrections to the attractive fluid-fluid and wall-fluid forces in inhomogeneous density distributions, which often previously have been accounted for by the disjoining pressure in an ad-hoc manner. We systematically derive a novel model for the description of a single-component liquid-vapor multiphase system which inherently incorporates these nonlocal effects. This derivation, which is inspired by statistical mechanics in the framework of colloidal density functional theory, is critically discussed with respect to its assumptions and restrictions. The model is then employed numerically to study a moving contact line of a liquid fluid displacing its vapor phase. We show how nonlocal physical effects are inherently incorporated by the model and describe how classical macroscopic results for the contact line motion are retrieved. We acknowledge financial support from ERC Advanced Grant No. 247031 and Imperial College through a DTG International Studentship.
McDonnell, Mark D; Mohan, Ashutosh; Stricker, Christian
2013-01-01
The release of neurotransmitter vesicles after arrival of a pre-synaptic action potential (AP) at cortical synapses is known to be a stochastic process, as is the availability of vesicles for release. These processes are known to also depend on the recent history of AP arrivals, and this can be described in terms of time-varying probabilities of vesicle release. Mathematical models of such synaptic dynamics frequently are based only on the mean number of vesicles released by each pre-synaptic AP, since if it is assumed there are sufficiently many vesicle sites, then variance is small. However, it has been shown recently that variance across sites can be significant for neuron and network dynamics, and this suggests the potential importance of studying short-term plasticity using simulations that do generate trial-to-trial variability. Therefore, in this paper we study several well-known conceptual models for stochastic availability and release. We state explicitly the random variables that these models describe and propose efficient algorithms for accurately implementing stochastic simulations of these random variables in software or hardware. Our results are complemented by mathematical analysis and statement of pseudo-code algorithms.
Kalugina, A V; Komarova, L N; Petin, V G
2002-01-01
For mathematical description of synergetic interaction of high environmental temperature and microwaves for animal heating, a simple semi-empirical model was used. In the model, it is suggested that the mechanism of synergistic interaction is caused by the additional effective damages resulting in more higher body temperature increment comparing with that expected for the independent action of each agents. These additional damages are supposed to be produced by the interaction of sublesions induces by each agent and which are ineffective for their separate action. Utilizing the results published for rabbits [15], it was demonstrated that the model describes experimental data, predicts the highest synergistic effect and the condition under which it can be achieved. The data obtained may be useful for the assessment of microwave exposure safe levels.
Description and Application of a Mathematical Method for the Analysis of Harmony.
Zuo, Qiting; Jin, Runfang; Ma, Junxia; Cui, Guotao
2015-01-01
Harmony issues are widespread in human society and nature. To analyze these issues, harmony theory has been proposed as the main theoretical approach for the study of interpersonal relationships and relationships between humans and nature. Therefore, it is of great importance to study harmony theory. After briefly introducing the basic concepts of harmony theory, this paper expounds the five elements that are essential for the quantitative description of harmony issues in water resources management: harmony participant, harmony objective, harmony regulation, harmony factor, and harmony action. A basic mathematical equation for the harmony degree, that is, a quantitative expression of harmony issues, is introduced in the paper: HD = ai - bj, where a is the uniform degree, b is the difference degree, i is the harmony coefficient, and j is the disharmony coefficient. This paper also discusses harmony assessment and harmony regulation and introduces some application examples.
ERIC Educational Resources Information Center
Jansen, Amanda; Spitzer, Sandy M.
2009-01-01
In this study, we examined prospective middle school mathematics teachers' reflective thinking skills to understand how they learned from their own teaching practice when engaging in a modified lesson study experience. Our goal was to identify variations among prospective teachers' descriptions of students' thinking and frequency of their…
Explosion-proof fiber optic fire detector: design and mathematical description
NASA Astrophysics Data System (ADS)
Kazakov, V. I.; Moskaletz, O. D.
2014-10-01
The problem of early fire detection in areas classified as potentially explosive is considered in this paper. These include, for example, some types of facilities and plants, which may cause environmental disasters in case of fires. Hard safety requirements impose serious terms for the technical performance the detectors for the protection of such objects from the fire. Detector itself should not cause a fire. The main danger is open conductive parts in the construction of the sensitive elements of detectors, which can lead to the generation of sparks and fire. The using of fiber-optic technology allows creating smoke and heating fire detectors, which only the sensors will be located in the protected area, and all electronic components generate signals and their processing may be removed at considerable distances measured by kilometers. The block diagram of the fire smoke point detector based on fiber-optic technology is considered, the mathematical description of the propagation of optical radiation through the sensing element of the detector is provided, sensitivity is analyzed.
NASA Astrophysics Data System (ADS)
Gurova, E. G.
2016-08-01
During the researches the mathematical description of the traction characteristics of the stiffness compensators of the vibration isolation devices, relatively of the each axis, has been done. Representation of the compensators properties considers the variable load, thereby provide the wide enough spectrum of the action of the suggested vibration isolators. The derived expressions are valid for all three axes of space at the different stiffnesses, i.e. basic basic and two compensating. The research was supported by the scholarships of Russian Federation President for young scientists №184 from 10th of March 2015.
NASA Astrophysics Data System (ADS)
Wang, Li-yong; Li, Le; Zhang, Zhi-hua
2016-09-01
Hot compression tests of Ti-6Al-4V alloy in a wide temperature range of 1023-1323 K and strain rate range of 0.01-10 s-1 were conducted by a servo-hydraulic and computer-controlled Gleeble-3500 machine. In order to accurately and effectively characterize the highly nonlinear flow behaviors, support vector regression (SVR) which is a machine learning method was combined with genetic algorithm (GA) for characterizing the flow behaviors, namely, the GA-SVR. The prominent character of GA-SVR is that it with identical training parameters will keep training accuracy and prediction accuracy at a stable level in different attempts for a certain dataset. The learning abilities, generalization abilities, and modeling efficiencies of the mathematical regression model, ANN, and GA-SVR for Ti-6Al-4V alloy were detailedly compared. Comparison results show that the learning ability of the GA-SVR is stronger than the mathematical regression model. The generalization abilities and modeling efficiencies of these models were shown as follows in ascending order: the mathematical regression model < ANN < GA-SVR. The stress-strain data outside experimental conditions were predicted by the well-trained GA-SVR, which improved simulation accuracy of the load-stroke curve and can further improve the related research fields where stress-strain data play important roles, such as speculating work hardening and dynamic recovery, characterizing dynamic recrystallization evolution, and improving processing maps.
A Description and Characterization of Student Activity in an Open, Online, Mathematics Help Forum
ERIC Educational Resources Information Center
van de Sande, Carla
2011-01-01
Free, open, online, calculus forums are websites where students from around the world can post course-related queries that may be viewed and responded to by anonymous others. These sites are an emergent resource for students seeking help and have become a part of many students' mathematical experience. The purpose of this paper is to introduce and…
Shape in Picture: Mathematical Description of Shape in Grey-Level Images
1992-09-11
vision, and artificial intelligence all make wue ot descriptiosf shape in grey-level images. Most aisting algorithms for the automatic recognition and...analy- sis, computer vision, and artificial intelligence . The NATO Advanced Rosearch WorsMhop "Shape in Picture" was organised with a twofd objective...Annals of Maths. and Artificial Intelligence , special issue on "Mathematics in Pattern Recognition", to appear. 46. Ronse, C. (1989). Fourier analysis
A general model for Io's neutral gas clouds. I - Mathematical description
NASA Technical Reports Server (NTRS)
Smyth, W. H.; Combi, M. R.
1988-01-01
A general mathematical formalism for calculating the physical properties of any of Io's neutral gas clouds (Na, K, O, S, SO2) is presented. The dynamical effects of both the gravitational fields of Io and Jupiter and solar radiation pressure are included, in addition to the many complex space- and time-dependent interactions that occur between the neutral clouds and the plasma torus. The importance of this new model in studying both the plasma conditions prevalent in the inner planetary magnetosphere and the nature of Io's local atmosphere is discussed. A numerical method for evaluating the physical properties of the neutral clouds using the new model is described.
NASA Technical Reports Server (NTRS)
Przekwas, A. J.; Singhal, A. K.; Tam, L. T.
1984-01-01
The capability of simulating three dimensional two phase reactive flows with combustion in the liquid fuelled rocket engines is demonstrated. This was accomplished by modifying an existing three dimensional computer program (REFLAN3D) with Eulerian Lagrangian approach to simulate two phase spray flow, evaporation and combustion. The modified code is referred as REFLAN3D-SPRAY. The mathematical formulation of the fluid flow, heat transfer, combustion and two phase flow interaction of the numerical solution procedure, boundary conditions and their treatment are described.
Entrainment Descriptions for Mathematical Modeling of Pumped-Storage Inflows in Reservoirs.
1985-10-01
demonstrated that the entrainment description can be ., one of the most important inputs to a PS reservoir simulation model. ..... Therefore, adequate...discharged into arbitrary stratifica- ............. tion. The results were then reduced to a form suitable for inclusion into reservoir simulation models...integral buoyant jet model, as adapted to the reservoir simulation code, is referred to as subroutine SBJET (Strongly Buoyant JET). 26. Fan and
NASA Astrophysics Data System (ADS)
Lavrikov, SV; Mikenina, OA; Revuzhenko, AF
2017-02-01
Under analysis is an approach to mathematical modeling of structurally inhomogeneous rocks considering structural hierarchy and internal self-balanced stresses. The fields of stresses and strains at various scale levels of rock mass medium are characterized using the non-Archimedean analysis methods. It is shown that such model describes accumulationtion of elastic energy in the form of internal self-balanced stresses on a micro-scale. The finite element algorithm and a computer program are developed to solve plane boundary-value problems. The calculated data on compression of a rock specimen are reported. The paper shows that the behavior of plastic strain zones largley depends on the pre-set initital micro-stresses.
Bespamyatnov, Igor O; Rowan, William L; Granetz, Robert S
2008-10-01
Charge exchange recombination spectroscopy on Alcator C-Mod relies on the use of the diagnostic neutral beam injector as a source of neutral particles which penetrate deep into the plasma. It employs the emission resulting from the interaction of the beam atoms with fully ionized impurity ions. To interpret the emission from a given point in the plasma as the density of emitting impurity ions, the density of beam atoms must be known. Here, an analysis of beam propagation is described which yields the beam density profile throughout the beam trajectory from the neutral beam injector to the core of the plasma. The analysis includes the effects of beam formation, attenuation in the neutral gas surrounding the plasma, and attenuation in the plasma. In the course of this work, a numerical simulation and an analytical approximation for beam divergence are developed. The description is made sufficiently compact to yield accurate results in a time consistent with between-shot analysis.
ERIC Educational Resources Information Center
Costellano, Janet; Scaffa, Matthew
The product of a Special Studies Institute, this teacher developed resource guide for the emotionally handicapped (K-6) presents 37 activities designed to develop mathematics concepts and skills utilizing the urban out-of-doors. Focus is on experiencing math models, patterns, problems, and relationships found in an urban environment. Activities…
SHETTY, ANIL N.; CHIANG, SHARON; MALETIC-SAVATIC, MIRJANA; KASPRIAN, GREGOR; VANNUCCI, MARINA; LEE, WESLEY
2016-01-01
In this article, we discuss the theoretical background for diffusion weighted imaging and diffusion tensor imaging. Molecular diffusion is a random process involving thermal Brownian motion. In biological tissues, the underlying microstructures restrict the diffusion of water molecules, making diffusion directionally dependent. Water diffusion in tissue is mathematically characterized by the diffusion tensor, the elements of which contain information about the magnitude and direction of diffusion and is a function of the coordinate system. Thus, it is possible to generate contrast in tissue based primarily on diffusion effects. Expressing diffusion in terms of the measured diffusion coefficient (eigenvalue) in any one direction can lead to errors. Nowhere is this more evident than in white matter, due to the preferential orientation of myelin fibers. The directional dependency is removed by diagonalization of the diffusion tensor, which then yields a set of three eigenvalues and eigenvectors, representing the magnitude and direction of the three orthogonal axes of the diffusion ellipsoid, respectively. For example, the eigenvalue corresponding to the eigenvector along the long axis of the fiber corresponds qualitatively to diffusion with least restriction. Determination of the principal values of the diffusion tensor and various anisotropic indices provides structural information. We review the use of diffusion measurements using the modified Stejskal–Tanner diffusion equation. The anisotropy is analyzed by decomposing the diffusion tensor based on symmetrical properties describing the geometry of diffusion tensor. We further describe diffusion tensor properties in visualizing fiber tract organization of the human brain. PMID:27441031
Mathematical Description of Complex Chemical Kinetics and Application to CFD Modeling Codes
NASA Technical Reports Server (NTRS)
Bittker, D. A.
1993-01-01
A major effort in combustion research at the present time is devoted to the theoretical modeling of practical combustion systems. These include turbojet and ramjet air-breathing engines as well as ground-based gas-turbine power generating systems. The ability to use computational modeling extensively in designing these products not only saves time and money, but also helps designers meet the quite rigorous environmental standards that have been imposed on all combustion devices. The goal is to combine the very complex solution of the Navier-Stokes flow equations with realistic turbulence and heat-release models into a single computer code. Such a computational fluid-dynamic (CFD) code simulates the coupling of fluid mechanics with the chemistry of combustion to describe the practical devices. This paper will focus on the task of developing a simplified chemical model which can predict realistic heat-release rates as well as species composition profiles, and is also computationally rapid. We first discuss the mathematical techniques used to describe a complex, multistep fuel oxidation chemical reaction and develop a detailed mechanism for the process. We then show how this mechanism may be reduced and simplified to give an approximate model which adequately predicts heat release rates and a limited number of species composition profiles, but is computationally much faster than the original one. Only such a model can be incorporated into a CFD code without adding significantly to long computation times. Finally, we present some of the recent advances in the development of these simplified chemical mechanisms.
Mathematical description of complex chemical kinetics and application to CFD modeling codes
NASA Technical Reports Server (NTRS)
Bittker, D. A.
1993-01-01
A major effort in combustion research at the present time is devoted to the theoretical modeling of practical combustion systems. These include turbojet and ramjet air-breathing engines as well as ground-based gas-turbine power generating systems. The ability to use computational modeling extensively in designing these products not only saves time and money, but also helps designers meet the quite rigorous environmental standards that have been imposed on all combustion devices. The goal is to combine the very complex solution of the Navier-Stokes flow equations with realistic turbulence and heat-release models into a single computer code. Such a computational fluid-dynamic (CFD) code simulates the coupling of fluid mechanics with the chemistry of combustion to describe the practical devices. This paper will focus on the task of developing a simplified chemical model which can predict realistic heat-release rates as well as species composition profiles, and is also computationally rapid. We first discuss the mathematical techniques used to describe a complex, multistep fuel oxidation chemical reaction and develop a detailed mechanism for the process. We then show how this mechanism may be reduced and simplified to give an approximate model which adequately predicts heat release rates and a limited number of species composition profiles, but is computationally much faster than the original one. Only such a model can be incorporated into a CFD code without adding significantly to long computation times. Finally, we present some of the recent advances in the development of these simplified chemical mechanisms.
NASA Astrophysics Data System (ADS)
Petoshin, V. I.; Chasovnikov, E. A.
2011-05-01
Aerodynamic loads in problems of flight dynamics of passenger aircraft in stalled flow regimes are described using a mathematical model that includes an ordinary linear first-order differential equation. A procedure for determining the parameters of the mathematical model is proposed which is based on approximating experimental frequency characteristics with the frequency characteristics of the linearized mathematical model. The mathematical model was verified by tests of a modern passenger aircraft model in a wind tunnel.
ERIC Educational Resources Information Center
Pagliaro, Claudia M.; Kritzer, Karen L.
2013-01-01
Over decades and across grade levels, deaf/hard-of-hearing (d/hh) student performance in mathematics has shown a gap in achievement. It is unclear, however, exactly when this gap begins to emerge and in what areas. This study describes preschool d/hh children's knowledge of early mathematics concepts. Both standardized and nonstandardized measures…
Pagliaro, Claudia M; Kritzer, Karen L
2013-04-01
Over decades and across grade levels, deaf/hard-of-hearing (d/hh) student performance in mathematics has shown a gap in achievement. It is unclear, however, exactly when this gap begins to emerge and in what areas. This study describes preschool d/hh children's knowledge of early mathematics concepts. Both standardized and nonstandardized measures were used to assess understanding in number, geometry, measurement, problem solving, and patterns, reasoning and algebra. Results present strong evidence that d/hh students' difficulty in mathematics may begin prior to the start of formal schooling. Findings also show areas of strength (geometry) and weakness (problem solving and measurement) for these children. Evidence of poor foundational performance may relate to later academic achievement.
Allan, M.E.; Wilson, M.L.; Wightman, J. )
1996-01-01
The Elk Hills giant oilfield, located in the southern San Joaquin Valley of California, has produced 1.1 billion barrels of oil from Miocene and shallow Pliocene reservoirs. 65% of the current 64,000 BOPD production is from the pressure-supported, deeper Miocene turbidite sands. In the turbidite sands of the 31 S structure, large porosity permeability variations in the Main Body B and Western 31 S sands cause problems with the efficiency of the waterflooding. These variations have now been quantified and visualized using geostatistics. The end result is a more detailed reservoir characterization for simulation. Traditional reservoir descriptions based on marker correlations, cross-sections and mapping do not provide enough detail to capture the short-scale stratigraphic heterogeneity needed for adequate reservoir simulation. These deterministic descriptions are inadequate to tie with production data as the thinly bedded sand/shale sequences blur into a falsely homogenous picture. By studying the variability of the geologic petrophysical data vertically within each wellbore and spatially from well to well, a geostatistical reservoir description has been developed. It captures the natural variability of the sands and shales that was lacking from earlier work. These geostatistical studies allow the geologic and petrophysical characteristics to be considered in a probabilistic model. The end-product is a reservoir description that captures the variability of the reservoir sequences and can be used as a more realistic starting point for history matching and reservoir simulation.
Allan, M.E.; Wilson, M.L.; Wightman, J.
1996-12-31
The Elk Hills giant oilfield, located in the southern San Joaquin Valley of California, has produced 1.1 billion barrels of oil from Miocene and shallow Pliocene reservoirs. 65% of the current 64,000 BOPD production is from the pressure-supported, deeper Miocene turbidite sands. In the turbidite sands of the 31 S structure, large porosity & permeability variations in the Main Body B and Western 31 S sands cause problems with the efficiency of the waterflooding. These variations have now been quantified and visualized using geostatistics. The end result is a more detailed reservoir characterization for simulation. Traditional reservoir descriptions based on marker correlations, cross-sections and mapping do not provide enough detail to capture the short-scale stratigraphic heterogeneity needed for adequate reservoir simulation. These deterministic descriptions are inadequate to tie with production data as the thinly bedded sand/shale sequences blur into a falsely homogenous picture. By studying the variability of the geologic & petrophysical data vertically within each wellbore and spatially from well to well, a geostatistical reservoir description has been developed. It captures the natural variability of the sands and shales that was lacking from earlier work. These geostatistical studies allow the geologic and petrophysical characteristics to be considered in a probabilistic model. The end-product is a reservoir description that captures the variability of the reservoir sequences and can be used as a more realistic starting point for history matching and reservoir simulation.
ERIC Educational Resources Information Center
Brizius, Martine G.; Luckey, Heather B.
This report summarizes the 1998 reporting year data on the National Science Foundation's (NSF's) Graduate Research Traineeship (GRT) program. The GRT program supports the research and education of talented students pursuing graduate degrees in critical and emerging areas of science, mathematics, engineering, and technology (SMET) and SMET…
Hara, Toshihide; Iriyama, Satoshi; Makino, Kimiko; Terada, Hiroshi; Ohya, Masanori
2010-01-01
It is known that Drug Delivery System (DDS) is useful to remedy against tumors for the reduction of side effects and the effective dosage. However the shape, in particular, the size of drug (medicine) is empirically decided in the present stage, which will be related to a question how much medicine should be dosed. Taking a particular reaction of tumor tissues called the EPR effect into consideration, we try to mathematically describe the behavior (dynamics) of drug in blood vessel by applying several techniques used in mathematics and physics. In this paper, we estimate the configuration of drug which is most effective to remedy for tumors under various conditions. As a result, this model and its simulation will be useful to design the drug in nano-level.
NASA Astrophysics Data System (ADS)
Namba, Masanobu; Nishino, Ryohei
The purpose of this paper is to study the effect of neighboring blade rows on the unsteady aerodynamic response of oscillating cascade blades on the basis of a genuine three-dimensional model. To this end, mathematical formulations based on the lifting surface theory are developed for a pair of contra-rotating annular cascades of oscillating blades. The mechanism of frequency scattering of blade loadings and mode scattering of acoustic waves resulting from interaction between the blade rows in relative rotational motions is mathematically explained. Simultaneous integral equations for all frequency components of blade loadings are derived from the flow tangency condition on the blade surfaces of both blade rows. The validity of the computation codes is verified.
1982-05-01
authorized documents. The citation of trade name. and names of manLfacturers in this report is not to be construed as official Government indorsement 4 or...ating the light which illuminatis it. For a target and background which are coincident , this is ntot a problem .rid a comparison of r;flectivities can...NBS Applied Mathematics, Series 55, U. S. Government Printing Office, 1046. Allen, G. and B. E. Simonson, 1970: Attenuation of infrared laser radia
Aksenov, L.N.; Bronshtein, A.P.; Zadorina, E.N.; Zagorets, A.M.; Makarov, G.N.; Polyakov, A.A.; Shlenskii, O.F.
1981-01-01
The determination of the most effective regimes for the thermal processing of solid fuels and the control of these processes requires a well-based selection of mathematical models for them. In the reported theoretical study, the question is considered of the possibility of using the traditional equations of chemical kinetics for describing the thermal degradation of the organic matter of coals. Various methods are proposed for the detemination of thermogravimetric curves. 14 refs.
Gray, W.G.
2001-01-25
This project has contributed to the improved understanding and precise physical description of multiphase subsurface flow by combining theoretical derivation of equations, lattice Boltzmann modeling of hydrodynamics to identify characteristics and parameters, and simplification of field-scale equations to assess the advantages and disadvantages of the complete theory.
NASA Astrophysics Data System (ADS)
Schwerdtfeger, Peter
2016-12-01
In the last two decades cold and hot fusion experiments lead to the production of new elements for the Periodic Table up to nuclear charge 118. Recent developments in relativistic quantum theory have made it possible to obtain accurate electronic properties for the trans-actinide elements with the aim to predict their potential chemical and physical behaviour. Here we report on first results of solid-state calculations for Og (element 118) to support future atom-at-a-time gas-phase adsorption experiments on surfaces such as gold or quartz.
NASA Astrophysics Data System (ADS)
Roy Choudhury, Raja; Roy Choudhury, Arundhati; Kanti Ghose, Mrinal
2013-01-01
A semi-analytical model with three optimizing parameters and a novel non-Gaussian function as the fundamental modal field solution has been proposed to arrive at an accurate solution to predict various propagation parameters of graded-index fibers with less computational burden than numerical methods. In our semi analytical formulation the optimization of core parameter U which is usually uncertain, noisy or even discontinuous, is being calculated by Nelder-Mead method of nonlinear unconstrained minimizations as it is an efficient and compact direct search method and does not need any derivative information. Three optimizing parameters are included in the formulation of fundamental modal field of an optical fiber to make it more flexible and accurate than other available approximations. Employing variational technique, Petermann I and II spot sizes have been evaluated for triangular and trapezoidal-index fibers with the proposed fundamental modal field. It has been demonstrated that, the results of the proposed solution identically match with the numerical results over a wide range of normalized frequencies. This approximation can also be used in the study of doped and nonlinear fiber amplifier.
NASA Technical Reports Server (NTRS)
Fortenbaugh, R. L.
1980-01-01
A mathematical model of a high performance airplane capable of vertical attitude takeoff and landing (VATOL) was developed. An off line digital simulation program incorporating this model was developed to provide trim conditions and dynamic check runs for the piloted simulation studies and support dynamic analyses of proposed VATOL configuration and flight control concepts. Development details for the various simulation component models and the application of the off line simulation program, Vertical Attitude Take-Off and Landing Simulation (VATLAS), to develop a baseline control system for the Vought SF-121 VATOL airplane concept are described.
Bagnasco, Annamaria; Galaverna, Lucia; Aleo, Giuseppe; Grugnetti, Anna Maria; Rosa, Francesca; Sasso, Loredana
2016-01-01
In the literature we found many studies that confirmed our concerns about nursing students' poor maths skills that directly impact on their ability to correctly calculate drug dosages with very serious consequences for patient safety. The aim of our study was to explore where students had most difficulty and identify appropriate educational interventions to bridge their mathematical knowledge gaps. This was a quali-quantitative descriptive study that included a sample of 726 undergraduate nursing students. We identified exactly where students had most difficulty and identified appropriate educational interventions to bridge their mathematical knowledge gaps. We found that the undergraduate nursing students mainly had difficulty with basic maths principles. Specific learning interventions are needed to improve their basic maths skills and their dosage calculation skills. For this purpose, we identified safeMedicate and eDose (Authentic World Ltd.), only that they are only available in English. In the near future we hope to set up a partnership to work together on the Italian version of these tools.
NASA Astrophysics Data System (ADS)
de Vicente, S.; Galiano, G.; Velasco, J.; Aróstegui, J. M.
Two-phase systems where a dense phase of small particles is fluidized with a gas flow appear in many industrial applications, among which the fluidized bed combustors are probably the most important. A homogenization technique allows us to formulate the mathematical model in form of the compressible Navier-Stokes system type with some particularities: 1) the volumetric fraction of the dense phase (analogous to the density in the Navier-Stokes equations) may vanish, 2) the constitutive viscosity law may depend in a nonlinear form on this density, 3) the source term is nonlinear and coupled with state equations involving drag forces and hydrodynamic pressure, and 4) the state equation for the collision pressure of dense phase blows up for finite values of the density. We develop a rigorous theory for a special kind of solutions we call stationary clouds. Such solutions exist only under restrictions on the geometry of combustor and on the boundary conditions that usually meet in engineering applications. In return, these solutions have a stationary one-dimensional structure very simple and, from them, it is possible to reconstruct much of the dynamics of the whole system, responding to most of the practical issues of interest. Finally, we study the linear stability for the trivial solutions corresponding to uniform fluidized states injecting plane wave perturbations in our equations. Depending on the parameters of the equations of state describing the collisions between solid particles, hydrodynamic pressure, and the values of blowing boundary condition, we can draw detailed abacus separating stable regions of unstable regions where bubbles appear. Then, we use the dispersion relations of this multidimensional linearized model, combined with the stationary phase theorem, to approach the profiles and the evolution of the bubbles appearing in unstable regimes, and verify that the obtained results adjust to the observations.
Borbás, Enikő; Sinkó, Bálint; Tsinman, Oksana; Tsinman, Konstantin; Kiserdei, Éva; Démuth, Balázs; Balogh, Attila; Bodák, Brigitta; Domokos, András; Dargó, Gergő; Balogh, György T; Nagy, Zsombor K
2016-11-07
The aim of this study was to investigate the impact of formulation excipients and solubilizing additives on dissolution, supersaturation, and membrane transport of an active pharmaceutical ingredient (API). When a poorly water-soluble API is formulated to enhance its dissolution, additives, such as surfactants, polymers, and cyclodextrins, have an effect not only on dissolution profile but also on the measured physicochemical properties (solubility, pKa, permeability) of the drug while the excipient is present, therefore also affecting the driving force of membrane transport. Meloxicam, a nonsteroidal anti-inflammatory drug, was chosen as a poorly water-soluble model drug and formulated in order to enhance its dissolution using solvent-based electrospinning. Three polyvinylpyrrolidone (PVP) derivatives (K30, K90, and VA 64), Soluplus, and (2-hydroxypropyl)-β-cyclodextrin were used to create five different amorphous solid dispersions of meloxicam. Through experimental design, the various formulation additives that could influence the characteristics of dissolution and permeation through artificial membrane were observed by carrying out a simultaneous dissolution-permeation study with a side-by-side diffusion cell, μFLUX. Although the dissolution profiles of the formulations were found to be very similar, in the case of Soluplus containing formulation the flux was superior, showing that the driving force of membrane transport cannot be simplified to the concentration gradient. Supersaturation gradient, the difference in degree of supersaturation (defined as the ratio of dissolved amount of the drug to its thermodynamic solubility) between the donor and acceptor side, was found to be the driving force of membrane transport. It was mathematically derived from Fick's first law, and experimentally proved to be universal on several meloxicam containing ASDs and DMSO stock solution.
Taggart, Peter; Srinivasan, Neil; Hayward, Martin; Lambiase, Pier D.
2016-01-01
Background The restitution of the action potential duration (APDR) and conduction velocity (CVR) are mechanisms whereby cardiac excitation and repolarization adapt to changes in heart rate. They modulate the vulnerability to dangerous arrhythmia, but the mechanistic link between restitution and arrhythmogenesis remains only partially understood. Methods This paper provides an experimental and theoretical study of repolarization and excitation restitution properties and their interactions in the intact human epicardium. The interdependence between excitation and repolarization dynamic is studied in 8 patients (14 restitution protocols, 1722 restitution curves) undergoing global epicardial mapping with multi-electrode socks before open heart surgery. A mathematical description of the contribution of both repolarization and conduction dynamics to the steepness of the APDR slope is proposed. Results This study demonstrates that the APDR slope is a function of both activation and repolarization dynamics. At short cycle length, conduction delay significantly increases the APDR slope by interacting with the diastolic interval. As predicted by the proposed mathematical formulation, the APDR slope was more sensitive to activation time prolongation than to the simultaneous shortening of repolarization time. A steep APDR slope was frequently identified, with 61% of all cardiac sites exhibiting an APDR slope > 1, suggesting that a slope > 1 may not necessarily promote electrical instability in the human epicardium. APDR slope did not change for different activation or repolarization times, and it was not a function of local baseline APD. However, it was affected by the spatial organization of electrical excitation, suggesting that in tissue APDR is not a unique function of local electrophysiological properties. Spatial heterogeneity in both activation and repolarization restitution contributed to the increase in the modulated dispersion of repolarization, which for short cycle
NASA Technical Reports Server (NTRS)
Gliese, U.; Avanov, L. A.; Barrie, A. C.; Kujawski, J. T.; Mariano, A. J.; Tucker, C. J.; Chornay, D. J.; Cao, N. T.; Gershman, D. J.; Dorelli, J. C.; Zeuch, M. A.; Pollock, C. J.; Jacques, A. D.
2015-01-01
system calibration method that enables accurate and repeatable measurement and calibration of MCP gain, MCP efficiency, signal loss due to variation in gain and efficiency, crosstalk from effects both above and below the MCP, noise margin, and stability margin in one single measurement. More precise calibration is highly desirable as the instruments will produce higher quality raw data that will require less post-acquisition data correction using results from in-flight pitch angle distribution measurements and ground calibration measurements. The detection system description and the fundamental concepts of this new calibration method, named threshold scan, will be presented. It will be shown how to derive all the individual detection system parameters and how to choose the optimum detection system operating point. This new method has been successfully applied to achieve a highly accurate calibration of the DESs and DISs of the MMS mission. The practical application of the method will be presented together with the achieved calibration results and their significance. Finally, it will be shown that, with further detailed modeling, this method can be extended for use in flight to achieve and maintain a highly accurate detection system calibration across a large number of instruments during the mission.
ERIC Educational Resources Information Center
Locklear, Tonja Motley
2012-01-01
The Sources of Middle School Mathematics Self-Efficacy Scale (Usher & Pajares, 2009) was adapted for use in this study investigating the impact that gender, race, sexual orientation, hometown location (rural, suburban, or urban), high school GPA, college GPA and letter grade of a mathematics course in the previous semester had on the four…
Langley Atmospheric Information Retrieval System (LAIRS): System description and user's guide
NASA Technical Reports Server (NTRS)
Boland, D. E., Jr.; Lee, T.
1982-01-01
This document presents the user's guide, system description, and mathematical specifications for the Langley Atmospheric Information Retrieval System (LAIRS). It also includes a description of an optimal procedure for operational use of LAIRS. The primary objective of the LAIRS Program is to make it possible to obtain accurate estimates of atmospheric pressure, density, temperature, and winds along Shuttle reentry trajectories for use in postflight data reduction.
Cooper, D.K.; Cooper, J.A.; Ferson, S.
1999-01-21
Calculating safety and reliability probabilities with functions of uncertain variables can yield incorrect or misleading results if some precautions are not taken. One important consideration is the application of constrained mathematics for calculating probabilities for functions that contain repeated variables. This paper includes a description of the problem and develops a methodology for obtaining an accurate solution.
Learning Together: Mathematics
ERIC Educational Resources Information Center
Her Majesty's Inspectorate of Education, 2010
2010-01-01
This guide is intended to stimulate professional reflection, dialogue and debate about mathematics and how to improve it. It draws together themes, features and characteristics of effective improvement in mathematics and descriptions of good practice. It offers a reference point for staff and teachers who are working together to improve…
Mathematics across the Curriculum.
ERIC Educational Resources Information Center
Kleiman, Glenn M.
1991-01-01
Except for its relationship to science, mathematics is the forgotten cousin in interdisciplinary teaching and learning. In the Journeys in Mathematics project, teachers engage children in imaginative activities that inspire them to identify patterns and relationships, solve problems, and communicate accurately, using Jonathan Swift's…
NASA Technical Reports Server (NTRS)
Zolotukhin, V. G.; Kolosov, B. I.; Usikov, D. A.; Borisenko, V. I.; Mosin, S. T.; Gorokhov, V. N.
1980-01-01
A description of a batch of programs for the YeS-1040 computer combined into an automated system for processing photo (and video) images of the Earth's surface, taken from spacecraft, is presented. Individual programs with the detailed discussion of the algorithmic and programmatic facilities needed by the user are presented. The basic principles for assembling the system, and the control programs are included. The exchange format within whose framework the cataloging of any programs recommended for the system of processing will be activated in the future is displayed.
The Emergence of Objects from Mathematical Practices
ERIC Educational Resources Information Center
Font, Vicenc; Godino, Juan D.; Gallardo, Jesus
2013-01-01
The nature of mathematical objects, their various types, the way in which they are formed, and how they participate in mathematical activity are all questions of interest for philosophy and mathematics education. Teaching in schools is usually based, implicitly or explicitly, on a descriptive/realist view of mathematics, an approach which is not…
Gray, W.G.; Tompson, A.; Soll, W.E.
1998-06-01
'Improved capabilities for modeling multiphase flow in the subsurface requires that several aspects of the system which impact the flow and transport processes be more properly accounted for. A distinguishing feature of multiphase flow in comparison to single phase flow is the existence of interfaces between fluids. At the microscopic (pore) scale, these interfaces are known to influence system behavior by supporting non-zero stresses such that the pressures in adjacent phases are not equal. In problems of interphase transport at the macroscopic (core) scale, knowledge of the total amount of interfacial area in the system provides a clue to the effectiveness of the communication between phases. Although interfacial processes are central to multiphase flow physics, their treatment in traditional porous-media theories has been implicit rather than explicit; and no attempts have been made to systematically account for the evolution of the interfacial area in dynamic systems or to include the dependence of constitutive functions, such as capillary pressure, on the interfacial area. This project implements a three-pronged approach to assessing the importance of various features of multiphase flow to its description. The research contributes to the improved understanding and precise physical description of multiphase subsurface flow by combining: (1) theoretical derivation of equations, (2) lattice Boltzmann modeling of hydrodynamics to identify characteristics and parameters, and (3) solution of the field-scale equations using a discrete numerical method to assess the advantages and disadvantages of the complete theory. This approach includes both fundamental scientific inquiry and a path for inclusion of the scientific results obtained in a technical tool that will improve assessment capabilities for multiphase flow situations that have arisen due to the introduction of organic materials in the natural environment. This report summarizes work after 1.5 years of a 3
Goddard trajectory determination subsystem: Mathematical specifications
NASA Technical Reports Server (NTRS)
Wagner, W. E. (Editor); Velez, C. E. (Editor)
1972-01-01
The mathematical specifications of the Goddard trajectory determination subsystem of the flight dynamics system are presented. These specifications include the mathematical description of the coordinate systems, dynamic and measurement model, numerical integration techniques, and statistical estimation concepts.
Computation and graphics in mathematical research
Hoffman, D.A.; Spruck, J.
1992-08-13
This report discusses: The description of the GANG Project and results for prior research; the center for geometry, analysis, numerics and graphics; description of GANG Laboratory; software development at GANG; and mathematical and scientific research activities.
A mathematical approach to human pterygium shape
Pajic, Bojan; Vastardis, Iraklis; Rajkovic, Predrag; Pajic-Eggspuehler, Brigitte; Aebersold, Daniel M; Cvejic, Zeljka
2016-01-01
Purpose Pterygium is a common lesion affecting the population in countries with high levels of ultraviolet exposure. The final shape of a pterygium is the result of a growth pattern, which remains poorly understood. This manuscript provides a mathematical analysis as a tool to determine the shape of human pterygia. Materials and methods Eighteen patients, all affected by nasal unilateral pterygia, were randomly selected from our patient database independently of sex, origin, or race. We included all primary or recurrent pterygia with signs of proliferation, dry eye, and induction of astigmatism. Pseudopterygia were excluded from this study. Pterygia were outlined and analyzed mathematically using a Cartesian coordinate system with two axes (X, Y) and five accurate landmarks of the pterygium. Results In 13 patients (72%), the shape of the pterygia was hyperbolic and in five patients (28%), the shape was rather elliptical. Conclusion This analysis gives a highly accurate mathematical description of the shape of human pterygia. This might help to better assess the clinical results and outcome of the great variety of therapeutic approaches concerning these lesions. PMID:27555741
ERIC Educational Resources Information Center
Luther, Kenneth H.
2012-01-01
Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…
Mathematical representations of turbulent mixing
NASA Technical Reports Server (NTRS)
Farmer, R. C.; Audeh, B.
1973-01-01
A basic description is given of the mathematical tools and models which are presently used to represent turbulent, free shear layers. Recommendations are included for ways in which current modeling techniques can be improved.
Mathematical epidemiology is not an oxymoron
2009-01-01
A brief description of the importance of communicable diseases in history and the development of mathematical modelling of disease transmission is given. This includes reasons for mathematical modelling, the history of mathematical modelling from the foundations laid in the late nineteenth century to the present, some of the accomplishments of mathematical modelling, and some challenges for the future. Our purpose is to demonstrate the importance of mathematical modelling for the understanding and management of infectious disease transmission. PMID:19922686
The Mathematics of Global Change
ERIC Educational Resources Information Center
Kreith, Kurt
2011-01-01
This paper is a descriptive and preliminary report on recent efforts to address two questions: 1) Can school mathematics be used to enhance our students' ability to understand their changing world? and 2) What role might computer technology play in this regard? After recounting some of the mathematical tools that led to a better understanding of…
Mathematics Teachers' Criteria of Dimension
ERIC Educational Resources Information Center
Ural, Alattin
2014-01-01
The aim of the study is to determine mathematics teachers' decisions about dimensions of the geometric figures, criteria of dimension and consistency of decision-criteria. The research is a qualitative research and the model applied in the study is descriptive method on the basis of general scanning model. 15 mathematics teachers attended the…
ERIC Educational Resources Information Center
Redlich, Otto
1972-01-01
The foundation of science, and of thermodynamics in particular, can be developed cogently and without arbitrariness. The goal of science, description of nature, is externally given; it requires a set of basic concepts as indispensable tools. Mathematics has no similar externally given goal. (Author/TS)
Fostering Creativity Through Mathematics.
ERIC Educational Resources Information Center
Lichtenberg, Betty K., Ed.; Troutman, Andria P., Ed.
The 26 activities described in this volume deal with a wide variety of mathematical ideas. Most of the activities are appropriate for grades 6-9; many could be used with older or younger groups as well. All activities are described in detail; some descriptions include sample worksheets, and several provide suggestions for followup activities. The…
Assessment Mathematics Teacher's Competencies
ERIC Educational Resources Information Center
Alnoor, A. G.; Yuanxiang, Guo; Abudhuim, F. S.
2007-01-01
This paper aimed to identifying the professional efficiencies for the intermediate schools mathematics teachers and tries to know at what level the math teachers experience those competencies. The researcher used a descriptive research approach, the study data collected from specialist educators and teacher's experts and previous studies to…
Simple and surprisingly accurate approach to the chemical bond obtained from dimensional scaling.
Svidzinsky, Anatoly A; Scully, Marlan O; Herschbach, Dudley R
2005-08-19
We present a new dimensional scaling transformation of the Schrödinger equation for the two electron bond. This yields, for the first time, a good description of the bond via D scaling. There also emerges, in the large-D limit, an intuitively appealing semiclassical picture, akin to a molecular model proposed by Bohr in 1913. In this limit, the electrons are confined to specific orbits in the scaled space, yet the uncertainty principle is maintained. A first-order perturbation correction, proportional to 1/D, substantially improves the agreement with the exact ground state potential energy curve. The present treatment is very simple mathematically, yet provides a strikingly accurate description of the potential curves for the lowest singlet, triplet, and excited states of H2. We find the modified D-scaling method also gives good results for other molecules. It can be combined advantageously with Hartree-Fock and other conventional methods.
ERIC Educational Resources Information Center
Reys, Robert; Reys, Rustin
2011-01-01
In their dual roles as mathematics teachers and tennis coaches, the authors have worked with tennis players who have never thought about how a knowledge of mathematics might help them become "better" tennis players. They have also worked with many mathematics students who have never considered how much mathematics is associated with tennis. This…
CARE 3 phase 2 report - mathematical description
NASA Technical Reports Server (NTRS)
Stiffler, J. J.; Bryant, L. A.
1982-01-01
CARE III (Computer-Aided Reliability Estimation, version three) a computer program designed to help estimate the reliability of complex, redundant systems is described. Although the program can model a wide variety of redundant structures, it was developed specifically for fault tolerant avionics systems. CARE III generalizes the class of system structures that can be modeled and greatly expands the coverage model to take into account such effects as intermittent and transient faults, latent faults, and error propagation.
Comment on ``The First Accurate Description of an Aurora''
NASA Astrophysics Data System (ADS)
Silverman, Sam
2007-11-01
Schröder [2006] discusses Das Buch der Natur (The Book of Nature), written by Konrad von Megenberg between 1348 and 1350. The Buch was the first encyclopedia of natural phenomena written in German. (For a contemporary German translation, see Schulz [1897] for definitions of Megenberg's astronomical terminology, see Deschler [1977]). Megenberg translated the Liber de Natura Rerum, written by Thomas of Cantimpré between 1225 and 1240.
Beauty as Fit: A Metaphor in Mathematics?
ERIC Educational Resources Information Center
Raman, Manya; Öhman, Lars-Daniel
2013-01-01
Beauty, which plays a central role in the practice of mathematics (Sinclair 2002), is almost absent in discussions of school mathematics (Dreyfus and Eisenberg 1986). This is problematic, because students will decide whether or not to continue their studies in mathematics without having an accurate picture of what the subject is about. In order to…
ERIC Educational Resources Information Center
Hanh, Vu Duc, Ed.
This document gives a listing of mathematical terminology in both the English and Vietnamese languages. Vocabulary used in algebra and geometry is included along with a translation of mathematical symbols. (DT)
ERIC Educational Resources Information Center
Jones, Thomas A.
1983-01-01
Mathematical techniques used to solve geological problems are briefly discussed (including comments on use of geostatistics). Highlights of conferences/meetings and conference papers in mathematical geology are also provided. (JN)
... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...
On accurate determination of contact angle
NASA Technical Reports Server (NTRS)
Concus, P.; Finn, R.
1992-01-01
Methods are proposed that exploit a microgravity environment to obtain highly accurate measurement of contact angle. These methods, which are based on our earlier mathematical results, do not require detailed measurement of a liquid free-surface, as they incorporate discontinuous or nearly-discontinuous behavior of the liquid bulk in certain container geometries. Physical testing is planned in the forthcoming IML-2 space flight and in related preparatory ground-based experiments.
ERIC Educational Resources Information Center
Kilpatrick, Jeremy
2014-01-01
This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…
Developmental Kindergarten: Definition and Description.
ERIC Educational Resources Information Center
Virginia State Dept. of Education, Richmond.
This paper sets forth a definition and operational description of a developmental program that should be of use as a guide, especially to Virginia's teachers and administrators. Also included in the paper are kindergarten curriculum objectives in the areas of language arts, mathematics, science, art, social studies, family life, health, mental…
Self-Efficacy Beliefs of Prospective Primary Mathematics Teachers about Mathematical Literacy
ERIC Educational Resources Information Center
Yavuz, Gunes; Gunhan, Berna Canturk; Ersoy, Esen; Narli, Serkan
2013-01-01
The aim of this study was to examine the self-efficacy beliefs about mathematical literacy among teachers of primary school mathematics and the relationship between the self-efficacy beliefs and attitudes towards mathematics. To that end, a descriptive research study was conducted with 550 prospective teachers studying primary school mathematics…
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…
Shi, Runhua; McLarty, Jerry W
2009-10-01
In this article, we introduced basic concepts of statistics, type of distributions, and descriptive statistics. A few examples were also provided. The basic concepts presented herein are only a fraction of the concepts related to descriptive statistics. Also, there are many commonly used distributions not presented herein, such as Poisson distributions for rare events and exponential distributions, F distributions, and logistic distributions. More information can be found in many statistics books and publications.
NASA Astrophysics Data System (ADS)
Stöltzner, Michael
Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.
Accurate Finite Difference Algorithms
NASA Technical Reports Server (NTRS)
Goodrich, John W.
1996-01-01
Two families of finite difference algorithms for computational aeroacoustics are presented and compared. All of the algorithms are single step explicit methods, they have the same order of accuracy in both space and time, with examples up to eleventh order, and they have multidimensional extensions. One of the algorithm families has spectral like high resolution. Propagation with high order and high resolution algorithms can produce accurate results after O(10(exp 6)) periods of propagation with eight grid points per wavelength.
Accurate monotone cubic interpolation
NASA Technical Reports Server (NTRS)
Huynh, Hung T.
1991-01-01
Monotone piecewise cubic interpolants are simple and effective. They are generally third-order accurate, except near strict local extrema where accuracy degenerates to second-order due to the monotonicity constraint. Algorithms for piecewise cubic interpolants, which preserve monotonicity as well as uniform third and fourth-order accuracy are presented. The gain of accuracy is obtained by relaxing the monotonicity constraint in a geometric framework in which the median function plays a crucial role.
Experimental Mathematics and Mathematical Physics
Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Zudilin, Wadim
2009-06-26
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.
Mathematics for modern precision engineering.
Scott, Paul J; Forbes, Alistair B
2012-08-28
The aim of precision engineering is the accurate control of geometry. For this reason, mathematics has a long association with precision engineering: from the calculation and correction of angular scales used in surveying and astronomical instrumentation to statistical averaging techniques used to increase precision. This study illustrates the enabling role the mathematical sciences are playing in precision engineering: modelling physical processes, instruments and complex geometries, statistical characterization of metrology systems and error compensation.
ERIC Educational Resources Information Center
Prochazka, Helen
2004-01-01
One section of this "scrapbook" section describes Pythagoras' belief in the connections between music and mathematics -- that everything in the universe was a series of harmonies and regulated by music. Another section explains why Phythagoras felt it important for women to be encouraged to learn mathematics. At least 28 women were involved in his…
ERIC Educational Resources Information Center
Langbort, Carol, Ed.; Curtis, Deborah, Ed.
2000-01-01
The focus of this special issue is mathematics education. All articles were written by graduates of the new masters Degree program in which students earn a Master of Arts degree in Education with a concentration in Mathematics Education at San Francisco State University. Articles include: (1) "Developing Teacher-Leaders in a Masters Degree Program…
ERIC Educational Resources Information Center
Flannery, Carol A.
This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…
ERIC Educational Resources Information Center
McClellan, Kathryn T.
Why mathematics should be learned is discussed. Its role as an important active force in the development of our civilization, and as the most useful subject taught in our schools, next to English, is noted. The primary objective of all mathematics work is to help man study nature, and some practical achievements of this connection are noted.…
ERIC Educational Resources Information Center
Martin, Hope
2007-01-01
"Mathematical literacy" implies that a person is able to reason, analyze, formulate, and solve problems in a real-world setting. Mathematically literate individuals are informed citizens and intelligent consumers. They have the ability to interpret and analyze the vast amount of information they are inundated with daily in newspapers, on…
ERIC Educational Resources Information Center
Beller, Charley
2013-01-01
The study of definite descriptions has been a central part of research in linguistics and philosophy of language since Russell's seminal work "On Denoting" (Russell 1905). In that work Russell quickly dispatches analyses of denoting expressions with forms like "no man," "some man," "a man," and "every…
Accurate ab Initio Spin Densities.
Boguslawski, Katharina; Marti, Konrad H; Legeza, Ors; Reiher, Markus
2012-06-12
We present an approach for the calculation of spin density distributions for molecules that require very large active spaces for a qualitatively correct description of their electronic structure. Our approach is based on the density-matrix renormalization group (DMRG) algorithm to calculate the spin density matrix elements as a basic quantity for the spatially resolved spin density distribution. The spin density matrix elements are directly determined from the second-quantized elementary operators optimized by the DMRG algorithm. As an analytic convergence criterion for the spin density distribution, we employ our recently developed sampling-reconstruction scheme [J. Chem. Phys.2011, 134, 224101] to build an accurate complete-active-space configuration-interaction (CASCI) wave function from the optimized matrix product states. The spin density matrix elements can then also be determined as an expectation value employing the reconstructed wave function expansion. Furthermore, the explicit reconstruction of a CASCI-type wave function provides insight into chemically interesting features of the molecule under study such as the distribution of α and β electrons in terms of Slater determinants, CI coefficients, and natural orbitals. The methodology is applied to an iron nitrosyl complex which we have identified as a challenging system for standard approaches [J. Chem. Theory Comput.2011, 7, 2740].
Accurate quantum chemical calculations
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.; Langhoff, Stephen R.; Taylor, Peter R.
1989-01-01
An important goal of quantum chemical calculations is to provide an understanding of chemical bonding and molecular electronic structure. A second goal, the prediction of energy differences to chemical accuracy, has been much harder to attain. First, the computational resources required to achieve such accuracy are very large, and second, it is not straightforward to demonstrate that an apparently accurate result, in terms of agreement with experiment, does not result from a cancellation of errors. Recent advances in electronic structure methodology, coupled with the power of vector supercomputers, have made it possible to solve a number of electronic structure problems exactly using the full configuration interaction (FCI) method within a subspace of the complete Hilbert space. These exact results can be used to benchmark approximate techniques that are applicable to a wider range of chemical and physical problems. The methodology of many-electron quantum chemistry is reviewed. Methods are considered in detail for performing FCI calculations. The application of FCI methods to several three-electron problems in molecular physics are discussed. A number of benchmark applications of FCI wave functions are described. Atomic basis sets and the development of improved methods for handling very large basis sets are discussed: these are then applied to a number of chemical and spectroscopic problems; to transition metals; and to problems involving potential energy surfaces. Although the experiences described give considerable grounds for optimism about the general ability to perform accurate calculations, there are several problems that have proved less tractable, at least with current computer resources, and these and possible solutions are discussed.
The Mathematics Laboratory in Engineering Studies.
ERIC Educational Resources Information Center
Quesada, Jose Fco. Carballido
1986-01-01
Discusses the need for mathematics laboratories to supplement classroom instruction in mathematics for engineering students. Provides a description of such a laboratory, including a listing of equipment and materials that are recommended. Describes the uses for personal computers and suggests various problems that could be explored in the…
Secondary School Mathematics Curriculum Improvement Study.
ERIC Educational Resources Information Center
Secondary School Mathematics Curriculum Improvement Study, New York, NY.
This bulletin contains: (1) a summary and conclusions of a study of mathematics curricula in Europe and Japan, and (2) a description of beginning efforts to evaluate the Secondary School Mathematics Curriculum Improvement Study (SSMCIS) project. Some of the conclusions of the European and Japanese study are: (1) the study of Euclidean synthetic…
Computer-Game-Based Tutoring of Mathematics
ERIC Educational Resources Information Center
Ke, Fengfeng
2013-01-01
This in-situ, descriptive case study examined the potential of implementing computer mathematics games as an anchor for tutoring of mathematics. Data were collected from middle school students at a rural pueblo school and an urban Hispanic-serving school, through in-field observation, content analysis of game-based tutoring-learning interactions,…
On the Role of Mathematics in Physics
ERIC Educational Resources Information Center
Quale, Andreas
2011-01-01
I examine the association between the observable physical world and the mathematical models of theoretical physics. These models will exhibit many entities that have no counterpart in the physical world, but which are still necessary for the mathematical description of physical systems. Moreover, when the model is applied to the analysis of a…
Rendón-Macías, Mario Enrique; Villasís-Keever, Miguel Ángel; Miranda-Novales, María Guadalupe
2016-01-01
Descriptive statistics is the branch of statistics that gives recommendations on how to summarize clearly and simply research data in tables, figures, charts, or graphs. Before performing a descriptive analysis it is paramount to summarize its goal or goals, and to identify the measurement scales of the different variables recorded in the study. Tables or charts aim to provide timely information on the results of an investigation. The graphs show trends and can be histograms, pie charts, "box and whiskers" plots, line graphs, or scatter plots. Images serve as examples to reinforce concepts or facts. The choice of a chart, graph, or image must be based on the study objectives. Usually it is not recommended to use more than seven in an article, also depending on its length.
ERIC Educational Resources Information Center
ROSEN, ELLEN F.; STOLUROW, LAWRENCE M.
MANIPULATION OF FRAMES WITHIN PROGRAMED MATHEMATICS TEXTS IN ORDER TO STUDY FOUR VARIABLES YIELDED, IN A PREVIOUSLY REPORTED PAPER, CORRELATIONAL DATA (FOR RELATIVELY SMALL TREATMENT GROUPS) THAT ARE PRESENTED HERE. FIRST, THE ORDER OF PRESENTATION OF PROGRAMED MATERIAL (BEFORE, AFTER, AND WITHOUT CONVENTIONAL INSTRUCTION) HAD NO EFFECT ON…
ERIC Educational Resources Information Center
Britton, Edward; Raizen, Senta; Kaser, Joyce; Porter, Andrew
When entering this new millennium, educators and researchers need to know much more about how to address the increasingly acute diversity and equity issues in educating children in mathematics and science. This headline was the conclusion of the over 200 distinguished panelists, chairs, discussants, featured speakers, and participants who…
BIOACCESSIBILITY TESTS ACCURATELY ESTIMATE ...
Hazards of soil-borne Pb to wild birds may be more accurately quantified if the bioavailability of that Pb is known. To better understand the bioavailability of Pb to birds, we measured blood Pb concentrations in Japanese quail (Coturnix japonica) fed diets containing Pb-contaminated soils. Relative bioavailabilities were expressed by comparison with blood Pb concentrations in quail fed a Pb acetate reference diet. Diets containing soil from five Pb-contaminated Superfund sites had relative bioavailabilities from 33%-63%, with a mean of about 50%. Treatment of two of the soils with P significantly reduced the bioavailability of Pb. The bioaccessibility of the Pb in the test soils was then measured in six in vitro tests and regressed on bioavailability. They were: the “Relative Bioavailability Leaching Procedure” (RBALP) at pH 1.5, the same test conducted at pH 2.5, the “Ohio State University In vitro Gastrointestinal” method (OSU IVG), the “Urban Soil Bioaccessible Lead Test”, the modified “Physiologically Based Extraction Test” and the “Waterfowl Physiologically Based Extraction Test.” All regressions had positive slopes. Based on criteria of slope and coefficient of determination, the RBALP pH 2.5 and OSU IVG tests performed very well. Speciation by X-ray absorption spectroscopy demonstrated that, on average, most of the Pb in the sampled soils was sorbed to minerals (30%), bound to organic matter 24%, or present as Pb sulfate 18%. Ad
New model accurately predicts reformate composition
Ancheyta-Juarez, J.; Aguilar-Rodriguez, E. )
1994-01-31
Although naphtha reforming is a well-known process, the evolution of catalyst formulation, as well as new trends in gasoline specifications, have led to rapid evolution of the process, including: reactor design, regeneration mode, and operating conditions. Mathematical modeling of the reforming process is an increasingly important tool. It is fundamental to the proper design of new reactors and revamp of existing ones. Modeling can be used to optimize operating conditions, analyze the effects of process variables, and enhance unit performance. Instituto Mexicano del Petroleo has developed a model of the catalytic reforming process that accurately predicts reformate composition at the higher-severity conditions at which new reformers are being designed. The new AA model is more accurate than previous proposals because it takes into account the effects of temperature and pressure on the rate constants of each chemical reaction.
ERIC Educational Resources Information Center
McCammon, Richard B.
1979-01-01
The year 1978 marked a continued trend toward practical applications in mathematical geology. Developments included work in interactive computer graphics, factor analysis, the vanishing tons problem, universal kriging, and resource estimating. (BB)
Elementary Statistics I--Mathematics 274 Course Syllabus, Fall 2001.
ERIC Educational Resources Information Center
Clark, Deborah L.
This document features the syllabus for a course in Elementary Statistics/Mathematics at Southern University in Baton Rouge, LA. The course textbook, a course description, readings, goals, and course requirements are presented. Basic descriptive analysis and mathematical concepts commonly used in statistics are emphasized in the course. Topics…
Accurate spectral color measurements
NASA Astrophysics Data System (ADS)
Hiltunen, Jouni; Jaeaeskelaeinen, Timo; Parkkinen, Jussi P. S.
1999-08-01
Surface color measurement is of importance in a very wide range of industrial applications including paint, paper, printing, photography, textiles, plastics and so on. For a demanding color measurements spectral approach is often needed. One can measure a color spectrum with a spectrophotometer using calibrated standard samples as a reference. Because it is impossible to define absolute color values of a sample, we always work with approximations. The human eye can perceive color difference as small as 0.5 CIELAB units and thus distinguish millions of colors. This 0.5 unit difference should be a goal for the precise color measurements. This limit is not a problem if we only want to measure the color difference of two samples, but if we want to know in a same time exact color coordinate values accuracy problems arise. The values of two instruments can be astonishingly different. The accuracy of the instrument used in color measurement may depend on various errors such as photometric non-linearity, wavelength error, integrating sphere dark level error, integrating sphere error in both specular included and specular excluded modes. Thus the correction formulas should be used to get more accurate results. Another question is how many channels i.e. wavelengths we are using to measure a spectrum. It is obvious that the sampling interval should be short to get more precise results. Furthermore, the result we get is always compromise of measuring time, conditions and cost. Sometimes we have to use portable syste or the shape and the size of samples makes it impossible to use sensitive equipment. In this study a small set of calibrated color tiles measured with the Perkin Elmer Lamda 18 and the Minolta CM-2002 spectrophotometers are compared. In the paper we explain the typical error sources of spectral color measurements, and show which are the accuracy demands a good colorimeter should have.
Science modelling in pre-calculus: how to make mathematics problems contextually meaningful
NASA Astrophysics Data System (ADS)
Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen
2011-04-01
of computer-based science simulations. Although there are several exceptional computer-based science simulations designed for mathematics classes (see, e.g. Kinetic Book (http://www.kineticbooks.com/) or Gizmos (http://www.explorelearning.com/)), we concentrate mainly on the PhET Interactive Simulations developed at the University of Colorado at Boulder (http://phet.colorado.edu/) in generating our argument that computer simulations more accurately represent the contextual characteristics of scientific phenomena than their textual descriptions.
Enhancing Mathematical Communication: "Bag of Tricks" Game
ERIC Educational Resources Information Center
Patahuddin, Sitti Maesuri; Ramful, Ajay; Greenlees, Jane
2015-01-01
An engaging activity which prompts students to listen, talk, reason and write about geometrical properties. The "Bag of Tricks" encourages students to clarify their thoughts and communicate precisely using accurate mathematical language.
Exploring Metacognition in Preservice Teachers: Problem Solving Processes in Elementary Mathematics
ERIC Educational Resources Information Center
Sparkman, Dana; Harris, Kymberly
2009-01-01
In Principles and Standards for School Mathematics (2000), the (U.S.) National Council of Teachers of Mathematics recommended that students communicate their mathematical thinking in a logical manner, and use the language of mathematics to express their thinking accurately and logically. Students should not only learn mathematics content, but…
ERIC Educational Resources Information Center
Bossé, Michael J.; Adu-Gyamfi, Kwaku; Chandler, Kayla; Lynch-Davis, Kathleen
2016-01-01
Dynamic mathematical environments allow users to reify mathematical concepts through multiple representations, transform mathematical relations and organically explore mathematical properties, investigate integrated mathematics, and develop conceptual understanding. Herein, we integrate Boolean algebra, the functionalities of a dynamic…
SKYMAP system description: Star catalog data base generation and utilization
NASA Technical Reports Server (NTRS)
Gottlieb, D. M.
1979-01-01
The specifications, design, software description, and use of the SKYMAP star catalog system are detailed. The SKYMAP system was developed to provide an accurate and complete catalog of all stars with blue or visual magnitudes brighter than 9.0 for use by attitude determination programs. Because of the large number of stars which are brighter than 9.0 magnitude, efficient techniques of manipulating and accessing the data were required. These techniques of staged distillation of data from a Master Catalog to a Core Catalog, and direct access of overlapping zone catalogs, form the basis of the SKYMAP system. The collection and tranformation of data required to produce the Master Catalog data base is described. The data flow through the main programs and levels of star catalogs is detailed. The mathematical and logical techniques for each program and the format of all catalogs are documented.
Educational assessment of mathematics skills and abilities.
Bryant, B R; Rivera, D P
1997-01-01
Mathematics assessments play a valuable role in identifying students' strengths and weaknesses and in developing and monitoring instructional practice. Over the last century, mathematics assessment has been refined as math content has changed as a result of curriculum reform. Today, researchers and practitioners use various assessment techniques to (a) identify students who have mathematics learning disabilities (LD), (b) target individual strengths and weaknesses across mathematics areas, (c) document the effects of mathematics instruction in a remedial or special program, (d) identify strategies that students employ during math activities, (e) conduct research about the characteristics of students with math LD, and (f) examine the technical characteristics of mathematics tests. This article provides an historical overview of the development of mathematics assessment and a description of specific strategies for conducting math evaluations.
Mathematical wit and mathematical cognition.
Aberdein, Andrew
2013-04-01
The published works of scientists often conceal the cognitive processes that led to their results. Scholars of mathematical practice must therefore seek out less obvious sources. This article analyzes a widely circulated mathematical joke, comprising a list of spurious proof types. An account is proposed in terms of argumentation schemes: stereotypical patterns of reasoning, which may be accompanied by critical questions itemizing possible lines of defeat. It is argued that humor is associated with risky forms of inference, which are essential to creative mathematics. The components of the joke are explicated by argumentation schemes devised for application to topic-neutral reasoning. These in turn are classified under seven headings: retroduction, citation, intuition, meta-argument, closure, generalization, and definition. Finally, the wider significance of this account for the cognitive science of mathematics is discussed.
Mathematics Framework for the 2005 National Assessment of Educational Progress
ERIC Educational Resources Information Center
Howe, Roger; Scheaffer, Richard; Lindquist, Mary; Philip, Frank; Halbrook, Arthur
2004-01-01
This document contains the framework and a set of recommendations for the 2005 NAEP mathematics assessment. It includes descriptions of the mathematical content of the test, the types of test questions, and recommendations for administration of the test. In broad terms, this framework attempts to answer the question: What mathematics should be…
Glimm, J.
2009-10-14
Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.
ERIC Educational Resources Information Center
Gafoor, Kunnathodi Abdul; Sarabi, M. K.
2015-01-01
This study relates factors in nature of Mathematics and its teaching learning to student difficulties for diverse mathematics tasks. Descriptive survey was done on a sample of 300 high school students in Kerala with a questionnaire on difficulties in learning. Student perception of difficulty on 26 types of tasks, under five heads that students…
Mathematical String Sculptures: A Case Study in Computationally-Enhanced Mathematical Crafts
ERIC Educational Resources Information Center
Eisenberg, Michael
2007-01-01
Mathematical string sculptures constitute an extremely beautiful realm of mathematical crafts. This snapshot begins with a description of a marvelous (and no longer manufactured) toy called Space Spider, which provided a framework with which children could experiment with string sculptures. Using a computer-controlled laser cutter to create frames…
Quotable Quotes in Mathematics
ERIC Educational Resources Information Center
Lo, Bruce W. N.
1983-01-01
As a way to dispel negative feelings toward mathematics, a variety of quotations are given. They are categorized by: what mathematics is, mathematicians, mathematics and other disciplines, different areas of mathematics, mathematics and humor, applications of mathematics, and pure versus applied mathematics. (MNS)
Mathematical and Numerical Techniques in Energy and Environmental Modeling
NASA Astrophysics Data System (ADS)
Chen, Z.; Ewing, R. E.
Mathematical models have been widely used to predict, understand, and optimize many complex physical processes, from semiconductor or pharmaceutical design to large-scale applications such as global weather models to astrophysics. In particular, simulation of environmental effects of air pollution is extensive. Here we address the need for using similar models to understand the fate and transport of groundwater contaminants and to design in situ remediation strategies. Three basic problem areas need to be addressed in the modeling and simulation of the flow of groundwater contamination. First, one obtains an effective model to describe the complex fluid/fluid and fluid/rock interactions that control the transport of contaminants in groundwater. This includes the problem of obtaining accurate reservoir descriptions at various length scales and modeling the effects of this heterogeneity in the reservoir simulators. Next, one develops accurate discretization techniques that retain the important physical properties of the continuous models. Finally, one develops efficient numerical solution algorithms that utilize the potential of the emerging computing architectures. We will discuss recent advances and describe the contribution of each of the papers in this book in these three areas. Keywords: reservoir simulation, mathematical models, partial differential equations, numerical algorithms
ERIC Educational Resources Information Center
Rogness, Jonathan
2011-01-01
Advances in computer graphics have provided mathematicians with the ability to create stunning visualizations, both to gain insight and to help demonstrate the beauty of mathematics to others. As educators these tools can be particularly important as we search for ways to work with students raised with constant visual stimulation, from video games…
ERIC Educational Resources Information Center
Hadlock, Charles R
2013-01-01
The movement of groundwater in underground aquifers is an ideal physical example of many important themes in mathematical modeling, ranging from general principles (like Occam's Razor) to specific techniques (such as geometry, linear equations, and the calculus). This article gives a self-contained introduction to groundwater modeling with…
ERIC Educational Resources Information Center
Kennard, Jackie
2007-01-01
One of the most interesting developments in teaching has been the growing importance of the outdoor environment. Whether it be playground, garden or field, the outdoors offers a range of challenging experiences, especially in the delivery of early mathematics. Oral feedback to parents, together with photographic displays, can show them that…
Constructing Meanings of Mathematical Registers Using Metaphorical Reasoning and Models
ERIC Educational Resources Information Center
Lai, Mun Yee
2013-01-01
Current debates about successful mathematics pedagogy suggest that mathematical learning and problem solving can be enhanced by using metaphors as they provide students with a tool for thinking. But assisting pre-service teachers to understand the importance of careful and accurate explanations for mathematical concepts remains an issue. This…
NASA Astrophysics Data System (ADS)
Ford, David; Huntsman, Steven
2006-06-01
Thermodynamics (in concert with its sister discipline, statistical physics) can be regarded as a data reduction scheme based on partitioning a total system into a subsystem and a bath that weakly interact with each other. Whereas conventionally, the systems investigated require this form of data reduction in order to facilitate prediction, a different problem also occurs, in the context of communication networks, markets, etc. Such “empirically accessible” systems typically overwhelm observers with the sort of information that in the case of (say) a gas is effectively unobtainable. What is required for such complex interacting systems is not prediction (this may be impossible when humans besides the observer are responsible for the interactions) but rather, description as a route to understanding. Still, the need for a thermodynamical data reduction scheme remains. In this paper, we show how an empirical temperature can be computed for finite, empirically accessible systems, and further outline how this construction allows the age-old science of thermodynamics to be fruitfully applied to them.
Mathematics Curriculum Guide. Mathematics IV.
ERIC Educational Resources Information Center
Gary City Public School System, IN.
GRADES OR AGES: Grade 12. SUBJECT MATTER: Mathematics. ORGANIZATION AND PHYSICAL APPEARANCE: The subject matter is presented in four columns: major areas, significant outcomes, observations and suggestions, and films and references. The topics include: sets-relations-functions, circular functions, graphs of circular functions, inverses of circular…
Mathematical Models of Gene Regulation
NASA Astrophysics Data System (ADS)
Mackey, Michael C.
2004-03-01
This talk will focus on examples of mathematical models for the regulation of repressible operons (e.g. the tryptophan operon), inducible operons (e.g. the lactose operon), and the lysis/lysogeny switch in phage λ. These ``simple" gene regulatory elements can display characteristics experimentally of rapid response to perturbations and bistability, and biologically accurate mathematical models capture these aspects of the dynamics. The models, if realistic, are always nonlinear and contain significant time delays due to transcriptional and translational delays that pose substantial problems for the analysis of the possible ranges of dynamics.
Three essays in mathematical finance
NASA Astrophysics Data System (ADS)
Wang, Ruming
This dissertation uses mathematical techniques to solve three problems in mathematical finance. The first two problems are on model-independent pricing and hedging of financial derivatives. We use asymptotic expansions to express derivative prices and implied volatilities. Then just by using the first few terms in the expansions, we get simple and accurate formulas, which can also help us find connections between different products. The last problem is on optimal trading strategies in a limit order book. Under a very general setup, we solve explicitly for a dynamic decision problem involving choosing between limit order and market order.
Dilemma in Teaching Mathematics
ERIC Educational Resources Information Center
Md Kamaruddin, Nafisah Kamariah; Md Amin, Zulkarnain
2012-01-01
The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…
Mathematics Worth Teaching, Mathematics Worth Understanding.
ERIC Educational Resources Information Center
Romberg, Thomas A.; Kaput, James J.
This chapter examines the scope of the mathematical content educators expect students to understand after they have participated in mathematics courses. It is organized under four headings: (1) Traditional School Mathematics, to clarify what the shift is away from; (2) Mathematics as Human Activity, to portray the direction the shift is toward;…
Teaching Mathematical Modeling in Mathematics Education
ERIC Educational Resources Information Center
Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant
2016-01-01
Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…
Sequentially Simulated Outcomes: Kind Experience versus Nontransparent Description
ERIC Educational Resources Information Center
Hogarth, Robin M.; Soyer, Emre
2011-01-01
Recently, researchers have investigated differences in decision making based on description and experience. We address the issue of when experience-based judgments of probability are more accurate than are those based on description. If description is well understood ("transparent") and experience is misleading ("wicked"), it…
Accurate Evaluation of Quantum Integrals
NASA Technical Reports Server (NTRS)
Galant, D. C.; Goorvitch, D.; Witteborn, Fred C. (Technical Monitor)
1995-01-01
Combining an appropriate finite difference method with Richardson's extrapolation results in a simple, highly accurate numerical method for solving a Schrodinger's equation. Important results are that error estimates are provided, and that one can extrapolate expectation values rather than the wavefunctions to obtain highly accurate expectation values. We discuss the eigenvalues, the error growth in repeated Richardson's extrapolation, and show that the expectation values calculated on a crude mesh can be extrapolated to obtain expectation values of high accuracy.
A Multifaceted Mathematical Approach for Complex Systems
Alexander, F.; Anitescu, M.; Bell, J.; Brown, D.; Ferris, M.; Luskin, M.; Mehrotra, S.; Moser, B.; Pinar, A.; Tartakovsky, A.; Willcox, K.; Wright, S.; Zavala, V.
2012-03-07
Applied mathematics has an important role to play in developing the tools needed for the analysis, simulation, and optimization of complex problems. These efforts require the development of the mathematical foundations for scientific discovery, engineering design, and risk analysis based on a sound integrated approach for the understanding of complex systems. However, maximizing the impact of applied mathematics on these challenges requires a novel perspective on approaching the mathematical enterprise. Previous reports that have surveyed the DOE's research needs in applied mathematics have played a key role in defining research directions with the community. Although these reports have had significant impact, accurately assessing current research needs requires an evaluation of today's challenges against the backdrop of recent advances in applied mathematics and computing. To address these needs, the DOE Applied Mathematics Program sponsored a Workshop for Mathematics for the Analysis, Simulation and Optimization of Complex Systems on September 13-14, 2011. The workshop had approximately 50 participants from both the national labs and academia. The goal of the workshop was to identify new research areas in applied mathematics that will complement and enhance the existing DOE ASCR Applied Mathematics Program efforts that are needed to address problems associated with complex systems. This report describes recommendations from the workshop and subsequent analysis of the workshop findings by the organizing committee.
Computation and graphics in mathematical research. Progress report, June 1, 1991--May 31, 1992
Hoffman, D.A.; Spruck, J.
1992-08-13
This report discusses: The description of the GANG Project and results for prior research; the center for geometry, analysis, numerics and graphics; description of GANG Laboratory; software development at GANG; and mathematical and scientific research activities.
Uses and abuses of mathematics in biology.
May, Robert M
2004-02-06
In the physical sciences, mathematical theory and experimental investigation have always marched together. Mathematics has been less intrusive in the life sciences, possibly because they have until recently been largely descriptive, lacking the invariance principles and fundamental natural constants of physics. Increasingly in recent decades, however, mathematics has become pervasive in biology, taking many different forms: statistics in experimental design; pattern seeking in bioinformatics; models in evolution, ecology, and epidemiology; and much else. I offer an opinionated overview of such uses--and abuses.
Mathematics and academic diversity in Japan.
Woodward, John; Ono, Yumiko
2004-01-01
Japanese education has been the subject of considerable research and educational commentary in the United States over the last 20 years. Since the early 1990s, there has been increased interest in Japanese methods for teaching mathematics, and the Third International Mathematics and Science Study has accelerated American interest in Japanese methods. Observational studies, teacher and student surveys, and analyses of classroom videotapes have provided a rich picture of how the Japanese teach the whole class. However, little has been written about how academically low-achieving math students fare in Japanese schools. This article briefly summarizes Japanese methods for teaching mathematics and describes how the educational system addresses academic diversity. It concludes with a description of a method for teaching mathematics that some Japanese mathematics educators feel has promise for students with learning disabilities.
Authenticity of Mathematical Modeling
ERIC Educational Resources Information Center
Tran, Dung; Dougherty, Barbara J.
2014-01-01
Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…
The College Entrance Examination Board and Mathematics Education.
ERIC Educational Resources Information Center
Jones, Chancey O.; Valentine, John A.
1984-01-01
To help explain the relationship between board activities and mathematics education today, the creation and evolution of the College Board are described. The development of the Advanced Placement computer science course description and examination are noted particularly. (MNS)
Number Sense in the Elementary School Mathematics Classroom.
ERIC Educational Resources Information Center
McBride, John W.; Lamb, Charles E.
1986-01-01
The number sense program in Texas was developed to help motivate students to learn mathematics and to literally develop "number sense." A description of the program, a 70-item exercise (with answers), and teaching tips are provided. (JN)
Accurate pose estimation for forensic identification
NASA Astrophysics Data System (ADS)
Merckx, Gert; Hermans, Jeroen; Vandermeulen, Dirk
2010-04-01
In forensic authentication, one aims to identify the perpetrator among a series of suspects or distractors. A fundamental problem in any recognition system that aims for identification of subjects in a natural scene is the lack of constrains on viewing and imaging conditions. In forensic applications, identification proves even more challenging, since most surveillance footage is of abysmal quality. In this context, robust methods for pose estimation are paramount. In this paper we will therefore present a new pose estimation strategy for very low quality footage. Our approach uses 3D-2D registration of a textured 3D face model with the surveillance image to obtain accurate far field pose alignment. Starting from an inaccurate initial estimate, the technique uses novel similarity measures based on the monogenic signal to guide a pose optimization process. We will illustrate the descriptive strength of the introduced similarity measures by using them directly as a recognition metric. Through validation, using both real and synthetic surveillance footage, our pose estimation method is shown to be accurate, and robust to lighting changes and image degradation.
Accurate basis set truncation for wavefunction embedding
NASA Astrophysics Data System (ADS)
Barnes, Taylor A.; Goodpaster, Jason D.; Manby, Frederick R.; Miller, Thomas F.
2013-07-01
Density functional theory (DFT) provides a formally exact framework for performing embedded subsystem electronic structure calculations, including DFT-in-DFT and wavefunction theory-in-DFT descriptions. In the interest of efficiency, it is desirable to truncate the atomic orbital basis set in which the subsystem calculation is performed, thus avoiding high-order scaling with respect to the size of the MO virtual space. In this study, we extend a recently introduced projection-based embedding method [F. R. Manby, M. Stella, J. D. Goodpaster, and T. F. Miller III, J. Chem. Theory Comput. 8, 2564 (2012)], 10.1021/ct300544e to allow for the systematic and accurate truncation of the embedded subsystem basis set. The approach is applied to both covalently and non-covalently bound test cases, including water clusters and polypeptide chains, and it is demonstrated that errors associated with basis set truncation are controllable to well within chemical accuracy. Furthermore, we show that this approach allows for switching between accurate projection-based embedding and DFT embedding with approximate kinetic energy (KE) functionals; in this sense, the approach provides a means of systematically improving upon the use of approximate KE functionals in DFT embedding.
The reasonable effectiveness of mathematics in the natural sciences
NASA Astrophysics Data System (ADS)
Harvey, Alex
2011-12-01
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism—mathematics exists and is discovered; Logicism—all mathematics may be deduced through pure logic; Formalism—mathematics is just the manipulation of formulas and rules invented for the purpose; Intuitionism—mathematics comprises mental constructs governed by self evident rules. The debate among the several schools has major importance in understanding what Eugene Wigner called, The Unreasonable Effectiveness of Mathematics in the Natural Sciences. In return, this `Unreasonable Effectiveness' suggests a possible resolution of the debate in favor of Realism. The crucial element is the extraordinary predictive capacity of mathematical structures descriptive of physical theories.
Values taught, values learned, attitude and performance in mathematics
NASA Astrophysics Data System (ADS)
Limbaco, K. S. A.
2015-03-01
The purpose of the study was to identify, describe and find the relationship among values taught, values learned, attitude and performance in mathematics. The researcher used descriptive-correlational method of research to gather information and to describe the nature of situation. The following instruments were used in this study: Math Attitude Inventory, Inventory of Values Taught and Learned which were content validated by experts in the field of Mathematics, Values and Education. Generally, most of the values were taught by the teachers. All of the values were learned by the students. The following got the highest mean ratings for values taught: moral strength, sharing, charity, valuing life, love of God, truth and honesty, reason, alternativism and articulation. The following got highest mean ratings for values learned: patience/tolerance, sharing, charity, valuing life, faith, love of God, truth and honesty, analogical thinking, confidence and individual liberty. Majority of the respondents have moderately positive attitude towards mathematics. Positive statements in the Mathematics Attitude Inventory are "Generally true" while negative statements are "Neutral." In conclusion, values were taught by mathematics teacher, thus, learned by the students. Therefore, mathematics is very much related to life. Values can be learned and strengthened through mathematics; there is a significant relationship between values taught by the teachers and values learned by the students and attitude towards mathematics and performance in mathematics; values taught does not affect attitude towards mathematics and performance in mathematics. A student may have a positive attitude towards mathematics or have an exemplary performance in mathematics even if the mathematics teacher did not teach values; values learned does not affect attitude towards mathematics and performance in mathematics. A student may have a positive attitude towards mathematics or have an exemplary performance
Success of Online Mathematics Courses at the Community College Level
ERIC Educational Resources Information Center
Lee, Lisa S.
2011-01-01
Low success rates in online mathematics courses at the community college level have raised concerns. The purpose of this study was to investigate the factors that contribute to student success in online mathematics courses at community colleges. The non-experimental quantitative design began with descriptive statistics to explore the quantitative…
Motivational Classroom Climate for Learning Mathematics: A Reversal Theory Perspective
ERIC Educational Resources Information Center
Lewis, Gareth
2015-01-01
In this article, a case is made that affect is central in determining students' experience of learning or not learning mathematics. I show how reversal theory (Apter, 2001), and particularly its taxonomy of motivations and emotions, provides a basis for a thick description of students' experiences of learning in a mathematics classroom. Using data…
The Necessary Teaching Competences for Mathematics Teachers in Middle Schools
ERIC Educational Resources Information Center
Alnoor, A. G.; xiang, G. Y.
2007-01-01
The professional competences of middle school mathematics teachers has been identified, also the significance extent of such competences for chinese and yemenies mathematics teachers has been studied. The researcher used descriptive research approach. The study data collected from Specialist educators and teachers experts to determine the…
Mathematics Framework for the 2007 National Assessment of Educational Progress
ERIC Educational Resources Information Center
Howe, Roger; Scheaffer, Richard; Lindquist, Mary
2006-01-01
This document contains the framework and a set of recommendations for the NAEP 2007 mathematics assessment, which will assess student achievement nationally and state-by-state, as well as in select urban districts, in grades 4 and 8. It includes descriptions of the mathematical content of the test, the types of test questions, and recommendations…
Mathematical Modelling Approach in Mathematics Education
ERIC Educational Resources Information Center
Arseven, Ayla
2015-01-01
The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…
Mathematical Story: A Metaphor for Mathematics Curriculum
ERIC Educational Resources Information Center
Dietiker, Leslie
2015-01-01
This paper proposes a theoretical framework for interpreting the content found in mathematics curriculum in order to offer teachers and other mathematics educators comprehensive conceptual tools with which to make curricular decisions. More specifically, it describes a metaphor of "mathematics curriculum as story" and defines and…
Discrete Mathematics and the Secondary Mathematics Curriculum.
ERIC Educational Resources Information Center
Dossey, John
Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…
Qualitative Graphing: A Construction in Mathematics.
ERIC Educational Resources Information Center
Narode, Ronald
This document argues that qualitative graphing is an effective introduction to mathematics as a construction for communication of ideas involving quantitative relationships. It is suggested that with little or no prior knowledge of Cartesian coordinates or analytic descriptions of graphs using equations students can successfully grasp concepts of…
Classroom Instruction and Students' Attitudes Towards Mathematics
ERIC Educational Resources Information Center
Tessema, Taddesse G.
2010-01-01
This quantitative study examined the association between classroom instruction and students' attitudes towards mathematics at the secondary level. Data were collected through a Likert-type survey of Hope High School students and then analyzed for statistical significance by utilizing descriptive statistics, tests of significance, and correlation…
ERIC Educational Resources Information Center
Dede, Yuksel
2013-01-01
This study reported the specific findings of a larger comparative study concerning Turkish and German mathematics teachers' values. The main focus was on the teaching experience of the mathematics teachers. Interactions related to nationality were also of interest. The research methodology employed in this study was a descriptive study. The…
Soft Biometrics; Human Identification Using Comparative Descriptions.
Reid, Daniel A; Nixon, Mark S; Stevenage, Sarah V
2014-06-01
Soft biometrics are a new form of biometric identification which use physical or behavioral traits that can be naturally described by humans. Unlike other biometric approaches, this allows identification based solely on verbal descriptions, bridging the semantic gap between biometrics and human description. To permit soft biometric identification the description must be accurate, yet conventional human descriptions comprising of absolute labels and estimations are often unreliable. A novel method of obtaining human descriptions will be introduced which utilizes comparative categorical labels to describe differences between subjects. This innovative approach has been shown to address many problems associated with absolute categorical labels-most critically, the descriptions contain more objective information and have increased discriminatory capabilities. Relative measurements of the subjects' traits can be inferred from comparative human descriptions using the Elo rating system. The resulting soft biometric signatures have been demonstrated to be robust and allow accurate recognition of subjects. Relative measurements can also be obtained from other forms of human representation. This is demonstrated using a support vector machine to determine relative measurements from gait biometric signatures-allowing retrieval of subjects from video footage by using human comparisons, bridging the semantic gap.
ASTP ranging system mathematical model
NASA Technical Reports Server (NTRS)
Ellis, M. R.; Robinson, L. H.
1973-01-01
A mathematical model is presented of the VHF ranging system to analyze the performance of the Apollo-Soyuz test project (ASTP). The system was adapted for use in the ASTP. The ranging system mathematical model is presented in block diagram form, and a brief description of the overall model is also included. A procedure for implementing the math model is presented along with a discussion of the validation of the math model and the overall summary and conclusions of the study effort. Detailed appendices of the five study tasks are presented: early late gate model development, unlock probability development, system error model development, probability of acquisition and model development, and math model validation testing.
ERIC Educational Resources Information Center
Mumcu, Hayal Yavuz
2016-01-01
The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…
ERIC Educational Resources Information Center
Lo, Jane-Jane; And Others
Calls for increased student involvement in mathematics classroom learning situations are due primarily to the recognition that a traditional lecture/demonstration format within school mathematics instruction is not effective in fostering and promoting students' problem-solving abilities, mathematical reasoning power, and mathematical communication…
ERIC Educational Resources Information Center
Ricks, Thomas E.
2010-01-01
Mathematics is motivating; at least, it should be. I argue that mathematical activity is an inherently attractive enterprise for human beings because as intellectual organisms, we are naturally enticed by the intellectual stimulation of mathematizing, and, as social beings, we are drawn to the socializing aspects of mathematical activity. These…
Computer Mathematics: An Introduction.
ERIC Educational Resources Information Center
New York City Board of Education, Brooklyn, NY. Div. of Curriculum and Instruction.
This document describes a mathematics course that uses the computer to solve mathematics problems. It was developed to be used with students who have completed at least one year of general mathematics or are not achieving success in the traditional mathematics program. The course is intended to review, reinforce, and extend concepts included in…
Students as Mathematics Consultants
ERIC Educational Resources Information Center
Jensen, Jennifer L.
2013-01-01
If students are going to develop reasoning and thinking skills, use their mathematical knowledge, and recognize the relevance of mathematics in their lives, they need to experience mathematics in meaningful ways. Only then will their mathematical skills be transferrable to all other parts of their lives. To promote such flexible mathematical…
NASA Astrophysics Data System (ADS)
Tegmark, Max
2014-02-01
The world can be described using mathematical equations and numbers, but why does maths do it so well? In his new book Our Mathematical Universe, a section of which is abridged and edited here, Max Tegmark makes the radical proposal that our reality isn't just described by mathematics - it is mathematics.
Mathematics Lessons without ...
ERIC Educational Resources Information Center
Cross, Kath; Hibbs, John
2006-01-01
In the Association of Teachers of Mathematics (ATM) Easter conference, 2006, the authors presented a list of important aspects of mathematics lessons, recommended for students to have a positive attitude to mathematics and for teachers to acquire effective teaching. The following are discussed in detail: (1) Mathematics lessons without good…
ERIC Educational Resources Information Center
Cain, David
2007-01-01
This article presents the first part of the closing address given by the author to the 2007 Association of Teachers of Mathematics (ATM) Easter conference at Loughborough. In his closing address, the author focuses on functioning mathematically as opposed to functional mathematics. His view of functional mathematics is that the focus is on someone…
Transforming Primary Mathematics
ERIC Educational Resources Information Center
Askew, Mike
2011-01-01
What is good mathematics teaching? What is mathematics teaching good for? Who is mathematics teaching for? These are just some of the questions addressed in "Transforming Primary Mathematics", a highly timely new resource for teachers which accessibly sets out the key theories and latest research in primary maths today. Under-pinned by findings…
Radiator standards for accurate IR calibrations in remote sensing based on heatpipe blackbodies
NASA Astrophysics Data System (ADS)
Hartmann, Juergen; Fischer, Joachim
1999-09-01
The demand of instrumentation in the field of remote sensing is increasing rapidly. For international compatibility, for reliable results and precise long-term investigation, necessary for example in the measurement of climatic trends, accurate traceability of the results to international standards or SI-units is mandatory. Additionally, interpretation of the results strongly requires a careful evaluation of the involved errors and the resulting uncertainties in order to allow for a rating of the obtained results. For that purpose quality assurance was introduced, not only for industrial fabrication, but also, and with increasing tendency, for industrial and scientific research. As an overview, the necessity and the possibilities of quality assurance in the area of remote sensing are discussed. Taking remote sensing of temperature as an example, the general approach is described. For that purpose, a description of heatpipe blackbodies used as standard radiation sources and of the apparatus for measuring the area of the beam limiting apertures is given. We also introduce the applied mathematical model for determination of the emissivity of the blackbodies, which crucially influenced the detected radiation temperature and the uncertainty. Finally the evaluation procedure of the uncertainties is described and a sophisticated estimation of the overall uncertainty is presented.
Minimal dynamical description of eye movements
NASA Astrophysics Data System (ADS)
Specht, Juan I.; Dimieri, Leonardo; Urdapilleta, Eugenio; Gasaneo, Gustavo
2017-02-01
In this paper we have addressed the question of whether a simple set of functions being the solution of a model, namely the damped harmonic oscillator with a general driving force, can satisfactorily describe data corresponding to ocular movements produced during a visual search task. Taking advantage of its mathematical tractability, we first focused on the simplest driving force compatible to the experimental data, a step-like activation. Under this hypothesis we were able to further simplify the system, once data from several experiments were fitted, producing an essentially parameter-free model that we plan to use in future applications. To increase the quality of the description of individual movements, we expanded the complexity in the forcing term and solved the inverse problem by using a proper mathematical formalism. Furthermore, additional terms, those arising from ocular drift and tremor, may be included within the same mathematical approach.
ERIC Educational Resources Information Center
Silver, Edward A.; Lane, Suzanne
Recent reports on mathematics education reform have focused the attention of educational practitioners and policymakers on new goals for mathematics education and new descriptions of mathematical proficiency. QUASAR is a national project (Quantitative Understanding: Amplifying Student Achievement and Reasoning) designed to improve the mathematics…
ERIC Educational Resources Information Center
Wasserman, Nicholas H.
2015-01-01
The work that mathematics teachers do is frequently mathematical in nature and different from other professions. Understanding and describing common ways that teachers draw upon their content knowledge in the practice of teaching is important. Building on the descriptions by McCrory et al. ("Journal for Research in Mathematics Education"…
Learning to Solve Story Problems--Supporting Transitions between Reality and Mathematics
ERIC Educational Resources Information Center
Große, Cornelia S.
2014-01-01
Applying mathematics to real problems is increasingly emphasized in school education; however, it is often complained that many students are not able to solve mathematical problems embedded in contexts. In order to solve story problems, a transition from a textual description to a mathematical notation has to be found, intra-mathematical…
ERIC Educational Resources Information Center
Salani, End
2013-01-01
Lesson starts are transitional events which may cause management problems for teachers. This study sought junior secondary school mathematics teachers' beliefs about calculator use in mathematics instruction in Botswana and was descriptive in nature adopting a survey design. The sample of seventeen (17) mathematics teachers from four (4) junior…
ERIC Educational Resources Information Center
Peschek, Werner; Schneider, Edith
2001-01-01
Discusses descriptive and normative perspectives of mathematics and of (general) mathematics education which can be found in the didactic literature. Contemplates and evaluates the use of computer algebra systems and offers suggestions for basic knowledge and basic skills in a modern technology-supported mathematics classroom. (Contains 12…
Getting Unstuck in Maths: Building Mathematical Memory with Rapid Reconstruction.
ERIC Educational Resources Information Center
Simpson, Jeff
This paper proposes that there are some students who understand mathematics but just can't remember the rules to use it, and others who have accurate rote memory but can't apply the facts they know or do not understand the concepts behind them. The guided discovery approach to teaching mathematics is introduced. This approach promotes a system of…
Mapping Pedagogical Opportunities Provided by Mathematics Analysis Software
ERIC Educational Resources Information Center
Pierce, Robyn; Stacey, Kaye
2010-01-01
This paper proposes a taxonomy of the pedagogical opportunities that are offered by mathematics analysis software such as computer algebra systems, graphics calculators, dynamic geometry or statistical packages. Mathematics analysis software is software for purposes such as calculating, drawing graphs and making accurate diagrams. However, its…
Mathematics of Information Processing and the Internet
ERIC Educational Resources Information Center
Hart, Eric W.
2010-01-01
The mathematics of information processing and the Internet can be organized around four fundamental themes: (1) access (finding information easily); (2) security (keeping information confidential); (3) accuracy (ensuring accurate information); and (4) efficiency (data compression). In this article, the author discusses each theme with reference to…
On numerically accurate finite element
NASA Technical Reports Server (NTRS)
Nagtegaal, J. C.; Parks, D. M.; Rice, J. R.
1974-01-01
A general criterion for testing a mesh with topologically similar repeat units is given, and the analysis shows that only a few conventional element types and arrangements are, or can be made suitable for computations in the fully plastic range. Further, a new variational principle, which can easily and simply be incorporated into an existing finite element program, is presented. This allows accurate computations to be made even for element designs that would not normally be suitable. Numerical results are given for three plane strain problems, namely pure bending of a beam, a thick-walled tube under pressure, and a deep double edge cracked tensile specimen. The effects of various element designs and of the new variational procedure are illustrated. Elastic-plastic computation at finite strain are discussed.
Studies in Mathematics Education. Volume 2. The Teaching of Basic Sciences, Mathematics.
ERIC Educational Resources Information Center
Morris, Robert, Ed.
This volume was geared to answering the question, does the teaching of mathematics correspond to the needs of the majority of pupils and the society. There are three types of chapters: (1) descriptions of goals reflecting some need of society; (2) case studies of national goal setting; and (3) a summary of the May 1980 meeting of the United…
ERIC Educational Resources Information Center
Barwell, Richard
2013-01-01
Climate change is one of the most pressing issues of the 21st Century. Mathematics is involved at every level of understanding climate change, including the description, prediction and communication of climate change. As a highly complex issue, climate change is an example of "post-normal" science -- it is urgent, complex and involves a…
Discover Mathematical Knowledge through Recreational Mathematics Problems
ERIC Educational Resources Information Center
Sodhi, Amar
2004-01-01
The way in which a mathematical problem was used as a vehicle to introduce the joy of mathematical research to a high school student is demonstrated. The student was interested in learning about other classical problems delighting an eager high school student.
Mathematics Coursework Regulates Growth in Mathematics Achievement
ERIC Educational Resources Information Center
Ma, Xin; Wilkins, Jesse L. M.
2007-01-01
Using data from the Longitudinal Study of American Youth (LSAY), we examined the extent to which students' mathematics coursework regulates (influences) the rate of growth in mathematics achievement during middle and high school. Graphical analysis showed that students who started middle school with higher achievement took individual mathematics…
Mathematics and Sports. Mathematical World. Volume 3.
ERIC Educational Resources Information Center
Sadovskii, L. E.; Sadovskii, A. L.
This volume contains some examples of mathematical applications in sports. Sports discussed include tennis, figure skating, gymnastics, track and field, soccer, skiing, hockey, and swimming. Problems and situations are posed and answers with thorough explanations are provided. Chapters include: (1) Mathematics and Sports; (2) What Is Applied…
Mathematics for Language, Language for Mathematics
ERIC Educational Resources Information Center
Prochazkova, Lenka Tejkalova
2013-01-01
The author discusses the balance and mutual influence of the language of instruction and mathematics in the context of CLIL, Content and Language Integrated Learning. Different aspects of the relationship of language and Mathematics teaching and learning are discussed: the benefits of using a foreign language of instruction, as well as the…
Mathematical and statistical analysis
NASA Technical Reports Server (NTRS)
Houston, A. Glen
1988-01-01
The goal of the mathematical and statistical analysis component of RICIS is to research, develop, and evaluate mathematical and statistical techniques for aerospace technology applications. Specific research areas of interest include modeling, simulation, experiment design, reliability assessment, and numerical analysis.
Developing My Mathematics Identity
ERIC Educational Resources Information Center
Gonzalez, Lidia
2016-01-01
Assuming the role of storyteller, the author uses her experiences as a graduate student and beginning teacher to reflect critically on issues related to mathematics, mathematics education, gender, and diversity.
ERIC Educational Resources Information Center
Gallian, Joseph A., Ed.
2010-01-01
"Mathematics and Sports", edited by Joseph A. Gallian, gathers 25 articles that illuminate the power and role of mathematics in the worlds of professional and recreational play. Divided into sections by the kind of sports, the book offers source materials for classroom use and student projects. Readers will encounter mathematical ideas from an…
Mathematics and Mobile Learning
ERIC Educational Resources Information Center
Sayed, Fayez
2015-01-01
The wide range of Mathematical Apps targeting different mathematical concepts and the various types of mobile devices available present a demanding and challenging problem to the teaching and learning in the field of mathematics. In an attempt to address this issue, a few Apps were selected, implemented and tested in this work. [For complete…
ERIC Educational Resources Information Center
Clary, Joseph R.; Nery, Karen P.
This set of 20 modules was designed for use primarily to help teach and reinforce the basic mathematics skills in electronics classes. The modules are based on electronics competencies that require mathematics skills, as determined by a panel of high school electronics and mathematics teachers. Each module consists of one or two pages of basic…
Defining Mathematical Giftedness
ERIC Educational Resources Information Center
Parish, Linda
2014-01-01
This theoretical paper outlines the process of defining "mathematical giftedness" for a present study on how primary school teaching shapes the mindsets of children who are mathematically gifted. Mathematical giftedness is not a badge of honour or some special value attributed to a child who has achieved something exceptional.…
Mathematics. [SITE 2001 Section].
ERIC Educational Resources Information Center
Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.
This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2001 conference: "Secondary Mathematics Methods Course with Technology Units: Encouraging Pre-Service Teachers To Use Technology" (Rajee Amarasinghe); "Competency Exams in College Mathematics"…
Mathematics, Programming, and STEM
ERIC Educational Resources Information Center
Yeh, Andy; Chandra, Vinesh
2015-01-01
Learning mathematics is a complex and dynamic process. In this paper, the authors adopt a semiotic framework (Yeh & Nason, 2004) and highlight programming as one of the main aspects of the semiosis or meaning-making for the learning of mathematics. During a 10- week teaching experiment, mathematical meaning-making was enriched when primary…
ERIC Educational Resources Information Center
Nisbet, Steven
1991-01-01
The relationship between mathematics and music has been investigated for thousands of years. Presented are the mathematical features of music through a study of melody, harmony, and rhythm, and the musical features of mathematics through a study of pattern, ratio, modular arithmetic, Pythagorean triples, and number sequences. (MDH)
ERIC Educational Resources Information Center
Ortiz-Franco, Luis
An historical perspective reveals that sophisticated mathematical activity has been going on in the Latino culture for thousands of years. This paper provides a general definition of the area of mathematics education that deals with issues of culture and mathematics (ethnomathematics) and defines what is meant by the term Latino in this essay.…
Translations toward Connected Mathematics
ERIC Educational Resources Information Center
Applebaum, Mark; Leikin, Roza
2010-01-01
The translation principle allows students to solve problems in different branches of mathematics and thus to develop connectedness in their mathematical knowledge. Successful application of the translation principle depends on the classroom mathematical norms for the development of discussions and the comparison of different solutions to one…
ERIC Educational Resources Information Center
Darlington, Ellie
2014-01-01
This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics…
Applied Vocational Mathematics.
ERIC Educational Resources Information Center
South Carolina State Dept. of Education, Columbia. Office of Vocational Education.
Developed for use in teaching a two-semester, one-unit course, this course guide is intended to aid the high school instructor in teaching mathematical problem-solving and computational skills to vocational education students. The state-adopted textbook for general mathematics III, "Applied General Mathematics" serves as the major…
Mathematical Discovery: Hadamard Resurected
ERIC Educational Resources Information Center
Liljedahl, Peter
2004-01-01
In 1943 Jacques Hadamard gave a series of lectures on mathematical invention at the Ecole Libre des Hautes Etudes in New York City. These talks were subsequently published as The Psychology of Mathematical Invention in the Mathematical Field (Hadamard, 1945). In this article I present a study that mirrors the work of Hadamard. Results both…
ERIC Educational Resources Information Center
Walshaw, Margaret
2014-01-01
This paper explores contemporary thinking about learning mathematics, and within that, social justice within mathematics education. The discussion first looks at mechanisms offered by conventional explanations on the emancipatory project and then moves towards more recent insights developed within mathematics education. Synergies are drawn between…
A "Mathematics Background Check"
ERIC Educational Resources Information Center
Hubisz, John
2009-01-01
Early in my career someone else reported that the best indicator of success in calculus-based physics (CBP) at our school was whether students had taken mathematics in a certain region of New Brunswick. I sat down with a very longtime mathematics teacher and asked him what he thought students should know in mathematics after high school to succeed…
Mathenger Hunt: Mathematics Matters.
ERIC Educational Resources Information Center
Falba, Christy J.; Weiss, Maria J.
1991-01-01
Presented is an activity which shows how mathematics is used in real life and helps to establish a need for mathematics in students' futures. Adapted from a scavenger-hunt idea, this activity helps students to discover that almost every career makes use of mathematics. (KR)
Students' Mathematical Noticing
ERIC Educational Resources Information Center
Lobato, Joanne; Hohensee, Charles; Rhodehamel, Bohdan
2013-01-01
Even in simple mathematical situations, there is an array of different mathematical features that students can attend to or notice. What students notice mathematically has consequences for their subsequent reasoning. By adapting work from both cognitive science and applied linguistics anthropology, we present a focusing framework, which treats…
Mathematics and Global Survival.
ERIC Educational Resources Information Center
Schwartz, Richard H.
This resource was written to provide students with an awareness of critical issues facing the world today. In courses for college students, it can motivate their study of mathematics, teach them how to solve mathematical problems related to current global issues, provide coherence to mathematical studies through a focus on issues of human…
ERIC Educational Resources Information Center
Martin, Tami S.; Speer, William R.
2009-01-01
This article describes features, consistent messages, and new components of "Mathematics Teaching Today: Improving Practice, Improving Student Learning" (NCTM 2007), an updated edition of "Professional Standards for Teaching Mathematics" (NCTM 1991). The new book describes aspects of high-quality mathematics teaching; offers a model for observing,…
Modern Versus Traditional Mathematics
ERIC Educational Resources Information Center
Roberts, A. M.
1974-01-01
The effect of different secondary school mathematics syllabi on first-year performance in college-level mathematics was studied in an attempt to evaluate the syllabus change. Students with a modern mathematics background performed sigficantly better on most first-year units. A topic-by-topic analysis of results is included. (DT)
The purpose of this book is to familiarize the reader with how mathematics can solve important problems in modern military affairs. The authors discuss and explain, without resorting to complex mathematical calculations, the essence of the basic methods which modern mathematics makes available to military problems, design and combat deployment of modern weapons.
ERIC Educational Resources Information Center
Henson, R.; Stumbles, A.
1977-01-01
The relationship between mathematics and chemistry has been changing rapidly in recent years. Some chemistry teachers have experienced difficulties in their teaching with the introduction of modern mathematics in the schools. Some suggestions for reinforcing the concepts and language of modern mathematics are put forth. (Author/MA)
ERIC Educational Resources Information Center
New York City Board of Education, Brooklyn, NY. Bureau of Curriculum Development.
The Materials in this bulletin indicate suggested teaching procedures needed to implement the teaching of "mathematics, 9th Year" as outlined in Curriculum Bulletin No. 3, 1958-59 series, Course of Study Mathematics 7-8-9. Whereas the course of study suggests the application of mathematical principles such as commutativity,…
Abraham, Ralph
2015-12-01
Is there a world of mathematics above and beyond ordinary reality, as Plato proposed? Or is mathematics a cultural construct? In this short article we speculate on the place of mathematical reality from the perspective of the mystical cosmologies of the ancient traditions of meditation, psychedelics, and divination.
ERIC Educational Resources Information Center
Galligan, Linda
2016-01-01
A "National Numeracy Report" and the Australian Curriculum (2014) have recognised the importance of language in mathematics. The general capabilities contained within the "Australian Curriculum: Mathematics" (2014) highlight literacy as an important tool in the teaching and learning of mathematics, from the interpretation of…
Scaffolding students' opportunities to learn mathematics through social interactions
NASA Astrophysics Data System (ADS)
Bell, Clare V.; Pape, Stephen J.
2012-12-01
In this study, we take a sociocultural perspective on teaching and learning to examine how teachers in an urban Algebra 1 classroom constructed opportunities to learn. Drawing on analyses of discourse practices, including videotaped classroom lessons as well as other classroom artifacts and telephone interviews, we describe ways that two teachers and their students interacted to develop mathematical understanding. Through descriptive narrative, we highlight practices that positioned students as competent mathematical thinkers and provided evidence of students' mathematical agency. This study suggests that critical awareness of discourse practices in conjunction with teacher mediation of other affordances for learning within the classroom environment might engage students in mathematical practices such as problem solving, explaining mathematical ideas, arguing for or against specific solutions to problems, and justifying mathematical thinking.
Multimedia content description framework
NASA Technical Reports Server (NTRS)
Bergman, Lawrence David (Inventor); Kim, Michelle Yoonk Yung (Inventor); Li, Chung-Sheng (Inventor); Mohan, Rakesh (Inventor); Smith, John Richard (Inventor)
2003-01-01
A framework is provided for describing multimedia content and a system in which a plurality of multimedia storage devices employing the content description methods of the present invention can interoperate. In accordance with one form of the present invention, the content description framework is a description scheme (DS) for describing streams or aggregations of multimedia objects, which may comprise audio, images, video, text, time series, and various other modalities. This description scheme can accommodate an essentially limitless number of descriptors in terms of features, semantics or metadata, and facilitate content-based search, index, and retrieval, among other capabilities, for both streamed or aggregated multimedia objects.
Experimental and Mathematical-Modeling Characterization of Trypanosoma cruzi Epimastigote Motility
Arias-del-Angel, Jorge A.; Dévora-Canales, Diego; Manning-Cela, Rebeca G.; Santana-Solano, Jesús; Santillán, Moisés
2015-01-01
The present work is aimed at characterizing the motility of parasite T. cruzi in its epimastigote form. To that end, we recorded the trajectories of two strains of this parasite (a wild-type strain and a stable transfected strain, which contains an ectopic copy of LYT1 gene and whose motility is known to be affected). We further extracted parasite trajectories from the recorded videos, and statistically analysed the following trajectory-step features: step length, angular change of direction, longitudinal and transverse displacements with respect to the previous step, and mean square displacement. Based on the resulting observations, we developed a mathematical model to simulate parasite trajectories. The fact that the model predictions closely match most of the experimentally observed parasite-trajectory characteristics, allows us to conclude that the model is an accurate description of T. cruzi motility. PMID:26544863
Towards Accurate Application Characterization for Exascale (APEX)
Hammond, Simon David
2015-09-01
Sandia National Laboratories has been engaged in hardware and software codesign activities for a number of years, indeed, it might be argued that prototyping of clusters as far back as the CPLANT machines and many large capability resources including ASCI Red and RedStorm were examples of codesigned solutions. As the research supporting our codesign activities has moved closer to investigating on-node runtime behavior a nature hunger has grown for detailed analysis of both hardware and algorithm performance from the perspective of low-level operations. The Application Characterization for Exascale (APEX) LDRD was a project concieved of addressing some of these concerns. Primarily the research was to intended to focus on generating accurate and reproducible low-level performance metrics using tools that could scale to production-class code bases. Along side this research was an advocacy and analysis role associated with evaluating tools for production use, working with leading industry vendors to develop and refine solutions required by our code teams and to directly engage with production code developers to form a context for the application analysis and a bridge to the research community within Sandia. On each of these accounts significant progress has been made, particularly, as this report will cover, in the low-level analysis of operations for important classes of algorithms. This report summarizes the development of a collection of tools under the APEX research program and leaves to other SAND and L2 milestone reports the description of codesign progress with Sandia’s production users/developers.
Accurate 3D quantification of the bronchial parameters in MDCT
NASA Astrophysics Data System (ADS)
Saragaglia, A.; Fetita, C.; Preteux, F.; Brillet, P. Y.; Grenier, P. A.
2005-08-01
The assessment of bronchial reactivity and wall remodeling in asthma plays a crucial role in better understanding such a disease and evaluating therapeutic responses. Today, multi-detector computed tomography (MDCT) makes it possible to perform an accurate estimation of bronchial parameters (lumen and wall areas) by allowing a quantitative analysis in a cross-section plane orthogonal to the bronchus axis. This paper provides the tools for such an analysis by developing a 3D investigation method which relies on 3D reconstruction of bronchial lumen and central axis computation. Cross-section images at bronchial locations interactively selected along the central axis are generated at appropriate spatial resolution. An automated approach is then developed for accurately segmenting the inner and outer bronchi contours on the cross-section images. It combines mathematical morphology operators, such as "connection cost", and energy-controlled propagation in order to overcome the difficulties raised by vessel adjacencies and wall irregularities. The segmentation accuracy was validated with respect to a 3D mathematically-modeled phantom of a pair bronchus-vessel which mimics the characteristics of real data in terms of gray-level distribution, caliber and orientation. When applying the developed quantification approach to such a model with calibers ranging from 3 to 10 mm diameter, the lumen area relative errors varied from 3.7% to 0.15%, while the bronchus area was estimated with a relative error less than 5.1%.
Physics 3204. Course Description.
ERIC Educational Resources Information Center
Newfoundland and Labrador Dept. of Education.
A description of the physics 3204 course in Newfoundland and Labrador is provided. The description includes: (1) statement of purpose, including general objectives of science education; (2) a list of six course objectives; (3) course content for units on sound, light, optical instruments, electrostatics, current electricity, Michael Faraday and…
Descriptive Metadata: Emerging Standards.
ERIC Educational Resources Information Center
Ahronheim, Judith R.
1998-01-01
Discusses metadata, digital resources, cross-disciplinary activity, and standards. Highlights include Standard Generalized Markup Language (SGML); Extensible Markup Language (XML); Dublin Core; Resource Description Framework (RDF); Text Encoding Initiative (TEI); Encoded Archival Description (EAD); art and cultural-heritage metadata initiatives;…
The History of Mathematics and Mathematical Education
ERIC Educational Resources Information Center
Grattan-Guinness, I.
1977-01-01
Answers to questions which were asked after the author's various lectures in Australia are gathered here. Topics touched upon include "new" mathematics, unknown constants and free variables, propositional functions, linear algebra, arithmetic and geometry, and student assessment. (MN)
Math Description Engine Software Development Kit
NASA Technical Reports Server (NTRS)
Shelton, Robert O.; Smith, Stephanie L.; Dexter, Dan E.; Hodgson, Terry R.
2010-01-01
The Math Description Engine Software Development Kit (MDE SDK) can be used by software developers to make computer-rendered graphs more accessible to blind and visually-impaired users. The MDE SDK generates alternative graph descriptions in two forms: textual descriptions and non-verbal sound renderings, or sonification. It also enables display of an animated trace of a graph sonification on a visual graph component, with color and line-thickness options for users having low vision or color-related impairments. A set of accessible graphical user interface widgets is provided for operation by end users and for control of accessible graph displays. Version 1.0 of the MDE SDK generates text descriptions for 2D graphs commonly seen in math and science curriculum (and practice). The mathematically rich text descriptions can also serve as a virtual math and science assistant for blind and sighted users, making graphs more accessible for everyone. The MDE SDK has a simple application programming interface (API) that makes it easy for programmers and Web-site developers to make graphs accessible with just a few lines of code. The source code is written in Java for cross-platform compatibility and to take advantage of Java s built-in support for building accessible software application interfaces. Compiled-library and NASA Open Source versions are available with API documentation and Programmer s Guide at http:/ / prim e.jsc.n asa. gov.
Mathematical simulation of centrifugal casting of pipes
Minosyan, Ya.P.; Gerasimov, V.G.; Ryadno, A.A.; Solov'yev, Yu.G.
1983-01-01
A mathematical description of centrifugal casting of long pipes in rapidly-rotating ingot molds is given. The effect of gravity force is neglected. A numerical solution is obtained for the solidification of a steel casting in a thermally insulated mold. The effect of the rate of metal pouring on the motion of the solidification interface is investigated. The disagreement with experimental data is less then 7 percent.
Conceptions of mathematics and student identity: implications for engineering education
NASA Astrophysics Data System (ADS)
Craig, Tracy S.
2013-10-01
Lecturers of first-year mathematics often have reason to believe that students enter university studies with naïve conceptions of mathematics and that more mature conceptions need to be developed in the classroom. Students' conceptions of the nature and role of mathematics in current and future studies as well as future career are pedagogically important as they can impact on student learning and have the potential to influence how and what we teach. As part of ongoing longitudinal research into the experience of a cohort of students registered at the author's institution, students' conceptions of mathematics were determined using a coding scheme developed elsewhere. In this article, I discuss how the cohort of students choosing to study engineering exhibits a view of mathematics as conceptual skill and as problem-solving, coherent with an accurate understanding of the role of mathematics in engineering. Parallel investigation shows, however, that the students do not embody designated identities as engineers.
Haase, Vitor G; Júlio-Costa, Annelise; Lopes-Silva, Júlia B; Starling-Alves, Isabella; Antunes, Andressa M; Pinheiro-Chagas, Pedro; Wood, Guilherme
2014-01-01
Mathematics learning difficulties are a highly comorbid and heterogeneous set of disorders linked to several dissociable mechanisms and endophenotypes. Two of these endophenotypes consist of primary deficits in number sense and verbal numerical representations. However, currently acknowledged endophenotypes are underspecified regarding the role of automatic vs. controlled information processing, and their description should be complemented. Two children with specific deficits in number sense and verbal numerical representations and normal or above-normal intelligence and preserved visuospatial cognition illustrate this point. Child H.V. exhibited deficits in number sense and fact retrieval. Child G.A. presented severe deficits in orally presented problems and transcoding tasks. A partial confirmation of the two endophenotypes that relate to the number sense and verbal processing was obtained, but a much more clear differentiation between the deficits presented by H.V. and G.A. can be reached by looking at differential impairments in modes of processing. H.V. is notably competent in the use of controlled processing but has problems with more automatic processes, such as nonsymbolic magnitude processing, speeded counting and fact retrieval. In contrast, G.A. can retrieve facts and process nonsymbolic magnitudes but exhibits severe impairment in recruiting executive functions and the concentration that is necessary to accomplish transcoding tasks and word problem solving. These results indicate that typical endophenotypes might be insufficient to describe accurately the deficits that are observed in children with mathematics learning abilities. However, by incorporating domain-specificity and modes of processing into the assessment of the endophenotypes, individual deficit profiles can be much more accurately described. This process calls for further specification of the endophenotypes in mathematics learning difficulties.
Haase, Vitor G.; Júlio-Costa, Annelise; Lopes-Silva, Júlia B.; Starling-Alves, Isabella; Antunes, Andressa M.; Pinheiro-Chagas, Pedro; Wood, Guilherme
2014-01-01
Mathematics learning difficulties are a highly comorbid and heterogeneous set of disorders linked to several dissociable mechanisms and endophenotypes. Two of these endophenotypes consist of primary deficits in number sense and verbal numerical representations. However, currently acknowledged endophenotypes are underspecified regarding the role of automatic vs. controlled information processing, and their description should be complemented. Two children with specific deficits in number sense and verbal numerical representations and normal or above-normal intelligence and preserved visuospatial cognition illustrate this point. Child H.V. exhibited deficits in number sense and fact retrieval. Child G.A. presented severe deficits in orally presented problems and transcoding tasks. A partial confirmation of the two endophenotypes that relate to the number sense and verbal processing was obtained, but a much more clear differentiation between the deficits presented by H.V. and G.A. can be reached by looking at differential impairments in modes of processing. H.V. is notably competent in the use of controlled processing but has problems with more automatic processes, such as nonsymbolic magnitude processing, speeded counting and fact retrieval. In contrast, G.A. can retrieve facts and process nonsymbolic magnitudes but exhibits severe impairment in recruiting executive functions and the concentration that is necessary to accomplish transcoding tasks and word problem solving. These results indicate that typical endophenotypes might be insufficient to describe accurately the deficits that are observed in children with mathematics learning abilities. However, by incorporating domain-specificity and modes of processing into the assessment of the endophenotypes, individual deficit profiles can be much more accurately described. This process calls for further specification of the endophenotypes in mathematics learning difficulties. PMID:24592243
The FLUKA Code: An Accurate Simulation Tool for Particle Therapy
Battistoni, Giuseppe; Bauer, Julia; Boehlen, Till T.; Cerutti, Francesco; Chin, Mary P. W.; Dos Santos Augusto, Ricardo; Ferrari, Alfredo; Ortega, Pablo G.; Kozłowska, Wioletta; Magro, Giuseppe; Mairani, Andrea; Parodi, Katia; Sala, Paola R.; Schoofs, Philippe; Tessonnier, Thomas; Vlachoudis, Vasilis
2016-01-01
Monte Carlo (MC) codes are increasingly spreading in the hadrontherapy community due to their detailed description of radiation transport and interaction with matter. The suitability of a MC code for application to hadrontherapy demands accurate and reliable physical models capable of handling all components of the expected radiation field. This becomes extremely important for correctly performing not only physical but also biologically based dose calculations, especially in cases where ions heavier than protons are involved. In addition, accurate prediction of emerging secondary radiation is of utmost importance in innovative areas of research aiming at in vivo treatment verification. This contribution will address the recent developments of the FLUKA MC code and its practical applications in this field. Refinements of the FLUKA nuclear models in the therapeutic energy interval lead to an improved description of the mixed radiation field as shown in the presented benchmarks against experimental data with both 4He and 12C ion beams. Accurate description of ionization energy losses and of particle scattering and interactions lead to the excellent agreement of calculated depth–dose profiles with those measured at leading European hadron therapy centers, both with proton and ion beams. In order to support the application of FLUKA in hospital-based environments, Flair, the FLUKA graphical interface, has been enhanced with the capability of translating CT DICOM images into voxel-based computational phantoms in a fast and well-structured way. The interface is capable of importing also radiotherapy treatment data described in DICOM RT standard. In addition, the interface is equipped with an intuitive PET scanner geometry generator and automatic recording of coincidence events. Clinically, similar cases will be presented both in terms of absorbed dose and biological dose calculations describing the various available features. PMID:27242956
The FLUKA Code: An Accurate Simulation Tool for Particle Therapy.
Battistoni, Giuseppe; Bauer, Julia; Boehlen, Till T; Cerutti, Francesco; Chin, Mary P W; Dos Santos Augusto, Ricardo; Ferrari, Alfredo; Ortega, Pablo G; Kozłowska, Wioletta; Magro, Giuseppe; Mairani, Andrea; Parodi, Katia; Sala, Paola R; Schoofs, Philippe; Tessonnier, Thomas; Vlachoudis, Vasilis
2016-01-01
Monte Carlo (MC) codes are increasingly spreading in the hadrontherapy community due to their detailed description of radiation transport and interaction with matter. The suitability of a MC code for application to hadrontherapy demands accurate and reliable physical models capable of handling all components of the expected radiation field. This becomes extremely important for correctly performing not only physical but also biologically based dose calculations, especially in cases where ions heavier than protons are involved. In addition, accurate prediction of emerging secondary radiation is of utmost importance in innovative areas of research aiming at in vivo treatment verification. This contribution will address the recent developments of the FLUKA MC code and its practical applications in this field. Refinements of the FLUKA nuclear models in the therapeutic energy interval lead to an improved description of the mixed radiation field as shown in the presented benchmarks against experimental data with both (4)He and (12)C ion beams. Accurate description of ionization energy losses and of particle scattering and interactions lead to the excellent agreement of calculated depth-dose profiles with those measured at leading European hadron therapy centers, both with proton and ion beams. In order to support the application of FLUKA in hospital-based environments, Flair, the FLUKA graphical interface, has been enhanced with the capability of translating CT DICOM images into voxel-based computational phantoms in a fast and well-structured way. The interface is capable of importing also radiotherapy treatment data described in DICOM RT standard. In addition, the interface is equipped with an intuitive PET scanner geometry generator and automatic recording of coincidence events. Clinically, similar cases will be presented both in terms of absorbed dose and biological dose calculations describing the various available features.
38 CFR 4.46 - Accurate measurement.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 38 Pensions, Bonuses, and Veterans' Relief 1 2013-07-01 2013-07-01 false Accurate measurement. 4... RATING DISABILITIES Disability Ratings The Musculoskeletal System § 4.46 Accurate measurement. Accurate measurement of the length of stumps, excursion of joints, dimensions and location of scars with respect...
38 CFR 4.46 - Accurate measurement.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 38 Pensions, Bonuses, and Veterans' Relief 1 2012-07-01 2012-07-01 false Accurate measurement. 4... RATING DISABILITIES Disability Ratings The Musculoskeletal System § 4.46 Accurate measurement. Accurate measurement of the length of stumps, excursion of joints, dimensions and location of scars with respect...
38 CFR 4.46 - Accurate measurement.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 38 Pensions, Bonuses, and Veterans' Relief 1 2010-07-01 2010-07-01 false Accurate measurement. 4... RATING DISABILITIES Disability Ratings The Musculoskeletal System § 4.46 Accurate measurement. Accurate measurement of the length of stumps, excursion of joints, dimensions and location of scars with respect...
38 CFR 4.46 - Accurate measurement.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 38 Pensions, Bonuses, and Veterans' Relief 1 2014-07-01 2014-07-01 false Accurate measurement. 4... RATING DISABILITIES Disability Ratings The Musculoskeletal System § 4.46 Accurate measurement. Accurate measurement of the length of stumps, excursion of joints, dimensions and location of scars with respect...
38 CFR 4.46 - Accurate measurement.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 38 Pensions, Bonuses, and Veterans' Relief 1 2011-07-01 2011-07-01 false Accurate measurement. 4... RATING DISABILITIES Disability Ratings The Musculoskeletal System § 4.46 Accurate measurement. Accurate measurement of the length of stumps, excursion of joints, dimensions and location of scars with respect...
On canonical cylinder sections for accurate determination of contact angle in microgravity
NASA Technical Reports Server (NTRS)
Concus, Paul; Finn, Robert; Zabihi, Farhad
1992-01-01
Large shifts of liquid arising from small changes in certain container shapes in zero gravity can be used as a basis for accurately determining contact angle. Canonical geometries for this purpose, recently developed mathematically, are investigated here computationally. It is found that the desired nearly-discontinuous behavior can be obtained and that the shifts of liquid have sufficient volume to be readily observed.
Mathematical modelling of microtumour infiltration based on in vitro experiments.
Luján, Emmanuel; Guerra, Liliana N; Soba, Alejandro; Visacovsky, Nicolás; Gandía, Daniel; Calvo, Juan C; Suárez, Cecilia
2016-08-08
The present mathematical models of microtumours consider, in general, volumetric growth and spherical tumour invasion shapes. Nevertheless in many cases, such as in gliomas, a need for more accurate delineation of tumour infiltration areas in a patient-specific manner has arisen. The objective of this study was to build a mathematical model able to describe in a case-specific way as well as to predict in a probabilistic way the growth and the real invasion pattern of multicellular tumour spheroids (in vitro model of an avascular microtumour) immersed in a collagen matrix. The two-dimensional theoretical model was represented by a reaction-convection-diffusion equation that considers logistic proliferation, volumetric growth, a rim with proliferative cells at the tumour surface and invasion with diffusive and convective components. Population parameter values of the model were extracted from the experimental dataset and a shape function that describes the invasion area was derived from each experimental case by image processing. New possible and aleatory shape functions were generated by data mining and Monte Carlo tools by means of a satellite EGARCH model, which were fed with all the shape functions of the dataset. Then the main model is used in two different ways: to reproduce the growth and invasion of a given experimental tumour in a case-specific manner when fed with the corresponding shape function (descriptive simulations) or to generate new possible tumour cases that respond to the general population pattern when fed with an aleatory-generated shape function (predictive simulations). Both types of simulations are in good agreement with empirical data, as it was revealed by area quantification and Bland-Altman analysis. This kind of experimental-numerical interaction has wide application potential in designing new strategies able to predict as much as possible the invasive behaviour of a tumour based on its particular characteristics and microenvironment.
Langevin description of nonequilibrium quantum fields
NASA Astrophysics Data System (ADS)
Gautier, F.; Serreau, J.
2012-12-01
We consider the nonequilibrium dynamics of a real quantum scalar field. We show the formal equivalence of the exact evolution equations for the statistical and spectral two-point functions with a fictitious Langevin process and examine the conditions under which a local Markovian dynamics is a valid approximation. In quantum field theory, the memory kernel and the noise correlator typically exhibit long time power laws and are thus highly nonlocal, thereby questioning the possibility of a local description. We show that despite this fact, there is a finite time range during which a local description is accurate. This requires the theory to be (effectively) weakly coupled. We illustrate the use of such a local description for studies of decoherence and entropy production in quantum field theory.
[Examination procedure and description of skin lesions].
Ochsendorf, Falk; Meister, Laura
2017-02-09
The dermatologic examination follows a clear structure. After a short history is taken, the whole skin is inspected. The description, which is ideally provided in writing, forces one to look at the skin more closely. The description should include an accurate description of the location, the distribution, the form, and the type of lesion. The article contains tables with internationally approved definitions to describe skin changes. The analysis of these findings allows one to deduce pathophysiologic mechanisms occurring in the skin and to deduce hypotheses, i. e., suspected and differential diagnoses. These are confirmed or excluded by further diagnostic measures. The expert comes to a diagnosis very quickly by a pattern-recognition process, whereby novices must still develop this kind of thinking. Experts can minimize cognitive bias by reflective analytical reasoning and reorganization of knowledge.
Early childhood mathematics intervention.
Clements, Douglas H; Sarama, Julie
2011-08-19
Preschool and primary grade children have the capacity to learn substantial mathematics, but many children lack opportunities to do so. Too many children not only start behind their more advantaged peers, but also begin a negative trajectory in mathematics. Interventions designed to facilitate their mathematical learning during ages 3 to 5 years have a strong positive effect on these children's lives for many years thereafter.
Hardware description languages
NASA Technical Reports Server (NTRS)
Tucker, Jerry H.
1994-01-01
Hardware description languages are special purpose programming languages. They are primarily used to specify the behavior of digital systems and are rapidly replacing traditional digital system design techniques. This is because they allow the designer to concentrate on how the system should operate rather than on implementation details. Hardware description languages allow a digital system to be described with a wide range of abstraction, and they support top down design techniques. A key feature of any hardware description language environment is its ability to simulate the modeled system. The two most important hardware description languages are Verilog and VHDL. Verilog has been the dominant language for the design of application specific integrated circuits (ASIC's). However, VHDL is rapidly gaining in popularity.
Philosophy and mathematics: interactions.
Rashed, Roshdi
From Plato to the beginnings of the last century, mathematics provided philosophers with methods of exposition, procedures of demonstration, and instruments of analysis. The unprecedented development of mathematics on the one hand, and the mathematicians' appropriation of Logic from the philosophers on the other hand, have given rise to two problems with which the philosophers have to contend: (1) Is there still a place for the philosophy of mathematics? and (2) To what extent is a philosophy of mathematics still possible? This article offers some reflections on these questions, which have preoccupied a good many philosophers and continue to do so.
Finite Mathematics and Discrete Mathematics: Is There a Difference?
ERIC Educational Resources Information Center
Johnson, Marvin L.
Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…
On Mathematical Understanding: Perspectives of Experienced Chinese Mathematics Teachers
ERIC Educational Resources Information Center
Cai, Jinfa; Ding, Meixia
2017-01-01
Researchers have long debated the meaning of mathematical understanding and ways to achieve mathematical understanding. This study investigated experienced Chinese mathematics teachers' views about mathematical understanding. It was found that these mathematics teachers embrace the view that understanding is a web of connections, which is a result…
Mathematics for Teaching: A Form of Applied Mathematics
ERIC Educational Resources Information Center
Stylianides, Gabriel J.; Stylianides, Andreas J.
2010-01-01
In this article we elaborate a conceptualisation of "mathematics for teaching" as a form of applied mathematics (using Bass's idea of characterising mathematics education as a form of applied mathematics) and we examine implications of this conceptualisation for the mathematical preparation of teachers. Specifically, we focus on issues of design…
Exploring Differential Effects of Mathematics Courses on Mathematics Achievement
ERIC Educational Resources Information Center
Ma, Xin; McIntyre, Laureen J.
2005-01-01
Using data from the Longitudinal Study of Mathematics Participation (N = 1,518 students from 34 schools), we investigated the effects of pure and applied mathematics courses on mathematics achievement, controlling for prior mathematics achievement. Results of multilevel modelling showed that the effects of pure mathematics were significant after…
A Capstone Mathematics Course for Prospective Secondary Mathematics Teachers
ERIC Educational Resources Information Center
Artzt, Alice F.; Sultan, Alan; Curcio, Frances R.; Gurl, Theresa
2012-01-01
This article describes an innovative capstone mathematics course that links college mathematics with school mathematics and pedagogy. It describes how college juniors in a secondary mathematics teacher preparation program engage in leadership experiences that enable them to learn mathematics for teaching while developing student-centered…
Using Mathematics Literature with Prospective Secondary Mathematics Teachers
ERIC Educational Resources Information Center
Jett, Christopher C.
2014-01-01
Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…
The use of experimental bending tests to more accurate numerical description of TBC damage process
NASA Astrophysics Data System (ADS)
Sadowski, T.; Golewski, P.
2016-04-01
Thermal barrier coatings (TBCs) have been extensively used in aircraft engines to protect critical engine parts such as blades and combustion chambers, which are exposed to high temperatures and corrosive environment. The blades of turbine engines are additionally exposed to high mechanical loads. These loads are created by the high rotational speed of the rotor (30 000 rot/min), causing the tensile and bending stresses. Therefore, experimental testing of coated samples is necessary in order to determine strength properties of TBCs. Beam samples with dimensions 50×10×2 mm were used in those studies. The TBC system consisted of 150 μm thick bond coat (NiCoCrAlY) and 300 μm thick top coat (YSZ) made by APS (air plasma spray) process. Samples were tested by three-point bending test with various loads. After bending tests, the samples were subjected to microscopic observation to determine the quantity of cracks and their depth. The above mentioned results were used to build numerical model and calibrate material data in Abaqus program. Brittle cracking damage model was applied for the TBC layer, which allows to remove elements after reaching criterion. Surface based cohesive behavior was used to model the delamination which may occur at the boundary between bond coat and top coat.
2014-10-08
Marenich, Christopher J. Cramer, Donald G. Truhlar, and Chang-Guo Zhan. Free Energies of Solvation with Surface , Volume, and Local Electrostatic...Effects and Atomic Surface Tensions to Represent the First Solvation Shell (Reprint), Journal of Chemical Theory and Computation, (01 2010): . doi...the Gibbs free energy of solvation and dissociation of HCl in water via Monte Carlo simulations and continuum solvation models, Physical Chemistry
NASA Astrophysics Data System (ADS)
Luo, Yi
2002-03-01
We have developed a new theoretical approach to characterize the electron transport process in molecular devices based on the elastic-scattering Green's function theory in connection with the hybrid density functional theory without using any fitting parameters. Two molecular devices with benzene-1,4-dithiol and octanedithiol molecules embedded between two gold electrodes have been studied. The calculated current-voltage characteristics are in very good agreement with existing experimental results reported by Reed et. al for benzene-1,4-dithiol [Science, 278(1997) 252] and by Cui et al. for octanedithiol [Science, 294(2001) 571]. Our approach is very straightforward and can apply to quite large systems. Most importantly, it provides a reliable way to design and optimize molecular devices theoretically, thereby avoiding extremely difficult, time consuming laboratory tests.
Accurate polarimeter with multicapture fitting for plastic lens evaluation
NASA Astrophysics Data System (ADS)
Domínguez, Noemí; Mayershofer, Daniel; Garcia, Cristina; Arasa, Josep
2016-02-01
Due to their manufacturing process, plastic injection molded lenses do not achieve a constant density throughout their volume. This change of density introduces tensions in the material, inducing local birefringence, which in turn is translated into a variation of the ordinary and extraordinary refractive indices that can be expressed as a retardation phase plane using the Jones matrix notation. The detection and measurement of the value of the retardation of the phase plane are therefore very useful ways to evaluate the quality of plastic lenses. We introduce a polariscopic device to obtain two-dimensional maps of the tension distribution in the bulk of a lens, based on detection of the local birefringence. In addition to a description of the device and the mathematical approach used, a set of initial measurements is presented that confirms the validity of the developed system for the testing of the uniformity of plastic lenses.
Mathematical models of diabetes progression.
De Gaetano, Andrea; Hardy, Thomas; Beck, Benoit; Abu-Raddad, Eyas; Palumbo, Pasquale; Bue-Valleskey, Juliana; Pørksen, Niels
2008-12-01
Few attempts have been made to model mathematically the progression of type 2 diabetes. A realistic representation of the long-term physiological adaptation to developing insulin resistance is necessary for effectively designing clinical trials and evaluating diabetes prevention or disease modification therapies. Writing a good model for diabetes progression is difficult because the long time span of the disease makes experimental verification of modeling hypotheses extremely awkward. In this context, it is of primary importance that the assumptions underlying the model equations properly reflect established physiology and that the mathematical formulation of the model give rise only to physically plausible behavior of the solutions. In the present work, a model of the pancreatic islet compensation is formulated, its physiological assumptions are presented, some fundamental qualitative characteristics of its solutions are established, the numerical values assigned to its parameters are extensively discussed (also with reference to available cross-sectional epidemiologic data), and its performance over the span of a lifetime is simulated under various conditions, including worsening insulin resistance and primary replication defects. The differences with respect to two previously proposed models of diabetes progression are highlighted, and therefore, the model is proposed as a realistic, robust description of the evolution of the compensation of the glucose-insulin system in healthy and diabetic individuals. Model simulations can be run from the authors' web page.
The roughness surface expressed by the mathematical model
NASA Astrophysics Data System (ADS)
Macurova, Anna
2010-07-01
The work investigates the effect of some characteristics of a cut surface and studies roughness of the cutting process. There is elaborated theoretical information and new aspects on calculation of the theoretical values of the roughness of the cut surface for the chosen materials are formulated. In the area of the experimental investigation, results on characteristics of the chosen materials are formulated in this work. Obtained results are fundamental for the mathematical modulation and mathematical analysis for the investigated dependencies for the cut surfaces. The mathematical model also represents the specific dependencies of the technological process. The characteristics of the observed parameters are approximated by characteristics of the quasi-linear models. The solution of this model offers acceptable results. The mathematical models of the roughness of the cut surface are a mathematical description of the dependency of the maximum roughness of the cut surface of the feed represented by the differential equation and by the integral curves.
On some classical problems of descriptive set theory
NASA Astrophysics Data System (ADS)
Kanovei, Vladimir G.; Lyubetskii, Vasilii A.
2003-10-01
The centenary of P.S. Novikov's birth provides an inspiring motivation to present, with full proofs and from a modern standpoint, the presumably definitive solutions of some classical problems in descriptive set theory which were formulated by Luzin [Lusin] and, to some extent, even earlier by Hadamard, Borel, and Lebesgue and relate to regularity properties of point sets. The solutions of these problems began in the pioneering works of Aleksandrov [Alexandroff], Suslin [Souslin], and Luzin (1916-17) and evolved in the fundamental studies of Gödel, Novikov, Cohen, and their successors. Main features of this branch of mathematics are that, on the one hand, it is an ordinary mathematical theory studying natural properties of point sets and functions and rather distant from general set theory or intrinsic problems of mathematical logic like consistency or Gödel's theorems, and on the other hand, it has become a subject of applications of the most subtle tools of modern mathematical logic.
A new sensor system for accurate and precise determination of sediment dynamics and position.
NASA Astrophysics Data System (ADS)
Maniatis, Georgios; Hoey, Trevor; Sventek, Joseph; Hodge, Rebecca
2014-05-01
Sediment transport processes control many significant geomorphological changes. Consequently, sediment transport dynamics are studied across a wide range of scales leading to application of a variety of conceptually different mathematical descriptions (models) and data acquisition techniques (sensing). For river sediment transport processes both Eulerian and Lagrangian formulations are used. Data are gathered using a very wide range of sensing techniques that are not always compatible with the conceptual formulation applied. We are concerned with small to medium sediment grain-scale motion in gravel-bed rivers, and other coarse-grained environments, and: a) are developing a customised environmental sensor capable of providing coherent data that reliably record the motion; and, b) provide a mathematical framework in which these data can be analysed and interpreted, this being compatible with current stochastic approaches to sediment transport theory. Here we present results from three different aspects of the above developmental process. Firstly, we present a requirement analysis for the sensor based on the state of the art of the existing technologies. We focus on the factors that enhance data coherence and representativeness, extending the common practice for optimization which is based exclusively on electronics/computing related criteria. This analysis leads to formalization of a method that permits accurate control on the physical properties of the sensor using contemporary rapid prototyping techniques [Maniatis et al. 2013]. Secondly the first results are presented from a series of entrainment experiments in a 5 x 0.8 m flume in which a prototype sensor was deployed to monitor entrainment dynamics under increasing flow conditions (0.037 m3.s-1). The sensor was enclosed in an idealized spherical case (111 mm diameter) and placed on a constructed bed of hemispheres of the same diameter. We measured 3-axial inertial acceleration (as a measure of flow stress
Automatic TLI recognition system, general description
Lassahn, G.D.
1997-02-01
This report is a general description of an automatic target recognition system developed at the Idaho National Engineering Laboratory for the Department of Energy. A user`s manual is a separate volume, Automatic TLI Recognition System, User`s Guide, and a programmer`s manual is Automatic TLI Recognition System, Programmer`s Guide. This system was designed as an automatic target recognition system for fast screening of large amounts of multi-sensor image data, based on low-cost parallel processors. This system naturally incorporates image data fusion, and it gives uncertainty estimates. It is relatively low cost, compact, and transportable. The software is easily enhanced to expand the system`s capabilities, and the hardware is easily expandable to increase the system`s speed. In addition to its primary function as a trainable target recognition system, this is also a versatile, general-purpose tool for image manipulation and analysis, which can be either keyboard-driven or script-driven. This report includes descriptions of three variants of the computer hardware, a description of the mathematical basis if the training process, and a description with examples of the system capabilities.
The Characteristics of Mathematical Creativity
ERIC Educational Resources Information Center
Sriraman, Bharath
2004-01-01
Mathematical creativity ensures the growth of mathematics as a whole. However, the source of this growth, the creativity of the mathematician, is a relatively unexplored area in mathematics and mathematics education. In order to investigate how mathematicians create mathematics, a qualitative study involving five creative mathematicians was…
Remedial Mathematics for Quantum Chemistry
ERIC Educational Resources Information Center
Koopman, Lodewijk; Brouwer, Natasa; Heck, Andre; Buma, Wybren Jan
2008-01-01
Proper mathematical skills are important for every science course and mathematics-intensive chemistry courses rely on a sound mathematical pre-knowledge. In the first-year quantum chemistry course at this university, it was noticed that many students lack basic mathematical knowledge. To tackle the mathematics problem, a remedial mathematics…
Experimenting with Impacts in a Conceptual Physics or Descriptive Astronomy Laboratory
ERIC Educational Resources Information Center
LoPresto, Michael C.
2016-01-01
What follows is a description of the procedure for and results of a simple experiment on the formation of impact craters designed for the laboratory portions of lower mathematical-level general education science courses such as conceptual physics or descriptive astronomy. The experiment provides necessary experience with data collection and…
Astronomy and Mathematics Education
NASA Astrophysics Data System (ADS)
Ros, Rosa M.
There are many European countries where Astronomy does not appear as a specific course on the secondary school. In these cases Astronomy content can be introduced by means of other subjects. There are some astronomical topics within the subject of Physics but this talk concerns introducing Astronomy in Mathematics classes. Teaching Astronomy through Mathematics would result in more exposure than through Physics as Mathematics is more prevalent in the curriculum. Generally it is not easy to motivate students in Mathematics but they are motivated to find out more about the universe and Astronomy current events than appears in the media. This situation can be an excellent introduction to several mathematics topics. The teachers in secondary and high school can use this idea in order to present more attractive mathematics courses. In particular some different examples will be offered regarding * Angles and spherical coordinates considering star traces * Logarithms and visual magnitudes * Plane trigonometry related orbital movements * Spherical trigonometry in connection with ecliptic obliquity * Conic curves related to sundial at several latitudes Some students do not enjoy studying Mathematics but they can be attracted by practical situations using Applied Mathematics: Astronomy is always very attractive to teenagers.
Mathematical techniques: A compilation
NASA Technical Reports Server (NTRS)
1975-01-01
Articles on theoretical and applied mathematics are introduced. The articles cover information that might be of interest to workers in statistics and information theory, computational aids that could be used by scientists and engineers, and mathematical techniques for design and control.
[Collected Papers on Mathematics.
ERIC Educational Resources Information Center
Connell, Michael L., Ed.
This document contains the following papers on issues related to mathematics in technology and teacher education: "A Case for Strong Conceptualization in Technology Enhanced Mathematics Instruction" (Michael L. Connell and Delwyn L. Harnisch); "Faculty/Student Collaboration in Education and Math--Using the Web To Improve Student…
The Applied Mathematics Laboratory.
ERIC Educational Resources Information Center
Siegel, Martha J.
This report describes the Applied Mathematics Laboratory (AML) operated by the Department of Mathematics at Towson State University, Maryland. AML is actually a course offered to selected undergraduates who are given the opportunity to apply their skills in investigating industrial and governmental problems. By agreement with sponsoring…
Mathematics. [SITE 2002 Section].
ERIC Educational Resources Information Center
Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.
This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2002 conference: (1) "Teachers' Learning of Mathematics in the Presence of Technology: Participatory Cognitive Apprenticeship" (Mara Alagic); (2) "A Fractal Is a Pattern in Your Neighborhood" (Craig N. Bach); (3)…
Developing Mathematically Promising Students.
ERIC Educational Resources Information Center
Sheffield, Linda Jensen, Ed.
This book, written on the recommendation of the Task Force on Mathematically Promising Students, investigates issues involving the development of promising mathematics students. Recommendations are made concerning topics such as the definition of promising students; the identification of such students; appropriate curriculum, instruction, and…
ERIC Educational Resources Information Center
Carr, Martha, Ed.
The purpose of this book is to bring together research and theory about motivation for mathematics from different perspectives. Chapters are included that present theory and research on the influence of gender, culture, the classroom environment, and curriculum on children's mathematical performance and motivation. Chapters are: (1) "Sociocultural…
Experimenting with Mathematical Biology
ERIC Educational Resources Information Center
Sanft, Rebecca; Walter, Anne
2016-01-01
St. Olaf College recently added a Mathematical Biology concentration to its curriculum. The core course, Mathematics of Biology, was redesigned to include a wet laboratory. The lab classes required students to collect data and implement the essential modeling techniques of formulation, implementation, validation, and analysis. The four labs…
Mathematics in Power Technology.
ERIC Educational Resources Information Center
Trombley, Carl; And Others
This mathematics curriculum is designed to be taught by the technology education teacher during the power technology class over a period of 2 years. It is intended to be elective in nature; upon successful completion of both years, one-half credit in mathematics is to be awarded. A list of the academic competencies contained in the curriculum…
ERIC Educational Resources Information Center
Bureau of Naval Personnel, Washington, DC.
The first of three volumes of a mathematics training course for Navy personnel, this document covers a wide range of basic mathematics. The text begins with number systems, signed numbers, fractions, decimals, and percentages and continues into algebra with exponents, polynomials, and linear equations. Early chapters were designed to give insight…
NASA Astrophysics Data System (ADS)
Rohrlich, Fritz
2011-12-01
Classical and the quantum mechanical sciences are in essential need of mathematics. Only thus can the laws of nature be formulated quantitatively permitting quantitative predictions. Mathematics also facilitates extrapolations. But classical and quantum sciences differ in essential ways: they follow different laws of logic, Aristotelian and non-Aristotelian logics, respectively. These are explicated.
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.
Solving Common Mathematical Problems
NASA Technical Reports Server (NTRS)
Luz, Paul L.
2005-01-01
Mathematical Solutions Toolset is a collection of five software programs that rapidly solve some common mathematical problems. The programs consist of a set of Microsoft Excel worksheets. The programs provide for entry of input data and display of output data in a user-friendly, menu-driven format, and for automatic execution once the input data has been entered.
ERIC Educational Resources Information Center
Morgan, John L.; Ginther, John L.
1994-01-01
Describes the effect, method, and mathematics of the following magic tricks which can be used in introducing mathematics lessons: the Ninth Card, Fibonacci Revealed, the Case of the Missing Area, I've Got Your Numbers, and the Card That Turns Inside Out. (MKR)
ERIC Educational Resources Information Center
Sharp, John
2012-01-01
This relationship is omnipresent to those who appreciate the shared attributes of these two areas of creativity. The dynamic nature of media, and further study, enable mathematicians and artists to present new and exciting manifestations of the "mathematics in art", and the "art in mathematics". The illustrative images of the relationship--that…
Business Mathematics Curriculum.
ERIC Educational Resources Information Center
EASTCONN Regional Educational Services Center, North Windham, CT.
This curriculum guide for teaching business mathematics in the Connecticut Vocational-Technical School System is based on the latest thinking of instructors in the field, suggestions from mathematics authorities, and current instructional approaches in education. The curriculum guide consists of six sections: (1) career relationships and…
Teaching Mathematical Modelling.
ERIC Educational Resources Information Center
Jones, Mark S.
1997-01-01
Outlines a course at the University of Glamorgan in the United Kingdom in which a computer algebra system (CAS) teaches mathematical modeling. The format is based on continual assessment of group and individual work stating the problem, a feature list, and formulation of the models. No additional mathematical word processing package is necessary.…
Mathematics Education in Argentina
ERIC Educational Resources Information Center
Varsavsky, Cristina; Anaya, Marta
2009-01-01
This article gives an overview of the state of mathematics education in Argentina across all levels, in the regional and world contexts. Statistics are drawn from Mercosur and UNESCO data bases, World Education Indicators and various national time-series government reports. Mathematics results in national testing programmes, Programme for…
ERIC Educational Resources Information Center
Heck, Andre; Van Gastel, Leendert
2006-01-01
Lowering the dropout rate of incoming mathematics and science students, and enhancing the provision of mathematics support for freshmen are two important aims of the University of Amsterdam. The approach recently adopted to support first year students is to set up a diagnostic pretest and posttest and use these tests to identify students being at…
Elementary Mathematics Leaders
ERIC Educational Resources Information Center
Fennell, Francis; Kobett, Beth McCord; Wray, Jonathan A.
2013-01-01
Elementary school mathematics leaders often come to the realization that their position, however titled and determined, although dedicated to addressing needs in math teaching and learning, also entails and directly involves leadership. Elementary school math specialists/instructional leaders (referenced here as elementary mathematics leaders, or…
ERIC Educational Resources Information Center
Fluellen, Jerry
This paper describes a mathematics-centered thematic unit for 5th graders which organizes all the topics in the Houghton Mifflin Mathematics Program by combining critical thinking and whole language frameworks to help students retain, understand, and make active use of knowledge within and across domains. The unit connects inquiry, goals, critical…
Quality Teaching in Mathematics
ERIC Educational Resources Information Center
Ediger, Marlow
2012-01-01
The best teaching possible needs to accrue in the mathematics curriculum. Pupils also need to become proficient in using mathematics in every day situations in life. Individuals buy goods and services. They pay for these in different ways, including cash. Here, persons need to be able to compute the total cost of items purchased and then pay for…
Designing Assessment for Mathematics
ERIC Educational Resources Information Center
Depka, Eileen
2007-01-01
Teaching mathematics in today's world requires practices and procedures integrated with performance tasks that actively involve students. In this second edition of Designing Rubrics for Mathematics, Eileen Depka clarifies the purpose of rubrics in math instruction and illustrates the relationship between assessment, rubrics, and the National…
The Impossible in Mathematics.
ERIC Educational Resources Information Center
Adler, Irving
The material in this reprint, with minor editorial changes, is from the chapter "Doing the Impossible" in MONKEY BUSINESS by Irving Adler. This 25-page booklet contains brief accounts of historical attempts to prove impossible problems in mathematics. The mathematical recreations in this booklet of geometric constructions include the trisection…
Integrating Writing and Mathematics
ERIC Educational Resources Information Center
Wilcox, Brad; Monroe, Eula Ewing
2011-01-01
Teachers often find it difficult to integrate writing and mathematics while honoring the integrity of both disciplines. In this article, the authors present two levels of integration that teachers may use as a starting point. The first level, writing without revision, can be worked into mathematics instruction quickly and readily. The second…
Building Mathematics Vocabulary
ERIC Educational Resources Information Center
Kovarik, Madeline
2010-01-01
Although mathematics is visual language of symbols and numbers it is also expressed and explained through written and spoken words. For students to excel in mathematics, they must recognize, comprehend and apply the requisite vocabulary. Thus, vocabulary instruction is as critical in content areas as it is in language arts. It is especially…
Under Threes' Mathematical Learning
ERIC Educational Resources Information Center
Franzén, Karin
2015-01-01
The article focuses on mathematics for toddlers in preschool, with the aim of challenging a strong learning discourse that mainly focuses on cognitive learning. By devoting more attention to other perspectives on learning, the hope is to better promote children's early mathematical development. Sweden is one of few countries to have a curriculum…
Mathematics Projects Handbook.
ERIC Educational Resources Information Center
Hess, Adrien L.
This handbook is designed as a guide for teachers and students in choosing and developing mathematics projects, from simple demonstrations of mathematical problems or principles that the teacher has assigned as classroom learning experiences to complex, sophisticated exhibits, intended for entrance in fairs and competitions. The use of projects to…
Psychology and Mathematics Education.
ERIC Educational Resources Information Center
Fischbein, Efraim
1999-01-01
Analyzes the relationship between cognitive psychology as a broad theoretical framework, and the psychology of mathematics education. Argues that mathematics education should not simply borrow from cognitive psychology; rather, it should provide its own psychological research problems, adapted investigation strategies, and adequate original…
Teaching Mathematics Using Steplets
ERIC Educational Resources Information Center
Bringslid, Odd; Norstein, Anne
2008-01-01
This article evaluates online mathematical content used for teaching mathematics in engineering classes and in distance education for teacher training students. In the EU projects Xmath and dMath online computer algebra modules (Steplets) for undergraduate students assembled in the Xmath eBook have been designed. Two questionnaires, a compulsory…
Philosophy of Teaching Mathematics.
ERIC Educational Resources Information Center
Ediger, Marlow
There are selected philosophies in the teaching of mathematics which can provide guidance to the teacher in developing the curriculum and also a framework for teaching and learning. This paper discusses four such philosophies of teaching mathematics: Idealism, Realism, Experimentalism, and Existentialism. Idealism stresses that students live in an…
Janssen, Paddy K.C.
2016-01-01
Purpose To find the most accurate mathematical description of the intravaginal ejaculation latency time (IELT) distribution in the general male population. Materials and Methods We compared the fitness of various well-known mathematical distributions with the IELT distribution of two previously published stopwatch studies of the Caucasian general male population and a stopwatch study of Dutch Caucasian men with lifelong premature ejaculation (PE). The accuracy of fitness is expressed by the Goodness of Fit (GOF). The smaller the GOF, the more accurate is the fitness. Results The 3 IELT distributions are gamma distributions, but the IELT distribution of lifelong PE is another gamma distribution than the IELT distribution of men in the general male population. The Lognormal distribution of the gamma distributions most accurately fits the IELT distribution of 965 men in the general population, with a GOF of 0.057. The Gumbel Max distribution most accurately fits the IELT distribution of 110 men with lifelong PE with a GOF of 0.179. There are more men with lifelong PE ejaculating within 30 and 60 seconds than can be extrapolated from the probability density curve of the Lognormal IELT distribution of men in the general population. Conclusions Men with lifelong PE have a distinct IELT distribution, e.g., a Gumbel Max IELT distribution, that can only be retrieved from the general male population Lognormal IELT distribution when thousands of men would participate in a IELT stopwatch study. The mathematical formula of the Lognormal IELT distribution is useful for epidemiological research of the IELT. PMID:26981594
Technical Mathematics: Restructure of Technical Mathematics.
ERIC Educational Resources Information Center
Flannery, Carol A.
Designed to accompany a series of videotapes, this textbook provides information, examples, problems, and solutions relating to mathematics and its applications in technical fields. Chapter I deals with basic arithmetic, providing information on fractions, decimals, ratios, proportions, percentages, and order of operations. Chapter II focuses on…
Business Mathematics. Mathematics Curriculum Guide (Career Oriented).
ERIC Educational Resources Information Center
Nuschler, Alexandra; And Others
The curriculum guide correlates concepts in business mathematics with career-oriented concepts and activities. The curriculum outline format gives the concepts to be taught, matched with related career-oriented performance objectives, concepts, and suggested instructional activities in facing page layouts. The outline is divided into the major…
Mathematical algorithms for approximate reasoning
NASA Technical Reports Server (NTRS)
Murphy, John H.; Chay, Seung C.; Downs, Mary M.
1988-01-01
Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away
Mathematical model for gyroscope effects
NASA Astrophysics Data System (ADS)
Usubamatov, Ryspek
2015-05-01
Gyroscope effects are used in many engineering calculations of rotating parts, and a gyroscope is the basic unit of numerous devices and instruments used in aviation, space, marine and other industries. The primary attribute of a gyroscope is a spinning rotor that persists in maintaining its plane of rotation, creating gyroscope effects. Numerous publications represent the gyroscope theory using mathematical models based on the law of kinetic energy conservation and the rate of change in angular momentum of a spinning rotor. Gyroscope theory still attracts many researchers who continue to discover new properties of gyroscopic devices. In reality, gyroscope effects are more complex and known mathematical models do not accurately reflect the actual motions. Analysis of forces acting on a gyroscope shows that four dynamic components act simultaneously: the centrifugal, inertial and Coriolis forces and the rate of change in angular momentum of the spinning rotor. The spinning rotor generates a rotating plane of centrifugal and Coriols forces that resist the twisting of the spinning rotor with external torque applied. The forced inclination of the spinning rotor generates inertial forces, resulting in precession torque of a gyroscope. The rate of change of the angular momentum creates resisting and precession torques which are not primary one in gyroscope effects. The new mathematical model for the gyroscope motions under the action of the external torque applied can be as base for new gyroscope theory. At the request of the author of the paper, this corrigendum was issued on 24 May 2016 to correct an incomplete Table 1 and errors in Eq. (47) and Eq. (48).
ERIC Educational Resources Information Center
Hebert, Michael A.; Powell, Sarah R.
2016-01-01
Increasingly, students are expected to write about mathematics. Mathematics writing may be informal (e.g., journals, exit slips) or formal (e.g., writing prompts on high-stakes mathematics assessments). In order to develop an effective mathematics-writing intervention, research needs to be conducted on how students organize mathematics writing and…
Hands-on mathematics: two cases from ancient Chinese mathematics
NASA Astrophysics Data System (ADS)
Wang, Youjun
2009-05-01
In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in ancient China is an abundant resource for materials to demonstrate mathematics by hands-on manipulation. In this article I shall present two cases that embody this idea of a hands-on approach in ancient Chinese mathematics, at the same time offering an opportunity to show how to utilize materials from the history of Chinese math in modern mathematical education.
A robust and accurate formulation of molecular and colloidal electrostatics.
Sun, Qiang; Klaseboer, Evert; Chan, Derek Y C
2016-08-07
This paper presents a re-formulation of the boundary integral method for the Debye-Hückel model of molecular and colloidal electrostatics that removes the mathematical singularities that have to date been accepted as an intrinsic part of the conventional boundary integral equation method. The essence of the present boundary regularized integral equation formulation consists of subtracting a known solution from the conventional boundary integral method in such a way as to cancel out the singularities associated with the Green's function. This approach better reflects the non-singular physical behavior of the systems on boundaries with the benefits of the following: (i) the surface integrals can be evaluated accurately using quadrature without any need to devise special numerical integration procedures, (ii) being able to use quadratic or spline function surface elements to represent the surface more accurately and the variation of the functions within each element is represented to a consistent level of precision by appropriate interpolation functions, (iii) being able to calculate electric fields, even at boundaries, accurately and directly from the potential without having to solve hypersingular integral equations and this imparts high precision in calculating the Maxwell stress tensor and consequently, intermolecular or colloidal forces, (iv) a reliable way to handle geometric configurations in which different parts of the boundary can be very close together without being affected by numerical instabilities, therefore potentials, fields, and forces between surfaces can be found accurately at surface separations down to near contact, and (v) having the simplicity of a formulation that does not require complex algorithms to handle singularities will result in significant savings in coding effort and in the reduction of opportunities for coding errors. These advantages are illustrated using examples drawn from molecular and colloidal electrostatics.
A robust and accurate formulation of molecular and colloidal electrostatics
NASA Astrophysics Data System (ADS)
Sun, Qiang; Klaseboer, Evert; Chan, Derek Y. C.
2016-08-01
This paper presents a re-formulation of the boundary integral method for the Debye-Hückel model of molecular and colloidal electrostatics that removes the mathematical singularities that have to date been accepted as an intrinsic part of the conventional boundary integral equation method. The essence of the present boundary regularized integral equation formulation consists of subtracting a known solution from the conventional boundary integral method in such a way as to cancel out the singularities associated with the Green's function. This approach better reflects the non-singular physical behavior of the systems on boundaries with the benefits of the following: (i) the surface integrals can be evaluated accurately using quadrature without any need to devise special numerical integration procedures, (ii) being able to use quadratic or spline function surface elements to represent the surface more accurately and the variation of the functions within each element is represented to a consistent level of precision by appropriate interpolation functions, (iii) being able to calculate electric fields, even at boundaries, accurately and directly from the potential without having to solve hypersingular integral equations and this imparts high precision in calculating the Maxwell stress tensor and consequently, intermolecular or colloidal forces, (iv) a reliable way to handle geometric configurations in which different parts of the boundary can be very close together without being affected by numerical instabilities, therefore potentials, fields, and forces between surfaces can be found accurately at surface separations down to near contact, and (v) having the simplicity of a formulation that does not require complex algorithms to handle singularities will result in significant savings in coding effort and in the reduction of opportunities for coding errors. These advantages are illustrated using examples drawn from molecular and colloidal electrostatics.
Accurate thermoelastic tensor and acoustic velocities of NaCl
NASA Astrophysics Data System (ADS)
Marcondes, Michel L.; Shukla, Gaurav; da Silveira, Pedro; Wentzcovitch, Renata M.
2015-12-01
Despite the importance of thermoelastic properties of minerals in geology and geophysics, their measurement at high pressures and temperatures are still challenging. Thus, ab initio calculations are an essential tool for predicting these properties at extreme conditions. Owing to the approximate description of the exchange-correlation energy, approximations used in calculations of vibrational effects, and numerical/methodological approximations, these methods produce systematic deviations. Hybrid schemes combining experimental data and theoretical results have emerged as a way to reconcile available information and offer more reliable predictions at experimentally inaccessible thermodynamics conditions. Here we introduce a method to improve the calculated thermoelastic tensor by using highly accurate thermal equation of state (EoS). The corrective scheme is general, applicable to crystalline solids with any symmetry, and can produce accurate results at conditions where experimental data may not exist. We apply it to rock-salt-type NaCl, a material whose structural properties have been challenging to describe accurately by standard ab initio methods and whose acoustic/seismic properties are important for the gas and oil industry.
Accurate thermoelastic tensor and acoustic velocities of NaCl
Marcondes, Michel L.; Shukla, Gaurav; Silveira, Pedro da; Wentzcovitch, Renata M.
2015-12-15
Despite the importance of thermoelastic properties of minerals in geology and geophysics, their measurement at high pressures and temperatures are still challenging. Thus, ab initio calculations are an essential tool for predicting these properties at extreme conditions. Owing to the approximate description of the exchange-correlation energy, approximations used in calculations of vibrational effects, and numerical/methodological approximations, these methods produce systematic deviations. Hybrid schemes combining experimental data and theoretical results have emerged as a way to reconcile available information and offer more reliable predictions at experimentally inaccessible thermodynamics conditions. Here we introduce a method to improve the calculated thermoelastic tensor by using highly accurate thermal equation of state (EoS). The corrective scheme is general, applicable to crystalline solids with any symmetry, and can produce accurate results at conditions where experimental data may not exist. We apply it to rock-salt-type NaCl, a material whose structural properties have been challenging to describe accurately by standard ab initio methods and whose acoustic/seismic properties are important for the gas and oil industry.
On the Role of Mathematics in Physics
NASA Astrophysics Data System (ADS)
Quale, Andreas
2011-03-01
I examine the association between the observable physical world and the mathematical models of theoretical physics. These models will exhibit many entities that have no counterpart in the physical world, but which are still necessary for the mathematical description of physical systems. Moreover, when the model is applied to the analysis of a physical system, it will sometimes produce solutions that are unphysical—i.e. describe a physical system that simply cannot exist in the real world. It is argued that this poses a problem for the epistemic position of realism in physics: a mathematical theory that professes to give a correct description of physical reality should not contain such unrealistic objects. Some concrete examples are examined, and their implications for physics are discussed from a relativist epistemic perspective. I argue that the appearance of the unphysical entities and solutions also has significance for the teaching of physics. It is recommended that the students be exposed from the start to a relativist ontology, as advocated by the theory of radical constructivism; here the unphysical objects do not pose an epistemic problem.
On Possible Uses of Traditional Angolan Sand Drawings in the Mathematics Classroom.
ERIC Educational Resources Information Center
Gerdes, Paulus
1988-01-01
Both industrialized and Third World countries see the need to "multi-culturalize" their mathematics curricula. Following a brief description of the drawing tradition of the Tchokwe people (Angola), some possible uses of their pictograms in the mathematics classroom are suggested. Examples given in this paper include the study of arithmetical…
Hidden Disparities: How Courses and Curricula Shape Opportunities in Mathematics during High School
ERIC Educational Resources Information Center
Schiller, Kathryn S.; Schmidt, William H.; Muller, Chandra; Houang, Richard T.
2010-01-01
Efforts to promote academic achievement by increasing access to courses, especially in mathematics, may mask educational disparities if variations in curriculum are not also monitored. A multi-dimensional description of students' mathematics curricula during high school was obtained from analyses of surveys, transcripts, and textbooks collected…
ERIC Educational Resources Information Center
Yenilmez, Kursat; Ersoy, Mehmet
2008-01-01
The purpose of this study was to determine opinions of mathematics teacher candidates towards applying 7E instructional model on computer aided instruction environments. The descriptive case study model was used in this study. The sample of the study consists of 52 mathematics teacher candidates which were selected randomly from Eskisehir…
Mathematics as verbal behavior.
Marr, M Jackson
2015-04-01
"Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk.
Nakhleh, Luay
2014-03-12
I proposed to develop computationally efficient tools for accurate detection and reconstruction of microbes' complex evolutionary mechanisms, thus enabling rapid and accurate annotation, analysis and understanding of their genomes. To achieve this goal, I proposed to address three aspects. (1) Mathematical modeling. A major challenge facing the accurate detection of HGT is that of distinguishing between these two events on the one hand and other events that have similar "effects." I proposed to develop a novel mathematical approach for distinguishing among these events. Further, I proposed to develop a set of novel optimization criteria for the evolutionary analysis of microbial genomes in the presence of these complex evolutionary events. (2) Algorithm design. In this aspect of the project, I proposed to develop an array of e cient and accurate algorithms for analyzing microbial genomes based on the formulated optimization criteria. Further, I proposed to test the viability of the criteria and the accuracy of the algorithms in an experimental setting using both synthetic as well as biological data. (3) Software development. I proposed the nal outcome to be a suite of software tools which implements the mathematical models as well as the algorithms developed.
ERIC Educational Resources Information Center
Brashers, H. C.
1968-01-01
As the inexperienced writer becomes aware of the issues involved in the composition of effective descriptive prose, he also develops a consistent control over his materials. The persona he chooses, if coherently thought out, can function as an index of many choices, helping him to manipulate the tone, intent, and mood of this style; to regulate…
Andrew integrated reservoir description
Todd, S.P.
1996-12-31
The Andrew field is an oil and gas accumulation in Palaeocene deep marine sands in the Central North Sea. It is currently being developed with mainly horizontal oil producers. Because of the field`s relatively small reserves (mean 118 mmbbls), the performance of each of the 10 or so horizontal wells is highly important. Reservoir description work at sanction time concentrated on supporting the case that the field could be developed commercially with the minimum number of wells. The present Integrated Reservoir Description (IRD) is focussed on delivering the next level of detail that will impact the understanding of the local reservoir architecture and dynamic performance of each well. Highlights of Andrew IRD Include: (1) Use of a Reservoir Uncertainty Statement (RUS) developed at sanction time to focus the descriptive effort of both asset, support and contract petrotechnical staff, (2) High resolution biostratigraphic correlation to support confident zonation of the reservoir, (3) Detailed sedimentological analysis of the core including the use of dipmeter to interpret channel/sheet architecture to provide new insights into reservoir heterogeneity; (4) Integrated petrographical and petrophysical investigation of the controls on Sw-Height and relative permeability of water; (5) Fluids description using oil geochemistry and Residual Salt Analysis Sr isotope studies. Andrew IRD has highlighted several important risks to well performance, including the influence of more heterolithic intervals on gas breakthrough and the controls on water coning exerted by suppressed water relative permeability in the transition zone.
Andrew integrated reservoir description
Todd, S.P.
1996-01-01
The Andrew field is an oil and gas accumulation in Palaeocene deep marine sands in the Central North Sea. It is currently being developed with mainly horizontal oil producers. Because of the field's relatively small reserves (mean 118 mmbbls), the performance of each of the 10 or so horizontal wells is highly important. Reservoir description work at sanction time concentrated on supporting the case that the field could be developed commercially with the minimum number of wells. The present Integrated Reservoir Description (IRD) is focussed on delivering the next level of detail that will impact the understanding of the local reservoir architecture and dynamic performance of each well. Highlights of Andrew IRD Include: (1) Use of a Reservoir Uncertainty Statement (RUS) developed at sanction time to focus the descriptive effort of both asset, support and contract petrotechnical staff, (2) High resolution biostratigraphic correlation to support confident zonation of the reservoir, (3) Detailed sedimentological analysis of the core including the use of dipmeter to interpret channel/sheet architecture to provide new insights into reservoir heterogeneity; (4) Integrated petrographical and petrophysical investigation of the controls on Sw-Height and relative permeability of water; (5) Fluids description using oil geochemistry and Residual Salt Analysis Sr isotope studies. Andrew IRD has highlighted several important risks to well performance, including the influence of more heterolithic intervals on gas breakthrough and the controls on water coning exerted by suppressed water relative permeability in the transition zone.
Mathematics-like Principles Inferred from the Petroglyphs.
ERIC Educational Resources Information Center
Moore, Charles G.
1988-01-01
Identifies certain principles of mathematics-like thought participated in by the carvers of the petroglyphs: (1) iteration; (2) recursion; (3) similitude; (4) tiling; and (5) symmetry. Provides illustrations and verbal descriptions of each process and concludes with four suggested classroom activities to help students appreciate the talents of the…
Engaging Students in Mathematical Modeling through Service-Learning
ERIC Educational Resources Information Center
Carducci, Olivia M.
2014-01-01
I have included a service-learning project in my mathematical modeling course for the last 6 years. This article describes my experience with service-learning in this course. The article includes a description of the course and the service-learning projects. There is a discussion of how to connect with community partners and identify…
Cultural Issues in the Communication of Research on Mathematics Education
ERIC Educational Resources Information Center
Bartolini Bussi, Maria G.; Martignone, Francesca
2013-01-01
It might be trite to observe that every research study is framed within a cultural background. In this paper we argue that the description of the cultural background is important for discussing, evaluating and exploiting internationally the findings of local educational studies. This issue is fundamental in every study in mathematics education…
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…
Eliciting Students' Beliefs about Who Is Good at Mathematics
ERIC Educational Resources Information Center
Morge, Shelby P.
2007-01-01
This article highlights a series of activities designed to elicit students' mathematics-related beliefs, particularly those related to gender. As a result of the activities, females in upper-level classes rated themselves as having less confidence than males, and viewing a movie clip was sufficient for some students to modify their descriptions of…
Workplace Mathematics Research: Reflections on Personal Practical Experiences
ERIC Educational Resources Information Center
Naresh, Nirmala; Chahine, Iman
2013-01-01
This article describes our transitions through three phases of a reflective cycle as a journey from the past to the future. In the descriptive phase, we delve into our past research experiences and address questions such as: What is the role of mathematics at work? In doing so, we uncovered additional venues for exploration that called for a new…
Preferences of Teaching Methods and Techniques in Mathematics with Reasons
ERIC Educational Resources Information Center
Ünal, Menderes
2017-01-01
In this descriptive study, the goal was to determine teachers' preferred pedagogical methods and techniques in mathematics. Qualitative research methods were employed, primarily case studies. 40 teachers were randomly chosen from various secondary schools in Kirsehir during the 2015-2016 educational terms, and data were gathered via…
Brain Hemisphericity and Mathematics Achievement of High School Students
ERIC Educational Resources Information Center
Fernandez, Sanny F.
2011-01-01
This study aimed to find out the brain hemisphericity and mathematics achievement of high school students. The respondents of the study were the 168 first year high school students of Colegio de San Jose, during school year 2010-2011 who were chosen through stratified random sampling. The descriptive and interview methods of research were used in…
Using Our Senses: MINNEMAST Coordinated Mathematics - Science Series, Unit 4.
ERIC Educational Resources Information Center
Page, Laura M.; Reed, Elizabeth W.
This volume is the fourth in a series of 29 coordinated MINNEMAST units in mathematics and science for kindergarten and the primary grades. Intended for use by kindergarten teachers, this unit guide provides a summary and overview of the unit, a list of materials needed, and descriptions of seven groups of activities. The purposes and procedures…
101 Environmental Education Activities. Booklet 3--Mathematics Activities.
ERIC Educational Resources Information Center
Schaljo, Roger, Comp.
Each of the 14 environment-related mathematics activities included in this publication by the Upper Mississippi River ECO-Center includes objectives, materials needed, preparation, and activity description. Occasionally, variations and helpful hints are added. Because the student can gain experience to help him with the practical application of…
Investigating Systems: MINNEMAST Coordinated Mathematics - Science Series, Unit 15.
ERIC Educational Resources Information Center
David, Edith, Ed.
This volume is the fifteenth in a series of 29 coordinated MINNEMAST units in mathematics and science for kindergarten and the primary grades. Intended for use by second-grade teachers, this unit guide provides a summary and overview of the unit, a list of materials needed, and descriptions of six groups of lessons. The purposes and procedures for…
Natural Systems: MINNEMAST Coordinated Mathematics - Science Series, Unit 29.
ERIC Educational Resources Information Center
Bakke, Jeannette; And Others
This volume is the last in a series of 29 coordinated MINNEMAST units in mathematics and science for kindergarten and the primary grades. Intended for use by third-grade teachers, this unit guide provides a summary and overview of the unit, a list of materials needed, and descriptions of three groups of lessons. The purposes and procedures for…
Developing Interactive Learning Objects for a Computing Mathematics Module
ERIC Educational Resources Information Center
Lim, Cher Ping; Lee, Siew Lie; Richards, Cameron
2006-01-01
Based on a case study of the online component of a Computing Mathematics module at a local polytechnic in Singapore, this article provides a descriptive account of the development and employment of interactive learning objects to enhance the learning experiences of the students in the course. The experimented learning objects were branded as…
Learning to Teach Mathematics with Reasoning and Sense Making
ERIC Educational Resources Information Center
Nebesniak, Amy L.
2012-01-01
This study uses teacher research to examine teacher learning in the context of instructional coaching. The author, a mathematics instructional coach, engaged in an intense three-week coaching relationship with a high school Algebra teacher. A detailed description of the teaching and learning of quadratics that took place during this research…
Mathematics Education Is Not an Enigma--Part 1
ERIC Educational Resources Information Center
Williams, Doug
2012-01-01
Doug Williams presented the opening address at Conference 2012 on the theme of "Enigmas". This is storytelling about the learning and teaching of mathematics at its best. The descriptions are of real classrooms with real teachers, and real learners. As with many good stories this is the narrative of a journey. A journey that seeks to change…
Mathematics Education Is Not an Enigma--Part 2
ERIC Educational Resources Information Center
Williams, Doug
2012-01-01
Doug Williams presented the opening address at Conference 2012 on the theme of "Enigmas". Here he continues storytelling about the learning and teaching of mathematics at its best. The descriptions are of real classrooms with real teachers, and real learners. As with many good stories this is the narrative of a journey. A journey that…
Merging Mathematics and English: One Approach to Bridging the Disciplines.
ERIC Educational Resources Information Center
Hansbarger, J. Clark; Stewart, Eric Lane
1996-01-01
Discusses two six-week projects for high school students involving qualitative and quantitative research methods to integrate mathematics and English. Students use descriptive statistics and prose to present findings about (1) their school space and (2) daily life for American troops in the Gulf War. (KMC)
Mathematical modeling in neuroendocrinology.
Bertram, Richard
2015-04-01
Mathematical models are commonly used in neuroscience, both as tools for integrating data and as devices for designing new experiments that test model predictions. The wide range of relevant spatial and temporal scales in the neuroendocrine system makes neuroendocrinology a branch of neuroscience with great potential for modeling. This article provides an overview of concepts that are useful for understanding mathematical models of the neuroendocrine system, as well as design principles that have been illuminated through the use of mathematical models. These principles are found over and over again in cellular dynamics, and serve as building blocks for understanding some of the complex temporal dynamics that are exhibited throughout the neuroendocrine system.
Mathematization in introductory physics
NASA Astrophysics Data System (ADS)
Brahmia, Suzanne M.
Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in
The Greatest Mathematical Discovery?
Bailey, David H.; Borwein, Jonathan M.
2010-05-12
What mathematical discovery more than 1500 years ago: (1) Is one of the greatest, if not the greatest, single discovery in the field of mathematics? (2) Involved three subtle ideas that eluded the greatest minds of antiquity, even geniuses such as Archimedes? (3) Was fiercely resisted in Europe for hundreds of years after its discovery? (4) Even today, in historical treatments of mathematics, is often dismissed with scant mention, or else is ascribed to the wrong source? Answer: Our modern system of positional decimal notation with zero, together with the basic arithmetic computational schemes, which were discovered in India about 500 CE.
Boisvert, Ronald F.; Donahue, Michael J.; Lozier, Daniel W.; McMichael, Robert; Rust, Bert W.
2001-01-01
In this paper we describe the role that mathematics plays in measurement science at NIST. We first survey the history behind NIST’s current work in this area, starting with the NBS Math Tables project of the 1930s. We then provide examples of more recent efforts in the application of mathematics to measurement science, including the solution of ill-posed inverse problems, characterization of the accuracy of software for micromagnetic modeling, and in the development and dissemination of mathematical reference data. Finally, we comment on emerging issues in measurement science to which mathematicians will devote their energies in coming years. PMID:27500024
Characterization of high school mathematics and physics language genres
NASA Astrophysics Data System (ADS)
Wallace, Michelle L.
Research indicates that language factors play a critical role in the learning of school mathematics and science. Symbols and language-forms have been created to represent and discuss mathematical ideas. Understanding language factors, therefore, is critical in improving the teaching and learning of school mathematics and science. The specific goal of this research was to characterize language genres found in secondary school mathematics and physics classrooms. The research presented here was conducted in two secondary school classrooms---one algebra and one physics---taught by the same teacher. The focus was on the discourse between the teacher and her students. In both mathematics and physics, the teacher attended to the meaning of mathematical concepts and processes, but the talk differed. Physics talk focused on developing meaning for the physics concepts through activities and discussion, which were accompanied by mathematical calculations and analyses. Algebra talk, on the other hand, was procedural and narrative in nature. Thus physics talk was more descriptive of individual concepts and situation, and was more explanatory and exploratory than algebra talk. All discourse inevitably reflects one's thinking and beliefs about the content of that discourse. Thus talking algebra and talking physics, as observed in this study, both represented the teacher's beliefs about teaching and learning and the nature of the school curriculum. Even for a teacher with a strong academic background in both mathematics and science, integrating across the curriculum can be hindered by the approved school curriculum and by the reality of the particular classroom context. Providing professional development and implementing one of several available integrated curricula would be needed if more integration were to be implemented. This study presents a literature-based description of the conceptual notion of language genre. It additionally presents a conceptualization of mathematics and
Mathematics, anxiety, and the brain.
Moustafa, Ahmed A; Tindle, Richard; Ansari, Zaheda; Doyle, Margery J; Hewedi, Doaa H; Eissa, Abeer
2017-02-03
Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.
ERIC Educational Resources Information Center
Jaji, Gail
Presents a detailed discussion of the data collected on calculator and computer use in schools in 20 countries. The document includes discussion of: (1) school policy on calculator use; (2) description of populations A (8th grade students) and B (12th grade students) in the United States; (3) uses of calculators in subjects other than mathematics;…
Using Mathematics in Science: Working with Your Mathematics Department
ERIC Educational Resources Information Center
Lyon, Steve
2014-01-01
Changes to the mathematics and science curriculums are designed to increase rigour in mathematics, and place greater emphasis on mathematical content in science subjects at key stages 3, 4 and 5 (ages 11-18). One way to meet the growing challenge of providing increased emphasis on mathematics in the science curriculum is greater collaboration…
Promoting Critical Mathematics Literacy in Secondary Mathematics Teacher Education
ERIC Educational Resources Information Center
Fish, Michael Charles
2012-01-01
This study examines how critical mathematical literacy teachers conceptualize their practices and how those practices were demonstrated in the classroom. Practices were considered from an ontology of mathematics education, specific to critical mathematical literacy, in which classroom interactions question what it means to do mathematics as an…
Elementary Mathematics Teachers' Perceptions and Lived Experiences on Mathematical Communication
ERIC Educational Resources Information Center
Kaya, Defne; Aydin, Hasan
2016-01-01
Mathematical thinking skills and meaningful mathematical understanding are among the goals of current mathematics education. There is a wide consensus among scholars about the purpose of developing mathematical understanding and higher order thinking skills in students. However, how to develop those skills in classroom settings is an area that…
Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches
ERIC Educational Resources Information Center
Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem
2014-01-01
Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…
The Applied Mathematics for Power Systems (AMPS)
Chertkov, Michael
2012-07-24
Increased deployment of new technologies, e.g., renewable generation and electric vehicles, is rapidly transforming electrical power networks by crossing previously distinct spatiotemporal scales and invalidating many traditional approaches for designing, analyzing, and operating power grids. This trend is expected to accelerate over the coming years, bringing the disruptive challenge of complexity, but also opportunities to deliver unprecedented efficiency and reliability. Our Applied Mathematics for Power Systems (AMPS) Center will discover, enable, and solve emerging mathematics challenges arising in power systems and, more generally, in complex engineered networks. We will develop foundational applied mathematics resulting in rigorous algorithms and simulation toolboxes for modern and future engineered networks. The AMPS Center deconstruction/reconstruction approach 'deconstructs' complex networks into sub-problems within non-separable spatiotemporal scales, a missing step in 20th century modeling of engineered networks. These sub-problems are addressed within the appropriate AMPS foundational pillar - complex systems, control theory, and optimization theory - and merged or 'reconstructed' at their boundaries into more general mathematical descriptions of complex engineered networks where important new questions are formulated and attacked. These two steps, iterated multiple times, will bridge the growing chasm between the legacy power grid and its future as a complex engineered network.
Benjamin Banneker's Mathematical Puzzles.
ERIC Educational Resources Information Center
Mahoney, John F.
2003-01-01
Benjamin Banneker, a self-taught African American mathematician, kept a journal containing a number of mathematical puzzles. Explores four of these puzzles, 200 years later, with the aid of 21st century technology. (Author/NB)
Fostering Mathematical Curiosity.
ERIC Educational Resources Information Center
Knuth, Eric J.
2002-01-01
Demonstrates what it might mean to engage students in problem posing and how teachers might begin to create classroom environments that encourage, develop, and foster mathematical curiosity. (Author/NB)
Mathematics: Contributions by Women.
ERIC Educational Resources Information Center
Dewar, Jacqueline M.
1991-01-01
Describes a core course in a women's-studies program at Loyola Marymount University. Provides information, resources, and an annotated bibliography useful for making students more aware of women's contributions to mathematics. Contains 38 references. (ASK)
Black African Traditional Mathematics
ERIC Educational Resources Information Center
Zaslavsky, Claudia
1970-01-01
Discusses the traditional number systems and the origin of the number names used by several African peoples living south of the Sahara. Also included are limitations in African mathematical development, and possible topics for research. (RP)
Mathematics Case Methods Project.
ERIC Educational Resources Information Center
Barnett, Carne S.
1998-01-01
Presents an overview and analysis of the Mathematics Case Methods Project, which uses cases in order to examine and reflect upon teaching. Focuses on a special kind of teacher knowledge, coined pedagogical-content knowledge. (ASK)
Ferrari, Pier Luigi
2003-01-01
Some current interpretations of abstraction in mathematical settings are examined from different perspectives, including history and learning. It is argued that abstraction is a complex concept and that it cannot be reduced to generalization or decontextualization only. In particular, the links between abstraction processes and the emergence of new objects are shown. The role that representations have in abstraction is discussed, taking into account both the historical and the educational perspectives. As languages play a major role in mathematics, some ideas from functional linguistics are applied to explain to what extent mathematical notations are to be considered abstract. Finally, abstraction is examined from the perspective of mathematics education, to show that the teaching ideas resulting from one-dimensional interpretations of abstraction have proved utterly unsuccessful. PMID:12903658
ERIC Educational Resources Information Center
Goos, Merrilyn
2000-01-01
Presents an activity using the familiar fairy tale "Cinderella" to provide the context for stimulating mathematical thinking about a real life problem. Makes use of graphing calculator technology to investigate the relationship between shoe sizes and shoe lengths. (ASK)
Accurate vessel width measurement from fundus photographs: a new concept.
Rassam, S M; Patel, V; Brinchmann-Hansen, O; Engvold, O; Kohner, E M
1994-01-01
Accurate determination of retinal vessel width measurement is important in the study of the haemodynamic changes that accompany various physiological and pathological states. Currently the width at the half height of the transmittance and densitometry profiles are used as a measure of retinal vessel width. A consistent phenomenon of two 'kick points' on the slopes of the transmittance and densitometry profiles near the base, has been observed. In this study, mathematical models have been formulated to describe the characteristic curves of the transmittance and the densitometry profiles. They demonstrate the kick points being coincident with the edges of the blood column. The horizontal distance across the kick points would therefore indicate the actual blood column width. To evaluate this hypothesis, blood was infused through two lengths of plastic tubing of known diameters, and photographed. In comparison with the known diameters, the half height underestimated the blood column width by 7.33% and 6.46%, while the kick point method slightly overestimated it by 1.40% and 0.34%. These techniques were applied to monochromatic fundus photographs. In comparison with the kick point method, the half height underestimated the blood column width in veins by 16.67% and in arteries by 15.86%. The characteristics of the kick points and their practicality have been discussed. The kick point method may provide the most accurate measurement of vessel width possible from these profiles. Images PMID:8110693
Landauer, C.; Bellman, K.L.
1996-12-31
In this paper, we study foundational issues that we believe will help us develop a theoretically sound approach to constructing complex systems. The two theoretical approaches that have helped us understand and develop computational systems in the past are mathematics and linguistics. We describe some differences and strengths of the approaches, and propose a research program to combine the richness of linguistic reasoning with the precision 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.
Mill profiler machines soft materials accurately
NASA Technical Reports Server (NTRS)
Rauschl, J. A.
1966-01-01
Mill profiler machines bevels, slots, and grooves in soft materials, such as styrofoam phenolic-filled cores, to any desired thickness. A single operator can accurately control cutting depths in contour or straight line work.
ERIC Educational Resources Information Center
Wilson, John Martin, Jr.
The purpose of this study was to investigate the interrelationship of general mathematics skills, modern mathematics skills, modern mathematics achievement, prior mathematical attitudes, and postmathematical attitudes of prospective elementary teachers. A sample of 206 students was drawn from 286 students enrolled in a modern mathematics course.…
The "Emerging" and "Emergent" Present: A View on the Indeterminate Nature of Mathematics Lessons
ERIC Educational Resources Information Center
Roth, Wolff-Michael; Maheux, Jean-François
2014-01-01
The notion of emergence has considerable currency in mathematics education. However, the notion tends to be used in a descriptive way rather than being theorized and developed as a phenomenon sui generis. The purpose of this article is to contribute to building a theory of "emergence." After providing an exemplifying description and…
Reasoning about scene descriptions
DiManzo, M.; Adorni, G.; Giunchiglia, F.
1986-07-01
When a scene is described by means of natural language sentences, many details are usually omitted, because they are not in the focus of the conversation. Moreover, natural language is not the best tool to define precisely positions and spatial relationships. The process of interpreting ambiguous statements and inferring missing details involves many types of knowledge, from linguistics to physics. This paper is mainly concerned with the problem of modeling the process of understanding descriptions of static scenes. The specific topics covered by this work are the analysis of the meaning of spatial prepositions, the problem of the reference system and dimensionality, the activation of expectations about unmentioned objects, the role of default knowledge about object positions and its integration with contextual information sources, and the problem of space representation. The issue of understanding dynamic scenes descriptions is briefly approached in the last section.
Reaching All Students with Mathematics.
ERIC Educational Resources Information Center
Cuevas, Gilbert, Ed.; Driscoll, Mark, Ed.
The National Council of Teachers of Mathematics'"Curriculum and Evaluation Standards for School Mathematics" and "Professional Standards for Teaching Mathematics" reflect the belief that all students can learn a significant core of high-quality mathematics. Recognizing the magnitude of the task of reaching all students, this…
Truth & Beauty: Mathematics in Literature
ERIC Educational Resources Information Center
Cohen, Marion D.
2013-01-01
Today there are many categories of mathematics literature, including fiction and poetry. Mathematics fiction appears in such anthologies as "Fantasia Mathematica" (Fadiman 1958, 1997) and "The Mathematical Magpie" (Fadiman 1962, 1997). In addition, mathematics fiction is featured at http://kasmana.people.cofc.edu/MATHFICT.…
Mathematical Modeling: A Structured Process
ERIC Educational Resources Information Center
Anhalt, Cynthia Oropesa; Cortez, Ricardo
2015-01-01
Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…
Semantic Processing of Mathematical Gestures
ERIC Educational Resources Information Center
Lim, Vanessa K.; Wilson, Anna J.; Hamm, Jeff P.; Phillips, Nicola; Iwabuchi, Sarina J.; Corballis, Michael C.; Arzarello, Ferdinando; Thomas, Michael O. J.
2009-01-01
Objective: To examine whether or not university mathematics students semantically process gestures depicting mathematical functions (mathematical gestures) similarly to the way they process action gestures and sentences. Semantic processing was indexed by the N400 effect. Results: The N400 effect elicited by words primed with mathematical gestures…
Celebrating Mathematics All Year 'Round
ERIC Educational Resources Information Center
Daire, Sandra Arguelles
2010-01-01
Celebrating mathematics should be a yearlong event in which students in mathematics classes of all levels engage in mathematics activities and competitions that will encourage growth in mathematical knowledge, enthusiasm for the subject, and collaboration among students of different abilities and backgrounds. Pi Day and Pi Week festivities--a good…
ERIC Educational Resources Information Center
Gough, John
2008-01-01
It is potentially arresting when a mathematical implication is offered in a non-mathematical book. This author contends that students are encouraged to develop mathematical thinking when they read mathematical challenges in books. Aspects of books such as time-lines, historical relationships, maps, journeys, cause-and-affect, deductive inference,…
A Course in Multicultural Mathematics
ERIC Educational Resources Information Center
Hall, Rachel W.
2007-01-01
The course described in this article, "Multicultural Mathematics," aims to strengthen and expand students' understanding of fundamental mathematics--number systems, arithmetic, geometry, elementary number theory, and mathematical reasoning--through study of the mathematics of world cultures. In addition, the course is designed to explore the…
Computers in the Mathematics Curriculum.
ERIC Educational Resources Information Center
Ediger, Marlow
This paper examines ways that mathematics teachers and supervisors can use computers in a quality mathematics curriculum in a school setting. Teachers and supervisors continually need to appraise the present mathematics curriculum and make necessary changes. A modern mathematics curriculum makes much use of technology. Society emphasizes heavy use…
Assessing Innovative Proposals in Mathematics.
ERIC Educational Resources Information Center
Ediger, Marlow
Mathematics is at the apex in priorities pertaining to state-mandated testing of students. With 49 out of 50 states having mandated the testing of students, all of these have mathematics in the testing format. This paper discusses the modern school mathematics movement, recent approaches in improving the teaching of mathematics, and specific…
A Mathematics Software Database Update.
ERIC Educational Resources Information Center
Cunningham, R. S.; Smith, David A.
1987-01-01
Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)
Spacelab J experiment descriptions
Miller, T.Y.
1993-08-01
Brief descriptions of the experiment investigations for the Spacelab J Mission which was launched from the Kennedy Space Center aboard the Endeavour in Sept. 1992 are presented. Experiments cover the following: semiconductor crystals; single crystals; superconducting composite materials; crystal growth; bubble behavior in weightlessness; microgravity environment; health monitoring of Payload Specialists; cultured plant cells; effect of low gravity on calcium metabolism and bone formation; and circadian rhythm. Separate abstracts have been prepared for articles from this report.
Spacelab J experiment descriptions
NASA Technical Reports Server (NTRS)
Miller, Teresa Y. (Editor)
1993-01-01
Brief descriptions of the experiment investigations for the Spacelab J Mission which was launched from the Kennedy Space Center aboard the Endeavour in Sept. 1992 are presented. Experiments cover the following: semiconductor crystals; single crystals; superconducting composite materials; crystal growth; bubble behavior in weightlessness; microgravity environment; health monitoring of Payload Specialists; cultured plant cells; effect of low gravity on calcium metabolism and bone formation; and circadian rhythm.
Management control system description
Bence, P. J.
1990-10-01
This Management Control System (MCS) description describes the processes used to manage the cost and schedule of work performed by Westinghouse Hanford Company (Westinghouse Hanford) for the US Department of Energy, Richland Operations Office (DOE-RL), Richland, Washington. Westinghouse Hanford will maintain and use formal cost and schedule management control systems, as presented in this document, in performing work for the DOE-RL. This MCS description is a controlled document and will be modified or updated as required. This document must be approved by the DOE-RL; thereafter, any significant change will require DOE-RL concurrence. Westinghouse Hanford is the DOE-RL operations and engineering contractor at the Hanford Site. Activities associated with this contract (DE-AC06-87RL10930) include operating existing plant facilities, managing defined projects and programs, and planning future enhancements. This document is designed to comply with Section I-13 of the contract by providing a description of Westinghouse Hanford's cost and schedule control systems used in managing the above activities. 5 refs., 22 figs., 1 tab.
Development of a Mathematical Ability Test: A Validity and Reliability Study
ERIC Educational Resources Information Center
Dündar, Sefa; Temel, Hasan; Gündüz, Nazan
2016-01-01
The identification of talented students accurately at an early age and the adaptation of the education provided to the students depending on their abilities are of great importance for the future of the countries. In this regard, this study aims to develop a mathematical ability test for the identification of the mathematical abilities of students…
ERIC Educational Resources Information Center
Taber, Mary R.
2013-01-01
Mathematics can be a difficult topic both to teach and to learn. Word problems specifically can be difficult for students with disabilities because they have to conceptualize what the problem is asking for, and they must perform the correct operation accurately. Current trends in mathematics instruction stem from the National Council of Teachers…
Mathematical studies of parasitic infection and immunity.
Anderson, R M
1994-06-24
The techniques that underpin modern molecular biology have been rapidly adopted by those interested in the major parasitic infections of humans. The parasitological literature is full of reports of genes and their amino acid sequences, of molecules, of cell membrane receptors and channels, and of the fine details of the immunological responses mounted by the host to combat infection. Much less enthusiasm has been shown for the mathematical techniques that facilitate the analysis and interpretation of dynamical processes such as transmission, evolution, and the interplay between parasite population growth and immunological responses within the host. Molecular techniques provide enormous opportunities for description, but ultimately, understanding biological systems with the precision that physicists and engineers aspire to in their own fields will require quantitative description of the many rate processes that dictate both an observed pattern and the dynamics of its change.
The Effect of Mathematics Research on Mathematics Majors' Mathematical Beliefs
ERIC Educational Resources Information Center
Goodson, Joshua E.
2012-01-01
This is a dissertation about the beliefs that mathematics majors have about mathematics and how their beliefs are affected by the introduction of mathematics research. The mathematics research presented to the students dealt with counting regular orbits of an action. Research has shown that the beliefs that teachers hold about mathematics…
ERIC Educational Resources Information Center
Clark, Kathleen Michelle
2012-01-01
The use of the history of mathematics in teaching has long been considered a tool for enriching students' mathematical learning. However, in the USA few, if any, research efforts have investigated how the study of history of mathematics contributes to a person's mathematical knowledge for teaching. In this article, I present the results of…
ERIC Educational Resources Information Center
Dickerson, David S.; Doerr, Helen M.
2014-01-01
Proof serves many purposes in mathematics. In this qualitative study of 17 high school mathematics teachers, we found that these teachers perceived that two of the most important purposes for proof in school mathematics were (a) to enhance students' mathematical understanding and (b) to develop generalized thinking skills that were…
Mathematical modelling of the MAP kinase pathway using proteomic datasets.
Tian, Tianhai; Song, Jiangning
2012-01-01
The advances in proteomics technologies offer an unprecedented opportunity and valuable resources to understand how living organisms execute necessary functions at systems levels. However, little work has been done up to date to utilize the highly accurate spatio-temporal dynamic proteome data generated by phosphoprotemics for mathematical modeling of complex cell signaling pathways. This work proposed a novel computational framework to develop mathematical models based on proteomic datasets. Using the MAP kinase pathway as the test system, we developed a mathematical model including the cytosolic and nuclear subsystems; and applied the genetic algorithm to infer unknown model parameters. Robustness property of the mathematical model was used as a criterion to select the appropriate rate constants from the estimated candidates. Quantitative information regarding the absolute protein concentrations was used to refine the mathematical model. We have demonstrated that the incorporation of more experimental data could significantly enhance both the simulation accuracy and robustness property of the proposed model. In addition, we used the MAP kinase pathway inhibited by phosphatases with different concentrations to predict the signal output influenced by different cellular conditions. Our predictions are in good agreement with the experimental observations when the MAP kinase pathway was inhibited by phosphatase PP2A and MKP3. The successful application of the proposed modeling framework to the MAP kinase pathway suggests that our method is very promising for developing accurate mathematical models and yielding insights into the regulatory mechanisms of complex cell signaling pathways.
Electrooculography: Connecting Mind, Brain, and Behavior in Mathematics Education Research
ERIC Educational Resources Information Center
Shipulina, Olga V.; Campbell, Stephen R.; Cimen, Arda O.
2009-01-01
This paper reports on the potential roles and importance of electrooculography (EOG) for mathematics educational neuroscience research. EOG enables accurate measurements of eye-related behavior (i.e., blinks & movements) by recording changes in voltage potentials generated by eye-related behavior. We identify and discuss three main uses of EOG.…
Gaber, David; Schlimm, Dirk
2015-01-01
Mathematics is a powerful tool for describing and developing our knowledge of the physical world. It informs our understanding of subjects as diverse as music, games, science, economics, communications protocols, and visual arts. Mathematical thinking has its roots in the adaptive behavior of living creatures: animals must employ judgments about quantities and magnitudes in the assessment of both threats (how many foes) and opportunities (how much food) in order to make effective decisions, and use geometric information in the environment for recognizing landmarks and navigating environments. Correspondingly, cognitive systems that are dedicated to the processing of distinctly mathematical information have developed. In particular, there is evidence that certain core systems for understanding different aspects of arithmetic as well as geometry are employed by humans and many other animals. They become active early in life and, particularly in the case of humans, develop through maturation. Although these core systems individually appear to be quite limited in application, in combination they allow for the recognition of mathematical properties and the formation of appropriate inferences based upon those properties. In this overview, the core systems, their roles, their limitations, and their interaction with external representations are discussed, as well as possibilities for how they can be employed together to allow us to reason about more complex mathematical domains.
Measuring Joint Stimulus Control by Complex Graph/Description Correspondences
ERIC Educational Resources Information Center
Fields, Lanny; Spear, Jack
2012-01-01
Joint stimulus control occurs when responding is determined by the correspondence of elements of a complex sample and a complex comparison stimulus. In academic settings, joint stimulus control of behavior would be evidenced by the selection of an accurate description of a complex graph in which each element of a graph corresponded to particular…
Mathematical challenges from theoretical/computational chemistry
1995-12-31
The committee believes that this report has relevance and potentially valuable suggestions for a wide range of readers. Target audiences include: graduate departments in the mathematical and chemical sciences; federal and private agencies that fund research in the mathematical and chemical sciences; selected industrial and government research and development laboratories; developers of software and hardware for computational chemistry; and selected individual researchers. Chapter 2 of this report covers some history of computational chemistry for the nonspecialist, while Chapter 3 illustrates the fruits of some past successful cross-fertilization between mathematical scientists and computational/theoretical chemists. In Chapter 4 the committee has assembled a representative, but not exhaustive, survey of research opportunities. Most of these are descriptions of important open problems in computational/theoretical chemistry that could gain much from the efforts of innovative mathematical scientists, written so as to be accessible introductions to the nonspecialist. Chapter 5 is an assessment, necessarily subjective, of cultural differences that must be overcome if collaborative work is to be encouraged between the mathematical and the chemical communities. Finally, the report ends with a brief list of conclusions and recommendations that, if followed, could promote accelerated progress at this interface. Recognizing that bothersome language issues can inhibit prospects for collaborative research at the interface between distinctive disciplines, the committee has attempted throughout to maintain an accessible style, in part by using illustrative boxes, and has included at the end of the report a glossary of technical terms that may be familiar to only a subset of the target audiences listed above.
The Genre of Technical Description.
ERIC Educational Resources Information Center
Jordan, Michael P.
1986-01-01
Summarizes recent research into systems of lexical and grammatical cohesion in technical description. Discusses various methods by which technical writers "re-enter" the topic of description back into the text in successive sentences. (HTH)
Accurate three-dimensional documentation of distinct sites
NASA Astrophysics Data System (ADS)
Singh, Mahesh K.; Dutta, Ashish; Subramanian, Venkatesh K.
2017-01-01
One of the most critical aspects of documenting distinct sites is acquiring detailed and accurate range information. Several three-dimensional (3-D) acquisition techniques are available, but each has its own limitations. This paper presents a range data fusion method with the aim to enhance the descriptive contents of the entire 3-D reconstructed model. A kernel function is introduced for supervised classification of the range data using a kernelized support vector machine. The classification method is based on the local saliency features of the acquired range data. The range data acquired from heterogeneous range sensors are transformed into a defined common reference frame. Based on the segmentation criterion, the fusion of range data is performed by integrating finer regions of range data acquired from a laser range scanner with the coarser region of Kinect's range data. After fusion, the Delaunay triangulation algorithm is applied to generate the highly accurate, realistic 3-D model of the scene. Finally, experimental results show the robustness of the proposed approach.
MCO Monitoring activity description
SEXTON, R.A.
1998-11-09
Spent Nuclear Fuel remaining from Hanford's N-Reactor operations in the 1970s has been stored under water in the K-Reactor Basins. This fuel will be repackaged, dried and stored in a new facility in the 200E Area. The safety basis for this process of retrieval, drying, and interim storage of the spent fuel has been established. The monitoring of MCOS in dry storage is a currently identified issue in the SNF Project. This plan outlines the key elements of the proposed monitoring activity. Other fuel stored in the K-Reactor Basins, including SPR fuel, will have other monitoring considerations and is not addressed by this activity description.
Three Approaches to Descriptive Research.
ERIC Educational Resources Information Center
Svensson, Lennart
This report compares three approaches to descriptive research, focusing on the kinds of descriptions developed and on the methods used to develop the descriptions. The main emphasis in all three approaches is on verbal data. In these approaches the importance of interpretation and its intuitive nature are emphasized. The three approaches, however,…
An accurate metric for the spacetime around rotating neutron stars.
NASA Astrophysics Data System (ADS)
Pappas, George
2017-01-01
The problem of having an accurate description of the spacetime around rotating neutron stars is of great astrophysical interest. For astrophysical applications, one needs to have a metric that captures all the properties of the spacetime around a rotating neutron star. Furthermore, an accurate appropriately parameterised metric, i.e., a metric that is given in terms of parameters that are directly related to the physical structure of the neutron star, could be used to solve the inverse problem, which is to infer the properties of the structure of a neutron star from astrophysical observations. In this work we present such an approximate stationary and axisymmetric metric for the exterior of rotating neutron stars, which is constructed using the Ernst formalism and is parameterised by the relativistic multipole moments of the central object. This metric is given in terms of an expansion on the Weyl-Papapetrou coordinates with the multipole moments as free parameters and is shown to be extremely accurate in capturing the physical properties of a neutron star spacetime as they are calculated numerically in general relativity. Because the metric is given in terms of an expansion, the expressions are much simpler and easier to implement, in contrast to previous approaches. For the parameterisation of the metric in general relativity, the recently discovered universal 3-hair relations are used to produce a 3-parameter metric. Finally, a straightforward extension of this metric is given for scalar-tensor theories with a massless scalar field, which also admit a formulation in terms of an Ernst potential.
Mathematics in modern immunology
Castro, Mario; Lythe, Grant; Molina-París, Carmen; Ribeiro, Ruy M.
2016-01-01
Mathematical and statistical methods enable multidisciplinary approaches that catalyse discovery. Together with experimental methods, they identify key hypotheses, define measurable observables and reconcile disparate results. We collect a representative sample of studies in T-cell biology that illustrate the benefits of modelling–experimental collaborations and that have proven valuable or even groundbreaking. We conclude that it is possible to find excellent examples of synergy between mathematical modelling and experiment in immunology, which have brought significant insight that would not be available without these collaborations, but that much remains to be discovered. PMID:27051512
Babylonian Mathematical Astronomy
NASA Astrophysics Data System (ADS)
Ossendrijver, Mathieu
The earliest known form of mathematical astronomy of the ancient world was developed in Babylonia in the 5th century BCE. It was used for predicting a wide range of phenomena of the Moon, the Sun, and the planets. After a brief discussion of the material evidence and historical context of Babylonian mathematical astronomy, its main concepts and methods are illustrated on the basis of a tablet with computed data for Jupiter. Finally, the past, present, and future directions of research are briefly addressed.
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.
Early modern mathematical instruments.
Bennett, Jim
2011-12-01
In considering the appropriate use of the terms "science" and "scientific instrument," tracing the history of "mathematical instruments" in the early modern period is offered as an illuminating alternative to the historian's natural instinct to follow the guiding lights of originality and innovation, even if the trail transgresses contemporary boundaries. The mathematical instrument was a well-defined category, shared across the academic, artisanal, and commercial aspects of instrumentation, and its narrative from the sixteenth to the eighteenth century was largely independent from other classes of device, in a period when a "scientific" instrument was unheard of.
Mathematics in modern immunology
Castro, Mario; Lythe, Grant; Molina-París, Carmen; ...
2016-02-19
Mathematical and statistical methods enable multidisciplinary approaches that catalyse discovery. Together with experimental methods, they identify key hypotheses, define measurable observables and reconcile disparate results. Here, we collect a representative sample of studies in T-cell biology that illustrate the benefits of modelling–experimental collaborations and that have proven valuable or even groundbreaking. Furthermore, we conclude that it is possible to find excellent examples of synergy between mathematical modelling and experiment in immunology, which have brought significant insight that would not be available without these collaborations, but that much remains to be discovered.
Computer programs: Operational and mathematical, a compilation
NASA Technical Reports Server (NTRS)
1973-01-01
Several computer programs which are available through the NASA Technology Utilization Program are outlined. Presented are: (1) Computer operational programs which can be applied to resolve procedural problems swiftly and accurately. (2) Mathematical applications for the resolution of problems encountered in numerous industries. Although the functions which these programs perform are not new and similar programs are available in many large computer center libraries, this collection may be of use to centers with limited systems libraries and for instructional purposes for new computer operators.
Theoretical Explanations in Mathematical Physics
NASA Astrophysics Data System (ADS)
Rivadulla, Andrés
Many physicists wonder at the usefulness of mathematics in physics. According Madrid to Einstein mathematics is admirably appropriate to the objects of reality. Wigner asserts that mathematics plays an unreasonable important role in physics. James Jeans affirms that God is a mathematician, and that the first aim of physics is to discover the laws of nature, which are written in mathematical language. Dirac suggests that God may have used very advanced mathematics in constructing the universe. And Barrow adheres himself to Wigner's claim about the unreasonable effectiveness of mathematics for the workings of the physical world.
Accurate pointing of tungsten welding electrodes
NASA Technical Reports Server (NTRS)
Ziegelmeier, P.
1971-01-01
Thoriated-tungsten is pointed accurately and quickly by using sodium nitrite. Point produced is smooth and no effort is necessary to hold the tungsten rod concentric. The chemically produced point can be used several times longer than ground points. This method reduces time and cost of preparing tungsten electrodes.
Can Mathematics Education and History of Mathematics Coexist?
NASA Astrophysics Data System (ADS)
Fried, Michael N.
Despite the wide interest in combining mathematics education and the history of mathematics, there are grave and fundamental problems in this effort. The main difficulty is that while one wants to see historical topics in the classroom or an historical approach in teaching, the commitment to teach the modern mathematics and modern mathematical techniques necessary in the pure and applied sciences forces one either to trivialize history or to distort it. In particular, this commitment forces one to adopt a Whiggish approach to the history of mathematics. Two possible resolutions of the difficulty are (1) radical separation - putting the history of mathematics on a separate track from the ordinary course of instruction, and (2) radical accommodation - turning the study of mathematics into the study of mathematical texts.
Supporting Mathematical Thinking
ERIC Educational Resources Information Center
Houssart, Jenny; Roaf, Caroline; Watson, Anne
2005-01-01
This book looks at how practitioners have focused on the fully educational application of intellect to the problem of developing mathematical thinking among one's pupils. Each chapter demonstrates reflective minds at work, relying on close observation, willingness to understand the student's thinking processes and patient commitment to students…
ERIC Educational Resources Information Center
Zack, Laurie; Fuselier, Jenny; Graham-Squire, Adam; Lamb, Ron; O'Hara, Karen
2015-01-01
Our study compared a flipped class with a standard lecture class in four introductory courses: finite mathematics, precalculus, business calculus, and calculus 1. The flipped sections watched video lectures outside of class and spent time in class actively working on problems. The traditional sections had lectures in class and did homework outside…
ERIC Educational Resources Information Center
Barger, Rita H.; Jarrah, Adeeb M.
2012-01-01
March 14 is special because it is Pi Day. Mathematics is celebrated on that day because the date, 3-14, replicates the first three digits of pi. Pi-related songs, websites, trivia facts, and more are at the fingertips of interested teachers and students. Less celebrated, but still fairly well known, is National Metric Day, which falls on October…
ERIC Educational Resources Information Center
Thornton, Steve
2000-01-01
Describes the most enduring link between Napoleon and mathematics as the geometric result known as Napoleon's Theorem, which states that if equilateral triangles are drawn on the three sides of any triangle, the line segments joining the centers of these equilateral triangles will themselves form an equilateral triangle. (ASK)
Designing a Mathematics Curriculum
ERIC Educational Resources Information Center
Yee, Lee Peng
2010-01-01
A decade of PMRI saw the changes in the classroom in some of the primary schools in Indonesia. Based on observation, we can say that though the mathematics syllabus in Indonesia did not change, its curriculum has changed under the movement of PMRI. In this article, we put in writing some of the experience gained through the involvement in…
Storytelling + Origami = Storigami Mathematics
ERIC Educational Resources Information Center
Mastin, Marla
2007-01-01
This article presents a way to engage students in mathematics learning by using the innovative instructional method of storigami. The author shares reactions from teachers who have used her storigami techniques in their classes and provides an example of storigami using the Norwegian fable "The Dog and the Mountain." (Contains 6 figures.)
ERIC Educational Resources Information Center
Popelka, Susan R.
2011-01-01
Tiny prisms in reflective road signs and safety vests have interesting geometrical properties that can be discussed at any level of high school mathematics. At the beginning of the school year, the author teaches a unit on these reflective materials in her precalculus class so that students can review and strengthen their geometry and trigonometry…
Personal Achievement Mathematics: Automotive.
ERIC Educational Resources Information Center
Baenziger, Betty
Utilizing word problems relevant to automotive mechanics, this workbook presents a concept-oriented approach to competency development in 13 areas of basic mathematics: (1) the expression of numbers as figures and words; (2) the addition, subtraction, multiplication, and division of whole numbers, fractions, and decimals; (3) scientific notation;…
Using and Applying Mathematics
ERIC Educational Resources Information Center
Knight, Rupert
2011-01-01
The Nobel prize winning physicist Richard Feynman (2007) famously enthused about "the pleasure of finding things out". In day-to-day classroom life, however, it is easy to lose and undervalue this pleasure in the process, as opposed to products, of mathematics. Finding things out involves a journey and is often where the learning takes place.…
Designing for Mathematical Abstraction
ERIC Educational Resources Information Center
Pratt, Dave; Noss, Richard
2010-01-01
Our focus is on the design of systems (pedagogical, technical, social) that encourage mathematical abstraction, a process we refer to as "designing for abstraction." In this paper, we draw on detailed design experiments from our research on children's understanding about chance and distribution to re-present this work as a case study in designing…
ERIC Educational Resources Information Center
Bureau of Naval Personnel, Washington, DC.
The second of three volumes of a mathematics training course for Navy personnel, this document contains material primarily found at the college level. Beginning with logarithms and trigonometry, the text moves into vectors and static equilibrium (physics). Coordinate geometry, conic sections, and the tangents, normals, and slopes of curves follow.…
Urban Mathematics Teacher Retention
ERIC Educational Resources Information Center
Hamdan, Kamal
2010-01-01
Mathematics teachers are both more difficult to attract and more difficult to retain than social sciences teachers. This fact is not unique to the United States; it is reported as being a problem in Europe as well (Howson, 2002). In the United States, however, the problem is particularly preoccupying. Because of the chronic teacher shortages and…
Mature Students Studying Mathematics.
ERIC Educational Resources Information Center
Hirst, Keith
1999-01-01
Discusses mature students in the single subject area of mathematics in a single institution and makes comparisons with traditional universities. Reviews some features of the age distribution, entry qualifications, degree-class distribution, non-completion rates and gender distribution. (Author/ASK)
Mathematics and Mobile Learning
ERIC Educational Resources Information Center
White, Tobin; Martin, Lee
2014-01-01
This paper argues for an approach to mobile learning that leverages students' informal digital practices as resources for designing mathematics classrooms activities. We briefly describe two exploratory designs along these lines, one featuring the use of photos taken by students outside class and the other centered on their recording and…
Teaching Vocational Mathematics.
ERIC Educational Resources Information Center
Thiering, Jeannette; And Others
This Australian document is a guide to teaching mathematics as it relates to specific work situations. After a brief introduction, chapter 1 looks at problem solving, advises teachers to lower the reading level and thus raise the understandability of written math problems, and describes a four-step problem-solving process. Chapter 2 outlines a…
Graders' Mathematics Achievement
ERIC Educational Resources Information Center
Bond, John B.; Ellis, Arthur K.
2013-01-01
The purpose of this experimental study was to investigate the effects of metacognitive reflective assessment instruction on student achievement in mathematics. The study compared the performance of 141 students who practiced reflective assessment strategies with students who did not. A posttest-only control group design was employed, and results…
ERIC Educational Resources Information Center
Bogdany, Melvin
The curriculum guide offers a course of training in the fundamentals of mathematics as applied to baking. Problems specifically related to the baking trade are included to maintain a practical orientation. The course is designed to help the student develop proficiency in the basic computation of whole numbers, fractions, decimals, percentage,…
ERIC Educational Resources Information Center
Taschow, Horst G.
Difficulties inherent in the reading of mathematics at secondary and college levels are discussed. Special emphasis is placed on the reading of arithmetic numerals, literal numbers, operational symbols, and expressions of relationships, as well as the reading of technical vocabularies and specialized meanings of general words. While each…
Problematising Mathematics Education
ERIC Educational Resources Information Center
Begg, Andy
2015-01-01
We assume many things when considering our practice, but our assumptions limit what we do. In this theoretical/philosophical paper I consider some assumptions that relate to our work. My purpose is to stimulate a debate, a search for alternatives, and to help us improve mathematics education by influencing our future curriculum documents and…
Defence Mechanisms against Mathematics.
ERIC Educational Resources Information Center
Nimier, Jaques
1993-01-01
Students (n=1420) from Belgium and Quebec and students (n=614) of the Marne department were questioned to study the different defense mechanisms they employed against mathematics. Six main ways of grouping the responses were identified: (1) phobic avoidance; (2) repression; (3) projection; (4) reparation; (5) introjection; and (6) reversal into…
ERIC Educational Resources Information Center
Leutzinger, Larry, Ed.
This book contains articles that help to further the process of reform in the middle grades, recognizing that the knowledge acquired during these years greatly affects how well the secondary school curriculum will attain its goals. Critical issues facing middle grade classes in particular and all mathematics classrooms in general are discussed.…
A Classroom Mathematics Utility.
ERIC Educational Resources Information Center
Williams, Michael
1984-01-01
Reviews CATUSPLOT, a mathematics utility aimed at high school algebra through college-level calculus. Basic program capabilities include plotting, tabulating, integrating, and locating of intersections of functions composed of combinations of polynomial, trigonometric, and exponential functions. Rated excellent on all areas examined…
Research in Mathematics Education
ERIC Educational Resources Information Center
Schoenfeld, Alan H.
2016-01-01
As one of the three Rs, "'rithmetic" has always been central to education and education research. By virtue of that centrality, research in mathematics education has often reflected and at times led trends in education research. This chapter provides some deep background on epistemological and other issues that shape current research,…
Verbalizing Mathematics Using APL.
ERIC Educational Resources Information Center
Matthews, George E.
The nature of "A Programing Language" (APL) is viewed as unambiguous, consistent, and powerful. It is based on the notion of functions as imperative verbs, and is used by a small but growing number of mathematicians and computer programers. Three areas of mathematical activity are addressed: calculation of arithmetic expressions,…
The Constructivist Mathematics Classroom
ERIC Educational Resources Information Center
Jones, Karrie; Jones, Jennifer L.; Vermette, Paul J.
2010-01-01
By examining how people learn, the educational theories of Dewey, Piaget, Vygotsky and Bruner can be synthesized to give this set of core Constructivist principles. Principles of effective mathematics teaching: (1) allows learning that is "active" and "reflective". Students are required to transfer key concepts to new situations; (2) allows…
ERIC Educational Resources Information Center
Schwartz, Richard
1992-01-01
Suggests that teachers use mathematics problems related to the "1992 World Population Data Sheet" to teach students about such population-related issues as hunger, resource scarcity, poverty, and pollution. Offers sample problems involving percents, ratios, basic calculations, sequences, variability, graphs, averages, and correlation. Includes a…
ERIC Educational Resources Information Center
Whitin, Phyllis; Whitin, David J.
2011-01-01
The habit of looking for patterns, the skills to find them, and the expectation that patterns have explanations is an essential mathematical habit of mind for young children (Goldenberg, Shteingold, & Feurzeig 2003, 23). Work with patterns leads to the ability to form generalizations, the bedrock of algebraic thinking, and teachers must nurture…
Exploratory Problems in Mathematics.
ERIC Educational Resources Information Center
Stevenson, Frederick W.
This book attempts to introduce students to the creative aspects of mathematics through exploratory problems. The introduction presents the criteria for the selection of the problems in the book. Criteria indicate that problems should: be immediately attractive, require data to be generated or gathered, appeal to students from junior high school…
ERIC Educational Resources Information Center
Cain, David
2007-01-01
In this article, the author looks at ways of creating conditions to bring about learning. If one is to "arrange conditions to bring about learning," one needs written guidance and support systems. Two books that discusses how to arrange these conditions are: "Thinking Mathematically" by John Mason with Leone Burton and Kaye Stacey and "Starting…
Mathematical Intrusions in Literatures
ERIC Educational Resources Information Center
Modica, Erasmo
2011-01-01
This article describes an activity that can be carried out in one of the final classes of Italian secondary schools. The aim of the activity is to stimulate pupil curiosity, demonstrating that Mathematics is not a barren subject and allowing the students, according to an interdisciplinary point of view, to investigate some literary works and the…
Celebrate Mathematical Curiosity
ERIC Educational Resources Information Center
Redford, Christine
2011-01-01
Children's mathematical questions are often based in real-world experiences, as they instinctively make connections to the world around them. In teaching math methods courses, this author recently started to emphasize the importance of fostering curiosity in, and activating the thinking of, the students. In this article, she describes how to tap…
ERIC Educational Resources Information Center
Noblitt, Bethany A.; Buckley, Brooke E.
2011-01-01
Teams, pit stops, clues, time limits, fast forwards, challenges, and prizes are all components of the CBS hit show "The Amazing Race." They were also elements of the Amazing Mathematical Race sponsored by the Math and Stats Club at Northern Kentucky University in April 2009. Held in recognition of Math Awareness Month, which is advocated…
New Technologies in Mathematics.
ERIC Educational Resources Information Center
Sarmiento, Jorge
An understanding of past technological advancements can help educators understand the influence of new technologies in education. Inventions such as the abacus, logarithms, the slide rule, the calculating machine, computers, and electronic calculators have all found their place in mathematics education. While new technologies can be very useful,…
The Changing Curriculum: Mathematics.
ERIC Educational Resources Information Center
Davis, Robert B.
In this 1967 booklet, influences of technology, the non-achiever and the culturally disadvantaged, and the revolt against formalism are discussed in relation to the modern mathematics curriculum. Some projects and school programs described include PLATO, the Nuffield Project, the Nova School Program, Advanced Placement Program, and teacher…
ERIC Educational Resources Information Center
Ediger, Marlow
2008-01-01
There was much enthusiasm when the phrase "Modern School Mathematics" was coined shortly after the 1958 National Defense Education Act was passed. Many federally funded study groups came into being. Presently, criticisms in secondary teaching are just as great as it was in 1958. The innovations recommended by federally funded study groups has had…
NEEDLE TRADES, MATHEMATICS - I.
ERIC Educational Resources Information Center
COLICCHIO, ANTOINETTE J.
THE NEEDLE TRADES INDUSTRY CONSISTS OF THREE TYPES OF ESTABLISHMENTS -- THE REGULAR MANUFACTURERS, THE APPAREL JOBBERS, AND THE CONTRACTORS. THE FUNCTIONS INCLUDED COVER A WIDE SCOPE FROM BUYING OF RAW MATERIAL TO SELLING OF THE FINISHED APPAREL. THE PURPOSE OF THIS STUDY GUIDE IS TO FURNISH BASIC KNOWLEDGE IN MATHEMATICS AND DEVELOP SKILL IN…
COMMERCIAL FOODS, MATHEMATICS - I.
ERIC Educational Resources Information Center
DORNFIELD, BLANCHE E.
THE UNDERSTANDING AND MASTERY OF FUNDAMENTAL MATHEMATICS IS A NECESSARY PART OF COMMERCIAL FOODS WORK. THIS STUDENT HANDBOOK WAS DESIGNED TO ACCOMPANY A COMMERCIAL FOODS COURSE AT THE HIGH SCHOOL LEVEL FOR STUDENTS WITH APPROPRIATE APTITUDES AND COMMERCIAL FOOD SERVICE GOALS. THE MATERIAL, TESTED IN VARIOUS INTERESTED CLASSROOMS, WAS PREPARED BY…
Activities: Some Colorful Mathematics.
ERIC Educational Resources Information Center
DeTemple, Duane W.; Walker, Dean A.
1996-01-01
Describes three activities in discrete mathematics that involve coloring geometric objects: counting colored regions of overlapping simple closed curves, counting colored triangulations of polygons, and determining the number of colors required to paint the plane so that no two points one inch apart are the same color. (MKR)
Mathematical model for corundum single crystal growth by Verneuil method
NASA Astrophysics Data System (ADS)
Grzymkowski, Radosław; Mochnacki, Bohdan; Suchy, Józef
1983-05-01
A mathematical model which is an attempt to describe the complex process of monocrystallization by the Verneuil method is presented. The problem has been solved through the method of finite differences and at the same time making use of a certain modification of the mathematical description of Stefan's problem called the the alternating phase truncation method [9]. The elaborated algorithm and the examples of solutions given at the end of the present study point at the usefulness of the presented method of numerical simulation for modern designing and controlling the processes of crystal production.
Chern-Simons terms and cocycles in physics and mathematics
Jackiw, R.
1984-12-01
Contemporary topological research in Yang-Mills theory is reviewed, emphasizing the Chern-Simons terms and their relatives. Three applications of the Chern-Simons terms in physical theory are described: to help understanding gauge theories in even dimensional space-time; gauge field dynamics in odd dimensional space-time; and mathematically coherent description of even-dimensional gauge theories with chiral fermions that are apparently inconsistent due to chiral anomalies. Discussion of these applications is preceded by explanation of the mathematical preliminaries and examples in simple quantum mechanical settings. 24 refs. (LEW)
Extended Analyses: Promoting Mathematical Inquiry with Preservice Mathematics Teachers
ERIC Educational Resources Information Center
Bloom, Irene
2007-01-01
This paper describes the implementation of extended analysis tasks (EATs) in a required mathematics course for prospective high school mathematics teachers, and investigates the mathematical discovery promoted through engagement with these tasks. Extended analysis tasks are designed to move students beyond the problem context to the underlying…
Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape
ERIC Educational Resources Information Center
Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.
2014-01-01
This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…
Between the Academic Mathematics and the Mathematics Education Worlds.
ERIC Educational Resources Information Center
Moreira, Candida Queiroz
1997-01-01
Investigated stresses confronted by Portuguese secondary mathematics teachers during the first semester in a master's course, Perspectives on Mathematics Education, noting how they negatively affected teachers' self-confidence and morale and discussing fundamental issues teachers addressed in bridging the academic mathematics and mathematics…
Mathematical Fiction: Its Place in Secondary-School Mathematics Learning
ERIC Educational Resources Information Center
Padula, Janice
2005-01-01
This article contains a small selection of mathematical fiction chosen with the teaching of mathematics in secondary school in mind. However, an attempt is made to classify the works and provide a few ideas about how these items may be used by mathematics teachers, sometimes, but not necessarily, in collaboration with science and humanities…
Adults' Use of Mathematics and Its Influence on Mathematical Competence
ERIC Educational Resources Information Center
Duchhardt, Christoph; Jordan, Anne-Katrin; Ehmke, Timo
2017-01-01
The Programme for the International Assessment of Adult Competencies (PIAAC) has recently drawn additional attention to "mathematical literacy" as an important influential factor for individuals' life chances. High levels of mathematical literacy have thereby been linked to using mathematics in daily and working life frequently. In this…
Teaching Mathematics to Non-Mathematics Majors through Applications
ERIC Educational Resources Information Center
Abramovich, Sergei; Grinshpan, Arcadii Z.
2008-01-01
This article focuses on the important role of applications in teaching mathematics to students with career paths other than mathematics. These include the fields as diverse as education, engineering, business, and life sciences. Particular attention is given to instructional computing as a means for concept development in mathematics education…
Middle School Mathematics Students' Perspectives on the Study of Mathematics
ERIC Educational Resources Information Center
Vaughn, Christy H.
2012-01-01
This qualitative study addressed the perceptions toward the study of mathematics by middle school students who had formerly been in a remedial mathematics program. The purpose of the study was to explore the past experiences of nine students in order to determine what is needed for them to feel successful in mathematics. The conceptual framework…
Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving
ERIC Educational Resources Information Center
Ayllón, María F.; Gómez, Isabel A.; Ballesta-Claver, Julio
2016-01-01
This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas), flexibility (range of ideas),…
Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.
ERIC Educational Resources Information Center
Suppes, Patrick
This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…
History of Modern Applied Mathematics in Mathematics Education
ERIC Educational Resources Information Center
Jankvist, Uffe Thomas
2009-01-01
This article discusses the integration of history of modern applied mathematics in mathematics education as well as the possible teaching and learning benefits of introducing a newer history of mathematics over an old(er) one--something that seems to be done most often when integrating history. Three cases of the history of modern applied…
Racial Differences in Mathematics Test Scores for Advanced Mathematics Students
ERIC Educational Resources Information Center
Minor, Elizabeth Covay
2016-01-01
Research on achievement gaps has found that achievement gaps are larger for students who take advanced mathematics courses compared to students who do not. Focusing on the advanced mathematics student achievement gap, this study found that African American advanced mathematics students have significantly lower test scores and are less likely to be…
Toward Precision Healthcare: Context and Mathematical Challenges
Colijn, Caroline; Jones, Nick; Johnston, Iain G.; Yaliraki, Sophia; Barahona, Mauricio
2017-01-01
Precision medicine refers to the idea of delivering the right treatment to the right patient at the right time, usually with a focus on a data-centered approach to this task. In this perspective piece, we use the term “precision healthcare” to describe the development of precision approaches that bridge from the individual to the population, taking advantage of individual-level data, but also taking the social context into account. These problems give rise to a broad spectrum of technical, scientific, policy, ethical and social challenges, and new mathematical techniques will be required to meet them. To ensure that the science underpinning “precision” is robust, interpretable and well-suited to meet the policy, ethical and social questions that such approaches raise, the mathematical methods for data analysis should be transparent, robust, and able to adapt to errors and uncertainties. In particular, precision methodologies should capture the complexity of data, yet produce tractable descriptions at the relevant resolution while preserving intelligibility and traceability, so that they can be used by practitioners to aid decision-making. Through several case studies in this domain of precision healthcare, we argue that this vision requires the development of new mathematical frameworks, both in modeling and in data analysis and interpretation. PMID:28377724
NASA Technical Reports Server (NTRS)
Papageorgiou, Demetrios T.
1996-01-01
In this article we review recent results on the breakup of cylindrical jets of a Newtonian fluid. Capillary forces provide the main driving mechanism and our interest is in the description of the flow as the jet pinches to form drops. The approach is to describe such topological singularities by constructing local (in time and space) similarity solutions from the governing equations. This is described for breakup according to the Euler, Stokes or Navier-Stokes equations. It is found that slender jet theories can be applied when viscosity is present, but for inviscid jets the local shape of the jet at breakup is most likely of a non-slender geometry. Systems of one-dimensional models of the governing equations are solved numerically in order to illustrate these differences.
NASA Technical Reports Server (NTRS)
Simmons, Reid; Apfelbaum, David
2005-01-01
Task Description Language (TDL) is an extension of the C++ programming language that enables programmers to quickly and easily write complex, concurrent computer programs for controlling real-time autonomous systems, including robots and spacecraft. TDL is based on earlier work (circa 1984 through 1989) on the Task Control Architecture (TCA). TDL provides syntactic support for hierarchical task-level control functions, including task decomposition, synchronization, execution monitoring, and exception handling. A Java-language-based compiler transforms TDL programs into pure C++ code that includes calls to a platform-independent task-control-management (TCM) library. TDL has been used to control and coordinate multiple heterogeneous robots in projects sponsored by NASA and the Defense Advanced Research Projects Agency (DARPA). It has also been used in Brazil to control an autonomous airship and in Canada to control a robotic manipulator.
NASA Astrophysics Data System (ADS)
Dunajewski, Adam; Dusza, Jacek J.; Rosado Muñoz, Alfredo
2014-11-01
The article presents a proposal for the description of human gait as a periodic and symmetric process. Firstly, the data for researches was obtained in the Laboratory of Group SATI in the School of Engineering of University of Valencia. Then, the periodical model - Mean Double Step (MDS) was made. Finally, on the basis of MDS, the symmetrical models - Left Mean Double Step and Right Mean Double Step (LMDS and RMDS) could be created. The method of various functional extensions was used. Symmetrical gait models can be used to calculate the coefficients of asymmetry at any time or phase of the gait. In this way it is possible to create asymmetry, function which better describes human gait dysfunction. The paper also describes an algorithm for calculating symmetric models, and shows exemplary results based on the experimental data.
YUCCA MOUNTAIN SITE DESCRIPTION
A.M. Simmons
2004-04-16
The ''Yucca Mountain Site Description'' summarizes, in a single document, the current state of knowledge and understanding of the natural system at Yucca Mountain. It describes the geology; geochemistry; past, present, and projected future climate; regional hydrologic system; and flow and transport within the unsaturated and saturated zones at the site. In addition, it discusses factors affecting radionuclide transport, the effect of thermal loading on the natural system, and tectonic hazards. The ''Yucca Mountain Site Description'' is broad in nature. It summarizes investigations carried out as part of the Yucca Mountain Project since 1988, but it also includes work done at the site in earlier years, as well as studies performed by others. The document has been prepared under the Office of Civilian Radioactive Waste Management quality assurance program for the Yucca Mountain Project. Yucca Mountain is located in Nye County in southern Nevada. The site lies in the north-central part of the Basin and Range physiographic province, within the northernmost subprovince commonly referred to as the Great Basin. The basin and range physiography reflects the extensional tectonic regime that has affected the region during the middle and late Cenozoic Era. Yucca Mountain was initially selected for characterization, in part, because of its thick unsaturated zone, its arid to semiarid climate, and the existence of a rock type that would support excavation of stable openings. In 1987, the United States Congress directed that Yucca Mountain be the only site characterized to evaluate its suitability for development of a geologic repository for high-level radioactive waste and spent nuclear fuel.
Older Adults’ Pain Descriptions
McDonald, Deborah Dillon
2008-01-01
The purpose of this study was to describe the types of pain information described by older adults with chronic osteoarthritis pain. Pain descriptions were obtained from older adults’ who participated in a posttest only double blind study testing how the phrasing of healthcare practitioners’ pain questions affected the amount of communicated pain information. The 207 community dwelling older adults were randomized to respond to either the open-ended or closed-ended pain question. They viewed and orally responded to a computer displayed videotape of a practitioner asking them the respective pain question. All then viewed and responded to the general follow up question, ““What else can you tell me?” and lastly, “What else can you tell me about your pain, aches, soreness or discomfort?” Audio-taped responses were transcribed and content analyzed by trained, independent raters using 16 a priori criteria from the American Pain Society (2002) Guidelines for the Management of Pain in Osteoarthritis, Rheumatoid Arthritis, and Juvenile Chronic Arthritis. Older adults described important but limited types of information primarily about pain location, timing, and intensity. Pain treatment information was elicited after repeated questioning. Therefore, practitioners need to follow up older adults’ initial pain descriptions with pain questions that promote a more complete pain management discussion. Routine use of a multidimensional pain assessment instrument that measures information such as functional interference, current pain treatments, treatment effects, and side effects would be one way of insuring a more complete pain management discussion with older adults. PMID:19706351
ERIC Educational Resources Information Center
Badami, Rokhsareh; VaezMousavi, Mohammad; Wulf, Gabriele; Namazizadeh, Mahdi
2012-01-01
One purpose of the present study was to examine whether self-confidence or anxiety would be differentially affected by feedback from more accurate rather than less accurate trials. The second purpose was to determine whether arousal variations (activation) would predict performance. On Day 1, participants performed a golf putting task under one of…
Mathematics Education in Hungary Today.
ERIC Educational Resources Information Center
Varga, Tamas
1988-01-01
Changes in mathematics education from the 1950s to the 1980s are briefly described by the author, who was a leading mathematics educator in Hungary. Illustrations focus on personal experience and small group interaction. (MNS)
Common Threads - Mathematics and Textiles.
ERIC Educational Resources Information Center
Harris, Mary
1988-01-01
Describes an exhibition of "mathematically rich" cloths. The themes chosen to be included were symmetry, number, creativity, information handling, and problem solving. The project was an outgrowth of work to take ordinary daily situations and analyze them mathematically. (PK)
Doing Mathematics with Your Child.
ERIC Educational Resources Information Center
Hartog, Martin D.; Diamantis, Maria; Brosnan, Patricia
1998-01-01
Presents resources to help parents develop their children's abilities to do mathematics while encouraging more positive attitudes toward mathematics and having fun in the process. Provides examples of activities that can be done at home with parents and children. (ASK)
Integrating Mathematics and Composition Instruction.
ERIC Educational Resources Information Center
Kirtland, Joseph; Hoh, Pau-San
2002-01-01
Describes the development of an integrated approach for teaching mathematics and writing to freshmen. The goals are to strengthen mathematical skills, develop writing competencies, and foster interdisciplinary awareness. (Author/MM)
NASA Technical Reports Server (NTRS)
Nobbs, Steven G.
1995-01-01
An overview of the performance seeking control (PSC) algorithm and details of the important components of the algorithm are given. The onboard propulsion system models, the linear programming optimization, and engine control interface are described. The PSC algorithm receives input from various computers on the aircraft including the digital flight computer, digital engine control, and electronic inlet control. The PSC algorithm contains compact models of the propulsion system including the inlet, engine, and nozzle. The models compute propulsion system parameters, such as inlet drag and fan stall margin, which are not directly measurable in flight. The compact models also compute sensitivities of the propulsion system parameters to change in control variables. The engine model consists of a linear steady state variable model (SSVM) and a nonlinear model. The SSVM is updated with efficiency factors calculated in the engine model update logic, or Kalman filter. The efficiency factors are used to adjust the SSVM to match the actual engine. The propulsion system models are mathematically integrated to form an overall propulsion system model. The propulsion system model is then optimized using a linear programming optimization scheme. The goal of the optimization is determined from the selected PSC mode of operation. The resulting trims are used to compute a new operating point about which the optimization process is repeated. This process is continued until an overall (global) optimum is reached before applying the trims to the controllers.
Accurate Guitar Tuning by Cochlear Implant Musicians
Lu, Thomas; Huang, Juan; Zeng, Fan-Gang
2014-01-01
Modern cochlear implant (CI) users understand speech but find difficulty in music appreciation due to poor pitch perception. Still, some deaf musicians continue to perform with their CI. Here we show unexpected results that CI musicians can reliably tune a guitar by CI alone and, under controlled conditions, match simultaneously presented tones to <0.5 Hz. One subject had normal contralateral hearing and produced more accurate tuning with CI than his normal ear. To understand these counterintuitive findings, we presented tones sequentially and found that tuning error was larger at ∼30 Hz for both subjects. A third subject, a non-musician CI user with normal contralateral hearing, showed similar trends in performance between CI and normal hearing ears but with less precision. This difference, along with electric analysis, showed that accurate tuning was achieved by listening to beats rather than discriminating pitch, effectively turning a spectral task into a temporal discrimination task. PMID:24651081
Accurate colorimetric feedback for RGB LED clusters
NASA Astrophysics Data System (ADS)
Man, Kwong; Ashdown, Ian
2006-08-01
We present an empirical model of LED emission spectra that is applicable to both InGaN and AlInGaP high-flux LEDs, and which accurately predicts their relative spectral power distributions over a wide range of LED junction temperatures. We further demonstrate with laboratory measurements that changes in LED spectral power distribution with temperature can be accurately predicted with first- or second-order equations. This provides the basis for a real-time colorimetric feedback system for RGB LED clusters that can maintain the chromaticity of white light at constant intensity to within +/-0.003 Δuv over a range of 45 degrees Celsius, and to within 0.01 Δuv when dimmed over an intensity range of 10:1.
Accurate guitar tuning by cochlear implant musicians.
Lu, Thomas; Huang, Juan; Zeng, Fan-Gang
2014-01-01
Modern cochlear implant (CI) users understand speech but find difficulty in music appreciation due to poor pitch perception. Still, some deaf musicians continue to perform with their CI. Here we show unexpected results that CI musicians can reliably tune a guitar by CI alone and, under controlled conditions, match simultaneously presented tones to <0.5 Hz. One subject had normal contralateral hearing and produced more accurate tuning with CI than his normal ear. To understand these counterintuitive findings, we presented tones sequentially and found that tuning error was larger at ∼ 30 Hz for both subjects. A third subject, a non-musician CI user with normal contralateral hearing, showed similar trends in performance between CI and normal hearing ears but with less precision. This difference, along with electric analysis, showed that accurate tuning was achieved by listening to beats rather than discriminating pitch, effectively turning a spectral task into a temporal discrimination task.
An Accurate, Simplified Model Intrabeam Scattering
Bane, Karl LF
2002-05-23
Beginning with the general Bjorken-Mtingwa solution for intrabeam scattering (IBS) we derive an accurate, greatly simplified model of IBS, valid for high energy beams in normal storage ring lattices. In addition, we show that, under the same conditions, a modified version of Piwinski's IBS formulation (where {eta}{sub x,y}{sup 2}/{beta}{sub x,y} has been replaced by {Eta}{sub x,y}) asymptotically approaches the result of Bjorken-Mtingwa.
An accurate registration technique for distorted images
NASA Technical Reports Server (NTRS)
Delapena, Michele; Shaw, Richard A.; Linde, Peter; Dravins, Dainis
1990-01-01
Accurate registration of International Ultraviolet Explorer (IUE) images is crucial because the variability of the geometrical distortions that are introduced by the SEC-Vidicon cameras ensures that raw science images are never perfectly aligned with the Intensity Transfer Functions (ITFs) (i.e., graded floodlamp exposures that are used to linearize and normalize the camera response). A technique for precisely registering IUE images which uses a cross correlation of the fixed pattern that exists in all raw IUE images is described.
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…
MAPP: A Mathematics Placement Program.
ERIC Educational Resources Information Center
Doblin, Stephen A.
1978-01-01
MAPP (A Mathematics Placement Program) uses two COBOL programs to place entering freshmen in mathematics courses which are commensurate with their backgrounds and abilities. Having been used for three years, the program is considered to be a viable alternative to the traditional mathematics placement process. (Author/JKS)
The Psychological Foundations of Mathematics.
ERIC Educational Resources Information Center
Suppes, Patrick
1967-01-01
This paper outlines problems which are central to the psychological foundations of mathematics. Discussed are the relations that exist between psychological and classical foundations of mathematics. It is shown how the inadequacies of current learning theories which account for complex mathematics learning may be made explicit for appropriate…
Ethical Dimensions of Mathematics Education
ERIC Educational Resources Information Center
Boylan, Mark
2016-01-01
The relationships between mathematics, mathematics education and issues such as social justice and equity have been addressed by the sociopolitical tradition in mathematics education. Others have introduced explicit discussion of ethics, advocating for its centrality. However, this is an area that is still under developed. There is a need for an…
Investigating Teachers' Images of Mathematics
ERIC Educational Resources Information Center
Sterenberg, Gladys
2008-01-01
Research suggests that understanding new images of mathematics is very challenging and can contribute to teacher resistance. An explicit exploration of personal views of mathematics may be necessary for pedagogical change. One possible way for exploring these images is through mathematical metaphors. As metaphors focus on similarities, they can be…
Mathematical Modelling in European Education
ERIC Educational Resources Information Center
Ferri, Rita Borromeo
2013-01-01
Teaching and learning of mathematical modelling has become a key competence within school curricula and educational standards in many countries of the world. The term mathematical modelling, its meaning, and how it can be implemented in mathematics lessons have been intensively discussed during several Conferences of the European Society for…
The Emergence of Mathematical Structures
ERIC Educational Resources Information Center
Hegedus, Stephen John; Moreno-Armella, Luis
2011-01-01
We present epistemological ruptures that have occurred in mathematical history and in the transformation of using technology in mathematics education in the twenty-first century. We describe how such changes establish a new form of digital semiotics that challenges learning paradigms and mathematical inquiry for learners today. We focus on drawing…
Assessment and Learning of Mathematics.
ERIC Educational Resources Information Center
Leder, Gilah C., Ed.
This book addresses the link between student learning of mathematics, the teaching method adopted in the mathematics classroom, and the assessment procedures used to determine and measure student knowledge. Fifteen chapters address issues that include a review of different models of mathematics learning and assessment practices, three contrasting…
A Primer for Mathematical Modeling
ERIC Educational Resources Information Center
Sole, Marla
2013-01-01
With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…
Collaboration in the Mathematical Community
ERIC Educational Resources Information Center
Bagnato, Robert A.
1974-01-01
Proliferation of mathematical knowledge prohibits individual reduplication of all results and causes mathematicians to accept much on faith. To convey the spirit of the mathematical community, and provide maximum content coverage, instruction should allow students to accept some theorems without proof. Students would then find mathematics less…
Identity as a Mathematical Thinker
ERIC Educational Resources Information Center
Owens, Kay
2008-01-01
I argue in this article that identity as a mathematical thinker develops through self-directed learning within a supportive community of practice. The dynamic nature of identity as a mathematical thinker is illustrated by considering the experiences of primary pre-service teachers who undertook a mathematics and technology subject in their…
Mathematical History, Philosophy and Education
ERIC Educational Resources Information Center
Otte, Michael
2007-01-01
History of mathematics occupies itself describing processes of growth and development, whereas philosophy of mathematics is concerned with questions of justification. Both play an essential role within the educational context. But there is a problem because genuine historical studies necessitate ever greater particularity whereas mathematics and…
Why Are Mathematical Investigations Important?
ERIC Educational Resources Information Center
Quinnell, Lorna
2010-01-01
"Research studies show that when students discover mathematical ideas and invent mathematical procedures, they have a stronger conceptual understanding of connections between mathematical ideas." Flewelling and Higginson state that inquiry, investigations, and problem solving "give students the opportunity to use their imagination…
Unlocking Mathematics Teaching. Second Edition
ERIC Educational Resources Information Center
Koshy, Valsa, Ed.; Murray, Jean, Ed.
2011-01-01
Now in a fully updated second edition, "Unlocking Mathematics Teaching" is a comprehensive guide to teaching mathematics in the primary school. Combining theory and practice, selected experts outline the current context of mathematics education. They suggest strategies, activities and examples to help develop readers understanding and confidence…
Mathematics in the Early Years.
ERIC Educational Resources Information Center
Copley, Juanita V., Ed.
Noting that young children are capable of surprisingly complex forms of mathematical thinking and learning, this book presents a collection of articles depicting children discovering mathematical ideas, teachers fostering students' informal mathematical knowledge, adults asking questions and listening to answers, and researchers examining…
Mathematics Unit Plans. PACE '94.
ERIC Educational Resources Information Center
Wiles, Clyde A., Ed.; Schoon, Kenneth J., Ed.
This booklet contains mathematics unit plans for Algebra 1, Geometry, Math for Technology, Mathematical Problem Solving, and Pre-Algebra developed by PACE (Promoting Academic Excellence In Mathematics, Science & Technology for Workers of the 21st Century). Each unit plan contains suggested timing, objectives, skills to be acquired, workplace…
Promoting and Assessing Mathematical Generalising
ERIC Educational Resources Information Center
Hill, Tiffany; Lannin, John; van Garderen, Delinda
2015-01-01
Helping students generalise mathematical ideas is an essential component of teaching and learning of mathematics (Lannin, Ellis, Elliott & Zbiek, 2011). However, it can be challenging for primary teachers to assess and promote generalisation. Because generalisation is an essential part of mathematics instruction, the authors highlight the…
Flawed Mathematical Conceptualizations: Marlon's Dilemma
ERIC Educational Resources Information Center
Garrett, Lauretta
2013-01-01
Adult developmental mathematics students often work under great pressure to complete the mathematics sequences designed to help them achieve success (Bryk & Treisman, 2010). Results of a teaching experiment demonstrate how the ability to reason can be impeded by flaws in students' mental representations of mathematics. The earnestness of the…
Fort Benton Mathematics Curriculum Outline.
ERIC Educational Resources Information Center
Fort Benton Public Schools, MT.
The mathematics curriculum of the Fort Benton school system was designed with funds under Title III of the Elementary and Secondary Education Act to present all students with a basic knowledge of mathematics and to provide the gifted child with an opportunity to develop to the best of his ability the mathematical skills and theory demanded by a…
Improve the Teaching of Mathematics
ERIC Educational Resources Information Center
Maslova, G.; And Others
1977-01-01
Describes the mathematics curriculum instituted in Soviet secondary schools in 1975-76. Emphases of the new curriculum are the role of mathematics in sicence, technology, production, and everyday life, and the potential of the mathematics course for instilling a materialist world view. (Author/DB)
Mathematical Modeling: Convoying Merchant Ships
ERIC Educational Resources Information Center
Mathews, Susann M.
2004-01-01
This article describes a mathematical model that connects mathematics with social studies. Students use mathematics to model independent versus convoyed ship deployments and sinkings to determine if the British should have convoyed their merchant ships during World War I. During the war, the British admiralty opposed sending merchant ships grouped…