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Sample records for principle mathematical solutions

  1. The inactivation principle: mathematical solutions minimizing the absolute work and biological implications for the planning of arm movements.

    PubMed

    Berret, Bastien; Darlot, Christian; Jean, Frédéric; Pozzo, Thierry; Papaxanthis, Charalambos; Gauthier, Jean Paul

    2008-10-01

    An important question in the literature focusing on motor control is to determine which laws drive biological limb movements. This question has prompted numerous investigations analyzing arm movements in both humans and monkeys. Many theories assume that among all possible movements the one actually performed satisfies an optimality criterion. In the framework of optimal control theory, a first approach is to choose a cost function and test whether the proposed model fits with experimental data. A second approach (generally considered as the more difficult) is to infer the cost function from behavioral data. The cost proposed here includes a term called the absolute work of forces, reflecting the mechanical energy expenditure. Contrary to most investigations studying optimality principles of arm movements, this model has the particularity of using a cost function that is not smooth. First, a mathematical theory related to both direct and inverse optimal control approaches is presented. The first theoretical result is the Inactivation Principle, according to which minimizing a term similar to the absolute work implies simultaneous inactivation of agonistic and antagonistic muscles acting on a single joint, near the time of peak velocity. The second theoretical result is that, conversely, the presence of non-smoothness in the cost function is a necessary condition for the existence of such inactivation. Second, during an experimental study, participants were asked to perform fast vertical arm movements with one, two, and three degrees of freedom. Observed trajectories, velocity profiles, and final postures were accurately simulated by the model. In accordance, electromyographic signals showed brief simultaneous inactivation of opposing muscles during movements. Thus, assuming that human movements are optimal with respect to a certain integral cost, the minimization of an absolute-work-like cost is supported by experimental observations. Such types of optimality

  2. The inactivation principle: mathematical solutions minimizing the absolute work and biological implications for the planning of arm movements.

    PubMed

    Berret, Bastien; Darlot, Christian; Jean, Frédéric; Pozzo, Thierry; Papaxanthis, Charalambos; Gauthier, Jean Paul

    2008-10-01

    An important question in the literature focusing on motor control is to determine which laws drive biological limb movements. This question has prompted numerous investigations analyzing arm movements in both humans and monkeys. Many theories assume that among all possible movements the one actually performed satisfies an optimality criterion. In the framework of optimal control theory, a first approach is to choose a cost function and test whether the proposed model fits with experimental data. A second approach (generally considered as the more difficult) is to infer the cost function from behavioral data. The cost proposed here includes a term called the absolute work of forces, reflecting the mechanical energy expenditure. Contrary to most investigations studying optimality principles of arm movements, this model has the particularity of using a cost function that is not smooth. First, a mathematical theory related to both direct and inverse optimal control approaches is presented. The first theoretical result is the Inactivation Principle, according to which minimizing a term similar to the absolute work implies simultaneous inactivation of agonistic and antagonistic muscles acting on a single joint, near the time of peak velocity. The second theoretical result is that, conversely, the presence of non-smoothness in the cost function is a necessary condition for the existence of such inactivation. Second, during an experimental study, participants were asked to perform fast vertical arm movements with one, two, and three degrees of freedom. Observed trajectories, velocity profiles, and final postures were accurately simulated by the model. In accordance, electromyographic signals showed brief simultaneous inactivation of opposing muscles during movements. Thus, assuming that human movements are optimal with respect to a certain integral cost, the minimization of an absolute-work-like cost is supported by experimental observations. Such types of optimality

  3. Classical and Weak Solutions for Two Models in Mathematical Finance

    NASA Astrophysics Data System (ADS)

    Gyulov, Tihomir B.; Valkov, Radoslav L.

    2011-12-01

    We study two mathematical models, arising in financial mathematics. These models are one-dimensional analogues of the famous Black-Scholes equation on finite interval. The main difficulty is the degeneration at the both ends of the space interval. First, classical solutions are studied. Positivity and convexity properties of the solutions are discussed. Variational formulation in weighted Sobolev spaces is introduced and existence and uniqueness of the weak solution is proved. Maximum principle for weak solution is discussed.

  4. Scaffolding Mathematical Modelling with a Solution Plan

    ERIC Educational Resources Information Center

    Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner

    2015-01-01

    In the study presented in this paper, we examined the possibility to scaffold mathematical modelling with strategies. The strategies were prompted using an instrument called "solution plan" as a scaffold. The effects of this step by step instrument on mathematical modelling competency and on self-reported strategies were tested using…

  5. Complementary variational principle and duality in mathematical programming.

    NASA Technical Reports Server (NTRS)

    Chan, W. L.; Leininger, G. G.; Farison, J. B.

    1973-01-01

    The relationship between the complementary variational principle and duality in mathematical programming is demonstrated through a geometric approach in a Hilbert space setting. A necessary and sufficient condition for the existence of such a principle is given in the case of a convex functional constrained by linear dynamics. Its relationship to the Kuhn-Tucker saddle point theory is indicated. Applications to various programming and control problems are discussed.

  6. Mathematical principles of reinforcement and resistance to change.

    PubMed

    Nevin, John A.

    2003-04-28

    Although Killeen's mathematical principles of reinforcement (MPR) apply to the asymptotic rate of a free operant after extended exposure to a single schedule of reinforcement, they can be extended to resistance to change in multiple schedules via alterations in the parameter representing the activating effects of reinforcers. MPR's predictions of resistance to change in relation to reinforcer rate on variable-interval (VI) schedules are empirically correct and agree with behavioral momentum theory (BMT). However, both MPR and BMT encounter problems in accounting for the effects of delayed reinforcement on resistance to change, relative to immediate reinforcement at the same rate. Further problems are raised by differences in resistance to change between variable-ratio (VR) and variable-interval performances maintained by the same reinforcer rate. With both delayed versus immediate reinforcement and variable-ratio versus variable-interval reinforcement, differential resistance to change is negatively correlated with the log ratios of baseline response rates when reinforcer rates are equated. Cases where resistance to change varies despite equated reinforcer rates, and the correlations among behavioral measures, provide challenges and opportunities for both MPR and BMT.

  7. Intellectual Engagement and Other Principles of Mathematics Instruction

    ERIC Educational Resources Information Center

    Peterson, Blake E.; Corey, Douglas L.; Lewis, Benjamin M.; Bukarau, Jared

    2013-01-01

    In this article, mathematics teachers in the United States were asked what constitutes a high-quality mathematics lesson. The returned responses varied greatly. This same question was asked of Japanese teachers also. For a clearer picture both American and Japanese teachers were directed to comment on videotaped mathematics lessons taught in both…

  8. Multidrug resistance: Physiological principles and nanomedical solutions.

    PubMed

    Kunjachan, Sijumon; Rychlik, Błażej; Storm, Gert; Kiessling, Fabian; Lammers, Twan

    2013-11-01

    Multidrug resistance (MDR) is a pathophysiological phenomenon employed by cancer cells which limits the prolonged and effective use of chemotherapeutic agents. MDR is primarily based on the over-expression of drug efflux pumps in the cellular membrane. Prominent examples of such efflux pumps, which belong to the ATP-binding cassette (ABC) superfamily of proteins, are Pgp (P-glycoprotein) and MRP (multidrug resistance-associated protein), nowadays officially known as ABCB1 and ABCC1. Over the years, several strategies have been evaluated to overcome MDR, based not only on the use of low-molecular-weight MDR modulators, but also on the implementation of 1-100(0) nm-sized drug delivery systems. In the present manuscript, after introducing the most important physiological principles of MDR, we summarize prototypic nanomedical strategies to overcome multidrug resistance, including the use of carrier materials with intrinsic anti-MDR properties, the use of nanomedicines to modify the mode of cellular uptake, and the co-formulation of chemotherapeutic drugs together with low- and high-molecular-weight MDR inhibitors within a single drug delivery system. While certain challenges still need to be overcome before such constructs and concepts can be widely applied in the clinic, the insights obtained and the progress made strongly suggest that nanomedicine formulations hold significant potential for improving the treatment of multidrug-resistant malignancies.

  9. Acceleration of neutrons in a scheme of a tautochronous mathematical pendulum (physical principles)

    SciTech Connect

    Rivlin, Lev A

    2010-12-09

    We consider the physical principles of neutron acceleration through a multiple synchronous interaction with a gradient rf magnetic field in a scheme of a tautochronous mathematical pendulum. (laser applications and other aspects of quantum electronics)

  10. Slope across the Curriculum: Principles and Standards for School Mathematics and Common Core State Standards

    ERIC Educational Resources Information Center

    Nagle, Courtney; Moore-Russo, Deborah

    2014-01-01

    This article provides an initial comparison of the Principles and Standards for School Mathematics and the Common Core State Standards for Mathematics by examining the fundamental notion of slope. Each set of standards is analyzed using eleven previously identified conceptualizations of slope. Both sets of standards emphasize Functional Property,…

  11. Nonparametric solutions to the variational principle of ideal magnetohydrodynamics

    NASA Technical Reports Server (NTRS)

    Betancourt, O. L.; Mcfadden, G.

    1985-01-01

    In an effort to gain a better understanding of MHD equilibria in three dimensions, the lower dimensional cases are studied. The solution of the three-dimensional problem is based on the classical variational principle of ideal magnetohydrodynamics. The crucial assumption for the numerical method is the existence of a nested set of toroidal flux surfaces, which is then used as a coordinate. This paper studies the nonparametric solutions to this variational problem in those cases when the direct solution is known to have islands. A form of the variational principle for the slab geometry is described; the one-dimensional problem is analyzed; and asymptotic expansions and numerical solutions to the two-dimensional problem are discussed. An example is presented which shows that the assumption of nested flux surfaces need not rule out the occurrence of islands.

  12. Student Engagement and Teacher Guidance in Meaningful Mathematics: Enduring Principles

    ERIC Educational Resources Information Center

    Freeman, Gregory D.; Lucius, Lisa B.

    2008-01-01

    In mathematics, developing a conceptual understanding and observing properly modeled methods rarely lead to successful student performance. The student must participate. As with bike riding, participation with monitoring and guidance makes initial efforts meaningful and beneficial. In this article, the authors share a bike riding experience and…

  13. Applying the Mean Proportional Principle to Graphical Solutions.

    ERIC Educational Resources Information Center

    Barton, Lyndon O.

    1991-01-01

    A graphical illustration is presented indicating how the mean proportional (geometric mean), once established for one set of conditions of a geometric identity, can be used to generate other sets of conditions for the same identity. Exemplified is the application of this principle in developing graphical solutions to engineering problems. (JJK)

  14. Use of the Mathematical Principle of Inversion in Young Children.

    ERIC Educational Resources Information Center

    Rasmussen, Carmen; Ho, Elaine; Bisanz, Jeffrey

    2003-01-01

    Presented preschoolers and first graders with 3-term inversion problems such as 3 + 2 - 2 and similar standard problems to examine whether children used the inversion principle and if use was based on qualitative identity, length, or quantity. Found that both age groups showed evidence of using inversion in a fully quantitative manner, indicating…

  15. A mathematical solution to a network designing problem.

    PubMed

    Takahashi, Y

    1996-01-01

    One of the major open issues in neural network research includes a Network Designing Problem (NDP): find a polynomial-time procedure that produces minimal structures (the minimum intermediate size, thresholds and synapse weights) of multilayer threshold feed-forward networks so that they can yield outputs consistent with given sample sets of input-output data. The NDP includes as a subproblem a Network Training Problem (NTP) where the intermediate size is given. The NTP has been studied mainly by use of iterative algorithms of network training. This paper, making use of both rate distortion theory in information theory and linear algebra, solves the NDP mathematically rigorously. On the basis of this mathematical solution, it furthermore develops a mathematical solution procedure to the NDP that computes the minimal structure straightforwardly from the sample set. The procedure precisely attains the minimum intermediate size, although its computational time complexity can be of nonpolynomial order at worst cases. The paper also refers to a polynomial-time shortcut of the procedure for practical use that can reach an approximate minimum intermediate size with its error measurable. The shortcut, when the intermediate size is prespecified, reduces to a promising alternative as well to current network training algorithms to the NTP.

  16. 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…

  17. A new mathematical solution for predicting char activation reactions

    USGS Publications Warehouse

    Rafsanjani, H.H.; Jamshidi, E.; Rostam-Abadi, M.

    2002-01-01

    The differential conservation equations that describe typical gas-solid reactions, such as activation of coal chars, yield a set of coupled second-order partial differential equations. The solution of these coupled equations by exact analytical methods is impossible. In addition, an approximate or exact solution only provides predictions for either reaction- or diffusion-controlling cases. A new mathematical solution, the quantize method (QM), was applied to predict the gasification rates of coal char when both chemical reaction and diffusion through the porous char are present. Carbon conversion rates predicted by the QM were in closer agreement with the experimental data than those predicted by the random pore model and the simple particle model. ?? 2002 Elsevier Science Ltd. All rights reserved.

  18. Mathematical, physical and numerical principles essential for models of turbulent mixing

    SciTech Connect

    Sharp, David Howland; Lim, Hyunkyung; Yu, Yan; Glimm, James G

    2009-01-01

    We propose mathematical, physical and numerical principles which are important for the modeling of turbulent mixing, especially the classical and well studied Rayleigh-Taylor and Richtmyer-Meshkov instabilities which involve acceleration driven mixing of a fluid discontinuity layer, by a steady accerleration or an impulsive force.

  19. Principles and Guidelines for Equitable Mathematics Teaching Practices and Materials for English Language Learners

    ERIC Educational Resources Information Center

    Moschkovich, Judit

    2013-01-01

    In this essay, the author describes principles for equitable mathematics teaching practices for English Language Learners (ELLs) and outlines guidelines for materials to support such practices. Although research cannot provide a recipe for equitable teaching practices for ELLs, teachers, educators, and administrators can use this set of…

  20. Design Principles for Creating Locally-Rooted National Science and Mathematics Curricula in Timor-Leste

    ERIC Educational Resources Information Center

    Gabrielson, Curtis A.; Hsi, Sherry

    2012-01-01

    This paper articulates and illustrates design principles that guided the development of a set of hands-on teaching activities for the national science and mathematics curricula at junior-high and high-school level education in Timor-Leste, a small, low-income nation in Southeast Asia. A partnership between a university, an international science…

  1. Mathematics Learning with Multiple Solution Methods: Effects of Types of Solutions and Learners' Activity

    ERIC Educational Resources Information Center

    Große, Cornelia S.

    2014-01-01

    It is commonly suggested to mathematics teachers to present learners different methods in order to solve one problem. This so-called "learning with multiple solution methods" is also recommended from a psychological point of view. However, existing research leaves many questions unanswered, particularly concerning the effects of…

  2. Mathematical models of polymer solutions motion and their symmetries

    NASA Astrophysics Data System (ADS)

    Bozhkov, Yu. D.; Pukhnachev, V. V.; Pukhnacheva, T. P.

    2015-10-01

    We consider three mathematical models describing motion of aqueous polymer solutions. All of them are derived from equations of Maxwell type viscoelastic medium at small relaxation time. Distinction consists in the choice of time derivative in the rheological constitutive law. Namely, we can choose (a) connective, (b) partial or (c) objective derivative of the strain tensor in time. We found widest symmetry groups admitted by each of these models. Systems (a) and (c) admit the extended Galilei group containing four arbitrary functions of time while the group admitted by system (b) is rather poor. Wide classes of exact solutions are obtained and their behaviors are analyzed if the relaxation viscosity tends to zero. Asymptotic expansion in this solution's parameter describing the flow near a critical point in planar and axially symmetric cases is derived. Analogs of the classical Hagen-Poiseuille and Nusselt solutions are studied too. We found difference in the pressure distribution between solutions calculated on the base of model (c) and two other models.

  3. Using Diagrams as Tools for the Solution of Non-Routine Mathematical Problems

    ERIC Educational Resources Information Center

    Pantziara, Marilena; Gagatsis, Athanasios; Elia, Iliada

    2009-01-01

    The Mathematics education community has long recognized the importance of diagrams in the solution of mathematical problems. Particularly, it is stated that diagrams facilitate the solution of mathematical problems because they represent problems' structure and information (Novick & Hurley, 2001; Diezmann, 2005). Novick and Hurley were the first…

  4. Effective Computer-Aided Assessment of Mathematics; Principles, Practice and Results

    ERIC Educational Resources Information Center

    Greenhow, Martin

    2015-01-01

    This article outlines some key issues for writing effective computer-aided assessment (CAA) questions in subjects with substantial mathematical or statistical content, especially the importance of control of random parameters and the encoding of wrong methods of solution (mal-rules) commonly used by students. The pros and cons of using CAA and…

  5. Robotic and mathematical modeling reveal general principles of appendage control and coordination in terrestrial locomotion

    NASA Astrophysics Data System (ADS)

    McInroe, Benjamin; Astley, Henry; Gong, Chaohui; Kawano, Sandy; Schiebel, Perrin; Choset, Howie; Goldman, Daniel I.

    The transition from aquatic to terrestrial life presented new challenges to early walkers, necessitating robust locomotion on complex, flowable substrates (e.g. sand, mud). Locomotion on such substrates is sensitive to limb morphology and kinematics. Although early walker morphologies are known, principles of appendage control remain elusive. To reveal limb control strategies that facilitated the invasion of land, we study both robotic and mathematical models. Robot experiments show that an active tail is critical for robust locomotion on granular media, enabling locomotion even with poor foot placement and limited ability to lift the body. Using a granular resistive force theory model, we construct connection vector fields that reveal how appendage coordination and terrain inclination impact locomotor performance. This model replicates experimental results, showing that moving limbs/tail in phase is most effective (suggesting a locomotor template). Varying limb trajectories and contacts, we find gaits for which tail use can be neutral or harmful, suggesting limb-tail coordination to be a nontrivial aspect of locomotion. Our findings show that robot experiments coupled with geometric mechanics provide a general framework to reveal principles of robust terrestrial locomotion. This work was supported by NSF PoLS.

  6. Threats to CETI-SETI - Possible solutions and anthropic principle

    NASA Astrophysics Data System (ADS)

    Subotowicz, M.

    1989-11-01

    The relevance of the anthropic principle to the character and viability of SETI efforts is discussed, in the course of a general evaluation of current and prospective threats to continuation of SETI research. Such impediments encompass anthropogenic radiation from earth sufficiently powerful to pollute microwave reception from deep space, cessation of governmental funding, lack of general cultural interest in SETI, and fear of contact with extraterrestrial civilizations.

  7. Hamilton's Principle and Approximate Solutions to Problems in Classical Mechanics

    ERIC Educational Resources Information Center

    Schlitt, D. W.

    1977-01-01

    Shows how to use the Ritz method for obtaining approximate solutions to problems expressed in variational form directly from the variational equation. Application of this method to classical mechanics is given. (MLH)

  8. Multiple Solutions to Problems in Mathematics Teaching: Do Teachers Really Value Them?

    ERIC Educational Resources Information Center

    Bingolbali, Erhan

    2011-01-01

    Solving problems in different ways is strongly advised for mathematics learning and teaching. There is, however, little data available on the examination of teachers' openness to and evaluation of different solutions to the problems. In this paper, the author examines classroom teachers' openness to different solutions (or to what extent they…

  9. Cytokinesis in Prokaryotes and Eukaryotes: Common Principles and Different Solutions

    PubMed Central

    Nanninga, Nanne

    2001-01-01

    Cytokinesis requires duplication of cellular structures followed by bipolarization of the predivisional cell. As a common principle, this applies to prokaryotes as well as eukaryotes. With respect to eukaryotes, the discussion has focused mainly on Saccharomyces cerevisiae and on Schizosaccharomyces pombe. Escherichia coli and to a lesser extent Bacillus subtilis have been used as prokaryotic examples. To establish a bipolar cell, duplication of a eukaryotic origin of DNA replication as well as its genome is not sufficient. Duplication of the microtubule-organizing center is required as a prelude to mitosis, and it is here that the dynamic cytoskeleton with all its associated proteins comes to the fore. In prokaryotes, a cytoskeleton that pervades the cytoplasm appears to be absent. DNA replication and the concomitant DNA segregation seem to occur without help from extensive cytosolic supramacromolecular assemblies but with help from the elongating cellular envelope. Prokaryotic cytokinesis proceeds through a contracting ring, which has a roughly 100-fold-smaller circumference than its eukaryotic counterpart. Although the ring contains proteins that can be considered as predecessors of actin, tubulin, and microtubule-associated proteins, its macromolecular composition is essentially different. PMID:11381104

  10. Computer Facilitated Mathematical Methods in Chemical Engineering--Similarity Solution

    ERIC Educational Resources Information Center

    Subramanian, Venkat R.

    2006-01-01

    High-performance computers coupled with highly efficient numerical schemes and user-friendly software packages have helped instructors to teach numerical solutions and analysis of various nonlinear models more efficiently in the classroom. One of the main objectives of a model is to provide insight about the system of interest. Analytical…

  11. Comparison between analytical and numerical solution of mathematical drying model

    NASA Astrophysics Data System (ADS)

    Shahari, N.; Rasmani, K.; Jamil, N.

    2016-02-01

    Drying is often related to the food industry as a process of shifting heat and mass inside food, which helps in preserving food. Previous research using a mass transfer equation showed that the results were mostly concerned with the comparison between the simulation model and the experimental data. In this paper, the finite difference method was used to solve a mass equation during drying using different kinds of boundary condition, which are equilibrium and convective boundary conditions. The results of these two models provide a comparison between the analytical and the numerical solution. The result shows a close match between the two solution curves. It is concluded that the two proposed models produce an accurate solution to describe the moisture distribution content during the drying process. This analysis indicates that we have confidence in the behaviour of moisture in the numerical simulation. This result demonstrated that a combined analytical and numerical approach prove that the system is behaving physically. Based on this assumption, the model of mass transfer was extended to include the temperature transfer, and the result shows a similar trend to those presented in the simpler case.

  12. Principles to Actions: Mathematics Programs as the Core for Student Learning

    ERIC Educational Resources Information Center

    Brahier, Daniel; Leinwand, Steve; Huniker, DeAnn

    2014-01-01

    The National Council of Teachers of Mathematics (NCTM) launched the "standards-based" education movement in North America in 1989 with the release of "Curriculum and Evaluation Standards for School Mathematics," an unprecedented action to promote systemic improvement in mathematics education. Now, twenty-five years later, the…

  13. Solutions of some problems in applied mathematics using MACSYMA

    NASA Technical Reports Server (NTRS)

    Punjabi, Alkesh; Lam, Maria

    1987-01-01

    Various Symbolic Manipulation Programs (SMP) were tested to check the functioning of their commands and suitability under various operating systems. Support systems for SMP were found to be relatively better than the one for MACSYMA. The graphics facilities for MACSYMA do not work as expected under the UNIX operating system. Not all commands for MACSYMA function as described in the manuals. Shape representation is a central issue in computer graphics and computer-aided design. Aside from appearance, there are other application dependent, desirable properties like continuity to certain order, symmetry, axis-independence, and variation-diminishing properties. Several shape representations are studied, which include the Osculatory Method, a Piecewise Cubic Polynomial Method using two different slope estimates, Piecewise Cubic Hermite Form, a method by Harry McLaughlin, and a Piecewise Bezier Method. They are applied to collected physical and chemical data. Relative merits and demerits of these methods are examined. Kinematics of a single link, non-dissipative robot arm is studied using MACSYMA. Lagranian is set-up and Lagrange's equations are derived. From there, Hamiltonian equations of motion are obtained. Equations suggest that bifurcation of solutions can occur, depending upon the value of a single parameter. Using the characteristic function W, the Hamilton-Jacobi equation is derived. It is shown that the H-J equation can be solved in closed form. Analytical solutions to the H-J equation are obtained.

  14. Solution of steady-state one-dimensional conservation laws by mathematical programming

    NASA Technical Reports Server (NTRS)

    Lavery, J. E.

    1989-01-01

    Solution techniques for a class of steady-state scalar conservation laws are developed analytically. Discretization by finite-volume formulas is employed to obtain an overdetermined system of algebraic equations, which are then perturbed nonsingularly (with perturbation coefficient = epsilon) and solved using the l(1) mathematical-programming algorithm of Seneta and Steiger (1984); this approach limits the matrix bandwidth to two, so that an explicit solution can be found efficiently. It is shown that, for small values of epsilon, the l(1) solutions exhibit sharp correctly located shocks and are nonoscillatory O(epsilon) approximations of the physically relevant solutions.

  15. The Way Adults with Orientation to Mathematics Teaching Cope with the Solution of Everyday Real-World Problems

    ERIC Educational Resources Information Center

    Gazit, Avikam; Patkin, Dorit

    2012-01-01

    The article aims to check the way adults, "some who are" practicing mathematics teachers at elementary school, "some who are" academicians making a career change to mathematics teachers at junior high school and the "rest who are" pre-service mathematics teachers at elementary school, cope with the solution of everyday real-world problems of…

  16. Tensor Arithmetic, Geometric and Mathematic Principles of Fluid Mechanics in Implementation of Direct Computational Experiments

    NASA Astrophysics Data System (ADS)

    Bogdanov, Alexander; Khramushin, Vasily

    2016-02-01

    The architecture of a digital computing system determines the technical foundation of a unified mathematical language for exact arithmetic-logical description of phenomena and laws of continuum mechanics for applications in fluid mechanics and theoretical physics. The deep parallelization of the computing processes results in functional programming at a new technological level, providing traceability of the computing processes with automatic application of multiscale hybrid circuits and adaptive mathematical models for the true reproduction of the fundamental laws of physics and continuum mechanics.

  17. A Study of the Relative Effectiveness of a Meaningful Concrete and a Meaningful Symbolic Model in Learning a Selected Mathematical Principle.

    ERIC Educational Resources Information Center

    Fennema, Elizabeth

    Reported is a study to determine the relative effectiveness of a meaningful concrete and a meaningful symbolic model in learning a selected mathematics principle. Subjects were from a second grade population and they were assigned to three treatments. Students assigned to Treatment 1 received instruction in the principle with a meaningful symbolic…

  18. Solute/impurity diffusivities in bcc Fe: A first-principles study

    NASA Astrophysics Data System (ADS)

    Zhang, Chong; Fu, Jie; Li, Ruihuan; Zhang, Pengbo; Zhao, Jijun; Dong, Chuang

    2014-12-01

    Chinese low activation martensitic steel (CLAM) has been designed with decreased W content and increased Ta content to improve performance. We performed first-principles calculations to investigate the diffusion properties of solute element (Cr, W, Mn, V, Ta) and C diffusion with a nearby solute element inside bcc Fe. The self-diffusion coefficients and solute diffusion coefficients in Fe host were derived using the nine-frequency model. A relatively lower diffusivity was observed for W in paramagnetic state, implying enriched W concentration inside Fe host. The solute atom interacts strongly with C impurity, depending on the interatomic distance. According to our calculations, formation of Ta carbide precipitates is energetically preferred by trapping C impurity around Ta atom. Our theoretical results are helpful for investigating the evolution of microstructure of steels for engineering applications.

  19. Grade 3 Students' Mathematization through Modeling: Situation Models and Solution Models with Mutli-Digit Subtraction Problem Solving

    ERIC Educational Resources Information Center

    Murata, Aki; Kattubadi, Sailaja

    2012-01-01

    In considering mathematics problem solving as a model-eliciting activity (Lesh & Doerr, 2003; Lesh & Harel, 2003; Lesh & Zawojewski, 2008), it is important to know "what" students are modeling for the problems: situations or solutions. This study investigated Grade 3 students' mathematization process by examining how they modeled different…

  20. Applications of Information Theory and Acceptance Sampling Principles to the Management of Mathematics Instruction, Part 2.

    ERIC Educational Resources Information Center

    Kriewall, Thomas E.

    This Technical Report is concerned with various problems of instructional management encountered in situations which stress self-selection and self-pacing principles. These problems deal primarily with the efficient utilization and allocation of human and material resource materials to formulate an operational, individualized, inquiry-learning…

  1. Applications of Information Theory and Acceptance Sampling Principles to the Management of Mathematics Instruction, Part 1.

    ERIC Educational Resources Information Center

    Kriewall, Thomas E.

    This Technical Report is concerned with various problems of instructional management encountered in situations which stress self-selection and self-pacing principles. These problems deal primarily with the efficient utilization and allocation of human and material resource materials to formulate an operational, individualized, inquiry-learning…

  2. Rocket injector anomalies study. Volume 1: Description of the mathematical model and solution procedure

    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.

  3. FROM THE HISTORY OF PHYSICS: Tricentenary of Isaac Newton's "Mathematical Principles of Natural Philosophy"

    NASA Astrophysics Data System (ADS)

    Ginzburg, Vitalii L.

    1987-01-01

    The first edition of Newton's "Philosophiae Naturalis Principia Mathematica" was published in 1687. The present paper is dedicated to the tricentenary of this event, which is important not just in the history of physics, but of science generally. After the Introduction, the paper continues with the following Sections: Before Newton, Principia, Principia and the method of principles, The nature of gravitation, Critique of Newtonian mechanics and its subsequent development, On Newton, Concluding remarks.

  4. Transition metal solute interactions with point defects in fcc iron from first principles

    NASA Astrophysics Data System (ADS)

    Hepburn, D. J.; MacLeod, E.; Ackland, G. J.

    2015-07-01

    We present a comprehensive set of first-principles electronic structure calculations of the properties of substitutional transition metal solutes and point defects in austenite (face-centered cubic, paramagnetic Fe). Clear trends were observed in these quantities across the transition metal series, with solute-defect interactions strongly related to atomic size, and only weakly related to more subtle details of magnetic or electronic structure. Oversized solutes act as strong traps for both vacancy and self-interstitial defects and as nucleation sites for the development of protovoids and small self-interstitial loops. The consequent reduction in defect mobility and net defect concentrations in the matrix explains the observation of reduced swelling and radiation-induced segregation. Our analysis of vacancy-mediated solute diffusion demonstrates that below about 400 K Ni and Co will be dragged by vacancies and their concentrations should be enhanced at defect sinks. Cr and Cu show opposite behavior and are depleted at defect sinks. The stable configuration of some oversized solutes is neither interstitial nor substitutional; rather they occupy two adjacent lattice sites. The diffusion of these solutes proceeds by a novel mechanism, which has important implications for the nucleation and growth of complex oxide nanoparticles contained in oxide dispersion strengthened steels. Interstitial-mediated solute diffusion is negligible for all except the magnetic solutes (Cr, Mn, Co, and Ni). Our results are consistent across several antiferromagnetic states and surprising qualitative similarities with ferromagnetic (body-centered cubic) Fe were observed; this implies that our conclusions will be valid for paramagnetic iron.

  5. Approximate smooth solutions of a mathematical model for the activation and clonal expansion of T cells.

    PubMed

    Criaco, D; Dolfin, M; Restuccia, L

    2013-02-01

    In a previous paper a mathematical model was developed for the dynamics of activation and clonal expansion of T cells during the immune response to a single type of antigen challenge, constructed phenomenologically in the macroscopic framework of a thermodynamic theory of continuum mechanics for reacting and proliferating fluid mixtures. The present contribution deals with approximate smooth solutions, called asymptotic waves, of the system of PDEs describing the introduced model, obtained using a suitable perturbative method. In particular, in the one-dimensional case, after deriving the expression of the velocity along the characteristic rays and the equation of the wave front, the transport equation for the first perturbation term of the asymptotic solution is obtained. Finally, it is shown that this transport equation can be reduced to an equation similar to Burgers equation.

  6. Direct calculation of thermodynamic properties of the barite/celestite solid solution from molecular principles

    NASA Astrophysics Data System (ADS)

    Becker, U.; Fernández-González, A.; Prieto, M.; Harrison, R.; Putnis, A.

    Thermodynamic properties of the barite-celestite solid solution were calculated using molecular principles. Cation-cation (Ba-Ba, Sr-Sr, and Ba-Sr) interaction energies were derived from a number of random and ordered cation distributions which were energy-optimized using force potentials as incorporated in the program package GULP. With these interaction energies, diagrams for the enthalpy and free energy of mixing could be computed for the entire range of the solid solution between the barite and celestite end members and for a number of annealing temperatures. These thermodynamic data show that the solid solution is nonideal. The system has a tendency for Ba2+ and Sr2+ cations to order onto alternating layers ||(100). However, this ordering scheme is thermodynamically only relevant for annealing temperatures below approximately 500K and systems that are kinetically inhibited during crystal growth. For sufficiently long annealing times at room temperature, the solid solution tends to exsolve with barite-celestite interfaces ||(100). The cell parameters a and c were calculated to have almost linear behavior for the whole solid solution, suggesting close to ideal behavior according to Vegard's law. In contrast, b tends to deviate positively from linearity, in agreement with experimental values.

  7. Lyapunov Stabilizability of Controlled Diffusions via a Superoptimality Principle for Viscosity Solutions

    SciTech Connect

    Cesaroni, Annalisa

    2006-01-15

    We prove optimality principles for semicontinuous bounded viscosity solutions of Hamilton-Jacobi-Bellman equations. In particular, we provide a representation formula for viscosity supersolutions as value functions of suitable obstacle control problems. This result is applied to extend the Lyapunov direct method for stability to controlled Ito stochastic differential equations. We define the appropriate concept of the Lyapunov function to study stochastic open loop stabilizability in probability and local and global asymptotic stabilizability (or asymptotic controllability). Finally, we illustrate the theory with some examples.

  8. Towards the Solution of Abysmal Performance in Mathematics in Junior High Schools: Comparing the Pedagogical Potential of Two Designed Interventions

    ERIC Educational Resources Information Center

    Sarfo, Frederick Kwaku; Eshun, Grace; Elen, Jan; Adentwi, Kobina Impraim

    2014-01-01

    Introduction: In this study, the effectiveness of two different interventions was investigated. The effects of a concrete abstract intervention and a regular method of teaching intervention were compared. Both interventions were designed in line with the specifications of classical principles of instructional design for learning mathematics in the…

  9. A unified electrostatic and cavitation model for first-principles molecular dynamics in solution

    SciTech Connect

    Scherlis, D A; Fattebert, J; Gygi, F; Cococcioni, M; Marzari, N

    2005-11-14

    The electrostatic continuum solvent model developed by Fattebert and Gygi is combined with a first-principles formulation of the cavitation energy based on a natural quantum-mechanical definition for the surface of a solute. Despite its simplicity, the cavitation contribution calculated by this approach is found to be in remarkable agreement with that obtained by more complex algorithms relying on a large set of parameters. The model allows for very efficient Car-Parrinello simulations of finite or extended systems in solution, and demonstrates a level of accuracy as good as that of established quantum-chemistry continuum solvent methods. They apply this approach to the study of tetracyanoethylene dimers in dichloromethane, providing valuable structural and dynamical insights on the dimerization phenomenon.

  10. Variational solutions for the thermal and real time propagator using the McLachlan variational principle

    NASA Astrophysics Data System (ADS)

    Messina, Michael; Garrett, Bruce C.; Schenter, Gregory K.

    1994-05-01

    A new approximation to the propagator is presented. The approximation as applied to the thermal propagator (coordinate space density matrix) is obtained by using an analog of the McLachlan variational principle for the solution of the Bloch equation. The approximation as applied to the real time propagator is obtained by using the McLachlan variational principle for the solution of the time-dependent Schrödinger equation. The approximate coordinate space density matrix has the same functional form of the high temperature limit of the density matrix, while the approximate real time propagator has the same functional form as the short time propagator. We present numerical results for the thermal propagator for several test systems and compare these results to previous work of Zhang, Levy, and Freisner [Chem. Phys. Lett. 144, 236 (1988)], Mak and Andersen [J. Chem. Phys. 92, 2953 (1990)], and Cao and Berne [J. Chem. Phys. 92, 7531 (1990)]. We also present numerical results for the approximate real time propagator for several test systems and compare to the exact results and results obtained by Gaussian wave packet propagation.

  11. Interesting and Difficult Mathematical Problems: Changing Teachers' Views by Employing Multiple-Solution Tasks

    ERIC Educational Resources Information Center

    Guberman, Raisa; Leikin, Roza

    2013-01-01

    The study considers mathematical problem solving to be at the heart of mathematics teaching and learning, while mathematical challenge is a core element of any educational process. The study design addresses the complexity of teachers' knowledge. It is aimed at exploring the development of teachers' mathematical and pedagogical conceptions…

  12. Multiphase flow experiments, mathematical modeling and numerical simulation of the water - gas - solute movement

    NASA Astrophysics Data System (ADS)

    Li, Y.; Ma, X.; Su, N.

    2013-12-01

    The movement of water and solute into and through the vadose zone is, in essence, an issue of immiscible displacement in pore-space network of a soil. Therefore, multiphase flow and transport in porous media, referring to three medium: air, water, and the solute, pose one of the largest unresolved challenges for porous medium fluid seepage. However, this phenomenon has always been largely neglected. It is expected that a reliable analysis model of the multi-phase flow in soil can truly reflect the process of natural movement about the infiltration, which is impossible to be observed directly. In such cases, geophysical applications of the nuclear magnetic resonance (NMR) provides the opportunity to measure the water movements into soils directly over a large scale from tiny pore to regional scale, accordingly enable it available both on the laboratory and on the field. In addition, the NMR provides useful information about the pore space properties. In this study, we proposed both laboratory and field experiments to measure the multi-phase flow parameters, together with optimize the model in computer programming based on the fractional partial differential equations (fPDE). In addition, we establish, for the first time, an infiltration model including solute flowing with water, which has huge influence on agriculture and soil environment pollution. Afterwards, with data collected from experiments, we simulate the model and analyze the spatial variability of parameters. Simulations are also conducted according to the model to evaluate the effects of airflow on water infiltration and other effects such as solute and absorption. It has significant meaning to oxygen irrigation aiming to higher crop yield, and shed more light into the dam slope stability. In summary, our framework is a first-time model added in solute to have a mathematic analysis with the fPDE and more instructive to agriculture activities.

  13. Mathematical model formulation and validation of water and solute transport in whole hamster pancreatic islets.

    PubMed

    Benson, James D; Benson, Charles T; Critser, John K

    2014-08-01

    Optimization of cryopreservation protocols for cells and tissues requires accurate models of heat and mass transport. Model selection often depends on the configuration of the tissue. Here, a mathematical and conceptual model of water and solute transport for whole hamster pancreatic islets has been developed and experimentally validated incorporating fundamental biophysical data from previous studies on individual hamster islet cells while retaining whole-islet structural information. It describes coupled transport of water and solutes through the islet by three methods: intracellularly, intercellularly, and in combination. In particular we use domain decomposition techniques to couple a transmembrane flux model with an interstitial mass transfer model. The only significant undetermined variable is the cellular surface area which is in contact with the intercellularly transported solutes, Ais. The model was validated and Ais determined using a 3×3 factorial experimental design blocked for experimental day. Whole islet physical experiments were compared with model predictions at three temperatures, three perfusing solutions, and three islet size groups. A mean of 4.4 islets were compared at each of the 27 experimental conditions and found to correlate with a coefficient of determination of 0.87±0.06 (mean ± SD). Only the treatment variable of perfusing solution was found to be significant (p<0.05). We have devised a model that retains much of the intrinsic geometric configuration of the system, and thus fewer laboratory experiments are needed to determine model parameters and thus to develop new optimized cryopreservation protocols. Additionally, extensions to ovarian follicles and other concentric tissue structures may be made. PMID:24950195

  14. Facial plastic surgery area acquisition method based on point cloud mathematical model solution.

    PubMed

    Li, Xuwu; Liu, Fei

    2013-09-01

    It is one of the hot research problems nowadays to find a quick and accurate method of acquiring the facial plastic surgery area to provide sufficient but irredundant autologous or in vitro skin source for covering extensive wound, trauma, and burnt area. At present, the acquisition of facial plastic surgery area mainly includes model laser scanning, point cloud data acquisition, pretreatment of point cloud data, three-dimensional model reconstruction, and computation of area. By using this method, the area can be computed accurately, but it is hard to control the random error, and it requires a comparatively longer computation period. In this article, a facial plastic surgery area acquisition method based on point cloud mathematical model solution is proposed. This method applies symmetric treatment to the point cloud based on the pretreatment of point cloud data, through which the comparison diagram color difference map of point cloud error before and after symmetry is obtained. The slicing mathematical model of facial plastic area is got through color difference map diagram. By solving the point cloud data in this area directly, the facial plastic area is acquired. The point cloud data are directly operated in this method, which can accurately and efficiently complete the surgery area computation. The result of the comparative analysis shows the method is effective in facial plastic surgery area.

  15. Defect and solute properties in dilute Fe-Cr-Ni austenitic alloys from first principles

    NASA Astrophysics Data System (ADS)

    Klaver, T. P. C.; Hepburn, D. J.; Ackland, G. J.

    2012-05-01

    We present results of an extensive set of first-principles density functional theory calculations of point defect formation, binding, and clustering energies in austenitic Fe with dilute concentrations of Cr and Ni solutes. A large number of possible collinear magnetic structures were investigated as appropriate reference states for austenite. We found that the antiferromagnetic single- and double-layer structures with tetragonal relaxation of the unit cell were the most suitable reference states and highlighted the inherent instabilities in the ferromagnetic states. Test calculations for the presence and influence of noncollinear magnetism were performed but proved mostly negative. We calculate the vacancy formation energy to be between 1.8 and 1.95 eV. Vacancy cluster binding was initially weak at 0.1 eV for divacancies but rapidly increased with additional vacancies. Clusters of up to six vacancies were studied and a highly stable octahedral cluster and stacking fault tetrahedron were found with total binding energies of 2.5 and 2.3 eV, respectively. The <100> dumbbell was found to be the most stable self-interstitial with a formation energy of between 3.2 and 3.6 eV and was found to form strongly bound clusters, consistent with other fcc metals. Pair interaction models were found to be capable of capturing the trends in the defect cluster binding energy data. Solute-solute interactions were found to be weak in general, with a maximal positive binding of 0.1 eV found for Ni-Ni pairs and maximum repulsion found for Cr-Cr pairs of -0.1 eV. Solute cluster binding was found to be consistent with a pair interaction model, with Ni-rich clusters being the most stable. Solute-defect interactions were consistent with Ni and Cr being modestly oversized and undersized solutes, respectively, which is exactly opposite to the experimentally derived size factors for Ni and Cr solutes in type 316 stainless steel and in the pure materials. Ni was found to bind to the vacancy and

  16. First principles study of the aggregation of oligo and polythiophene cations in solution

    SciTech Connect

    Scherlis, D A; Fattebert, J; Marzari, N

    2005-11-14

    The stacking of positively charged (or doped) terthiophene oligomers and quaterthiophene polymers in solution is investigated applying a recently developed unified electrostatic and cavitation model for first-principles calculations in a continuum solvent. The thermodynamic and structural patterns of the dimerization are explored in different solvents, and the distinctive roles of polarity and surface tension are characterized and analyzed. Interestingly, we discover a saturation in the stabilization effect of the dielectric screening that takes place at rather small values of {epsilon}{sub 0}. Moreover, we address the interactions in trimers of terthiophene cations, with the aim of generalizing the results obtained for the dimers to the case of higher order stacks and nanoaggregates.

  17. A new sensitive method of dissociation constants determination based on the isohydric solutions principle.

    PubMed

    Michałowski, Tadeusz; Pilarski, Bogusław; Asuero, Agustin G; Dobkowska, Agnieszka

    2010-10-15

    The paper provides a new formulation and analytical proposals based on the isohydric solutions concept. It is particularly stated that a mixture formed, according to titrimetric mode, from a weak acid (HX, C(0)mol/L) and a strong acid (HB, Cmol/L) solutions, assumes constant pH, independently on the volumes of the solutions mixed, provided that the relation C(0)=C+C(2)·10(pK(1)) is valid, where pK(1)=-log K(1), K(1) the dissociation constant for HX. The generalized formulation, referred to the isohydric solutions thus obtained, was extended also to more complex acid-base systems. Particularly in the (HX, HB) system, the titration occurs at constant ionic strength (I) value, not resulting from presence of a basal electrolyte. This very advantageous conjunction of the properties provides, among others, a new, very sensitive method for verification of pK(1) value. The new method is particularly useful for weak acids HX characterized by low pK(1) values. The method was tested experimentally on four acid-base systems (HX, HB), in aqueous and mixed-solvent media and compared with the literature data. Some useful (linear and hyperbolic) correlations were stated and applied for validation of pK(1) values. Finally, some practical applications of analytical interest of the isohydricity (pH constancy) principle as one formulated in this paper were enumerated, proving the usefulness of such a property which has its remote roots in the Arrhenius concept.

  18. Design principles for high-pressure force fields: Aqueous TMAO solutions from ambient to kilobar pressures

    NASA Astrophysics Data System (ADS)

    Hölzl, Christoph; Kibies, Patrick; Imoto, Sho; Frach, Roland; Suladze, Saba; Winter, Roland; Marx, Dominik; Horinek, Dominik; Kast, Stefan M.

    2016-04-01

    Accurate force fields are one of the major pillars on which successful molecular dynamics simulations of complex biomolecular processes rest. They have been optimized for ambient conditions, whereas high-pressure simulations become increasingly important in pressure perturbation studies, using pressure as an independent thermodynamic variable. Here, we explore the design of non-polarizable force fields tailored to work well in the realm of kilobar pressures - while avoiding complete reparameterization. Our key is to first compute the pressure-induced electronic and structural response of a solute by combining an integral equation approach to include pressure effects on solvent structure with a quantum-chemical treatment of the solute within the embedded cluster reference interaction site model (EC-RISM) framework. Next, the solute's response to compression is taken into account by introducing pressure-dependence into selected parameters of a well-established force field. In our proof-of-principle study, the full machinery is applied to N,N,N-trimethylamine-N-oxide (TMAO) in water being a potent osmolyte that counteracts pressure denaturation. EC-RISM theory is shown to describe well the charge redistribution upon compression of TMAO(aq) to 10 kbar, which is then embodied in force field molecular dynamics by pressure-dependent partial charges. The performance of the high pressure force field is assessed by comparing to experimental and ab initio molecular dynamics data. Beyond its broad usefulness for designing non-polarizable force fields for extreme thermodynamic conditions, a good description of the pressure-response of solutions is highly recommended when constructing and validating polarizable force fields.

  19. Design principles for high-pressure force fields: Aqueous TMAO solutions from ambient to kilobar pressures.

    PubMed

    Hölzl, Christoph; Kibies, Patrick; Imoto, Sho; Frach, Roland; Suladze, Saba; Winter, Roland; Marx, Dominik; Horinek, Dominik; Kast, Stefan M

    2016-04-14

    Accurate force fields are one of the major pillars on which successful molecular dynamics simulations of complex biomolecular processes rest. They have been optimized for ambient conditions, whereas high-pressure simulations become increasingly important in pressure perturbation studies, using pressure as an independent thermodynamic variable. Here, we explore the design of non-polarizable force fields tailored to work well in the realm of kilobar pressures--while avoiding complete reparameterization. Our key is to first compute the pressure-induced electronic and structural response of a solute by combining an integral equation approach to include pressure effects on solvent structure with a quantum-chemical treatment of the solute within the embedded cluster reference interaction site model (EC-RISM) framework. Next, the solute's response to compression is taken into account by introducing pressure-dependence into selected parameters of a well-established force field. In our proof-of-principle study, the full machinery is applied to N,N,N-trimethylamine-N-oxide (TMAO) in water being a potent osmolyte that counteracts pressure denaturation. EC-RISM theory is shown to describe well the charge redistribution upon compression of TMAO(aq) to 10 kbar, which is then embodied in force field molecular dynamics by pressure-dependent partial charges. The performance of the high pressure force field is assessed by comparing to experimental and ab initio molecular dynamics data. Beyond its broad usefulness for designing non-polarizable force fields for extreme thermodynamic conditions, a good description of the pressure-response of solutions is highly recommended when constructing and validating polarizable force fields.

  20. Design principles for high-pressure force fields: Aqueous TMAO solutions from ambient to kilobar pressures.

    PubMed

    Hölzl, Christoph; Kibies, Patrick; Imoto, Sho; Frach, Roland; Suladze, Saba; Winter, Roland; Marx, Dominik; Horinek, Dominik; Kast, Stefan M

    2016-04-14

    Accurate force fields are one of the major pillars on which successful molecular dynamics simulations of complex biomolecular processes rest. They have been optimized for ambient conditions, whereas high-pressure simulations become increasingly important in pressure perturbation studies, using pressure as an independent thermodynamic variable. Here, we explore the design of non-polarizable force fields tailored to work well in the realm of kilobar pressures--while avoiding complete reparameterization. Our key is to first compute the pressure-induced electronic and structural response of a solute by combining an integral equation approach to include pressure effects on solvent structure with a quantum-chemical treatment of the solute within the embedded cluster reference interaction site model (EC-RISM) framework. Next, the solute's response to compression is taken into account by introducing pressure-dependence into selected parameters of a well-established force field. In our proof-of-principle study, the full machinery is applied to N,N,N-trimethylamine-N-oxide (TMAO) in water being a potent osmolyte that counteracts pressure denaturation. EC-RISM theory is shown to describe well the charge redistribution upon compression of TMAO(aq) to 10 kbar, which is then embodied in force field molecular dynamics by pressure-dependent partial charges. The performance of the high pressure force field is assessed by comparing to experimental and ab initio molecular dynamics data. Beyond its broad usefulness for designing non-polarizable force fields for extreme thermodynamic conditions, a good description of the pressure-response of solutions is highly recommended when constructing and validating polarizable force fields. PMID:27083705

  1. Structure and dynamics of aqueous solutions from PBE-based first-principles molecular dynamics simulations

    NASA Astrophysics Data System (ADS)

    Pham, Tuan Anh; Ogitsu, Tadashi; Lau, Edmond Y.; Schwegler, Eric

    2016-10-01

    Establishing an accurate and predictive computational framework for the description of complex aqueous solutions is an ongoing challenge for density functional theory based first-principles molecular dynamics (FPMD) simulations. In this context, important advances have been made in recent years, including the development of sophisticated exchange-correlation functionals. On the other hand, simulations based on simple generalized gradient approximation (GGA) functionals remain an active field, particularly in the study of complex aqueous solutions due to a good balance between the accuracy, computational expense, and the applicability to a wide range of systems. Such simulations are often performed at elevated temperatures to artificially "correct" for GGA inaccuracies in the description of liquid water; however, a detailed understanding of how the choice of temperature affects the structure and dynamics of other components, such as solvated ions, is largely unknown. To address this question, we carried out a series of FPMD simulations at temperatures ranging from 300 to 460 K for liquid water and three representative aqueous solutions containing solvated Na+, K+, and Cl- ions. We show that simulations at 390-400 K with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional yield water structure and dynamics in good agreement with experiments at ambient conditions. Simultaneously, this computational setup provides ion solvation structures and ion effects on water dynamics consistent with experiments. Our results suggest that an elevated temperature around 390-400 K with the PBE functional can be used for the description of structural and dynamical properties of liquid water and complex solutions with solvated ions at ambient conditions.

  2. First-principles molecular dynamics modeling of the molten fluoride salt with Cr solute

    NASA Astrophysics Data System (ADS)

    Nam, H. O.; Bengtson, A.; Vörtler, K.; Saha, S.; Sakidja, R.; Morgan, D.

    2014-06-01

    Fluoride salts and their interactions with metals are of wide interest for the nuclear community. In this work, first-principles molecular dynamics (FPMD) was employed to study both pure molten fluoride salt and fluoride salt with dissolved solute Cr ions (a common corrosion product) at high temperature (823-1423 K). Two types of molten fluoride salts, namely flibe (LiF-BeF2) and flinak (LiF-NaF-KF), with the Cr0, Cr2+ and Cr3+ ions were chosen as a target system for the FPMD modeling. The prediction of thermo-kinetic properties of pure fluoride salt, such as the equilibrium volume, density, bulk modulus, coefficient of thermal expansion, and self-diffusion coefficient, provide useful extensions of existing data and verify the accuracy of the FPMD simulation in modeling of fluoride salts. The FPMD modeling of solute Cr in fluoride salt shows the effect of Cr valence on diffusivity and local structure in the salt.

  3. Analytical solution for multi-singular vortex Gaussian beams: the mathematical theory of scattering modes

    NASA Astrophysics Data System (ADS)

    Ferrando, A.; García-March, M. A.

    2016-06-01

    We present a novel procedure for solving the Schrödinger equation, which in optics is the paraxial wave equation, with an initial multisingular vortex Gaussian beam. This initial condition has a number of singularities in a plane transversal to propagation embedded in a Gaussian beam. We use scattering modes, which are solutions to the paraxial wave equation that can be combined straightforwardly to express the initial condition and therefore allow the problem to be solved. To construct the scattering modes one needs to obtain a particular set of polynomials, which play an analogous role to Laguerre polynomials for Laguerre-Gaussian modes. We demonstrate here the recurrence relations needed to determine these polynomials. To stress the utility and strength of the method we solve first the problem of an initial Gaussian beam with two positive singularities and a negative one embedded in it. We show that the solution permits one to obtain analytical expressions. These can used to obtain mathematical expressions for meaningful quantities, such as the distance at which the positive and negative singularities merge, closing the loop of a vortex line. Furthermore, we present an example of the calculation of an specific discrete-Gauss state, which is the solution of the diffraction of a Laguerre-Gauss state showing definite angular momentum (that is, a highly charged vortex) by a thin diffractive element showing certain discrete symmetry. We show that this problem is therefore solved in a much simpler way than by using the previous procedure based on the integral Fresnel diffraction method.

  4. Predicting Raman Spectra of Aqueous Silica and Alumina Species in Solution From First Principles

    NASA Astrophysics Data System (ADS)

    Hunt, J. D.; Schauble, E. A.; Manning, C. E.

    2006-12-01

    Dissolved silica and alumina play an important role in lithospheric fluid chemistry. Silica concentrations in aqueous fluids vary over the range of crustal temperatures and pressures enough to allow for significant mass transport of silica via fluid-rock interaction. The polymerization of silica, and the possible incorporation of alumina into the polymer structure, could afford crystal-like or melt-like sites to otherwise insoluble elements such as titanium, leading to enhanced mobility. Raman spectroscopy in a hydrothermal diamond anvil cell (HDAC) has been used to study silica polymerization at elevated pressure and temperature [Ref. 1, 2], but Raman spectra of expected solutes are not fully understood. We calculated Raman spectra of H4SiO4 monomers, H6Si2O7 dimers, and H6SiAlO_7^- dimers, from first principles using hybrid density functional theory (B3LYP). These spectra take into account the variation in bridging angle (Si-O-Si and Si-O-Al angles) that the dimers will have at a given temperature by calculating a potential energy surface of the dimer as the bridging angle varies, and using a Boltzmann distribution at that temperature to determine relative populations at each geometry. Solution effects can be incorporated by using a polarizable continuum model (PCM), and a potential energy surface has been constructed for the silica dimer using a PCM. The bridging angle variation explains the broadness of the 630 cm^-^1 silica dimer peak observed in HDAC experiments [Ref. 1, 2] at high temperatures. The silica-alumina dimer bridging angle is shown to be stiffer than the silica dimer bridging angle, which results in a much narrower main peak. The synthetic spectrum obtained for the silica-alumina dimer suggests that there may be a higher ratio of complexed alumina to free alumina in solution at highly basic pH than previously estimated [Ref. 3]. References: 1. Zotov, N. and H. Keppler, Chemical Geology, 2002. 184: p. 71-82. 2. Zotov, N. and H. Keppler, American

  5. Three-dimensional inverse problem of geometrical optics: a mathematical comparison between Fermat's principle and the eikonal equation.

    PubMed

    Borghero, Francesco; Demontis, Francesco

    2016-09-01

    In the framework of geometrical optics, we consider the following inverse problem: given a two-parameter family of curves (congruence) (i.e., f(x,y,z)=c1,g(x,y,z)=c2), construct the refractive-index distribution function n=n(x,y,z) of a 3D continuous transparent inhomogeneous isotropic medium, allowing for the creation of the given congruence as a family of monochromatic light rays. We solve this problem by following two different procedures: 1. By applying Fermat's principle, we establish a system of two first-order linear nonhomogeneous PDEs in the unique unknown function n=n(x,y,z) relating the assigned congruence of rays with all possible refractive-index profiles compatible with this family. Moreover, we furnish analytical proof that the family of rays must be a normal congruence. 2. By applying the eikonal equation, we establish a second system of two first-order linear homogeneous PDEs whose solutions give the equation S(x,y,z)=const. of the geometric wavefronts and, consequently, all pertinent refractive-index distribution functions n=n(x,y,z). Finally, we make a comparison between the two procedures described above, discussing appropriate examples having exact solutions. PMID:27607492

  6. First-Principles Determination of Molecular Conformations of Indolizidine (−)-235B′ in Solution

    PubMed Central

    Zheng, Fang; Dwoskin, Linda P.; Crooks, Peter A.; Zhan, Chang-Guo

    2009-01-01

    Indolizidine (−)-235B′ is a particularly interesting natural product, as it is the currently known, most potent and subtype-selective open-channel blocker of the α4β2 nicotinic acetylcholine receptor (nAChR). In the current study, extensive first-principles electronic structure calculations have been carried out in order to determine the stable molecular conformations and their relative free energies of the protonated and deprotonated states of (−)-235B′ in the gas phase, in chloroform, and in aqueous solution. The 1H and 13C NMR chemical shifts calculated using the computationally determined dominant molecular conformation of the deprotonated state are all consistent with available experimental NMR spectra of (−)-235B′ in chloroform, which suggests that the computationally determined molecular conformations are reasonable. Our computational results reveal for the first time that two geminal H atoms on carbon-3 (C3) of (−)-235B′ have remarkably different chemical shifts (i.e. 3.24 and 2.03 ppm). The computational results help one to better understand and analyze the experimental 1H NMR spectra of (−)-235B′. The finding of remarkably different chemical shifts of two C3 geminal H atoms in a certain molecular conformation of (−)-235B′ may also be valuable in analysis of NMR spectra of other related ring-containing compounds. In addition, the pKa of (−)-235B′ in aqueous solution is predicted to be ~9.7. All of the computational results provide a solid basis for future studies of the microscopic and phenomenological binding of various receptor proteins with the protonated and deprotonated structures of this unique open-channel blocker of α4β2 nAChRs. This computational study also demonstrates how one can appropriately use computational modeling and spectroscopic analysis to address the structural and spectroscopic problems that cannot be addressed by experiments alone. PMID:20161506

  7. Microencapsulation of Bioactive Principles with an Airless Spray-Gun Suitable for Processing High Viscous Solutions

    PubMed Central

    Cocchietto, Moreno; Blasi, Paolo; Lapasin, Romano; Moro, Chiara; Gallo, Davide; Sava, Gianni

    2013-01-01

    Purpose: to design, assemble and test a prototype of a novel production plant, suitable for producing microparticles (MPs) by processing highly viscous feed solutions (FSs). Methods: the prototype has been built using a commercial air compressor, a piston pump, an airless spray-gun, a customized air-treatment section, a timer, a rotating base, and a filtration section. Preliminary prototype parameter setting was carried out to individuate the best performing nozzle’s dimension, the nebulization timing, and the CaCl2 concentration in the gelation fluid. In addition, prototype throughput (1 L to 5 L) and the range of practicable feed solution (FS) viscosities were assayed. A set of four batches was prepared in order to characterize the MPs, in terms of mean particle size and distribution, flow properties, swelling, encapsulation efficiency and release. Results: according to a qualitative scoring, the large nozzle was suitable to nebulize FSs at a higher alginate concentration. Conversely, the small nozzle performed better in the processing of FSs with an alginate concentration up to 2% w/v. Only at the highest degree of viscosity, corresponding to 5% w/v of alginate, the FS processing was not technically possible. Among the CaCl2 concentrations considered, 15% w/v was recognized as the most versatile. The prototype appears to be convenient and suitable to grant a high yield starting from 2 L of FS. The flow behavior of the FSs assayed can be satisfactorily described with the Carreau-Yasuda equation and the throughput begins to slightly decrease for FSs at alginate concentrations exceeding 3% w/v. MP morphology was irregular with crumpled shape. The angle of repose indicates a good flowability and the release studies showed gastro-resistance and potential prolonged release applications. Conclusions: the novel prototype of production plant is suitable to process large amounts (2 L or more) of FSs, characterized by a high viscosity, to produce MPs suitable for

  8. Material degradation due to moisture and temperature. Part 1: mathematical model, analysis, and analytical solutions

    NASA Astrophysics Data System (ADS)

    Xu, C.; Mudunuru, M. K.; Nakshatrala, K. B.

    2016-06-01

    The mechanical response, serviceability, and load-bearing capacity of materials and structural components can be adversely affected due to external stimuli, which include exposure to a corrosive chemical species, high temperatures, temperature fluctuations (i.e., freezing-thawing), cyclic mechanical loading, just to name a few. It is, therefore, of paramount importance in several branches of engineering—ranging from aerospace engineering, civil engineering to biomedical engineering—to have a fundamental understanding of degradation of materials, as the materials in these applications are often subjected to adverse environments. As a result of recent advancements in material science, new materials such as fiber-reinforced polymers and multi-functional materials that exhibit high ductility have been developed and widely used, for example, as infrastructural materials or in medical devices (e.g., stents). The traditional small-strain approaches of modeling these materials will not be adequate. In this paper, we study degradation of materials due to an exposure to chemical species and temperature under large strain and large deformations. In the first part of our research work, we present a consistent mathematical model with firm thermodynamic underpinning. We then obtain semi-analytical solutions of several canonical problems to illustrate the nature of the quasi-static and unsteady behaviors of degrading hyperelastic solids.

  9. Material degradation due to moisture and temperature. Part 1: mathematical model, analysis, and analytical solutions

    NASA Astrophysics Data System (ADS)

    Xu, C.; Mudunuru, M. K.; Nakshatrala, K. B.

    2016-11-01

    The mechanical response, serviceability, and load-bearing capacity of materials and structural components can be adversely affected due to external stimuli, which include exposure to a corrosive chemical species, high temperatures, temperature fluctuations (i.e., freezing-thawing), cyclic mechanical loading, just to name a few. It is, therefore, of paramount importance in several branches of engineering—ranging from aerospace engineering, civil engineering to biomedical engineering—to have a fundamental understanding of degradation of materials, as the materials in these applications are often subjected to adverse environments. As a result of recent advancements in material science, new materials such as fiber-reinforced polymers and multi-functional materials that exhibit high ductility have been developed and widely used, for example, as infrastructural materials or in medical devices (e.g., stents). The traditional small-strain approaches of modeling these materials will not be adequate. In this paper, we study degradation of materials due to an exposure to chemical species and temperature under large strain and large deformations. In the first part of our research work, we present a consistent mathematical model with firm thermodynamic underpinning. We then obtain semi-analytical solutions of several canonical problems to illustrate the nature of the quasi-static and unsteady behaviors of degrading hyperelastic solids.

  10. X-ray cone-beam computed tomography: principles, applications, challenges and solutions

    NASA Astrophysics Data System (ADS)

    Noo, Frederic

    2010-03-01

    In the nineties, x-ray computed tomography, commonly referred to as CT, seemed to be on the track to become old technology, bound to be replaced by more sophisticated techniques such as magnetic resonance imaging, due in particular to the harmful effects of x-ray radiation exposure. Yet, the new century brought with it new technology that allowed a complete change in trends and re-affirmed CT as an essential tool in radiology. For instance, the popularity of CT in 2007 was such that approximately 68.7 million CT examinations were performed in the United States, which was nearly 2.5 times the number of magnetic resonance (MRI) examinations. More than that, CT has expanded beyond its conventional diagnostic role; CT is now used routinely in interventional radiology and also in radiation therapy treatment. The technology advances that allowed the revival of CT are those that made fast, accurate cone-beam data acquisition possible. Nowadays, cone-beam data acquisition allows scanning large volumes with isotropic sub-millimeter spatial resolution in a very fast time, which can be as short as 500ms for cardiac imaging. The principles of cone-beam imaging will be first reviewed. Then a discussion of its applications will be given. Old and new challenges will be presented along the way with current solutions.

  11. First-Principles Design of Hydrogen Dissociation Catalysts Based on Isoelectronic Metal Solid Solutions.

    PubMed

    Seo, Dong-Hwa; Shin, Hyeyoung; Kang, Kisuk; Kim, Hyungjun; Han, Sang Soo

    2014-06-01

    We report an innovative route for designing novel functional alloys based on first-principles calculations, which is an isoelectronic solid solution (ISS) of two metal elements to create new characteristics that are not native to the constituent elements. Neither Rh nor Ag exhibits hydrogen storage properties, whereas the Rh50Ag50 ISS exhibits properties similar to Pd; furthermore, Au cannot dissociate H2, and Ir has a higher energy barrier for the H2 dissociation reaction than Pt, whereas the Ir50Au50 ISS can dissociate H2 in a similar way to Pt. In the periodic table, Pd is located between Rh and Ag, and Pt is located between Ir and Au, leading to similar atomic and electronic structures between the pure metals (Pd and Pt) and the ISS alloys (Rh50Ag50 and Ir50Au50). From a practical perspective, the Ir-Au ISS would be more cost-effective to use than pure Pt, and could exhibit catalytic activity equivalent to Pt. Therefore, the Ir50Au50 ISS alloy can be a potential catalyst candidate for the replacement of Pt. PMID:26273859

  12. DSMC method consistent with the Pauli exclusion principle and comparison with deterministic solutions for charge transport in graphene

    NASA Astrophysics Data System (ADS)

    Romano, Vittorio; Majorana, Armando; Coco, Marco

    2015-12-01

    A new algorithm for Monte Carlo simulations of charge transport in semiconductors is devised in order to properly deal with Pauli's exclusion principle in the degenerate case. Applications are presented in the case of monolayer graphene and comparisons with solutions of the Boltzmann equation obtained by using a discontinuous Galerkin method furnish a cross-validation of the proposed approach.

  13. The Problem Is the Solution: Creating Original Problems in Gifted Mathematics Classes

    ERIC Educational Resources Information Center

    Matsko, Vince; Thomas, Jerald

    2014-01-01

    The purpose of this exploratory study was to assess the effect of a novel approach to mathematics instruction on gifted high school students' engagement, motivation, and metacognition. Participants in this study included gifted students who were enrolled in a 3-year, residential, specialized mathematics and science high school. Rather than…

  14. First Year Pre-Service Teachers' Mathematical Content Knowledge: Methods of Solution for a Ratio Question

    ERIC Educational Resources Information Center

    Livy, Sharyn; Vale, Colleen

    2011-01-01

    In this article, pre-service teachers' mathematics content knowledge is explored through the analysis of two items about ratio from a Mathematical Competency, Skills and Knowledge Test. Pre-service teachers' thinking strategies, common errors and misconceptions in their responses are presented and discussed. Of particular interest was the range…

  15. First-principles study on stability of transition metal solutes in aluminum by analyzing the underlying forces

    SciTech Connect

    Liu, Wei; Xu, Yichun; Li, Xiangyan; Wu, Xuebang Liu, C. S.; Liang, Yunfeng; Wang, Zhiguang

    2015-05-07

    Although there have been some investigations on behaviors of solutes in metals under strain, the underlying mechanism of how strain changes the stability of a solute is still unknown. To gain such knowledge, first-principles calculations are performed on substitution energy of transition metal solutes in fcc Al host under rhombohedral strain (RS). Our results show that under RS, substitution energy decreases linearly with the increase of outermost d radius r{sub d} of the solute due to Pauli repulsion. The screened Coulomb interaction increases or decreases the substitution energy of a solute on condition that its Pauling electronegativity scale ϕ{sub P} is less or greater than that of Al under RS. This paper verifies a linear relation of substitution energy change versus r{sub d} and ϕ{sub P} under RS, which might be instructive for composition design of long life alloys serving in high stress condition.

  16. Maximum principle solutions for time-optimal half-loop maneuvers of a high alpha fighter aircraft

    NASA Technical Reports Server (NTRS)

    Stalford, Harold; Hoffman, Eric

    1989-01-01

    An investigation was conducted of maximum principle solutions for an initial 0.6 Mach number and 15,000-ft altitude. The authors generate these solutions for a family of prescribed final times tf, starting with tf = 0.5 s. Using a nonlinear wind-tunnel model they construct maximum principle solutions. Above tf = 1.2 s some small nonlinear variations in the aerodynamic pitching moment coefficient presented difficulty with respect to numerical convergence. This was circumvented by fitting analytical models to the aerodynamic coefficients of the wind-tunnel model at Mach 0.4. Maximum principle solutions of the analytical model are shown to compare well with those obtained for tf of less than 1.2 s. Using the analytical model the authors extended the prescribed final time to a value of 13.65 s at which time the aircraft completes the half-loop maneuver. This is 0.53 s longer than that obtained using the singular perturbation feedback control law.

  17. Thermodynamic properties of CexTh1-xO2 solid solution from first-principles calculations

    SciTech Connect

    Xiao, Haiyan Y.; Zhang, Yanwen; Weber, William J.

    2012-11-02

    A systematic study based on first-principles calculations along with a quasi-harmonic approximation has been conducted to calculate the thermodynamic properties of the CexTh1xO2 solid solution. The predicted density, thermal expansion coefficients, heat capacity and thermal conductivity for the CexTh1xO2 solid solution all agree well with the available experimental data. The thermal expansion coefficient for ThO2 increases with CeO2 substitution, and complete substitution shows the highest expansion coefficient. On the other hand, the mixed CexTh1xO2 (0 < x < 1) solid solution generally exhibits lower heat capacity and thermal conductivity than the ThO2 and CeO2 end members. Our calculations indicate a strong effect of Ce concentration on the thermodynamic properties of the CexTh1xO2 solid solution.

  18. Thermodynamic properties of CexTh1-xO2 solid solution from first-principles calculations

    SciTech Connect

    Xiao, Haiyan; Zhang, Yanwen; Weber, William J

    2013-01-01

    A systematic study based on first-principles calculations along with the quasi-harmonic approximation has been conducted to calculate the thermodynamic properties of the CexTh1-xO2 solid solution. The predicted density, thermal expansion coefficients, heat capacity and thermal conductivity for the CexTh1-xO2 solid solution all agree well with available experimental data. The thermal expansion coefficient for ThO2 increases with CeO2 substitution, and complete substitution shows the highest expansion coefficient. On the other hand, the mixed CexTh1-xO2 (0solution generally exhibits lower heat capacity and thermal conductivity than the ThO2 and CeO2 end members. Our calculations indicate a strong effect of Ce concentration on the thermodynamic properties of the CexTh1-xO2 solid solution.

  19. First-Year Urban Mathematics and Science Middle School Teachers: Classroom Challenges and Reflective Solutions

    ERIC Educational Resources Information Center

    Kelly, Angela M.; Gningue, Serigne M.; Qian, Gaoyin

    2015-01-01

    This study explored the challenges facing 1st-year alternatively certified teachers of mathematics and science in urban middle schools. Four teachers, participants in a National Science Foundation (NSF)-funded Robert Noyce Scholarship Program, were followed from preservice training through their 1st year of teaching, having taken part in…

  20. Equity in the Reform of Mathematics and Science Education: A Look at Issues and Solutions.

    ERIC Educational Resources Information Center

    Powell, Mary Jo; Boethel, Martha, Ed.

    The current push for reform in mathematics and science education cannot succeed unless it addresses the critical and persistent issue of equity. This report reviews the literature regarding that issue. Its purpose is to provide a reference tool for those who are working to change educational policy and practice. Part 1 of the review discusses the…

  1. Determination of minimum enzymatic decolorization time of reactive dye solution by spectroscopic & mathematical approach.

    PubMed

    Celebi, Mithat; Ozdemir, Zafer Omer; Eroglu, Emre; Altikatoglu, Melda; Guney, Ibrahim

    2015-02-01

    Synthetic dyes are very important for textile dyeing, paper printing, color photography and petroleum products. Traditional methods of dye removal include biodegradation, precipitation, adsorption, chemical degradation, photo degradation, and chemical coagulation. Dye decolorization with enzymatic reaction is an important issue for several research field (chemistry, environment) In this study, minimum decolorization time of Remazol Brilliant Blue R dye with Horseradish peroxidase enzyme was calculated using with mathematical equation depending on experimental data. Dye decolorization was determined by monitoring the absorbance decrease at the specific maximum wavelength for dye. All experiments were carried out with different initial dye concentrations of Remazol Brilliant Blue R at 25 degrees C constant temperature for 30 minutes. The development of the least squares estimators for a nonlinear model brings about complications not encountered in the case of the linear model. Decolorization times for completely removal of dye were calculated according to equation. It was shown that mathematical equation was conformed exponential curve for dye degradation.

  2. Study and numerical solution of a generalized mathematical model of isothermal adsorption

    SciTech Connect

    Komissarov, Yu.A.; Vetokhin, V.N.; Tsenev, V.A.; Gordeeva, E.L.

    1995-06-01

    A generalized mathematical model of isothermal adsorption that takes into account mass transfer on the surface of a particle, diffusion in micro- and macropores, and dispersion along the length of the apparatus is considered The parameters {lambda} and {var_phi}{sup 2} determine the dominating effect of any of the mass transfer mechanisms of the adsorption process. A numerical algorithm for solving the generalized adsorption model is suggested.

  3. A first principle particle mesh method for solution SAXS of large bio-molecular systems.

    PubMed

    Marchi, Massimo

    2016-07-28

    This paper will show that the solution small angle X-ray scattering (SAXS) intensity of globular and membrane proteins can be efficiently and accurately computed from molecular dynamics trajectories using 3D fast Fourier transforms (FFTs). A suitable particle meshing interpolation, similar to the one used in smooth particle mesh Ewald for electrostatic energies and forces, was combined with a uniform solvent density FFT padding scheme to obtain a convenient SAXS spectral resolution. The CPU time scaling of the method, as a function of system size, is highly favorable and its application to large systems such as solutions of solvated membrane proteins is computationally undemanding. Differently from other approaches, all contributions from the simulation cell are included. This means that the subtraction of the buffer from the solution scattering intensity is straightforward and devoid of artifact due to ad hoc definitions of proximal and distal solvent intensity contributions. PMID:27475396

  4. A first principle particle mesh method for solution SAXS of large bio-molecular systems

    NASA Astrophysics Data System (ADS)

    Marchi, Massimo

    2016-07-01

    This paper will show that the solution small angle X-ray scattering (SAXS) intensity of globular and membrane proteins can be efficiently and accurately computed from molecular dynamics trajectories using 3D fast Fourier transforms (FFTs). A suitable particle meshing interpolation, similar to the one used in smooth particle mesh Ewald for electrostatic energies and forces, was combined with a uniform solvent density FFT padding scheme to obtain a convenient SAXS spectral resolution. The CPU time scaling of the method, as a function of system size, is highly favorable and its application to large systems such as solutions of solvated membrane proteins is computationally undemanding. Differently from other approaches, all contributions from the simulation cell are included. This means that the subtraction of the buffer from the solution scattering intensity is straightforward and devoid of artifact due to ad hoc definitions of proximal and distal solvent intensity contributions.

  5. First-principles study of interactions between substitutional solutes in bcc iron

    NASA Astrophysics Data System (ADS)

    Gorbatov, O. I.; Delandar, A. Hosseinzadeh; Gornostyrev, Yu N.; Ruban, A. V.; Korzhavyi, P. A.

    2016-07-01

    Using density functional theory based calculations, employing the locally self-consistent Green's function method and the projected augmented wave method, we develop a database of solute-solute interactions in dilute alloys of bcc Fe. Interactions within the first three coordination shells are computed for the ferromagnetic state as well as for the paramagnetic (disordered local moment) state of the iron matrix. The contribution of lattice relaxations to the defect interaction energy is investigated in the ferromagnetic state. Implications of the obtained results for modeling the phenomena of point defect clustering and phase precipitation in bcc Fe-based alloys and steel are discussed.

  6. Fostering Solutions: Bringing Brief-Therapy Principles and Practices to the Child Welfare System

    ERIC Educational Resources Information Center

    Flemons, Douglas; Liscio, Michele; Gordon, Arlene Brett; Hibel, James; Gutierrez-Hersh, Annette; Rebholz, Cynthia L.

    2010-01-01

    This article describes a 15-month university-community collaboration that was designed to fast-track children out of foster care. The developers of the project initiated resource-oriented "systems facilitations," allowing wraparound professionals and families to come together in large meetings to solve problems and find solutions. Families also…

  7. Some notes on the numerical solution of shear-lag and mathematically related problems

    NASA Technical Reports Server (NTRS)

    Kuhn, Paul

    1939-01-01

    The analysis of box beams with shear deformation of the flanges can be reduced to the solution of a differential equation. The same equation is met in other problems of stress analysis. No analytical solutions of this equation can be given for practical cases, and numerical methods of evaluation must be used. Available methods are briefly discussed. Two numerical examples show the application of the step-by-step method of integration to shear-lag problems.

  8. New Solutions of Three Nonlinear Space- and Time-Fractional Partial Differential Equations in Mathematical Physics

    NASA Astrophysics Data System (ADS)

    Yao, Ruo-Xia; Wang, Wei; Chen, Ting-Hua

    2014-11-01

    Motivated by the widely used ansätz method and starting from the modified Riemann—Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper.

  9. Mathematical analysis of steady-state solutions in compartment and continuum models of cell polarization.

    PubMed

    Zheng, Zhenzhen; Chou, Ching-Shan; Yi, Tau-Mu; Nie, Qing

    2011-10-01

    Cell polarization, in which substances previously uniformly distributed become asymmetric due to external or/and internal stimulation, is a fundamental process underlying cell mobility, cell division, and other polarized functions. The yeast cell S. cerevisiae has been a model system to study cell polarization. During mating, yeast cells sense shallow external spatial gradients and respond by creating steeper internal gradients of protein aligned with the external cue. The complex spatial dynamics during yeast mating polarization consists of positive feedback, degradation, global negative feedback control, and cooperative effects in protein synthesis. Understanding such complex regulations and interactions is critical to studying many important characteristics in cell polarization including signal amplification, tracking dynamic signals, and potential trade-off between achieving both objectives in a robust fashion. In this paper, we study some of these questions by analyzing several models with different spatial complexity: two compartments, three compartments, and continuum in space. The step-wise approach allows detailed characterization of properties of the steady state of the system, providing more insights for biological regulations during cell polarization. For cases without membrane diffusion, our study reveals that increasing the number of spatial compartments results in an increase in the number of steady-state solutions, in particular, the number of stable steady-state solutions, with the continuum models possessing infinitely many steady-state solutions. Through both analysis and simulations, we find that stronger positive feedback, reduced diffusion, and a shallower ligand gradient all result in more steady-state solutions, although most of these are not optimally aligned with the gradient. We explore in the different settings the relationship between the number of steady-state solutions and the extent and accuracy of the polarization. Taken together

  10. Phase Stability for the Pd-Si System: First-Principles, Experiments, and Solution-Based Modeling

    NASA Astrophysics Data System (ADS)

    Zhou, S. H.; Huo, Y.; Napolitano, Ralph E.

    2016-01-01

    The relative stabilities of the compounds in the binary Pd-Si system were assessed using first-principles calculations and experimental methods. Calculations of lattice parameters and enthalpy of formation indicate that Pd5Si-{μ }, Pd9Si_2-{α }, Pd_3Si-{β }, Pd_2Si-{γ }, and PdSi-{δ } are the stable phases at 0 K (-273 °C). X-ray diffraction analyses (XRD) and electron probe microanalysis (EPMA) of the as-solidified and heat-treated samples support the computational findings, except that the PdSi-{δ } phase was not observed at low temperature. Considering both experimental data and first-principles results, the compounds Pd5Si-{μ }, Pd9Si2-{α }, Pd3Si-{β }, and Pd_2Si-{γ } are treated as stable phases down to 0 K (-273 °C), while the PdSi-{δ } is treated as being stable over a limited range, exhibiting a lower bound. Using these findings, a comprehensive solution-based thermodynamic model is formulated for the Pd-Si system, permitting phase diagram calculation. The liquid phase is described using a three-species association model and other phases are treated as solid solutions, where a random substitutional model is adopted for Pd-fcc and Si-dia, and a two-sublattice model is employed for Pd5Si-{μ }, Pd9Si_2-{α }, Pd_3Si-{β }, Pd_2Si-{γ }, and PdSi-{δ }. Model parameters are fitted using available experimental data and first-principles data, and the resulting phase diagram is reported over the full range of compositions.

  11. Phase Stability for the Pd-Si System. First-Principles, Experiments, and Solution-Based Modeling

    DOE PAGES

    Zhou, S. H.; Huo, Y.; Napolitano, Ralph E.

    2015-11-05

    Relative stabilities of the compounds in the binary Pd-Si system were assessed using first-principles calculations and experimental methods. Calculations of lattice parameters and enthalpy of formation indicate that Pd5Si-μ, Pd9Si2-α, Pd3 Si-β, Pd2 Si-γ, and PdSi-δ are the stable phases at 0 K (-273 °C). X-ray diffraction analyses (XRD) and electron probe microanalysis (EPMA) of the as-solidified and heat-treated samples support the computational findings, except that the PdSi-δ phase was not observed at low temperature. Considering both experimental data and first-principles results, the compounds Pd 5 Si-μ, Pd9 Si2-α, Pd3Si-β, and Pd2Si-γ are treated as stable phases down to 0more » K (-273 °C), while the PdSi-δ is treated as being stable over a limited range, exhibiting a lower bound. Using these findings, a comprehensive solution-based thermodynamic model is formulated for the Pd-Si system, permitting phase diagram calculation. Moreover, the liquid phase is described using a three-species association model and other phases are treated as solid solutions, where a random substitutional model is adopted for Pd-fcc and Si-dia, and a two-sublattice model is employed for Pd5Si-μ, Pd9Si2-α, Pd3Si-β, Pd2Si-γ, and PdSi-δ. Model parameters are fitted using available experimental data and first-principles data, and the resulting phase diagram is reported over the full range of compositions.« less

  12. A mathematical model for the transport of a solute through a porous-walled tube

    NASA Astrophysics Data System (ADS)

    Griffiths, Ian; Shipley, Rebecca

    2012-02-01

    Predicting the distribution of solutes or particles in flows within porous-walled tubes is essential to inform the design of cross-flow filtration devices. Here we use Taylor-dispersion theory to derive a radially averaged model for solute transport in a tube with porous walls, where the wall Darcy permeability may vary both spatially and in time. Crucially, this model includes solute advection via both radial and axial flow components, as well as diffusion, and the advection, diffusion and uptake coefficients in the averaged equation are explicitly derived. The model is used to explore the specific example of a hollow-fibre membrane bioreactor for tissue engineering applications - here membrane fouling and cell population expansion mean that the effective membrane permeability is intrinsically coupled to both fluid flow and nutrient transport. We conclude by presenting design considerations that promote spatially uniform cell population growth.

  13. Experimental validation of new mathematical solutions for orthotropic plates with clamped edges

    NASA Astrophysics Data System (ADS)

    Sprinťu, Iuliana; Roateşi, Simona

    2013-10-01

    This paper deals with analytical solutions for the bending deformation of rectangular orthotropic elastic composite plates with various boundary conditions. The models are based on the classical laminated plate theory (CLPT). The Ritz method, in conjunction with the weighted residue method for the coefficients calculation is used to analytically determine the bending solutions of orthotropic laminated plates subjected to uniform pressure on the bottom laminate, having clamped edges or possessing two opposite edges simply supported and the remaining two edges clamped, respectively. Numerical examples of laminated plates considering similar boundary value problems as treated analytically are presented. It is presented the experimental device and the experimental test results, as well. Thorough comparison between analytical solutions, numerical results and experimental data is performed and a good agreement is obtained.

  14. ASYMPTOTICS AS t\\to\\infty OF SOLUTIONS OF A PROBLEM OF MATHEMATICAL PHYSICS

    NASA Astrophysics Data System (ADS)

    Skazka, V. V.

    1986-02-01

    Solutions are considered of the mixed problem of S. L. Sobolev \\displaystyle \\frac{\\partial^2}{\\partial t^2}\\bigg(\\frac{\\partial^2u}{\\partial ......partial x_2^2}=0\\textrm{\\quad in\\quad }\\Omega,\\u\\vert _{\\partial\\Omega}=0, u\\vert _{t=0}=u_0, u_t\\vert _{t=0}=u_1, where \\Omega is the complement of a simply connected, compact, convex set in R^2. Asymptotic representations are given for a solution of this problem as t\\to\\infty. A boundary-layer phenomenon is discovered in a neighborhood of \\partial\\Omega.Bibliography: 15 titles.

  15. Mathematical apparatus for boundary value problems in gravity field studies and the geometry of the solution domain

    NASA Astrophysics Data System (ADS)

    Holota, Petr; Nesvadba, Otakar

    2014-05-01

    In geodesy mathematical techniques for gravity field studies that rest on the concept of the so-called classical solution of boundary value problems, have a rather traditional position. Nevertheless, the range of the tools for treating problems in this field is much wider. For instance the concept of the weak solution met with a considerable attention. From this point of view the approach is associated with constructing the respective integral kernels or Green's function in case we consider the classical solution concept or with the choice and constructing basis functions in case we are lucking for the weak solution of the problem. Within the tools considered we discuss also the use of reproducing kernels. In both the cases (classical or weak) the construction of the apparatus above represents and important technical step. It is not elementary, but for a number of fundamental boundary value problems the solution is known, in particular in the case of a spherical solution domain. The sphere, however, is rather far from the real shape of the Earth, which is interpreted here in terms of a functional analytic norm. The distance has a negative effect on any attempt to reach the solution of the boundary value problems considered (and to bridge the departure of the Earth's surface from the sphere) by an iteration procedure based on a successive application of a solution technique developed for the spherical boundary. From this point of view the construction of the integral kernels and basis functions for an oblate ellipsoid of revolution means a step closer towards reality. In this contribution we on the one hand give an overview of the results already achieved and subsequently develop the topic. The summation of series of ellipsoidal harmonics is one of the key problems in this connection. Hypergeometric functions and series are applied too. We also show where the use of Legendre elliptic integrals adds to the solution of the problem. It is interesting that they do not

  16. Computing the inhomogeneous broadening of electronic transitions in solution: a first-principle quantum mechanical approach.

    PubMed

    Avila Ferrer, Francisco José; Improta, Roberto; Santoro, Fabrizio; Barone, Vincenzo

    2011-10-14

    Starting from Marcus's relationship connecting the inhomogeneous broadening with the solvent reorganization energy and exploiting recent state-specific developments in PCM/TD-DFT calculations, we propose a procedure to estimate the polar broadening of optical transitions. When applied to two representative molecular probes, coumarin C153 and 4-aminophthalimide, in different solvents, our approach provides for the polar broadening values fully consistent with the experimental ones. Thanks to these achievements, for the first time fully ab initio vibrationally resolved absorption spectra in solution are computed, obtaining spectra for coumarin C153 in remarkable agreement with experiments.

  17. Variational principles and optimal solutions of the inverse problems of creep bending of plates

    NASA Astrophysics Data System (ADS)

    Bormotin, K. S.; Oleinikov, A. I.

    2012-09-01

    It is shown that inverse problems of steady-state creep bending of plates in both the geometrically linear and nonlinear formulations can be represented in a variational formulation. Steady-state values of the obtained functionals corresponding to the solutions of the problems of inelastic deformation and elastic unloading are determined by applying a finite element procedure to the functionals. Optimal laws of creep deformation are formulated using the criterion of minimizing damage in the functionals of the inverse problems. The formulated problems are reduced to the problems solved by the finite element method using MSC.Marc software.

  18. What to Trust: Reconciling Mathematical Work Done by Hand with Conflicting Graphing Calculator Solutions

    ERIC Educational Resources Information Center

    McCulloch, Allison W.; Kenney, Rachael H.; Keene, Karen Allen

    2013-01-01

    This paper reports on a mixed-methods study of 111 Advanced Placement calculus students' self-reports of their graphing calculator use, comfort, and rationale for trusting a solution produced with or without a graphing calculator when checking written work. It was found that there was no association between gender, teacher-reported…

  19. First principles calculation of the effects of solute atom on electromigration resistance of Al interconnects

    NASA Astrophysics Data System (ADS)

    Yu, Chun; Jijin, Xu; Yang, Yang; Lu, Hao

    2009-06-01

    Electromigration (EM) resistance of Al could be improved through the addition of a small amount of alloying elements, such as copper and magnesium. In this paper, an Al31X (X = Sc-Zn and Mg) supercell model was constructed to calculate the effects of a solute element on the properties of face central cubic Al, including the heat of formation, diffusion energy and electronic structure, etc, by employing the density functional theory. It is found that the diffusion energy of Al near Ti, V, Cr, Cu, Zn and Mg solutes could be enhanced. Likewise, the value of the density of states of the system at the Fermi level (N(EF)), as well as that of the Al atoms at the specific sites, could also be reduced slightly by the addition of Sc, Ni, Cu, Zn and Mg. These two results indicate that the nearest neighbour Al atoms could be stabilized by Cu, Zn and Mg. Thus they would be beneficial in prolonging the EM lifetime of Al interconnects. Our calculations are in good agreement with the previous calculations and the experimental phenomenon to some extent.

  20. An evaluation of mathematical models of the transport of biologically reacting solutes in saturated soils and aquifers

    NASA Astrophysics Data System (ADS)

    Baveye, Philippe; Valocchi, Albert

    1989-06-01

    Three different conceptual frameworks have been adopted in the past for the development of mathematical models of bacterial growth and biologically reacting solute transport in saturated porous media. Two schools of thought are based upon assuming that the pore scale geometrical configuration of the attached bacteria consists of biofilms or microcolonies; the third school of thought represents the traditional approach where pore scale processes are neglected and the bacteria are assumed to respond to the macroscopic bulk fluid substrate concentration. On the basis of a schematic block diagram representation of a saturated porous medium hosting a microbial population, it is shown that these frameworks share a common theoretical foundation, and that they differ only by the choice of particular constitutive equations for several transfer parameters. Using one possible option in this respect, we derive a mathematical model that involves no unwarranted assumption about the distribution of the microorganisms in the pore space. The governing equations of this latter model are shown to be formally identical to those obtained by F.J. Molz et al. (1986), using the concept of microcolony, and to those that would result from adopting a simple form of biofilm model to describe bacterial growth in the pore space. Some of the consequences of this formal similarity between macroscopic transport equations obtained in different conceptual frameworks are discussed from an operational standpoint and in terms of model validation.

  1. A mathematical model for the transfer of soil solutes to runoff under water scouring.

    PubMed

    Yang, Ting; Wang, Quanjiu; Wu, Laosheng; Zhang, Pengyu; Zhao, Guangxu; Liu, Yanli

    2016-11-01

    The transfer of nutrients from soil to runoff often causes unexpected pollution in water bodies. In this study, a mathematical model that relates to the detachment of soil particles by water flow and the degree of mixing between overland flow and soil nutrients was proposed. The model assumes that the mixing depth is an integral of average water flow depth, and it was evaluated by experiments with three water inflow rates to bare soil surfaces and to surfaces with eight treatments of different stone coverages. The model predicted outflow rates were compared with the experimentally observed data to test the accuracy of the infiltration parameters obtained by curve fitting the models to the data. Further analysis showed that the comprehensive mixing coefficient (ke) was linearly correlated with Reynolds' number Re (R(2)>0.9), and this relationship was verified by comparing the simulated potassium concentration and cumulative mass with observed data, respectively. The best performance with the bias error analysis (Nash Sutcliffe coefficient of efficiency (NS), relative error (RE) and the coefficient of determination (R(2))) showed that the predicted data by the proposed model was in good agreement with the measured data. Thus the model can be used to guide soil-water and fertilization management to minimize nutrient runoff from cropland. PMID:27344122

  2. Solution-based thermodynamic modeling of the Ni-Al-Mo system using first-principles calculations

    SciTech Connect

    Zhou, S H; Wang, Y; Chen, L -Q; Liu, Z -K; Napolitano, R E

    2014-09-01

    A solution-based thermodynamic description of the ternary Ni–Al–Mo system is developed here, incorporating first-principles calculations and reported modeling of the binary Ni–Al, Ni–Mo and Al–Mo systems. To search for the configurations with the lowest energies of the N phase, the Alloy Theoretic Automated Toolkit (ATAT) was employed and combined with VASP. The liquid, bcc and γ-fcc phases are modeled as random atomic solutions, and the γ'-Ni3Al phase is modeled by describing the ordering within the fcc structure using two sublattices, summarized as (Al,Mo,Ni)0.75(Al,Mo,Ni)0.25. Thus, γ-fcc and γ'-Ni3Al are modeled with a single Gibbs free energy function with appropriate treatment of the chemical ordering contribution. In addition, notable improvements are the following: first, the ternary effects of Mo and Al in the B2-NiAl and D0a-Ni3Mo phases, respectively, are considered; second, the N-NiAl8Mo3 phase is described as a solid solution using a three-sublattice model; third, the X-Ni14Al75Mo11 phase is treated as a stoichiometric compound. Model parameters are evaluated using first-principles calculations of zero-Kelvin formation enthalpies and reported experimental data. In comparison with the enthalpies of formation for the compounds ψ-AlMo, θ-Al8Mo3 and B2-NiAl, the first-principles results indicate that the N-NiAl8Mo3 phase, which is stable at high temperatures, decomposes into other phases at low temperature. Resulting phase equilibria are summarized in the form of isothermal sections and liquidus projections. To clearly identify the relationship between the γ-fcc and γ'-Ni3Al phases in the ternary Ni–Al–Mo system, the specific γ-fcc and γ'-Ni3Al phase fields are plotted in x(Al)–x(Mo)–T space for a temperature range 1200–1800 K.

  3. Fostering solutions: bringing brief-therapy principles and practices to the child welfare system.

    PubMed

    Flemons, Douglas; Liscio, Michele; Gordon, Arlene Brett; Hibel, James; Gutierrez-Hersh, Annette; Rebholz, Cynthia L

    2010-01-01

    This article describes a 15-month university-community collaboration that was designed to fast-track children out of foster care. The developers of the project initiated resource-oriented "systems facilitations," allowing wraparound professionals and families to come together in large meetings to solve problems and find solutions. Families also participated in strength-based brief-therapy sessions. The authors describe the history, structure, and process of the project, and they provide a case study to illustrate the approach and exemplify the kinds of changes that occurred throughout the system. In the final section of the article, the authors reflect on what they learned about their university-community partnership, what they would do differently the next time, and the implications of such larger-system involvements for American Association for Marriage and Family Therapy's Core Competencies.

  4. First-principles study of band gap engineering via oxygen vacancy doping in perovskite ABB'O₃ solid solutions

    DOE PAGES

    Qi, Tingting; Curnan, Matthew T.; Kim, Seungchul; Bennett, Joseph W.; Grinberg, Ilya; Rappe, Andrew M.

    2011-12-15

    Oxygen vacancies in perovskite oxide solid solutions are fundamentally interesting and technologically important. However, experimental characterization of the vacancy locations and their impact on electronic structure is challenging. We have carried out first-principles calculations on two Zr-modified solid solutions, Pb(Zn1/3Nb2/3)O₃ and Pb(Mg1/3Nb2/3)O₃, in which vacancies are present. We find that the vacancies are more likely to reside between low-valent cation-cation pairs than high-valent cation-cation pairs. Based on the analysis of our results, we formulate guidelines that can be used to predict the location of oxygen vacancies in perovskite solid solutions. Our results show that vacancies can have a significant impactmore » on both the conduction and valence band energies, in some cases lowering the band gap by ≈0.5 eV. The effects of vacancies on the electronic band structure can be understood within the framework of crystal field theory.« less

  5. First-principles study of band gap engineering via oxygen vacancy doping in perovskite ABB'O₃ solid solutions

    SciTech Connect

    Qi, Tingting; Curnan, Matthew T.; Kim, Seungchul; Bennett, Joseph W.; Grinberg, Ilya; Rappe, Andrew M.

    2011-12-15

    Oxygen vacancies in perovskite oxide solid solutions are fundamentally interesting and technologically important. However, experimental characterization of the vacancy locations and their impact on electronic structure is challenging. We have carried out first-principles calculations on two Zr-modified solid solutions, Pb(Zn1/3Nb2/3)O₃ and Pb(Mg1/3Nb2/3)O₃, in which vacancies are present. We find that the vacancies are more likely to reside between low-valent cation-cation pairs than high-valent cation-cation pairs. Based on the analysis of our results, we formulate guidelines that can be used to predict the location of oxygen vacancies in perovskite solid solutions. Our results show that vacancies can have a significant impact on both the conduction and valence band energies, in some cases lowering the band gap by ≈0.5 eV. The effects of vacancies on the electronic band structure can be understood within the framework of crystal field theory.

  6. Thermoelectric coefficients of n -doped silicon from first principles via the solution of the Boltzmann transport equation

    NASA Astrophysics Data System (ADS)

    Fiorentini, Mattia; Bonini, Nicola

    2016-08-01

    We present a first-principles computational approach to calculate thermoelectric transport coefficients via the exact solution of the linearized Boltzmann transport equation, also including the effect of nonequilibrium phonon populations induced by a temperature gradient. We use density functional theory and density functional perturbation theory for an accurate description of the electronic and vibrational properties of a system, including electron-phonon interactions; carriers' scattering rates are computed using standard perturbation theory. We exploit Wannier interpolation (both for electronic bands and electron-phonon matrix elements) for an efficient sampling of the Brillouin zone, and the solution of the Boltzmann equation is achieved via a fast and stable conjugate gradient scheme. We discuss the application of this approach to n -doped silicon. In particular, we discuss a number of thermoelectric properties such as the thermal and electrical conductivities of electrons, the Lorenz number and the Seebeck coefficient, including the phonon drag effect, in a range of temperatures and carrier concentrations. This approach gives results in good agreement with experimental data and provides a detailed characterization of the nature and the relative importance of the individual scattering mechanisms. Moreover, the access to the exact solution of the Boltzmann equation for a realistic system provides a direct way to assess the accuracy of different flavors of relaxation time approximation, as well as of models that are popular in the thermoelectric community to estimate transport coefficients.

  7. Identifying glucose thresholds for incident diabetes by physiological analysis: a mathematical solution.

    PubMed

    Ferrannini, Ele; Manca, Maria Laura

    2015-04-01

    Plasma glucose thresholds for diagnosis of type 2 diabetes are currently based on outcome data (risk of retinopathy), an inherently ill-conditioned approach. A radically different approach is to consider the mechanisms that control plasma glucose, rather than its relation to an outcome. We developed a constraint optimization algorithm to find the minimal glucose levels associated with the maximized combination of insulin sensitivity and β-cell function, the two main mechanisms of glucose homeostasis. We used a training cohort of 1,474 subjects (22% prediabetic, 7.7% diabetic) in whom insulin sensitivity was measured by the clamp technique and β-cell function was determined by mathematical modeling of an oral glucose tolerance test. Optimized fasting glucose levels were ≤ 87 and ≤ 89 mg/dl in ≤ 45-yr-old women and men, respectively, and ≤ 92 and ≤ 95 mg/dl in >45-yr-old women and men, respectively; the corresponding optimized 2-h glucose levels were ≤ 96, ≤ 98, ≤ 103, and ≤ 105 mg/dl. These thresholds were validated in three prospective cohorts of nondiabetic subjects (Relationship Between Insulin Sensitivity and Cardiovascular Disease Study, Botnia Study, and Mexico City Diabetes Study) with baseline and follow-up oral glucose tolerance tests. Of 5,593 participants, 452 progressed to diabetes. Similarly, in the three cohorts, subjects with glucose levels above the estimated thresholds had an odds ratio of 3.74 (95% confidence interval = 2.64-5.48) of progressing, substantially higher than the risk carried by baseline conventionally defined prediabetes [odds ratio = 2.32 (95% confidence interval = 1.91-2.81)]. The concept that optimization of glucose concentrations by direct measures of insulin sensitivity and β-cell function identifies gender- and age-specific thresholds that bear on disease progression is proven in a physiologically sound, quantifiable manner.

  8. Identifying glucose thresholds for incident diabetes by physiological analysis: a mathematical solution.

    PubMed

    Ferrannini, Ele; Manca, Maria Laura

    2015-04-01

    Plasma glucose thresholds for diagnosis of type 2 diabetes are currently based on outcome data (risk of retinopathy), an inherently ill-conditioned approach. A radically different approach is to consider the mechanisms that control plasma glucose, rather than its relation to an outcome. We developed a constraint optimization algorithm to find the minimal glucose levels associated with the maximized combination of insulin sensitivity and β-cell function, the two main mechanisms of glucose homeostasis. We used a training cohort of 1,474 subjects (22% prediabetic, 7.7% diabetic) in whom insulin sensitivity was measured by the clamp technique and β-cell function was determined by mathematical modeling of an oral glucose tolerance test. Optimized fasting glucose levels were ≤ 87 and ≤ 89 mg/dl in ≤ 45-yr-old women and men, respectively, and ≤ 92 and ≤ 95 mg/dl in >45-yr-old women and men, respectively; the corresponding optimized 2-h glucose levels were ≤ 96, ≤ 98, ≤ 103, and ≤ 105 mg/dl. These thresholds were validated in three prospective cohorts of nondiabetic subjects (Relationship Between Insulin Sensitivity and Cardiovascular Disease Study, Botnia Study, and Mexico City Diabetes Study) with baseline and follow-up oral glucose tolerance tests. Of 5,593 participants, 452 progressed to diabetes. Similarly, in the three cohorts, subjects with glucose levels above the estimated thresholds had an odds ratio of 3.74 (95% confidence interval = 2.64-5.48) of progressing, substantially higher than the risk carried by baseline conventionally defined prediabetes [odds ratio = 2.32 (95% confidence interval = 1.91-2.81)]. The concept that optimization of glucose concentrations by direct measures of insulin sensitivity and β-cell function identifies gender- and age-specific thresholds that bear on disease progression is proven in a physiologically sound, quantifiable manner. PMID:25552659

  9. Development of A General Principle Solution Forisoagrinet Compliant Networking System Components in Animal Husbandry

    NASA Astrophysics Data System (ADS)

    Kuhlmann, Arne; Herd, Daniel; Röβler, Benjamin; Gallmann, Eva; Jungbluth, Thomas

    In pig production software and electronic systems are widely used for process control and management. Unfortunately most devices on farms are proprietary solutions and autonomically working. To unify data communication of devices in agricultural husbandry, the international standard ISOagriNET (ISO 17532:2007) was developed. It defines data formats and exchange protocols, to link up devices like climate controls, feeding systems and sensors, but also management software. The aim of the research project, "Information and Data Collection in Livestock Systems" is to develop an ISOagriNET compliant IT system, a so called Farming Cell. It integrates all electronic components to acquire the available data and information for pig fattening. That way, an additional benefit to humans, animals and the environment regarding process control and documentation, can be generated. Developing the Farming Cell is very complex; in detail it is very difficult and long-winded to integrate hardware and software by various vendors into an ISOagriNET compliant IT system. This ISOagriNET prototype shows as a test environment the potential of this new standard.

  10. First-principles calculation of pKa for cocaine, nicotine, neurotransmitters, and anilines in aqueous solution.

    PubMed

    Lu, Haiting; Chen, Xi; Zhan, Chang-Guo

    2007-09-01

    The absolute pKa values of 24 representative amine compounds, including cocaine, nicotine, 10 neurotransmitters, and 12 anilines, in aqueous solution were calculated by performing first-principles electronic structure calculations that account for the solvent effects using four different solvation models, i.e., the surface and volume polarization for electrostatic interaction (SVPE) model, the standard polarizable continuum model (PCM), the integral equation formalism for the polarizable continuum model (IEFPCM), and the conductor-like screening solvation model (COSMO). Within the examined computational methods, the calculations using the SVPE model lead to the absolute pKa values with the smallest root-mean-square-deviation (rmsd) value (1.18). When the SVPE model was replaced by the PCM, IEFPCM, and COSMO, the rmsd value of the calculated absolute pKa values became 3.21, 2.72, and 3.08, respectively. All types of calculated pKa values linearly correlate with the experimental pKa values very well. With the empirical corrections using the linear correlation relationships, the theoretical pKa values are much closer to the corresponding experimental data and the rmsd values become 0.51-0.83. The smallest rmsd value (0.51) is also associated with the SVPE model. All of the results suggest that the first-principles electronic structure calculations using the SVPE model are a reliable approach to the pKa prediction for the amine compounds. PMID:17691837

  11. First-principles calculation of pKa for cocaine, nicotine, neurotransmitters, and anilines in aqueous solution

    PubMed Central

    Lu, Haiting; Chen, Xi; Zhan, Chang-Guo

    2010-01-01

    The absolute pKa values of 24 representative amine compounds, including cocaine, nicotine, 10 neurotransmitters, and 12 anilines, in aqueous solution were calculated by performing first-principles electronic structure calculations that account for the solvent effects using four different solvation models, i.e. the surface and volume polarization for electrostatic interaction (SVPE) model, the standard polarizable continuum model (PCM), the integral equation formalism for the polarizable continuum model (IEFPCM), and the conductor-like screening solvation model (COSMO). Within the examined computational methods, the calculations using the SVPE model lead to the absolute pKa values with the smallest root-mean-square-deviation (RMSD) value (1.18). When the SVPE model was replaced by the PCM, IEFPCM, and COSMO, the RMSD value of the calculated absolute pKa values became 3.21, 2.72, and 3.08, respectively. All types of calculated pKa values linearly correlate with the experimental pKa values very well. With the empirical corrections using the linear correlation relationships, the theoretical pKa values are much closer to the corresponding experimental data and the RMSD values become 0.51 to 0.83. The smallest RMSD value (0.51) is also associated with the SVPE model. All of the results suggest that the first-principles electronic structure calculations using the SVPE model are a reliable approach to the pKa prediction for the amine compounds. PMID:17691837

  12. Prediction of the copper (II) ions dynamic removal from a medium by using mathematical models with analytical solution.

    PubMed

    Borba, Carlos Eduardo; da Silva, Edson Antônio; Fagundes-Klen, Márcia R; Kroumov, Alexander D; Guirardello, Reginaldo

    2008-03-21

    A copper (II) ions biosorption by Sargassum sp. biomass was studied in a fixed bed column at 30 degrees C and pH 3.5. The experimental curves were obtained for the following feed concentrations -2.08, 4.16, 6.42 and 12.72mmol/L of the copper ions. The mathematical models developed by Thomas and Bohart-Adams were used for description of ions sorption process in the column. The models principle hypothesis is that the mass transfer controlling stage of the process is the adsorption kinetics between sorbate and adsorbent. The phenomena such as intraparticle diffusion, a mass transfer external resistance and axial dispersion effects were out of considerations. Some of the models parameters were experimentally determined (rho(B), epsilon, u(0), C(0)) and the others were evaluated on the bases of the experimental data (k(a1), k(a2)). The unique fitting parameter in all models was the adsorption kinetic constant. The identification procedure was based on the least square statistical method. Simulation results show that the models describe well a copper ions sorption process in a fixed bed column. The used models can be considered as useful tools for adsorption process design and optimization in fixed bed column by using algae biomass of Sargassum sp. as an adsorbent.

  13. Phase Stability for the Pd-Si System. First-Principles, Experiments, and Solution-Based Modeling

    SciTech Connect

    Zhou, S. H.; Huo, Y.; Napolitano, Ralph E.

    2015-11-05

    Relative stabilities of the compounds in the binary Pd-Si system were assessed using first-principles calculations and experimental methods. Calculations of lattice parameters and enthalpy of formation indicate that Pd5Si-μ, Pd9Si2-α, Pd3 Si-β, Pd2 Si-γ, and PdSi-δ are the stable phases at 0 K (-273 °C). X-ray diffraction analyses (XRD) and electron probe microanalysis (EPMA) of the as-solidified and heat-treated samples support the computational findings, except that the PdSi-δ phase was not observed at low temperature. Considering both experimental data and first-principles results, the compounds Pd 5 Si-μ, Pd9 Si2-α, Pd3Si-β, and Pd2Si-γ are treated as stable phases down to 0 K (-273 °C), while the PdSi-δ is treated as being stable over a limited range, exhibiting a lower bound. Using these findings, a comprehensive solution-based thermodynamic model is formulated for the Pd-Si system, permitting phase diagram calculation. Moreover, the liquid phase is described using a three-species association model and other phases are treated as solid solutions, where a random substitutional model is adopted for Pd-fcc and Si-dia, and a two-sublattice model is employed for Pd5Si-μ, Pd9Si2-α, Pd3Si-β, Pd2Si-γ, and PdSi-δ. Model parameters are fitted using available experimental data and first-principles data, and the resulting phase diagram is reported over the full range of compositions.

  14. Solution of steady-state, two-dimensional conservation laws by mathematical programming

    NASA Technical Reports Server (NTRS)

    Lavery, John E.

    1991-01-01

    A truly two-dimensional algorithm is created for solving the steady-state two-dimensional conservation-law problem. An overdetermined system of algebraic equations is obtained through discretization by finite-volume formulas. These equations are perturbed nonsingularly and are solved by an efficient geometrically oriented l(1) procedure. The basic algorithm and the theory for the linear case f(u) = u are presented, and computational results for the nonlinear case f(u) = sq u are also analyzed. It is noted that the l(1) procedure captures boundary shocks as well as oblige and zigzag interior shocks in bands that are one cell wide, and the solution values are accurate up to the edge of the shock.

  15. Accuracy of color prediction of anthraquinone dyes in methanol solution estimated from first principle quantum chemistry computations.

    PubMed

    Cysewski, Piotr; Jeliński, Tomasz

    2013-10-01

    The electronic spectrum of four different anthraquinones (1,2-dihydroxyanthraquinone, 1-aminoanthraquinone, 2-aminoanthraquinone and 1-amino-2-methylanthraquinone) in methanol solution was measured and used as reference data for theoretical color prediction. The visible part of the spectrum was modeled according to TD-DFT framework with a broad range of DFT functionals. The convoluted theoretical spectra were validated against experimental data by a direct color comparison in terms of CIE XYZ and CIE Lab tristimulus model color. It was found, that the 6-31G** basis set provides the most accurate color prediction and there is no need to extend the basis set since it does not improve the prediction of color. Although different functionals were found to give the most accurate color prediction for different anthraquinones, it is possible to apply the same DFT approach for the whole set of analyzed dyes. Especially three functionals seem to be valuable, namely mPW1LYP, B1LYP and PBE0 due to very similar spectra predictions. The major source of discrepancies between theoretical and experimental spectra comes from L values, representing the lightness, and the a parameter, depicting the position on green→magenta axis. Fortunately, the agreement between computed and observed blue→yellow axis (parameter b) is very precise in the case of studied anthraquinone dyes in methanol solution. Despite discussed shortcomings, color prediction from first principle quantum chemistry computations can lead to quite satisfactory results, expressed in terms of color space parameters.

  16. Mathematical Models, Analytical Solutions and Numerical Simulations of Self-Assembled Magnetic Colloidal Structures

    NASA Astrophysics Data System (ADS)

    Piet, David L.

    Ferromagnetic microparticles suspended at the interface between immiscible liquids and energized by an external alternating magnetic field show a rich variety of self-assembled structures, from linear snakes to radial asters, elongated wires to spinning chains to less dense clouds of particles called snails. In order to obtain insight into the fundamental physical mechanisms and the overall balance of forces governing self-assembly, we develop a modeling approach based on analytical solutions of the time-averaged Navier-Stokes equations. These analytical expressions for the self-consistent hydrodynamic flows are then employed to modify effective interactions between the particles, which in turn are formulated in terms of the time-averaged quantities. Our method allows effective computational verification of the mechanisms of self-assembly and leads to a testable predictions on the transitions between various self-assembled patterns. In one set of experiments, it was observed that viscosity is the primary driving force that determines whether asters or snakes appear at steady state. In the second set of experiments where hydrodynamics are less critical, the amplitude and frequency of the applied magnetic field determine whether wires, spinners or snails will appear. The ability to better understand what drives self-assembly and how to control which dynamic structures appear is necessary for further development of such structures and their applications.

  17. Underground Mathematics

    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…

  18. A Process for Testing a Mathematical Model for the Solution of a Practical Problem: Application to Test Equating. LES Paper on Learning and Teaching. Paper #79.

    ERIC Educational Resources Information Center

    Douglass, James B.

    A general process for testing the feasibility of applying alternative mathematical or statistical models to the solution of a practical problem is presented and flowcharted. The system is used to develop a plan to compare models for test equating. The five alternative models to be considered for equating are: (1) anchor test equating using…

  19. Tutoring Mathematical Word Problems Using Solution Trees: Text Comprehension, Situation Comprehension, and Mathematization in Solving Story Problems. Research Report No. 8.

    ERIC Educational Resources Information Center

    Reusser, Kurt; And Others

    The main concern of this paper is on the psychological processes of how students understand and solve mathematical word problems, and on how this knowledge can be applied to computer-based tutoring. It is argued that only a better understanding of the psychological requirements for understanding and solving those problems will lead to…

  20. A possible solution to the B → ππ puzzle using the principle of maximum conformality

    NASA Astrophysics Data System (ADS)

    Qiao, Cong-Feng; Zhu, Rui-Lin; Wu, Xing-Gang; Brodsky, Stanley J.

    2015-09-01

    The measured Bd →π0π0 branching fraction deviates significantly from conventional QCD predictions, a puzzle which has persisted for more than 10 years. This may be a hint of new physics beyond the Standard Model; however, as we shall show in this paper, the pQCD prediction is highly sensitive to the choice of the renormalization scales which enter the decay amplitude. In the present paper, we show that the renormalization scale uncertainties for B → ππ can be greatly reduced by applying the Principle of Maximum Conformality (PMC), and more precise predictions for CP-averaged branching ratios B (B → ππ) can be achieved. Combining the errors in quadrature, we obtain B (Bd →π0π0)|PMC = (0.98-0.31+0.44) ×10-6 by using the light-front holographic low-energy model for the running coupling. All of the CP-averaged B → ππ branching fractions predicted by the PMC are consistent with the Particle Data Group average values and the recent Belle data. Thus, the PMC provides a possible solution for the Bd →π0π0 puzzle.

  1. Limitations and Extensions of the Lock-and-Key Principle: Differences between Gas State, Solution and Solid State Structures

    PubMed Central

    Schneider, Hans-Jörg

    2015-01-01

    The lock-and-key concept is discussed with respect to necessary extensions. Formation of supramolecular complexes depends not only, and often not even primarily on an optimal geometric fit between host and guest. Induced fit and allosteric interactions have long been known as important modifications. Different binding mechanisms, the medium used and pH effects can exert a major influence on the affinity. Stereoelectronic effects due to lone pair orientation can lead to variation of binding constants by orders of magnitude. Hydrophobic interactions due to high-energy water inside cavities modify the mechanical lock-and-key picture. That optimal affinities are observed if the cavity is only partially filled by the ligand can be in conflict with the lock-and-key principle. In crystals other forces than those between host and guest often dominate, leading to differences between solid state and solution structures. This is exemplified in particular with calixarene complexes, which by X-ray analysis more often than other hosts show guest molecules outside their cavity. In view of this the particular problems with the identification of weak interactions in crystals is discussed. PMID:25815592

  2. The principle of superposition and its application in ground-water hydraulics

    USGS Publications Warehouse

    Reilly, Thomas E.; Franke, O. Lehn; Bennett, Gordon D.

    1987-01-01

    The principle of superposition, a powerful mathematical technique for analyzing certain types of complex problems in many areas of science and technology, has important applications in ground-water hydraulics and modeling of ground-water systems. The principle of superposition states that problem solutions can be added together to obtain composite solutions. This principle applies to linear systems governed by linear differential equations. This report introduces the principle of superposition as it applies to ground-water hydrology and provides background information, discussion, illustrative problems with solutions, and problems to be solved by the reader.

  3. A New Principle in Physiscs: the Principle "Finiteness", and Some Consequences

    SciTech Connect

    Abraham Sternlieb

    2010-06-25

    In this paper I propose a new principle in physics: the principle of "finiteness". It stems from the definition of physics as a science that deals (among other things) with measurable dimensional physical quantities. Since measurement results, including their errors, are always finite, the principle of finiteness postulates that the mathematical formulation of "legitimate" laws of physics should prevent exactly zero or infinite solutions. Some consequences of the principle of finiteness are discussed, in general, and then more specifically in the fields of special relativity, quantum mechanics, and quantum gravity. The consequences are derived independently of any other theory or principle in physics. I propose "finiteness" as a postulate (like the constancy of the speed of light in vacuum, "c"), as opposed to a notion whose validity has to be corroborated by, or derived theoretically or experimentally from other facts, theories, or principles.

  4. Mathematical modelling in Matlab of the experimental results shows the electrochemical potential difference - temperature of the WC coatings immersed in a NaCl solution

    NASA Astrophysics Data System (ADS)

    Benea, M. L.; Benea, O. D.

    2016-02-01

    The method used for purchasing the corrosion behaviour the WC coatings deposited by plasma spraying, on a martensitic stainless steel substrate consists in measuring the electrochemical potential of the coating, respectively that of the substrate, immersed in a NaCl solution as corrosive agent. The mathematical processing of the obtained experimental results in Matlab allowed us to make some correlations between the electrochemical potential of the coating and the solution temperature is very well described by some curves having equations obtained by interpolation order 4.

  5. Mathematical Perspectives

    SciTech Connect

    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.

  6. Mathematical modeling and simulation in animal health - Part II: principles, methods, applications, and value of physiologically based pharmacokinetic modeling in veterinary medicine and food safety assessment.

    PubMed

    Lin, Z; Gehring, R; Mochel, J P; Lavé, T; Riviere, J E

    2016-10-01

    This review provides a tutorial for individuals interested in quantitative veterinary pharmacology and toxicology and offers a basis for establishing guidelines for physiologically based pharmacokinetic (PBPK) model development and application in veterinary medicine. This is important as the application of PBPK modeling in veterinary medicine has evolved over the past two decades. PBPK models can be used to predict drug tissue residues and withdrawal times in food-producing animals, to estimate chemical concentrations at the site of action and target organ toxicity to aid risk assessment of environmental contaminants and/or drugs in both domestic animals and wildlife, as well as to help design therapeutic regimens for veterinary drugs. This review provides a comprehensive summary of PBPK modeling principles, model development methodology, and the current applications in veterinary medicine, with a focus on predictions of drug tissue residues and withdrawal times in food-producing animals. The advantages and disadvantages of PBPK modeling compared to other pharmacokinetic modeling approaches (i.e., classical compartmental/noncompartmental modeling, nonlinear mixed-effects modeling, and interspecies allometric scaling) are further presented. The review finally discusses contemporary challenges and our perspectives on model documentation, evaluation criteria, quality improvement, and offers solutions to increase model acceptance and applications in veterinary pharmacology and toxicology.

  7. Structural and magnetic properties of NiCx and NiNx (x=0 to (1)/(3)) solid solutions from first-principles calculations

    NASA Astrophysics Data System (ADS)

    Fang, C. M.; Sluiter, M. H. F.; van Huis, M. A.; Zandbergen, H. W.

    2012-10-01

    First-principles calculations have been performed for a variety of Ni3X (X = C, N) phases, as well as for NiXy (y = 0 to (1)/(3)) solid solutions to clarify the persistent controversy regarding its magnetic state. The calculations show that the solid solution phases based on hexagonal-close-packed (hcp or ɛ-) Ni have relatively high stability for X concentrations greater than about 0.1 whereas the face-centered-cubic (fcc or γ-) Ni phases are favored for smaller X concentration. Hence, during carburization or nitridization of Ni, a phase transformation is to be expected. In spite of the close-packed nature of both hcp- and fcc-based solid solutions, X quenches the magnetization more effectively in fcc than in hcp-based solid solutions. These findings resolve many apparently contradictory experimental observations concerning C- and N-containing Ni alloys in the literature.

  8. Mathematical modeling of molecular diffusion through mucus

    PubMed Central

    Cu, Yen; Saltzman, W. Mark

    2008-01-01

    The rate of molecular transport through the mucus gel can be an important determinant of efficacy for therapeutic agents delivered by oral, intranasal, intravaginal/rectal, and intraocular routes. Transport through mucus can be described by mathematical models based on principles of physical chemistry and known characteristics of the mucus gel, its constituents, and of the drug itself. In this paper, we review mathematical models of molecular diffusion in mucus, as well as the techniques commonly used to measure diffusion of solutes in the mucus gel, mucus gel mimics, and mucosal epithelia. PMID:19135488

  9. A correspondence principle

    NASA Astrophysics Data System (ADS)

    Hughes, Barry D.; Ninham, Barry W.

    2016-02-01

    A single mathematical theme underpins disparate physical phenomena in classical, quantum and statistical mechanical contexts. This mathematical "correspondence principle", a kind of wave-particle duality with glorious realizations in classical and modern mathematical analysis, embodies fundamental geometrical and physical order, and yet in some sense sits on the edge of chaos. Illustrative cases discussed are drawn from classical and anomalous diffusion, quantum mechanics of single particles and ideal gases, quasicrystals and Casimir forces.

  10. Equity in the Reform of Mathematics and Science Education: A Look at Issues and Solutions. Executive Summary.

    ERIC Educational Resources Information Center

    Powell, Mary Jo; Boethel, Martha, Ed.

    The current push for reform in mathematics and science education cannot succeed unless it addresses the critical and persistent issue of equity. This executive summary reviews the literature regarding that issue. Its purpose is to provide a reference tool for those who are working to change educational policy and practice. Part 1 of the review…

  11. Creating Problems and Their Solutions: Service-Learning through Trinity Mathematics Triathlons, Math Nights, and Math Centers

    ERIC Educational Resources Information Center

    Klanderman, David B.; Moore, Mary Webster; Maxwell, Mandi S.; Robbert, Sharon K.

    2013-01-01

    We describe several service-learning initiatives implemented by the mathematics and education departments. College students with majors and minors in math and math education have helped to design and implement math events for elementary and middle school students. Formal and informal reflections on these service-related experiences have…

  12. The Nature of Mathematical Modeling

    NASA Astrophysics Data System (ADS)

    Gershenfeld, Neil

    2011-06-01

    Preface; 1. Introduction; Part I. Analytical Models: 2. Ordinary differential and difference equations; 3. Partial differential equations; 4. Variational principles; 5. Random systems; Part II. Numerical Models: 6. Finite differences: ordinary difference equations; 7. Finite differences: partial differential equations; 8. Finite elements; 9. Cellular automata and lattice gases; Part III. Observational Models: 10. Function fitting; 11. Transforms; 12. Architectures; 13. Optimization and search; 14. Clustering and density estimation; 15. Filtering and state estimation; 16. Linear and nonlinear time series; Appendix 1. Graphical and mathematical software; Appendix 2. Network programming; Appendix 3. Benchmarking; Appendix 4. Problem solutions; Bibliography.

  13. On the Dirichlet's Box Principle

    ERIC Educational Resources Information Center

    Poon, Kin-Keung; Shiu, Wai-Chee

    2008-01-01

    In this note, we will focus on several applications on the Dirichlet's box principle in Discrete Mathematics lesson and number theory lesson. In addition, the main result is an innovative game on a triangular board developed by the authors. The game has been used in teaching and learning mathematics in Discrete Mathematics and some high schools in…

  14. Proton transfer from water to ketyl radical anion: Assessment of critical size of hydrated cluster and free energy barrier in solution from first principles simulations

    NASA Astrophysics Data System (ADS)

    Biswas, Sohag; Dasgupta, Teesta; Mallik, Bhabani S.

    2016-09-01

    We present the reactivity of an organic intermediate by studying the proton transfer process from water to ketyl radical anion using gas phase electronic structure calculations and the metadynamics method based first principles molecular dynamics (FPMD) simulations. Our results indicate that during the micro solvation of anion by water molecules systematically, the presence of minimum three water molecules in the gas phase cluster is sufficient to observe the proton transfer event. The analysis of trajectories obtained from initial FPMD simulation of an aqueous solution of the anion does not show any evident of complete transfer of the proton from water. The cooperativity of water molecules and the relatively weak anion-water interaction in liquid state prohibit the full release of the proton. Using biasing potential through first principles metadynamics simulations, we report the observation of proton transfer reaction from water to ketyl radical anion with a barrier height of 16.0 kJ/mol.

  15. The Kinetics and Mechanism of the Decomposition of Murexide in Acid Solution: An Experiment for Teaching Principles of Chemical Kinetics.

    ERIC Educational Resources Information Center

    Knoche, Wilhelm; Rees, Norman H.

    1984-01-01

    Background information, procedures, and typical results are provided for an experiment on the decomposition of murexide in acid solution. The experiment, suitable for advanced courses, can be easily performed in a 6-hour laboratory period. (JN)

  16. [FREE CONSUMPTION OF GLUCOSE SOLUTION BY RATS AS A CRITERION FOR EVALUATION ITS ABSORPTION IN THE SMALL INTESTINE (Experimental study and mathematical modeling)].

    PubMed

    Gruzdkov, A A; Gromova, L V; Dmitrieva, Yu V; Alekseeva, A S

    2015-06-01

    The aim of the work is to analyze the relationship between consumption of glucose solution by rats and its absorption, and to use this fact for assessment of the absorptive capacity of the small intestine in non anesthetized animals in vivo. Consumption of glucose solution (200 g/l) by fasted rats was recorded in the control, and after administration of phloridzin--inhibitor of glucose active transport- or 3 hours after the restriction stress. On the mathematical model we studied the relative role of factors that can influence the temporal dynamics of glucose consumption by rats. The rate of glucose consumption was observed being decreased in the presence of phloridzin (1 mM), and be increased after the stress. The results of modeling are consistent with the experimental data and show that the rate of consumption of glucose solutions considerably more depends on the transport activity of the small intestine than on glucose concentration in the solution, or on the substrate regulation of the stomach emptying. Analysis of dynamics of consumption of glucose solution by intact rats may be considered as one of promising approaches to assessing the absorptive capacity of the small intestine under natural conditions.

  17. Relative motion of orbiting particles under the influence of perturbing forces. Volume 2: Analytical results. [equations of motion and mathematical solutions

    NASA Technical Reports Server (NTRS)

    Eades, J. B., Jr.

    1974-01-01

    The mathematical developments carried out for this investigation are reported. In addition to describing and discussing the solutions which were acquired, there are compendia of data presented herein which summarize the equations and describe them as representative trace geometries. In this analysis the relative motion problems have been referred to two particular frames of reference; one which is inertially aligned, and one which is (local) horizon oriented. In addition to obtaining the classical initial values solutions, there are results which describe cases having applied specific forces serving as forcing functions. Also, in order to provide a complete state representation the speed components, as well as the displacements, have been described. These coordinates are traced on representative planes analogous to the displacement geometries. By this procedure a complete description of a relative motion is developed; and, as a consequence range rate as well as range information is obtained.

  18. Effects of dilute substitutional solutes on interstitial carbon in α-Fe: Interactions and associated carbon diffusion from first-principles calculations

    NASA Astrophysics Data System (ADS)

    Liu, Peitao; Xing, Weiwei; Cheng, Xiyue; Li, Dianzhong; Li, Yiyi; Chen, Xing-Qiu

    2014-07-01

    By means of first-principles calculations coupled with the kinetic Monte Carlo simulations, we have systematically investigated the effects of dilute substitutional solutes on the behaviors of carbon in α-Fe. Our results uncover the following. (i) Without the Fe vacancy the interactions between most solutes and carbon are repulsive due to the strain relief, whereas Mn has a weak attractive interaction with its nearest-neighbor carbon due to the local ferromagnetic coupling effect. (ii) The presence of the Fe vacancy results in attractive interactions of all the solutes with carbon. In particular, the Mn-vacancy pair shows an exceptionally large binding energy of -0.81 eV with carbon. (iii) The alloying addition significantly impacts the atomic-scale concentration distributions and chemical potential of carbon in the Fe matrix. Among them, Mn and Cr increase the carbon chemical potential, whereas Al and Si reduce it. (iv) Within the dilute scale of the alloying solution, the solute concentration- and temperature-dependent carbon diffusivities demonstrate that Mn has a little impact on the carbon diffusion, whereas Cr (Al or Si) remarkably retards the carbon diffusion. Our results provide a certain implication for better understanding the experimental observations related with the carbon solubility limit, carbon microsegregation, and carbide precipitations in the ferritic steels.

  19. Structural and Thermodynamic Properties of TiC x N y O z Solid Solution: Experimental Study and First-Principles Approaches

    NASA Astrophysics Data System (ADS)

    Xiao, Jiusan; Jiang, Bo; Huang, Kai; Jiao, Shuqiang; Zhu, Hongmin

    2016-09-01

    A series of TiC x N y O z solid solutions were synthesized via solid-state reaction and XRD patterns exhibited a single phase of FCC structure over the whole concentration range. The structural and thermodynamic properties of TiC x N y O z solid solutions were studied using experimental method and first-principles calculations. The difference between the calculated and experimental lattice parameters could be attributed to the vacancies segregated in TiO part. The fitting formulae for lattice parameters and mixing enthalpies were firstly given for TiC x N y O z solid solution over the whole concentration range. The obtained thermodynamic data for TiC x N y O z solid solution properly explained the reaction sequence of the carbothermal reduction of TiO2, providing theoretical foundation for TiC x N y O z solid solution as a kind of prospective material for consuming anode utilized in USTB titanium electrolysis process.

  20. 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…

  1. Toddlers' Opportunities to Learn Mathematics

    ERIC Educational Resources Information Center

    Bjorklund, Camilla

    2008-01-01

    Mathematical knowledge has developed from human activities through thousands of years and is bound to the world and cultures that men and women experience. One can say that mathematics is rooted in humans' everyday life, an environment where people reach agreement regarding principles in mathematics. Through interaction with worldly phenomena and…

  2. STEM Gives Meaning to Mathematics

    ERIC Educational Resources Information Center

    Hefty, Lukas J.

    2015-01-01

    The National Council of Teachers of Mathematics' (NCTM's) "Principles and Standards for School Mathematics" (2000) outlines fi ve Process Standards that are essential for developing deep understanding of mathematics: (1) Problem Solving; (2) Reasoning and Proof; (3) Communication; (4) Connections; and (5) Representation. The Common Core…

  3. Hybrid molecular dynamics and first-principles study on the work function of a Pt(111) electrode immersed in aqueous solution at room temperature

    NASA Astrophysics Data System (ADS)

    Duan, Sai; Xu, Xin; Tian, Zhong-Qun; Luo, Yi

    2012-07-01

    With a combined molecular dynamics simulation and first-principles calculations, we have investigated a metal surface immersed in aqueous solution at room temperature using a Pt(111) electrode as an example. With the inclusion of thermal average effects at room temperature, the calculated averaged work function is found to be in good agreement with the experimental measurements. The electron redistribution at the interface of the topmost Pt(111) slab layer and the first water layer plays an important role in controlling the work function. A broad distribution of calculated work functions caused by the thermal motions of the dipolar solvents is obtained from statistical sampling, which implies that the chemical reactivity of a metal electrode in aqueous solution is a dynamic property at least in the nanoscale. Such a microscopic understanding helps to understand the behavior of complex electrochemical double layers.

  4. Ibuprofen removal from aqueous solution by in situ electrochemically generated ferrate(VI): proof-of-principle.

    PubMed

    Nikolić-Bujanović, Ljiljana; Čekerevac, Milan; Tomić, Milena; Zdravković, Mladen

    2016-01-01

    The possibility of removing pharmaceuticals from aqueous solutions was examined using ibuprofen (Ibu) oxidation as an example, using in situ electrochemically synthesized ferrate(VI), a strong oxidant and coagulant, with forming of non-harmful byproducts. A solution of ibuprofen of 206 mg/L in 0.1 M phosphate buffer solution was treated with different amounts of fresh, electrochemically synthesized ferrate(VI). The changes of ibuprofen concentration in samples were determined using a UV-Vis spectrophotometer. The extent of mineralization was estimated using the changes in chemical oxygen demand (COD) values and total organic carbon (TOC) values of test samples. The largest reduction of the concentration of Ibu (41.75%) was obtained by adding 69.2 mg/L ferrate(VI) as Fe (Ibu: Fe = 1: 0.34). An effective removal of ibuprofen from aqueous solutions was recorded up to 68% and it can be done by using ferrate(VI) in the ratio Ibu: Fe = 1:3 as Fe. The possibility of ibuprofen removal by ferrate(VI) was confirmed by COD and TOC results, which demonstrated reduction up to 65% and 63.6%, respectively.

  5. Theoretical investigations into the nucleation of silica growth in basic solution part II--derivation and benchmarking of a first principles kinetic model of solution chemistry.

    PubMed

    McIntosh, Grant J

    2013-10-28

    A kinetic model of silicate oligomerization in water, up to and including tetramer formation, has been compiled exclusively from rate constants derived from transition state theory based on either quantum chemical data (derived under a hybrid solvation framework) for all bond breaking-forming reactions, or using empirically-based approximated pKa's and diffusion coefficients for rate constants of pH-based and bimolecular steps. The rate constants, based on an exhaustive search of all relevant elementary steps, form the basis of our kinetic model; numerical solution of the resulting rate equations allows the simulation of the reaction system, given a set of initial conditions and with almost no restriction on concentrations, pH, or reaction time, in a matter of only minutes. The model, which we believe contains all possible isomers of both neutral and singly anionic clusters, has been extensively benchmarked and reproduces a number of important experimental observations in the range pH ≈ 4-10. In particular, it provides a good description of the dominant products; product yields and reaction times (also as a function of pH) are in agreement with experiment; the linear relationship between the log of the rate of silica dissolution and pH is well reproduced; the origin of silica scaling naturally arises; and we can also simulate the observed fourth order dependence of the rate of monomer consumption on H4SiO4 concentration. This should be a general approach to exploring solution phase chemistry, and could be a useful complement to more conventional molecular dynamics and Monte Carlo modelling approaches in understanding complex reaction networks in solution.

  6. Existence of Solutions for a Mathematical Model Related to Solid-Solid Phase Transitions in Shape Memory Alloys

    NASA Astrophysics Data System (ADS)

    Bonetti, Elena; Colli, Pierluigi; Fabrizio, Mauro; Gilardi, Gianni

    2016-01-01

    We consider a strongly nonlinear PDE system describing solid-solid phase transitions in shape memory alloys. The system accounts for the evolution of an order parameter χ (related to different symmetries of the crystal lattice in the phase configurations), of the stress (and the displacement u), and of the absolute temperature ϑ. The resulting equations present several technical difficulties to be tackled; in particular, we emphasize the presence of nonlinear coupling terms, higher order dissipative contributions, possibly multivalued operators. As for the evolution of temperature, a highly nonlinear parabolic equation has to be solved for a right hand side that is controlled only in L 1. We prove the existence of a solution for a regularized version by use of a time discretization technique. Then, we perform suitable a priori estimates which allow us pass to the limit and find a weak global-in-time solution to the system.

  7. Formal mathematical solutions of the force-free equations, spontaneous discontinuities, and dissipation in large-scale magnetic fields

    NASA Technical Reports Server (NTRS)

    Parker, E. N.

    1990-01-01

    Direct integration of the force-free field equation del x B = alpha B, in the simple case of the local deformation of a laminar field, produces field configurations containing tangential discontinuities (current sheets). Whereas continuous solutions allow only restricted field topologies, the discontinuities provide the necessary release from those restrictions in more general topologies. Magnetic fields in nature are strongly deformed by convection, so as to contain significant internal discontinuities. The bipolar magnetic fields containing the active X-ray corona of the sun are a case in point. It appears that the dissipation caused by the discontinuities may be the primary heat source producing the X-ray corona.

  8. Solutions for complex, multi data type and multi tool analysis: principles and applications of using workflow and pipelining methods.

    PubMed

    Munro, Robin E J; Guo, Yike

    2009-01-01

    Analytical workflow technology, sometimes also called data pipelining, is the fundamental component that provides the scalable analytical middleware that can be used to enable the rapid building and deployment of an analytical application. Analytical workflows enable researchers, analysts and informaticians to integrate and access data and tools from structured and non-structured data sources so that analytics can bridge different silos of information; compose multiple analytical methods and data transformations without coding; rapidly develop applications and solutions by visually constructing analytical workflows that are easy to revise should the requirements change; access domain-specific extensions for specific projects or areas, for example, text extraction, visualisation, reporting, genetics, cheminformatics, bioinformatics and patient-based analytics; automatically deploy workflows directly into web portals and as web services to be part of a service-oriented architecture (SOA). By performing workflow building, using a middleware layer for data integration, it is a relatively simple exercise to visually design an analytical process for data analysis and then publish this as a service to a web browser. All this is encapsulated into what can be referred to as an 'Embedded Analytics' methodology which will be described here with examples covering different scientifically focused data analysis problems.

  9. Making Mathematical Connections by Constructing Tetrahedra

    ERIC Educational Resources Information Center

    Bergner, Jennifer A.; Groth, Randall E.

    2005-01-01

    This article describes a polyhedra construction project that illustrates how one activity can address several of the mathematics content standards in the NCTM Principles and Standards for School Mathematics.

  10. What is behind small deviations of quantum mechanics theory from experiments? Observer's mathematics point of view

    NASA Astrophysics Data System (ADS)

    Khots, Boris; Khots, Dmitriy

    2014-12-01

    Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We consider the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.

  11. What is behind small deviations of quantum mechanics theory from experiments? Observer's mathematics point of view

    SciTech Connect

    Khots, Boris; Khots, Dmitriy

    2014-12-10

    Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We consider the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.

  12. 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.

  13. Study of Mo (VI) removal from aqueous solution: application of different mathematical models to continuous biosorption data

    PubMed Central

    2013-01-01

    Molybdenum (VI) biosorption process was investigated by marine algae Cystoseria indica pretreated with 0.1 M CaCl2 solution in a packed bed column. The biosorbent was characterized by FTIR, BET and SEM analyses. The results showed that Mo (VI) ions should be chelated with the hydroxyl, carboxyl and amine groups of the biomass. The effects of inlet metal concentration and flow rate on biosorption process were investigated and the experimental breakthrough curves were obtained. Results showed that the maximum biosorption capacity of Ca-pretreated C. indica for Mo (VI) was found to be 18.32 mg/g at optimum flow rate of (1.4 mL/min). The controlled-rate step shifted from external to internal mass transfer limitations, as the flow rate increased. Also, it was observed that the breakthrough and exhaustion time decreased from 17.14 hr to 9.05 hr and from 0.006 h to 0.002 hr respectively, with the increase of flow rate from 0.7 to 2.1 ML/min. The increase in the initial concentration of Mo (VI) solution from 30 to 95 ml min-1 increases the adsorption capacity from 18.32 to 30.19 mg/g and decreases the percentage of Mo (VI) removal from 61 to 38%. Also, the treated volume was the greatest (1.42 L) at the lowest inlet concentration. Column data obtained under different conditions were described using the Thomas, Yoon and Nelson, Yan and Belter models. The breakthrough curve predictions by Belter model were found to be very satisfactory. PMID:23369379

  14. Mathematics Underground

    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…

  15. 1st principle simulations of ions in water solutions: Bond structure and chemistry in the hydration shells of highly charged ions

    NASA Astrophysics Data System (ADS)

    Weare, John

    2012-02-01

    Methods of direct simulation (Monte Carlo and molecular dynamics) have provided new insights into the structure and dynamics of electrolyte solutions. However, these methods are limited by the difficulty of developing reliable ion-solvent and solvent-solvent potential interactions in the highly perturbed hydration region. To model the interactions in this region methods of simulation that are based on the direct on the fly solution to the electronic Schr"odinger equation (ab-initio molecular dynamics, AIMD) are being developed. However, 1st principle methods have their own problems because the solution to the electronic structure problem is intractable unless rather uncontrolled approximations are made (e.g. density functional theory, DFT) and there is high computational cost to the solution to the Schr"odinger equation. To test the accuracy of AIMD methods we have directly simulated the XAFS spectra for a series of transition metal ions Ca^2+, Cr^3+, Mn^2+, Fe^3+, Co^2+, Ni^2+, Cu^2+, and Zn^2+. Despite DFT's well know deficiencies, the agreement between the calculated XAFS spectra and the data is almost quantitative for these test ions. This agreement supports the extension of the interpretation well beyond that of the usual XAFS analysis to include higher-order multiple scattering signals in the XAFS spectra, which provide a rigorous probe of the first shell distances and disorders. Less well resolved features of the spectra can still be analyzed and are related to 2nd shell structure. The combination of XAFS measurements and the parameter free AIMD method leads to new insights into the hydration structure of these ions. While strictly local DFT +gga provides excellent agreement with data, the addition of exact exchange seems to provide slightly better structural agreement. The computational complexity of these calculations requires the development of simulation tools that scale to high processor number on massively parallel supercomputers. Our present algorithm

  16. Resisting Reductionism in Mathematics Pedagogy

    ERIC Educational Resources Information Center

    Foster, Colin

    2013-01-01

    Although breaking down a mathematical problem into smaller parts can often be an effective solution strategy, when the same reductionist approach is applied to mathematics pedagogy the effects are far from beneficial for students. Mathematics pedagogy in UK schools is gaining an increasingly reductionist flavour, as seen in an excessive focus on…

  17. Developing Mathematical Content Knowledge for Teaching Elementary School Mathematics

    ERIC Educational Resources Information Center

    Thanheiser, Eva; Browning, Christine A.; Moss, Meg; Watanabe, Tad; Garza-Kling, Gina

    2010-01-01

    In this paper the authors present three design principles they use to develop preservice teachers' mathematical content knowledge for teaching in their mathematics content and/or methods courses: (1) building on currently held conceptions, (2) modeling teaching for understanding, (3) focusing on connections between content knowledge and other…

  18. English for Students of Mathematics.

    ERIC Educational Resources Information Center

    Bensoussan, Marsha; Golan, Jonathan

    A curriculum unit on English for mathematics students at the University of Haifa is presented. The text content concerns mathematics while integrating language principles. Exercises are included that involve comprehension of geometric diagrams, reading comprehension, word meanings, and restructuring sentences. The 12 sections cover: projective…

  19. Solving Geometry Problems via Mechanical Principles

    ERIC Educational Resources Information Center

    Man, Yiu Kwong

    2004-01-01

    The application of physical principles in solving mathematics problems have often been neglected in the teaching of physics or mathematics, especially at the secondary school level. This paper discusses how to apply the mechanical principles to geometry problems via concrete examples, which aims at providing insight and inspirations to physics or…

  20. The Collective Black and "Principles to Actions"

    ERIC Educational Resources Information Center

    Martin, Danny Bernard

    2015-01-01

    In this commentary, Danny Martin describes five key take-aways and two sets of questions that arose from his reading of "Principles to Actions: Ensuring Mathematics Success for All (National Council of Teachers of Mathematics [NCTM], 2014). Martin begins by noting that "Principles to Actions" is clearly a political document that…

  1. First-principles studies of effects of interstitial boron and carbon on the structural, elastic, and electronic properties of Ni solution and Ni3Al intermetallics

    NASA Astrophysics Data System (ADS)

    Huang, Meng-Li; Wang, Chong-Yu

    2016-10-01

    The effects of boron and carbon on the structural, elastic, and electronic properties of both Ni solution and Ni3Al intermetallics are investigated using first-principles calculations. The results agree well with theoretical and experimental data from previous studies and are analyzed based on the density of states and charge density. It is found that both boron and carbon are inclined to occupy the Ni-rich interstices in Ni3Al, which gives rise to a cubic interstitial phase. In addition, the interstitial boron and carbon have different effects on the elastic moduli of Ni and Ni3Al. The calculation results for the G/B and Poisson’s ratios further demonstrate that interstitial boron and carbon can both reduce the brittleness of Ni, thereby increasing its ductility. Meanwhile, boron can also enhance the ductility of the Ni3Al while carbon hardly has an effect on its brittleness or ductility. Project supported by the National Basic Research Program of China (Grant No. 2011CB606402).

  2. Mathematics, Anyone?

    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…

  3. Physical Principle for Generation of Randomness

    NASA Technical Reports Server (NTRS)

    Zak, Michail

    2009-01-01

    A physical principle (more precisely, a principle that incorporates mathematical models used in physics) has been conceived as the basis of a method of generating randomness in Monte Carlo simulations. The principle eliminates the need for conventional random-number generators. The Monte Carlo simulation method is among the most powerful computational methods for solving high-dimensional problems in physics, chemistry, economics, and information processing. The Monte Carlo simulation method is especially effective for solving problems in which computational complexity increases exponentially with dimensionality. The main advantage of the Monte Carlo simulation method over other methods is that the demand on computational resources becomes independent of dimensionality. As augmented by the present principle, the Monte Carlo simulation method becomes an even more powerful computational method that is especially useful for solving problems associated with dynamics of fluids, planning, scheduling, and combinatorial optimization. The present principle is based on coupling of dynamical equations with the corresponding Liouville equation. The randomness is generated by non-Lipschitz instability of dynamics triggered and controlled by feedback from the Liouville equation. (In non-Lipschitz dynamics, the derivatives of solutions of the dynamical equations are not required to be bounded.)

  4. A Novel Hybridization of Applied Mathematical, Operations Research and Risk-based Methods to Achieve an Optimal Solution to a Challenging Subsurface Contamination Problem

    NASA Astrophysics Data System (ADS)

    Johnson, K. D.; Pinder, G. F.

    2013-12-01

    The objective of the project is the creation of a new, computationally based, approach to the collection, evaluation and use of data for the purpose of determining optimal strategies for investment in the solution of remediation of contaminant source areas and similar environmental problems. The research focuses on the use of existing mathematical tools assembled in a unique fashion. The area of application of this new capability is optimal (least-cost) groundwater contamination source identification; we wish to identify the physical environments wherein it may be cost-prohibitive to identify a contaminant source, the optimal strategy to protect the environment from additional insult and formulate strategies for cost-effective environmental restoration. The computational underpinnings of the proposed approach encompass the integration into a unique of several known applied-mathematical tools. The resulting tool integration achieves the following: 1) simulate groundwater flow and contaminant transport under uncertainty, that is when the physical parameters such as hydraulic conductivity are known to be described by a random field; 2) define such a random field from available field data or be able to provide insight into the sampling strategy needed to create such a field; 3) incorporate subjective information, such as the opinions of experts on the importance of factors such as locations of waste landfills; 4) optimize a search strategy for finding a potential source location and to optimally combine field information with model results to provide the best possible representation of the mean contaminant field and its geostatistics. Our approach combines in a symbiotic manner methodologies found in numerical simulation, random field analysis, Kalman filtering, fuzzy set theory and search theory. Testing the algorithm for this stage of the work, we will focus on fabricated field situations wherein we can a priori specify the degree of uncertainty associated with the

  5. The Acquisition of Problem-Solving Skills in Mathematics: How Animations Can Aid Understanding of Structural Problem Features and Solution Procedures

    ERIC Educational Resources Information Center

    Scheiter, Katharina; Gerjets, Peter; Schuh, Julia

    2010-01-01

    In this paper the augmentation of worked examples with animations for teaching problem-solving skills in mathematics is advocated as an effective instructional method. First, in a cognitive task analysis different knowledge prerequisites are identified for solving mathematical word problems. Second, it is argued that so called hybrid animations…

  6. The Principle of General Tovariance

    NASA Astrophysics Data System (ADS)

    Heunen, C.; Landsman, N. P.; Spitters, B.

    2008-06-01

    We tentatively propose two guiding principles for the construction of theories of physics, which should be satisfied by a possible future theory of quantum gravity. These principles are inspired by those that led Einstein to his theory of general relativity, viz. his principle of general covariance and his equivalence principle, as well as by the two mysterious dogmas of Bohr's interpretation of quantum mechanics, i.e. his doctrine of classical concepts and his principle of complementarity. An appropriate mathematical language for combining these ideas is topos theory, a framework earlier proposed for physics by Isham and collaborators. Our principle of general tovariance states that any mathematical structure appearing in the laws of physics must be definable in an arbitrary topos (with natural numbers object) and must be preserved under so-called geometric morphisms. This principle identifies geometric logic as the mathematical language of physics and restricts the constructions and theorems to those valid in intuitionism: neither Aristotle's principle of the excluded third nor Zermelo's Axiom of Choice may be invoked. Subsequently, our equivalence principle states that any algebra of observables (initially defined in the topos Sets) is empirically equivalent to a commutative one in some other topos.

  7. 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…

  8. Using Calculators in Mathematics 12. Student Text.

    ERIC Educational Resources Information Center

    Rising, Gerald R.; And Others

    This student textbook is designed to incorporate programable calculators in grade 12 mathematics. The seven chapters contained in this document are: (1) Using Calculators in Mathematics; (2) Sequences, Series, and Limits; (3) Iteration, Mathematical Induction, and the Binomial Theorem; (4) Applications of the Fundamental Counting Principle; (5)…

  9. On Fences, Forms and Mathematical Modeling

    ERIC Educational Resources Information Center

    Lege, Jerry

    2009-01-01

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

  10. Improving Mathematics Education: Resources for Decision Making.

    ERIC Educational Resources Information Center

    Leinwand, Steve, Ed.; Burrill, Gail, Ed.

    This report describes the message of current publications in mathematics education. Eight documents were selected to be reviewed which provides a starting point for readers. Papers include: (1) "Principles and Standards for School Mathematics"; (2) "Adding It Up: Helping Children Learn Mathematics"; (3) "How People Learn: Brain, Mind, Experience,…

  11. School Mathematics in the Era of Globalization

    ERIC Educational Resources Information Center

    Namukasa, Immaculate

    2004-01-01

    This essay reviews the principles motivating contemporary"critical mathematics" discourses. Drawing from varied critical discourses including ethno-mathematics, critical theory, post-structural theory, and situated and ecological cognition, the essay examines the pragmatics of critiques to the privileged role of school mathematics in the era of…

  12. Leadership in Mathematics Education: Roles and Responsibilities

    ERIC Educational Resources Information Center

    Posamentier, Alfred S.

    2013-01-01

    This article partitions leadership in mathematics education into two categories: leadership in defining and maintaining important principles in teaching mathematics, and leadership in informing the public about the importance of mathematics today and in the future. Examples of both types of leadership are given in the article. Teacher leaders in…

  13. Compressed modes for variational problems in mathematics and physics

    PubMed Central

    Ozoliņš, Vidvuds; Lai, Rongjie; Caflisch, Russel; Osher, Stanley

    2013-01-01

    This article describes a general formalism for obtaining spatially localized (“sparse”) solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems, such as the important case of Schrödinger’s equation in quantum mechanics. Sparsity is achieved by adding an regularization term to the variational principle, which is shown to yield solutions with compact support (“compressed modes”). Linear combinations of these modes approximate the eigenvalue spectrum and eigenfunctions in a systematically improvable manner, and the localization properties of compressed modes make them an attractive choice for use with efficient numerical algorithms that scale linearly with the problem size. PMID:24170861

  14. Compressed modes for variational problems in mathematics and physics.

    PubMed

    Ozolins, Vidvuds; Lai, Rongjie; Caflisch, Russel; Osher, Stanley

    2013-11-12

    This article describes a general formalism for obtaining spatially localized ("sparse") solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems, such as the important case of Schrödinger's equation in quantum mechanics. Sparsity is achieved by adding an regularization term to the variational principle, which is shown to yield solutions with compact support ("compressed modes"). Linear combinations of these modes approximate the eigenvalue spectrum and eigenfunctions in a systematically improvable manner, and the localization properties of compressed modes make them an attractive choice for use with efficient numerical algorithms that scale linearly with the problem size.

  15. Identification of the noise using mathematical modelling

    NASA Astrophysics Data System (ADS)

    Dobeš, Josef; Kozubková, Milada; Mahdal, Miroslav

    2016-03-01

    In engineering applications the noisiness of a component or the whole device is a common problem. Currently, a lot of effort is put to eliminate noise of the already produced devices, to prevent generation of acoustic waves during the design of new components, or to specify the operating problems based on noisiness change. The experimental method and the mathematical modelling method belong to these identification methods. With the power of today's computers the ability to identify the sources of the noise on the mathematical modelling level is a very appreciated tool for engineers. For example, the noise itself may be generated by the vibration of the solid object, combustion, shock, fluid flow around an object or cavitation at the fluid flow in an object. For the given task generating the noise using fluid flow on the selected geometry and propagation of the acoustic waves and their subsequent identification are solved and evaluated. In this paper the principle of measurement of variables describing the fluid flow field and acoustic field are described. For the solution of fluid flow a mathematical model implemented into the CFD code is used. The mathematical modelling evaluation of the flow field is compared to the experimental data.

  16. Bernoulli's Principle

    ERIC Educational Resources Information Center

    Hewitt, Paul G.

    2004-01-01

    Some teachers have difficulty understanding Bernoulli's principle particularly when the principle is applied to the aerodynamic lift. Some teachers favor using Newton's laws instead of Bernoulli's principle to explain the physics behind lift. Some also consider Bernoulli's principle too difficult to explain to students and avoid teaching it…

  17. Mathematics and Measurement

    PubMed Central

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

    2001-01-01

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

  18. Mathematical Geology.

    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)

  19. Mathematical foundations of biomechanics.

    PubMed

    Niederer, Peter F

    2010-01-01

    The aim of biomechanics is the analysis of the structure and function of humans, animals, and plants by means of the methods of mechanics. Its foundations are in particular embedded in mathematics, physics, and informatics. Due to the inherent multidisciplinary character deriving from its aim, biomechanics has numerous connections and overlapping areas with biology, biochemistry, physiology, and pathophysiology, along with clinical medicine, so its range is enormously wide. This treatise is mainly meant to serve as an introduction and overview for readers and students who intend to acquire a basic understanding of the mathematical principles and mechanics that constitute the foundation of biomechanics; accordingly, its contents are limited to basic theoretical principles of general validity and long-range significance. Selected examples are included that are representative for the problems treated in biomechanics. Although ultimate mathematical generality is not in the foreground, an attempt is made to derive the theory from basic principles. A concise and systematic formulation is thereby intended with the aim that the reader is provided with a working knowledge. It is assumed that he or she is familiar with the principles of calculus, vector analysis, and linear algebra. PMID:21303323

  20. Mathematics anxiety and mathematics achievement

    NASA Astrophysics Data System (ADS)

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

    2003-09-01

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

  1. Rainforest Mathematics

    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…

  2. First Principles Simulation of the Bonding, Vibrational, and Electronic Properties of the Hydration Shells of the High-Spin Fe 3+ Ion in Aqueous Solutions

    SciTech Connect

    Bogatko, Stuart A.; Bylaska, Eric J.; Weare, John H.

    2010-02-11

    Results of parameter-free first principles simulations of a spin up 3d5 Fe3+ ion hydrated in an aqueous solution (64 waters, 30 ps, 300 K) are reported. The first hydration shell associated with the first maximum of the radial distribution function, gFeO(r), at d(Fe-OI) = 2.11-2.15 Å, contains 6 waters with average d(OH) = 0.99 Å, in good agreement with observations. A second shell with average coordination number 13.3 can be identified with average shell radius of d(Fe-OII) = 4.21-4.32 Å. The waters in this hydration shell are coordinated to the first shell via a trigonal H-bond network with d(OI-OII) = 2.7-2.9 Å, also in agreement with experimental measurements. The first shell tilt angle average is 33.4° as compared to the reported value of 41°. Wannier-Boys orbitals (WBO) show an interaction between the unoccupied 3d orbitals of the Fe3+ valence (spin up, 3d5) and the occupied spin down lone pair orbitals of first shell waters. The effect of the spin ordering of the Fe3+ ion on the WBO is not observed beyond the first shell. From this local bond analysis and consistent with other observations, the electronic structure of waters in the second shell is similar to that of a bulk water even in this strongly interacting system. H-bond decomposition shows significant bulk-like structure within the second shell for Fe3+. The vibrational density of states shows a first shell red shift of 230 cm-1 for the v1,2v2,v3 overtone, in reasonable agreement with experimental estimates for trivalent cations (300 cm-1). No exchanges between first and second shell were observed. Waters in the second shell exchanged with bulk waters via dissociative and associative mechanisms. Results are compared with an AIMD study of Al3+ and 64 waters. For Fe3+ the average first shell tilt angle is larger and the tilt angle distribution wider. H-bond decomposition shows that second shell to second shell H-bonding is enhanced in Fe3+ suggesting an earlier onset of bulk

  3. 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…

  4. Geometrical Analogies in Mathematics Lessons

    ERIC Educational Resources Information Center

    Eid, Wolfram

    2007-01-01

    A typical form of thinking to approach problem solutions humanly is thinking in analogous structures. Therefore school, especially mathematical lessons should help to form and to develop corresponding heuristic abilities of the pupils. In the contribution, a summary of possibilities of mathematics lessons regarding this shall particularly be…

  5. The principle of finiteness - a guideline for physical laws

    NASA Astrophysics Data System (ADS)

    Sternlieb, Abraham

    2013-04-01

    I propose a new principle in physics-the principle of finiteness (FP). It stems from the definition of physics as a science that deals with measurable dimensional physical quantities. Since measurement results including their errors, are always finite, FP postulates that the mathematical formulation of legitimate laws in physics should prevent exactly zero or infinite solutions. I propose finiteness as a postulate, as opposed to a statement whose validity has to be corroborated by, or derived theoretically or experimentally from other facts, theories or principles. Some consequences of FP are discussed, first in general, and then more specifically in the fields of special relativity, quantum mechanics, and quantum gravity. The corrected Lorentz transformations include an additional translation term depending on the minimum length epsilon. The relativistic gamma is replaced by a corrected gamma, that is finite for v=c. To comply with FP, physical laws should include the relevant extremum finite values in their mathematical formulation. An important prediction of FP is that there is a maximum attainable relativistic mass/energy which is the same for all subatomic particles, meaning that there is a maximum theoretical value for cosmic rays energy. The Generalized Uncertainty Principle required by Quantum Gravity is actually a necessary consequence of FP at Planck's scale. Therefore, FP may possibly contribute to the axiomatic foundation of Quantum Gravity.

  6. Mathematics Education.

    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…

  7. Making Mathematics.

    ERIC Educational Resources Information Center

    Huckstep, Peter

    2002-01-01

    Contends teachers must resist the temptation to suggest that, while children can create stories and melodies, they cannot create mathematics. Quotes mathematician G. H. Hardy: "A mathematician, like a painter or poet, is a 'maker' of patterns." Considers mathematics should be able to stand up for itself. (BT)

  8. Technical Mathematics.

    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…

  9. Mathematics Scrapbook

    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…

  10. Principled Narrative

    ERIC Educational Resources Information Center

    MacBeath, John; Swaffield, Sue; Frost, David

    2009-01-01

    This article provides an overview of the "Carpe Vitam: Leadership for Learning" project, accounting for its provenance and purposes, before focusing on the principles for practice that constitute an important part of the project's legacy. These principles framed the dialogic process that was a dominant feature of the project and are presented,…

  11. Buridan's Principle

    NASA Astrophysics Data System (ADS)

    Lamport, Leslie

    2012-08-01

    Buridan's principle asserts that a discrete decision based upon input having a continuous range of values cannot be made within a bounded length of time. It appears to be a fundamental law of nature. Engineers aware of it can design devices so they have an infinitessimal probability of not making a decision quickly enough. Ignorance of the principle could have serious consequences.

  12. Approximate solution of two-term fractional-order diffusion, wave-diffusion, and telegraph models arising in mathematical physics using optimal homotopy asymptotic method

    NASA Astrophysics Data System (ADS)

    Sarwar, S.; Rashidi, M. M.

    2016-07-01

    This paper deals with the investigation of the analytical approximate solutions for two-term fractional-order diffusion, wave-diffusion, and telegraph equations. The fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], (1,2), and [1,2], respectively. In this paper, we extended optimal homotopy asymptotic method (OHAM) for two-term fractional-order wave-diffusion equations. Highly approximate solution is obtained in series form using this extended method. Approximate solution obtained by OHAM is compared with the exact solution. It is observed that OHAM is a prevailing and convergent method for the solutions of nonlinear-fractional-order time-dependent partial differential problems. The numerical results rendering that the applied method is explicit, effective, and easy to use, for handling more general fractional-order wave diffusion, diffusion, and telegraph problems.

  13. Mathematical Geology.

    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)

  14. Mathematical Games

    ERIC Educational Resources Information Center

    Gardner, Martin

    1978-01-01

    Describes the life and work of Charles Peirce, U.S. mathematician and philosopher. His accomplishments include contributions to logic, the foundations of mathematics and scientific method, and decision theory and probability theory. (MA)

  15. Mathematics of Experimentally Generated Chemoattractant Gradients.

    PubMed

    Postma, Marten; van Haastert, Peter J M

    2016-01-01

    Many eukaryotic cells move in the direction of a chemical gradient. Several assays have been developed to measure this chemotactic response, but no complete mathematical models of the spatial and temporal gradients are available to describe the fundamental principles of chemotaxis. Here we provide analytical solutions for the gradients formed by release of chemoattractant from a point source by passive diffusion or forced flow (micropipettes) and gradients formed by laminar diffusion in a Zigmond chamber. The results show that gradients delivered with a micropipette are formed nearly instantaneously, are very steep close to the pipette, and have a steepness that is strongly dependent on the distance from the pipette. In contrast, gradients in a Zigmond chamber are formed more slowly, are nearly independent of the distance from the source, and resemble the temporal and spatial properties of the natural cAMP wave that Dictyostelium cells experience during cell aggregation. PMID:27271915

  16. Mathematics of Experimentally Generated Chemoattractant Gradients.

    PubMed

    Postma, Marten; van Haastert, Peter J M

    2016-01-01

    Many eukaryotic cells move in the direction of a chemical gradient. Several assays have been developed to measure this chemotactic response, but no complete mathematical models of the spatial and temporal gradients are available to describe the fundamental principles of chemotaxis. Here we provide analytical solutions for the gradients formed by release of chemoattractant from a point source by passive diffusion or forced flow (micropipettes) and gradients formed by laminar diffusion in a Zigmond chamber. The results show that gradients delivered with a micropipette are formed nearly instantaneously, are very steep close to the pipette, and have a steepness that is strongly dependent on the distance from the pipette. In contrast, gradients in a Zigmond chamber are formed more slowly, are nearly independent of the distance from the source, and resemble the temporal and spatial properties of the natural cAMP wave that Dictyostelium cells experience during cell aggregation.

  17. Technology in K-12 Mathematics Classrooms

    ERIC Educational Resources Information Center

    Ozel, Serkan; Yetkiner, Zeynep Ebrar; Capraro, Robert M.

    2008-01-01

    Technology integration in mathematics classrooms is important to the field of education, not only because today's society is becoming more and more advanced and reliant upon technology but also because schools are beginning to embrace technology as an essential part of their curricula. The Principles and Standards for School Mathematics (National…

  18. Building Blocks for Young Children's Mathematical Development.

    ERIC Educational Resources Information Center

    Sarama, Julie; Clements, Douglas H.

    2002-01-01

    Describes the design principles behind a set of research-based software microworlds included in the "Building Blocks" program, a pre-kindergarten to grade 2 software-based mathematics curriculum. Discusses how to help children extend and mathematize their everyday activities and presents the nine-step design process model used. (Author/LRW)

  19. Influence of the nature of the alcohol on the principles of the photocatalytic liberation of hydrogen from aqueous-organic solutions of europium salts

    SciTech Connect

    Myakon'kii, A.G.; Rozenkevich, M.B.; Potapova, G.V.

    1988-09-01

    The process of photocatalytic liberation of hydrogen from aqueous alcohol (ROH - CH/sub 3/OH, C/sub 2/H/sub 5/OH, C/sub 3/H/sub 7/OH, iso-C/sub 3/H/sub 7/OH) solutions of europium salts was investigated. In solutions containing sodium formate as a second organic component, HCOONa and ROH take part in the photoreduction of Eu(III), whereas the main role in the photooxidation of Eu(II) is played by ROH molecules. Such behavior of the system is explained by transfer of an electron in these reactions according to outer- and inner-sphere mechanism, respectively.

  20. From Square Dance to Mathematics

    ERIC Educational Resources Information Center

    Bremer, Zoe

    2010-01-01

    In this article, the author suggests a cross-curricular idea that can link with PE, dance, music and history. Teacher David Schmitz, a maths teacher in Illinois who was also a square dance caller, had developed a maths course that used the standard square dance syllabus to teach mathematical principles. He presents an intensive, two-week course…

  1. Lessons in Developing Mathematical Courseware.

    ERIC Educational Resources Information Center

    Harding, R. D.; And Others

    1995-01-01

    As part of a cross-disciplinary project to develop interactive, multimedia college instruction, a mathematics team developed a hypertext version of an existing textbook and created seven modules in basic calculus. Lessons and principles learned about courseware development are presented here to help faculty without previous software experience to…

  2. Problems of Mathematical Finance by Stochastic Control Methods

    NASA Astrophysics Data System (ADS)

    Stettner, Łukasz

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

  3. Dynamic Boolean Mathematics

    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…

  4. Mathematical wit and mathematical cognition.

    PubMed

    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. PMID:23512504

  5. Quantum Mechanics and the Principle of Least Radix Economy

    NASA Astrophysics Data System (ADS)

    Garcia-Morales, Vladimir

    2015-03-01

    A new variational method, the principle of least radix economy, is formulated. The mathematical and physical relevance of the radix economy, also called digit capacity, is established, showing how physical laws can be derived from this concept in a unified way. The principle reinterprets and generalizes the principle of least action yielding two classes of physical solutions: least action paths and quantum wavefunctions. A new physical foundation of the Hilbert space of quantum mechanics is then accomplished and it is used to derive the Schrödinger and Dirac equations and the breaking of the commutativity of spacetime geometry. The formulation provides an explanation of how determinism and random statistical behavior coexist in spacetime and a framework is developed that allows dynamical processes to be formulated in terms of chains of digits. These methods lead to a new (pre-geometrical) foundation for Lorentz transformations and special relativity. The Parker-Rhodes combinatorial hierarchy is encompassed within our approach and this leads to an estimate of the interaction strength of the electromagnetic and gravitational forces that agrees with the experimental values to an error of less than one thousandth. Finally, it is shown how the principle of least-radix economy naturally gives rise to Boltzmann's principle of classical statistical thermodynamics. A new expression for a general (path-dependent) nonequilibrium entropy is proposed satisfying the Second Law of Thermodynamics.

  6. Some unsolved problems in discrete mathematics and mathematical cybernetics

    NASA Astrophysics Data System (ADS)

    Korshunov, Aleksei D.

    2009-10-01

    There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.

  7. Thermodynamics of Dilute Solutions.

    ERIC Educational Resources Information Center

    Jancso, Gabor; Fenby, David V.

    1983-01-01

    Discusses principles and definitions related to the thermodynamics of dilute solutions. Topics considered include dilute solution, Gibbs-Duhem equation, reference systems (pure gases and gaseous mixtures, liquid mixtures, dilute solutions), real dilute solutions (focusing on solute and solvent), terminology, standard states, and reference systems.…

  8. Effects of the Multiple Solutions and Question Prompts on Generalization and Justification for Non-Routine Mathematical Problem Solving in a Computer Game Context

    ERIC Educational Resources Information Center

    Lee, Chun-Yi; Chen, Ming-Jang; Chang, Wen-Long

    2014-01-01

    The aim of this study is to investigate the effects of solution methods and question prompts on generalization and justification of non-routine problem solving for Grade 9 students. The learning activities are based on the context of the frog jumping game. In addition, related computer tools were used to support generalization and justification of…

  9. Motivational Qualities of Mathematical Experiences for Turkish Preservice Kindergarten Teachers

    ERIC Educational Resources Information Center

    Bintas, Jale

    2008-01-01

    This study is based on the principle that the mathematical anxiety in preservice kindergarten teachers-to-be should be removed and they should be encouraged towards mathematics. It is expected from teachers-to-be who are able to construct this confidence to prepare exercises improving mathematical ideas for their students. This study was carried…

  10. Teaching Gifted Children Mathematics in Grades Four Through Six.

    ERIC Educational Resources Information Center

    Gensley, Juliana T.

    Intended for teachers of gifted students in grades 4-6, the guide emphasizes the need for specialized instruction in mathematics, suggests methods for teaching mathematical facts and concepts, describes approaches and materials to develop students' understanding of mathematical principles, and explores ways to build skills and creativity. Stressed…

  11. How Bob Barker Would (Probably) Teach Discrete Mathematics

    ERIC Educational Resources Information Center

    Urness, Timothy

    2010-01-01

    This article proposes a discrete mathematics course in which games from "The Price Is Right" are used to engage students in a deeper, practical study of discrete mathematics. The games themselves are not the focus of the course; rather, the mathematical principles of the games give motivation for the concepts being taught. The game examples are…

  12. Dissociative Binding of Carboxylic Acid Ligand on Nanoceria Surface in Aqueous Solution: A Joint in Situ Spectroscopic Characterization and First-Principles Study

    SciTech Connect

    Lu, Zhou; Karakoti, Ajay S.; Velarde Ruiz Esparza, Luis A.; Wang, Weina; Yang, Ping; Thevuthasan, Suntharampillai; Wang, Hongfei

    2013-11-21

    Carboxylic acid is a common ligand anchoring group to functionalize nanoparticle surfaces. Its binding structures and mechanisms as a function of the oxidation states of metal oxide nanoparticle surfaces are not well characterized experimentally. We present an in situ sum frequency generation vibrational spectroscopy (SFG-VS) study on the binding of deuterated acetic acid on ceria nanoparticles in the aqueous solution. In the SFG experiment, ceria nanoparticles were deposited on the flat surface of a CaF2 hemisphere in contact with acetic acid solutions. While the ceria nanoparticle deprotonated the acetic acid, the CaF2 surface could not. Thus, the binding of the deprotonated acetic acid on ceria can be selectively probed. SFG spectra revealed that the binding modes of the carboxylate group depend on the oxidation states of the ceria surfaces. SFG polarization analysis suggested that the bidentate chelating and bridging binding modes co-exist on the reduced ceria surfaces, while the oxidized ceria surfaces are dominated by the bidentate bridging mode. The direct spectroscopic evidence helps to clarify the binding structures and mechanisms on the ceria nanoparticles. Furthermore, the middle-infrared (IR) transparent CaF2 and its chemical inertness make CaF2 and similar substrate materials good candidates for direct SFG-VS measurement of nanoparticle surface reactions and binding chem-istry.

  13. Modulation of the interstitial fluid pressure by high intensity focused ultrasound as a way to alter local fluid and solute movement: insights from a mathematical model.

    PubMed

    Sassaroli, E; O'Neill, B E

    2014-11-21

    High intensity focused ultrasound (HIFU) operated in thermal mode has been reported to reduce interstitial fluid pressure and improve the penetration of large macromolecules and nanoparticles in tumor and normal tissue. Little is understood about how the interstitial fluid pressure and velocity as well as the interstitial macromolecule transport are affected by HIFU exposure. A mathematical model is presented here which sheds light on the initial biophysical changes brought about HIFU. Our continuum model treats tissue as an effective poro-elastic material that reacts to elevated temperatures with a rapid drop in interstitial elastic modulus. Using parameters from the literature, the model is extrapolated to derive information on the effect in tumors, and to predict its impact on the convective and diffusive transport of macromolecular drugs. The model is first solved using an analytical approximation with step-wise changes at each boundary, and then solved numerically starting from a Gaussian beam approximation of the ultrasound treatment. Our results indicate that HIFU causes a rapid drop in interstitial fluid pressure that may be exploited to facilitate convection of macromolecules from vasculature to the exposed region. However, following a short recovery period in which the interstitial fluid pressure is normalized, transport returns to normal and the advantages disappear over time. The results indicate that this effect is strongest for the delivery of large molecules and nanoparticles that are in the circulation at the time of treatment. The model may be easily applied to more complex situations involving effects on vascular permeability and diffusion. PMID:25327766

  14. Kinetics on Demand Is a Simple Mathematical Solution that Fits Recorded Caffeine-Induced Luminal SR Ca2+ Changes in Smooth Muscle Cells

    PubMed Central

    Perez-Rosas, Norma C.; Gomez-Viquez, Norma L.; Dagnino-Acosta, Adan; Santillan, Moises; Guerrero-Hernandez, Agustín

    2015-01-01

    The process of Ca2+ release from sarcoplasmic reticulum (SR) comprises 4 phases in smooth muscle cells. Phase 1 is characterized by a large increase of the intracellular Ca2+ concentration ([Ca2+]i) with a minimal reduction of the free luminal SR [Ca2+] ([Ca2+]FSR). Importantly, active SR Ca2+ ATPases (SERCA pumps) are necessary for phase 1 to occur. This situation cannot be explained by the standard kinetics that involves a fixed amount of luminal Ca2+ binding sites. A new mathematical model was developed that assumes an increasing SR Ca2+ buffering capacity in response to an increase of the luminal SR [Ca2+] that is called Kinetics-on-Demand (KonD) model. This approach can explain both phase 1 and the refractory period associated with a recovered [Ca2+]FSR. Additionally, our data suggest that active SERCA pumps are a requisite for KonD to be functional; otherwise luminal SR Ca2+ binding proteins switch to standard kinetics. The importance of KonD Ca2+ binding properties is twofold: a more efficient Ca2+ release process and that [Ca2+]FSR and Ca2+-bound to SR proteins ([Ca2+]BSR) can be regulated separately allowing for Ca2+ release to occur (provided by Ca2+-bound to luminal Ca2+ binding proteins) without an initial reduction of the [Ca2+]FSR. PMID:26390403

  15. Genetic principles.

    PubMed

    Abuelo, D

    1987-01-01

    The author discusses the basic principles of genetics, including the classification of genetic disorders and a consideration of the rules and mechanisms of inheritance. The most common pitfalls in clinical genetic diagnosis are described, with emphasis on the problem of the negative or misleading family history.

  16. Mathematical Visualization

    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…

  17. Relevant Mathematics.

    ERIC Educational Resources Information Center

    Catterton, Gene; And Others

    This material was developed to be used with the non college-bound student in the senior high school. It provides the student with everyday problems and experiences in which practical mathematical applications are made. The package includes worksheets pertaining to letterhead invoices, sales slips, payroll sheets, inventory sheets, carpentry and…

  18. Is the promise of methadone Kenya’s solution to managing HIV and addiction? A mixed-method mathematical modelling and qualitative study

    PubMed Central

    Rhodes, Tim; Guise, Andy; Ndimbii, James; Strathdee, Steffanie; Ngugi, Elizabeth; Platt, Lucy; Kurth, Ann; Cleland, Charles; Vickerman, Peter

    2015-01-01

    Background and objectives Promoted globally as an evidence-based intervention in the prevention of HIV and treatment of heroin addiction among people who inject drugs (PWID), opioid substitution treatment (OST) can help control emerging HIV epidemics among PWID. With implementation in December 2014, Kenya is the third Sub-Saharan African country to have introduced OST. We combine dynamic mathematical modelling with qualitative sociological research to examine the ‘promise of methadone’ to Kenya. Methods, setting and participants We model the HIV prevention impact of OST in Nairobi, Kenya, at different levels of intervention coverage. We draw on thematic analyses of 109 qualitative interviews with PWID, and 43 with stakeholders, to chart their narratives of expectation in relation to the promise of methadone. Results The modelled impact of OST shows relatively slight reductions in HIV incidence (5–10%) and prevalence (2–4%) over 5 years at coverage levels (around 10%) anticipated in the planned roll-out of OST. However, there is a higher impact with increased coverage, with 40% coverage producing a 20% reduction in HIV incidence, even when accounting for relatively high sexual transmissions. Qualitative findings emphasise a culture of ‘rationed expectation’ in relation to access to care and a ‘poverty of drug treatment opportunity’. In this context, the promise of methadone may be narrated as a symbol of hope—both for individuals and community—in relation to addiction recovery. Conclusions Methadone offers HIV prevention potential, but there is a need to better model the effects of sexual HIV transmission in mediating the impact of OST among PWID in settings characterised by a combination of generalised and concentrated epidemics. We find that individual and community narratives of methadone as hope for recovery coexist with policy narratives positioning methadone primarily in relation to HIV prevention. Our analyses show the value of mixed

  19. 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…

  20. The Nature and Use of Open Problems in Mathematics Education: Mathematical and Pedagogical Perspectives.

    ERIC Educational Resources Information Center

    Silver, Edward A.

    1995-01-01

    Discusses varieties of open-ended problems in mathematics, including problems that are unsolved in the field of mathematics, are open with respect to solution method, are open to interpretation of the problem or solutions, or that invite other problems as follow-up. (Author/MKR)

  1. First principles studies on the impact of point defects on the phase stability of (AlxCr1-x)2O3 solid solutions

    NASA Astrophysics Data System (ADS)

    Koller, C. M.; Koutná, N.; Ramm, J.; Kolozsvári, S.; Paulitsch, J.; Holec, D.; Mayrhofer, P. H.

    2016-02-01

    Density Functional Theory applying the generalised gradient approximation is used to study the phase stability of (AlxCr1-x)2O3 solid solutions in the context of physical vapour deposition (PVD). Our results show that the energy of formation for the hexagonal α phase is lower than for the metastable cubic γ and B1-like phases-independent of the Al content x. Even though this suggests higher stability of the α phase, its synthesis by physical vapour deposition is difficult for temperatures below 800 °C. Aluminium oxide and Al-rich oxides typically exhibit a multi-phased, cubic-dominated structure. Using a model system of (Al0.69Cr0.31)2O3 which experimentally yields larger fractions of the desired hexagonal α phase, we show that point defects strongly influence the energetic relationships. Since defects and in particular point defects, are unavoidably present in PVD coatings, they are important factors and can strongly influence the stability regions. We explicitly show that defects with low formation energies (e.g. metal Frenkel pairs) are strongly preferred in the cubic phases, hence a reasonable factor contributing to the observed thermodynamically anomalous phase composition.

  2. Radar principles

    NASA Technical Reports Server (NTRS)

    Sato, Toru

    1989-01-01

    Discussed here is a kind of radar called atmospheric radar, which has as its target clear air echoes from the earth's atmosphere produced by fluctuations of the atmospheric index of refraction. Topics reviewed include the vertical structure of the atmosphere, the radio refractive index and its fluctuations, the radar equation (a relation between transmitted and received power), radar equations for distributed targets and spectral echoes, near field correction, pulsed waveforms, the Doppler principle, and velocity field measurements.

  3. A mathematical model of post-instability in fluid mechanics

    NASA Technical Reports Server (NTRS)

    Zak, M. A.

    1982-01-01

    Postinstability of fluids is eliminated in numerical models by introducing multivalued velocity fields after discarding the principle of impenetrability. Smooth functions are shown to be incapable of keeping the derivatives from going towards infinity when iterating solutions for the governing equations such as those defined by Navier-Stokes. Enlarging the class of functions is shown to be necessary to eliminate the appearance of imaginary characteristic roots in the systems of arbitrary partial differential equations, a condition which leads to physically impossible motions. The enlarging is demonstrated to be achievable by allowing several individual particles with different velocities to appear at the same point of space, and the subsequent multivaluedness of the solutions is purely a mathematical concern, rather than one of actual physical existence. Applications are provided for an inviscid fluid and for turbulence.

  4. Fluorescence recovery after photobleaching (FRAP) experiments under conditions of uniform disk illumination. Critical comparison of analytical solutions, and a new mathematical method for calculation of diffusion coefficient D.

    PubMed Central

    Lopez, A; Dupou, L; Altibelli, A; Trotard, J; Tocanne, J F

    1988-01-01

    A simple fluorescence recovery after photobleaching (FRAP) apparatus using a fluorescence microscope with a conventional mercury arc lamp, working under conditions of "uniform disk illumination" is described. This set-up was designed essentially for the use of anthracene as fluorescent probe, which is bleached (photodimerization reaction) by illumination in the near ultraviolet range (360 nm). It is shown that the lateral diffusion coefficients D can be readily calculated from fluorescence recovery curves using a finite differentiate method in combination with statistical analysis of the data. In contrast to the analytical solutions so far described, this numerical approach is particularly versatile. With a minimization algorithm, D and the probe mobile fraction can be readily calculated for any recovery time under various experimental conditions. These include different probe concentration profiles in the illuminated area after the bleaching step, and situations of infinite or noninfinite reservoir in the diffusion area outside the illuminated area. PMID:3395663

  5. 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…

  6. Generating Problems from Problems and Solutions from Solutions

    ERIC Educational Resources Information Center

    Arcavi, Abraham; Resnick, Zippora

    2008-01-01

    This article describes a geometrical solution to a problem that is usually solved geometrically as an example of how alternative solutions may enrich the teaching and learning of mathematics. (Contains 11 figures.)

  7. THERMAL-GRAVITATIONAL WIND EQUATION FOR THE WIND-INDUCED GRAVITATIONAL SIGNATURE OF GIANT GASEOUS PLANETS: MATHEMATICAL DERIVATION, NUMERICAL METHOD, AND ILLUSTRATIVE SOLUTIONS

    SciTech Connect

    Zhang, Keke; Kong, Dali; Schubert, Gerald E-mail: D.Kong@exeter.ac.uk

    2015-06-20

    The standard thermal wind equation (TWE) relating the vertical shear of a flow to the horizontal density gradient in an atmosphere has been used to calculate the external gravitational signature produced by zonal winds in the interiors of giant gaseous planets. We show, however, that in this application the TWE needs to be generalized to account for an associated gravitational perturbation. We refer to the generalized equation as the thermal-gravitational wind equation (TGWE). The generalized equation represents a two-dimensional kernel integral equation with the Green’s function in its integrand and is hence much more difficult to solve than the standard TWE. We develop an extended spectral method for solving the TGWE in spherical geometry. We then apply the method to a generic gaseous Jupiter-like object with idealized zonal winds. We demonstrate that solutions of the TGWE are substantially different from those of the standard TWE. We conclude that the TGWE must be used to estimate the gravitational signature of zonal winds in giant gaseous planets.

  8. Thermal-gravitational Wind Equation for the Wind-induced Gravitational Signature of Giant Gaseous Planets: Mathematical Derivation, Numerical Method, and Illustrative Solutions

    NASA Astrophysics Data System (ADS)

    Zhang, Keke; Kong, Dali; Schubert, Gerald

    2015-06-01

    The standard thermal wind equation (TWE) relating the vertical shear of a flow to the horizontal density gradient in an atmosphere has been used to calculate the external gravitational signature produced by zonal winds in the interiors of giant gaseous planets. We show, however, that in this application the TWE needs to be generalized to account for an associated gravitational perturbation. We refer to the generalized equation as the thermal-gravitational wind equation (TGWE). The generalized equation represents a two-dimensional kernel integral equation with the Green’s function in its integrand and is hence much more difficult to solve than the standard TWE. We develop an extended spectral method for solving the TGWE in spherical geometry. We then apply the method to a generic gaseous Jupiter-like object with idealized zonal winds. We demonstrate that solutions of the TGWE are substantially different from those of the standard TWE. We conclude that the TGWE must be used to estimate the gravitational signature of zonal winds in giant gaseous planets.

  9. Bistable solutions for the electron energy distribution function in electron swarms in xenon: a comparison between the results of first-principles particle simulations and conventional Boltzmann equation analysis

    NASA Astrophysics Data System (ADS)

    Dyatko, Nikolay; Donkó, Zoltán

    2015-08-01

    At low reduced electric fields the electron energy distribution function in heavy noble gases can take two distinct shapes. This ‘bistability effect’—in which electron-electron (Coulomb) collisions play an essential role—is analyzed here for Xe with a Boltzmann equation approach and with a first principles particle simulation method. The solution of the Boltzmann equation adopts the usual approximations of (i) searching for the distribution function in the form of two terms (‘two-term approximation’), (ii) neglecting the Coulomb part of the collision integral for the anisotropic part of the distribution function, (iii) treating Coulomb collisions as binary events, and (iv) truncating the range of the electron-electron interaction beyond a characteristic distance. The particle-based simulation method avoids these approximations: the many-body interactions within the electron gas with a true (un-truncated) Coulomb potential are described by a molecular dynamics algorithm, while the collisions between electrons and the background gas atoms are treated with Monte Carlo simulation. We find a good general agreement between the results of the two techniques, which confirms, to a certain extent, the approximations used in the solution of the Boltzmann equation. The differences observed between the results are believed to originate from these approximations and from the presence of statistical noise in the particle simulations.

  10. 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…

  11. Principles of Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Landé, Alfred

    2013-10-01

    Preface; Introduction: 1. Observation and interpretation; 2. Difficulties of the classical theories; 3. The purpose of quantum theory; Part I. Elementary Theory of Observation (Principle of Complementarity): 4. Refraction in inhomogeneous media (force fields); 5. Scattering of charged rays; 6. Refraction and reflection at a plane; 7. Absolute values of momentum and wave length; 8. Double ray of matter diffracting light waves; 9. Double ray of matter diffracting photons; 10. Microscopic observation of ρ (x) and σ (p); 11. Complementarity; 12. Mathematical relation between ρ (x) and σ (p) for free particles; 13. General relation between ρ (q) and σ (p); 14. Crystals; 15. Transition density and transition probability; 16. Resultant values of physical functions; matrix elements; 17. Pulsating density; 18. General relation between ρ (t) and σ (є); 19. Transition density; matrix elements; Part II. The Principle of Uncertainty: 20. Optical observation of density in matter packets; 21. Distribution of momenta in matter packets; 22. Mathematical relation between ρ and σ; 23. Causality; 24. Uncertainty; 25. Uncertainty due to optical observation; 26. Dissipation of matter packets; rays in Wilson Chamber; 27. Density maximum in time; 28. Uncertainty of energy and time; 29. Compton effect; 30. Bothe-Geiger and Compton-Simon experiments; 31. Doppler effect; Raman effect; 32. Elementary bundles of rays; 33. Jeans' number of degrees of freedom; 34. Uncertainty of electromagnetic field components; Part III. The Principle of Interference and Schrödinger's equation: 35. Physical functions; 36. Interference of probabilities for p and q; 37. General interference of probabilities; 38. Differential equations for Ψp (q) and Xq (p); 39. Differential equation for фβ (q); 40. The general probability amplitude Φβ' (Q); 41. Point transformations; 42. General theorem of interference; 43. Conjugate variables; 44. Schrödinger's equation for conservative systems; 45. Schr

  12. Mathematizing Darwin.

    PubMed

    Edwards, A W F

    2011-03-01

    Ernst Mayr called the first part of the evolutionary synthesis the 'Fisherian synthesis' on account of the dominant role played by R.A. Fisher in forging a mathematical theory of natural selection together with J.B.S. Haldane and Sewall Wright in the decade 1922-1932. It is here argued that Fisher's contribution relied on a close reading of Darwin's work to a much greater extent than did the contributions of Haldane and Wright, that it was synthetic in contrast to their analytic approach and that it was greatly influenced by his friendship with the Darwin family, particularly with Charles's son Leonard. PMID:21423339

  13. A Study of Visualization for Mathematics Education

    NASA Technical Reports Server (NTRS)

    Daugherty, Sarah C.

    2008-01-01

    Graphical representations such as figures, illustrations, and diagrams play a critical role in mathematics and they are equally important in mathematics education. However, graphical representations in mathematics textbooks are static, Le. they are used to illustrate only a specific example or a limited set. of examples. By using computer software to visualize mathematical principles, virtually there is no limit to the number of specific cases and examples that can be demonstrated. However, we have not seen widespread adoption of visualization software in mathematics education. There are currently a number of software packages that provide visualization of mathematics for research and also software packages specifically developed for mathematics education. We conducted a survey of mathematics visualization software packages, summarized their features and user bases, and analyzed their limitations. In this survey, we focused on evaluating the software packages for their use with mathematical subjects adopted by institutions of secondary education in the United States (middle schools and high schools), including algebra, geometry, trigonometry, and calculus. We found that cost, complexity, and lack of flexibility are the major factors that hinder the widespread use of mathematics visualization software in education.

  14. Minimum Principles in Motor Control.

    PubMed

    Engelbrecht, Sascha E.

    2001-06-01

    Minimum (or minimal) principles are mathematical laws that were first used in physics: Hamilton's principle and Fermat's principle of least time are two famous example. In the past decade, a number of motor control theories have been proposed that are formally of the same kind as the minimum principles of physics, and some of these have been quite successful at predicting motor performance in a variety of tasks. The present paper provides a comprehensive review of this work. Particular attention is given to the relation between minimum theories in motor control and those used in other disciplines. Other issues around which the review is organized include: (1) the relation between minimum principles and structural models of motor planning and motor control, (2) the empirically-driven development of minimum principles and the danger of circular theorizing, and (3) the design of critical tests for minimum theories. Some perspectives for future research are discussed in the concluding section of the paper. Copyright 2001 Academic Press. PMID:11401453

  15. Tasks to Advance the Learning of Mathematics

    ERIC Educational Resources Information Center

    Greenes, Carole

    2014-01-01

    Tasks to Advance the Learning of Mathematics (TALMs) were developed to stimulate grades 5-8 students' curiosity about complex mathematical relationships, inspire them to reason abstractly and quantitatively, encourage them to consider and create alternative solution approaches, develop their skills to persuade others about the viability of one…

  16. Mathematics and Molecules: Exploring Connections via Programming.

    ERIC Educational Resources Information Center

    Ploger, Don; Carlock, Margaret

    1996-01-01

    Examines the self-directed activity of two students who learned about molecular structure by writing computer programs. The programs displayed the solution of a mathematics problem, then the programs were extended to represent several classes of organic molecules. Different ways to enhance mathematical connections to chemistry education are…

  17. Using Simulations in the Mathematics Class

    ERIC Educational Resources Information Center

    Santulli, Thomas V.

    2006-01-01

    The understanding and a liking towards mathematics can be very effectively developed in students by allowing them to find out the solutions for any basic problem or simulations, which are basically mathematical reenactments of nearly or completely hypothetical situations. The nontransitive relation of Efron's dice or the assignment of numbers in a…

  18. Teachers Promoting Student Mathematical Reasoning

    ERIC Educational Resources Information Center

    Mueller, Mary; Yankelewitz, Dina; Maher, Carolyn

    2014-01-01

    During an informal, after-school, math program, a group of middle school students worked collaboratively on open-ended problems. The students co-constructed arguments, provided justifications for their solutions, and engaged in mathematical reasoning. This paper describes the specific teacher moves that promoted this phenomenon. The findings of…

  19. Mathematical Reasoning in Teachers' Presentations

    ERIC Educational Resources Information Center

    Bergqvist, Tomas; Lithner, Johan

    2012-01-01

    This paper presents a study of the opportunities presented to students that allow them to learn different types of mathematical reasoning during teachers' ordinary task solving presentations. The characteristics of algorithmic and creative reasoning that are seen in the presentations are analyzed. We find that most task solutions are based on…

  20. Learning to Calculate and Learning Mathematics.

    ERIC Educational Resources Information Center

    Fearnley-Sander, Desmond

    1980-01-01

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

  1. Causal theories of evolution and wave propagation in mathematical physics

    SciTech Connect

    Kranys, M. )

    1989-11-01

    There are still many phenomena, especially in continuum physics, that are described by means of parabolic partial differential equations whose solution are not compatible with the causality principle. Compatibility with this principle is required also by the theory of relativity. A general form of hyperbolic operators for the most frequently occurring linear governing equations in mathematical physics is written down. It is then easy to convert any given parabolic equation to the hyperbolic form without necessarily entering into the cause of the inadequacy of the governing equation. The method is verified on the well-known example of Timoshenko's correction of the Bernoulli-Euler-Rayleigh beam equation for flexural motion. The Love-Rayleigh fourth-order differential equations for the longitudinal and torsional wave propagation in the rod is generalized with this method. The hyperbolic version (not to mention others) of the linear Korteweg-deVries equation and of the telegraph equation governing electromagnetic wave propagation through relaxing material are given. Lagrangians of all the equations studied are listed. For all the reasons given the author believes the hyperbolic governing equations to be physically and mathematically more realistic and adequate.

  2. 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…

  3. Quantum Superposition, Collapse, and the Default Specification Principle

    NASA Astrophysics Data System (ADS)

    Nikkhah Shirazi, Armin

    2014-03-01

    Quantum Superposition and collapse lie at the heart of the difficulty in understanding what quantum mechanics is exactly telling us about reality. We present here a principle which permits one to formulate a simple and general mathematical model that abstracts these features out of quantum theory. A precise formulation of this principle in terms of a set-theoretic axiom added to standard set theory may directly connect the foundations of physics to the foundations of mathematics.

  4. New computer system simplifies programming of mathematical equations

    NASA Technical Reports Server (NTRS)

    Reinfelds, J.; Seitz, R. N.; Wood, L. H.

    1966-01-01

    Automatic Mathematical Translator /AMSTRAN/ permits scientists or engineers to enter mathematical equations in their natural mathematical format and to obtain an immediate graphical display of the solution. This automatic-programming, on-line, multiterminal computer system allows experienced programmers to solve nonroutine problems.

  5. A Call for Mathematics Education Colleagues and Stakeholders to Collaboratively Engage with NCTM: In Response to Martin's Commentary

    ERIC Educational Resources Information Center

    Briars, Diane J.; Larson, Matt; Strutchens, Marilyn E.; Barnes, David

    2015-01-01

    In his commentary "The Collective Black and 'Principles to Actions,'" Martin (2015) offers a thought-provoking critique of "Principles to Actions: Ensuring Mathematical Success for All" (National Council of Teachers of Mathematics [NCTM], 2014). Martin (2015) states that the mathematics education community, in general, and the…

  6. Least Action Principle on an Air Table

    ERIC Educational Resources Information Center

    Provost, J. P.

    1975-01-01

    Presents a mathematical demonstration that the least action principle enables both the trajectories and the conservation laws (of energy, momentum, and angular momentum) to be obtained without using Lagrange's equations. Discusses an experimental procedure which utilizes air tables to demonstrate the conservation laws and interactions at a…

  7. Transcranial Electrical Neuromodulation Based on the Reciprocity Principle

    PubMed Central

    Fernández-Corazza, Mariano; Turovets, Sergei; Luu, Phan; Anderson, Erik; Tucker, Don

    2016-01-01

    A key challenge in multi-electrode transcranial electrical stimulation (TES) or transcranial direct current stimulation (tDCS) is to find a current injection pattern that delivers the necessary current density at a target and minimizes it in the rest of the head, which is mathematically modeled as an optimization problem. Such an optimization with the Least Squares (LS) or Linearly Constrained Minimum Variance (LCMV) algorithms is generally computationally expensive and requires multiple independent current sources. Based on the reciprocity principle in electroencephalography (EEG) and TES, it could be possible to find the optimal TES patterns quickly whenever the solution of the forward EEG problem is available for a brain region of interest. Here, we investigate the reciprocity principle as a guideline for finding optimal current injection patterns in TES that comply with safety constraints. We define four different trial cortical targets in a detailed seven-tissue finite element head model, and analyze the performance of the reciprocity family of TES methods in terms of electrode density, targeting error, focality, intensity, and directionality using the LS and LCMV solutions as the reference standards. It is found that the reciprocity algorithms show good performance comparable to the LCMV and LS solutions. Comparing the 128 and 256 electrode cases, we found that use of greater electrode density improves focality, directionality, and intensity parameters. The results show that reciprocity principle can be used to quickly determine optimal current injection patterns in TES and help to simplify TES protocols that are consistent with hardware and software availability and with safety constraints. PMID:27303311

  8. Transcranial Electrical Neuromodulation Based on the Reciprocity Principle.

    PubMed

    Fernández-Corazza, Mariano; Turovets, Sergei; Luu, Phan; Anderson, Erik; Tucker, Don

    2016-01-01

    A key challenge in multi-electrode transcranial electrical stimulation (TES) or transcranial direct current stimulation (tDCS) is to find a current injection pattern that delivers the necessary current density at a target and minimizes it in the rest of the head, which is mathematically modeled as an optimization problem. Such an optimization with the Least Squares (LS) or Linearly Constrained Minimum Variance (LCMV) algorithms is generally computationally expensive and requires multiple independent current sources. Based on the reciprocity principle in electroencephalography (EEG) and TES, it could be possible to find the optimal TES patterns quickly whenever the solution of the forward EEG problem is available for a brain region of interest. Here, we investigate the reciprocity principle as a guideline for finding optimal current injection patterns in TES that comply with safety constraints. We define four different trial cortical targets in a detailed seven-tissue finite element head model, and analyze the performance of the reciprocity family of TES methods in terms of electrode density, targeting error, focality, intensity, and directionality using the LS and LCMV solutions as the reference standards. It is found that the reciprocity algorithms show good performance comparable to the LCMV and LS solutions. Comparing the 128 and 256 electrode cases, we found that use of greater electrode density improves focality, directionality, and intensity parameters. The results show that reciprocity principle can be used to quickly determine optimal current injection patterns in TES and help to simplify TES protocols that are consistent with hardware and software availability and with safety constraints. PMID:27303311

  9. Transcranial Electrical Neuromodulation Based on the Reciprocity Principle.

    PubMed

    Fernández-Corazza, Mariano; Turovets, Sergei; Luu, Phan; Anderson, Erik; Tucker, Don

    2016-01-01

    A key challenge in multi-electrode transcranial electrical stimulation (TES) or transcranial direct current stimulation (tDCS) is to find a current injection pattern that delivers the necessary current density at a target and minimizes it in the rest of the head, which is mathematically modeled as an optimization problem. Such an optimization with the Least Squares (LS) or Linearly Constrained Minimum Variance (LCMV) algorithms is generally computationally expensive and requires multiple independent current sources. Based on the reciprocity principle in electroencephalography (EEG) and TES, it could be possible to find the optimal TES patterns quickly whenever the solution of the forward EEG problem is available for a brain region of interest. Here, we investigate the reciprocity principle as a guideline for finding optimal current injection patterns in TES that comply with safety constraints. We define four different trial cortical targets in a detailed seven-tissue finite element head model, and analyze the performance of the reciprocity family of TES methods in terms of electrode density, targeting error, focality, intensity, and directionality using the LS and LCMV solutions as the reference standards. It is found that the reciprocity algorithms show good performance comparable to the LCMV and LS solutions. Comparing the 128 and 256 electrode cases, we found that use of greater electrode density improves focality, directionality, and intensity parameters. The results show that reciprocity principle can be used to quickly determine optimal current injection patterns in TES and help to simplify TES protocols that are consistent with hardware and software availability and with safety constraints.

  10. Using the Breathalyzer to Integrate Science and Mathematics.

    ERIC Educational Resources Information Center

    Foster, Brian C.; And Others

    1991-01-01

    Described is how the construction of a breathalyzer was used by high school students to focus on a variety of concepts and principles of science and mathematics. The procedure for constructing the breathalyzer, related material, and summary are included. (KR)

  11. Mathematical Language and Advanced Mathematics Learning

    ERIC Educational Resources Information Center

    Ferrari, Pier Luigi

    2004-01-01

    This paper is concerned with the role of language in mathematics learning at college level. Its main aim is to provide a perspective on mathematical language appropriate to effectively interpret students' linguistic behaviors in mathematics and to suggest new teaching ideas. Examples are given to show that the explanation of students' behaviors…

  12. 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…

  13. Mathematics for Life: Sustainable Mathematics Education

    ERIC Educational Resources Information Center

    Renert, Moshe

    2011-01-01

    Ecological sustainability has not been a major focus of mathematics education research, even though it has attracted considerable attention in other areas of educational research in the past decade. The connections between mathematics education and ecological sustainability are not readily apparent. This paper explores how mathematics educators…

  14. 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…

  15. Mathematics Anxiety and Attitudes toward Mathematics.

    ERIC Educational Resources Information Center

    Rounds, James B., Jr.; Hendel, Darwin D.

    1980-01-01

    Results indicate that the Mathematics Anxiety Rating Scale and the Math Anxiety Scale measure similar components of mathematics-anxiety domain. Mathematics-anxiety scales and Fennema-Sherman scales of Confidence and Effectance Motivation measure similar affective domains and are approximately equal predictors of arithmetic performance. (Author)

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

    ERIC Educational Resources Information Center

    Keleher, Lori A.

    2006-01-01

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

  17. Effect of Difference in Word Formulation and Mathematical Characteristics of Story Problems on Mathematics Preservice Teachers and Practising Teachers

    ERIC Educational Resources Information Center

    Patkin, Dorit; Gazit, Avikam

    2011-01-01

    This article aims to present the findings of a research which investigated the effect of a difference in word formulation and mathematical characteristics of story problems on their successful solution by preservice mathematics teachers (students) and practising mathematics teachers. The findings show that in the case of a problem with a…

  18. A mathematical model of a computational problem solving system

    NASA Astrophysics Data System (ADS)

    Aris, Teh Noranis Mohd; Nazeer, Shahrin Azuan

    2015-05-01

    This paper presents a mathematical model based on fuzzy logic for a computational problem solving system. The fuzzy logic uses truth degrees as a mathematical model to represent vague algorithm. The fuzzy logic mathematical model consists of fuzzy solution and fuzzy optimization modules. The algorithm is evaluated based on a software metrics calculation that produces the fuzzy set membership. The fuzzy solution mathematical model is integrated in the fuzzy inference engine that predicts various solutions to computational problems. The solution is extracted from a fuzzy rule base. Then, the solutions are evaluated based on a software metrics calculation that produces the level of fuzzy set membership. The fuzzy optimization mathematical model is integrated in the recommendation generation engine that generate the optimize solution.

  19. Granularity analysis for mathematical proofs.

    PubMed

    Schiller, Marvin R G

    2013-04-01

    Mathematical proofs generally allow for various levels of detail and conciseness, such that they can be adapted for a particular audience or purpose. Using automated reasoning approaches for teaching proof construction in mathematics presupposes that the step size of proofs in such a system is appropriate within the teaching context. This work proposes a framework that supports the granularity analysis of mathematical proofs, to be used in the automated assessment of students' proof attempts and for the presentation of hints and solutions at a suitable pace. Models for granularity are represented by classifiers, which can be generated by hand or inferred from a corpus of sample judgments via machine-learning techniques. This latter procedure is studied by modeling granularity judgments from four experts. The results provide support for the granularity of assertion-level proofs but also illustrate a degree of subjectivity in assessing step size.

  20. The Effects of Comprehension Intervention on Mathematics Problem Solving for Students with Mathematics Disability

    ERIC Educational Resources Information Center

    Moran, Amber Squire

    2011-01-01

    The purpose of this study was to examine the effectiveness of a mathematics problem solving intervention strategies for 3rd grade students identified as having a Mathematics Disability and students who are English Learners. The intervention targeted specific proposition within word problems as a means to enhance solution accuracy. Three…

  1. Financial Mathematical Tasks in a Middle School Mathematics Textbook Series: A Content Analysis

    ERIC Educational Resources Information Center

    Hamburg, Maryanna P.

    2009-01-01

    This content analysis examined the distribution of financial mathematical tasks (FMTs), mathematical tasks that contain financial terminology and require financially related solutions, across the National Standards in K-12 Personal Finance Education categories (JumpStart Coalition, 2007), the thinking skills as identified by "A Taxonomy for…

  2. Hamilton's principle in stochastic mechanics

    NASA Astrophysics Data System (ADS)

    Pavon, Michele

    1995-12-01

    In this paper we establish three variational principles that provide new foundations for Nelson's stochastic mechanics in the case of nonrelativistic particles without spin. The resulting variational picture is much richer and of a different nature with respect to the one previously considered in the literature. We first develop two stochastic variational principles whose Hamilton-Jacobi-like equations are precisely the two coupled partial differential equations that are obtained from the Schrödinger equation (Madelung equations). The two problems are zero-sum, noncooperative, stochastic differential games that are familiar in the control theory literature. They are solved here by means of a new, absolutely elementary method based on Lagrange functionals. For both games the saddle-point equilibrium solution is given by the Nelson's process and the optimal controls for the two competing players are precisely Nelson's current velocity v and osmotic velocity u, respectively. The first variational principle includes as special cases both the Guerra-Morato variational principle [Phys. Rev. D 27, 1774 (1983)] and Schrödinger original variational derivation of the time-independent equation. It also reduces to the classical least action principle when the intensity of the underlying noise tends to zero. It appears as a saddle-point action principle. In the second variational principle the action is simply the difference between the initial and final configurational entropy. It is therefore a saddle-point entropy production principle. From the variational principles it follows, in particular, that both v(x,t) and u(x,t) are gradients of appropriate principal functions. In the variational principles, the role of the background noise has the intuitive meaning of attempting to contrast the more classical mechanical features of the system by trying to maximize the action in the first principle and by trying to increase the entropy in the second. Combining the two variational

  3. Mathematics education for social justice

    NASA Astrophysics Data System (ADS)

    Suhendra

    2016-02-01

    Mathematics often perceived as a difficult subject with many students failing to understand why they learn mathematics. This situation has been further aggravated by the teaching and learning processes used, which is mechanistic without considering students' needs. The learning of mathematics tends to be just a compulsory subject, in which all students have to attend its classes. Social justice framework facilitates individuals or groups as a whole and provides equitable approaches to achieving equitable outcomes by recognising disadvantage. Applying social justice principles in educational context is related to how the teachers treat their students, dictates that all students the right to equal treatment regardless of their background and completed with applying social justice issues integrated with the content of the subject in order to internalise the principles of social justice simultaneously the concepts of the subject. The study examined the usefulness of implementing the social justice framework as a means of improving the quality of mathematics teaching in Indonesia involved four teacher-participants and their mathematics classes. The study used action research as the research methodology in which the teachers implemented and evaluated their use of social justice framework in their teaching. The data were collected using multiple research methods while analysis and interpretation of the data were carried out throughout the study. The findings of the study indicated that there were a number of challengesrelated to the implementation of the social justice framework. The findings also indicated that, the teachers were provided with a comprehensive guide that they could draw on to make decisions about how they could improve their lessons. The interactions among students and between the teachers and the students improved, they became more involved in teaching and learning process. Using social justice framework helped the teachers to make mathematics more

  4. Handbook of Research Design in Mathematics and Science Education.

    ERIC Educational Resources Information Center

    Kelly, Anthony E., Ed.; Lesh, Richard A., Ed.

    This book attempts to clarify the nature of principles that govern the effective use of merging new research designs in mathematics and science education. A primary goal is to describe several of the most important types of research design that have been pioneered recently by mathematics and science educators, have distinctive characteristics when…

  5. Helping Continuation High School Student Become Successful in Mathematics

    ERIC Educational Resources Information Center

    Villegas, Ramon R.

    2011-01-01

    The focus of this research is to understand how to engage at risk students at a continuation high school in mastering mathematics. These students typically fail math classes, and, as a result, are unmotivated to attempt to learn principles of mathematics. The purpose of the study is to develop strategies that build their understanding of Algebra…

  6. A "Chilling" Project Integrating Mathematics, Science, and Technology

    ERIC Educational Resources Information Center

    Schooler, Susan Rodgers

    2004-01-01

    "Principles and Standards for School Mathematics" states that in the middle grades "measurement concepts and skills can be developed and used throughout the school year rather than treated exclusively as a separate unit of study" (National Council of Teachers of Mathematics 200, p. 241). This article describes a collaborative activity that…

  7. A Literature Review of Pedagogical Research on Mathematical Induction

    ERIC Educational Resources Information Center

    Michaelson, Matthew T.

    2008-01-01

    Many students experience considerable difficulties when they learn and then attempt to construct and communicate proofs of conjectures using the principle of mathematical induction. Although research on the pedagogy of mathematical induction has gained only occasional attention since the 1970s, there has been an increasing interest in this field…

  8. Mathematics analysis of polymerase chain reaction kinetic curves.

    PubMed

    Sochivko, D G; Fedorov, A A; Varlamov, D A; Kurochkin, V E; Petrov, R V

    2016-01-01

    The paper reviews different approaches to the mathematical analysis of polymerase chain reaction (PCR) kinetic curves. The basic principles of PCR mathematical analysis are presented. Approximation of PCR kinetic curves and PCR efficiency curves by various functions is described. Several PCR models based on chemical kinetics equations are suggested. Decision criteria for an optimal function to describe PCR efficiency are proposed.

  9. Mathematics and Living Things. Student Text. Revised Edition.

    ERIC Educational Resources Information Center

    Faber, Norman J.; And Others

    This document is designed for grade eight to enrich and supplement the usual courses of instruction. Mathematics and Living Things (MALT) utilizes exercises in biological science to derive data through which mathematical concepts and principles may be introduced and expanded. Chapters included are: (1) Leaves and Natural Variation: Measurement of…

  10. Lensless ghost imaging based on mathematical simulation and experimental simulation

    NASA Astrophysics Data System (ADS)

    Liu, Yanyan; Wang, Biyi; Zhao, Yingchao; Dong, Junzhang

    2014-02-01

    The differences of conventional imaging and correlated imaging are discussed in this paper. The mathematical model of lensless ghost imaging system is set up and the image of double slits is computed by mathematical simulation. The results are also testified by the experimental verification. Both the theory simulation and experimental verifications results shows that the mathematical model based on statistical optical principle are keeping consistent with real experimental results.

  11. Energy Transfer and a Recurring Mathematical Function

    ERIC Educational Resources Information Center

    Atkin, Keith

    2013-01-01

    This paper extends the interesting work of a previous contributor concerning the analogies between physical phenomena such as mechanical collisions and the transfer of power in an electric circuit. Emphasis is placed on a mathematical function linking these different areas of physics. This unifying principle is seen as an exciting opportunity to…

  12. RULE GENERALITY AND CONSISTENCY IN MATHEMATICS LEARNING.

    ERIC Educational Resources Information Center

    SCANDURA, JOSEPH M.

    PSYCHOLOGICAL PRINCIPLES INVOLVED WITH RULE GENERALITY (DEGREE OF NONSPECIFICITY) AND PERFORMANCE CONSISTENCY IN MATHEMATICAL PRESENTATIONS WERE STUDIED. SPECIFICALLY, THE PURPOSES WERE (1) TO DETERMINE IF TEST BEHAVIOR CONFORMS TO THE SCOPE OF A VERBALLY ADMINISTERED TEST RULE, (2) TO EXPLORE THE INTERPRETABILITY OF VERBAL TEST RULES, AND (3) TO…

  13. Mathematics Teachers at Work: Connecting Curriculum Materials and Classroom Instruction. Studies in Mathematical Thinking and Learning Series

    ERIC Educational Resources Information Center

    Remillard, Janine T., Ed.; Herbel-Eisenmann, Beth A., Ed.; Lloyd, Gwendolyn M., Ed.

    2011-01-01

    This book compiles and synthesizes existing research on teachers' use of mathematics curriculum materials and the impact of curriculum materials on teaching and teachers, with a particular emphasis on--but not restricted to--those materials developed in the 1990s in response to the NCTM's Principles and Standards for School Mathematics. Despite…

  14. 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…

  15. 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…

  16. Mathematics for Real Life.

    ERIC Educational Resources Information Center

    Morsy, Zaghloul, Ed.; Draxler, Alexandra, Ed.

    1979-01-01

    A set of articles with the theme "Mathematics for Real Life" is presented. These article titles are: (1) Teaching Mathematics as a Tool for Problem Solving; (2) New Math or New Education; (3) Hand Calculators and Math in Primary School; (4) Mass Media in the Mathematical Training of Polish Primary Teachers; (5) The Goals of Mathematics Teaching in…

  17. Mathematical Epistemologies at Work.

    ERIC Educational Resources Information Center

    Noss, Richard

    2002-01-01

    Investigates young people's expression of mathematical ideas with a computer, the nature of mathematical practices, and the problem of mathematical meaning from cognitive and socio-cultural perspectives. Describes a mathematical activity system designed for learning and the role of digital technologies in helping to understand and reshape the…

  18. Functioning Mathematically: 1

    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…

  19. 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…

  20. Equivalence principles and electromagnetism

    NASA Technical Reports Server (NTRS)

    Ni, W.-T.

    1977-01-01

    The implications of the weak equivalence principles are investigated in detail for electromagnetic systems in a general framework. In particular, it is shown that the universality of free-fall trajectories (Galileo weak equivalence principle) does not imply the validity of the Einstein equivalence principle. However, the Galileo principle plus the universality of free-fall rotation states does imply the Einstein principle.

  1. Classical Solution Thermodynamics: A Retrospective View.

    ERIC Educational Resources Information Center

    Van Ness, H. C.; Abbott, M. M.

    1985-01-01

    Examines topics related to classical solution thermodynamics, considering energy, enthalpy, and the Gibbs function. Applicable mathematical equations are introduced and discussed when appropriate. (JN)

  2. Qualitative uncertainty principles for the generalized Fourier transform associated to a Dunkl type operator on the real line

    NASA Astrophysics Data System (ADS)

    Mejjaoli, Hatem; Trimèche, Khalifa

    2016-06-01

    In this paper, we prove various mathematical aspects of the qualitative uncertainty principle, including Hardy's, Cowling-Price's theorem, Morgan's theorem, Beurling, Gelfand-Shilov, Miyachi theorems.

  3. Science Modelling in Pre-Calculus: How to Make Mathematics Problems Contextually Meaningful

    ERIC Educational Resources Information Center

    Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

    2011-01-01

    "Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum" [National Council of Teachers of Mathematics (NCTM), "Principles and Standards for School Mathematics", NCTM, Reston, VA, 2000]. Commonly used pre-calculus textbooks provide a…

  4. Riding the Mathematical Merry-Go-Round to Foster Conceptual Understanding of Angle

    ERIC Educational Resources Information Center

    Tzur, Ron; Clark, Matthew R.

    2006-01-01

    This article presents playful activities for fostering students' conceptual understanding of angle--a root concept in mathematics--that revolve around the Mathematical Merry-Go-Round game. The authors focus on activities for two reasons. On one hand, NCTM's Principles and Standards for School Mathematics (2000) stresses the central role of student…

  5. The Learning of Mathematics: 69th NCTM Yearbook [2007 NCTM Yearbook (69th)

    ERIC Educational Resources Information Center

    National Council of Teachers of Mathematics, 2007

    2007-01-01

    Learning mathematics is the central goal of mathematics education, yet it is the least frequently addressed of the National Council of Teachers of Mathematics' (NCTM's) Principles and Standards. With an increasing population of English language learners and the inclusion of students with learning disabilities into the regular mathematics…

  6. An Examination of the Instructional Practices of Mathematics Teachers in Urban Schools

    ERIC Educational Resources Information Center

    McKinney, Sueanne E.; Chappell, Shannan; Berry, Robert Q.; Hickman, Bythella T.

    2009-01-01

    Researchers have given increased attention to the teaching and learning of mathematics since the release of the National Council of Teachers of Mathematics (NCTM)'s Principles and Standards for School Mathematics (PSSM). Despite the clear and focused goals, recommendations, and standards set by the NCTM (2000), a majority of classrooms continue to…

  7. Mathematical Understanding 5-11: A Practical Guide to Creative Communication in Maths

    ERIC Educational Resources Information Center

    Cockburn, Anne D.

    2007-01-01

    Children's mathematical misconceptions very often arise as a result of poor communication. This practical and innovative book presents a range of creative strategies to help teachers communicate effectively in the mathematics classroom, offering some new ways of presenting the fundamental concepts and principles of mathematics, and clearly…

  8. Hobbes on natural philosophy as "True Physics" and mixed mathematics.

    PubMed

    Adams, Marcus P

    2016-04-01

    In this paper, I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for Hobbes is mixed because an explanation may combine observations from experience (the 'that') with causal principles from geometry (the 'why'). My argument shows that Hobbesian natural philosophy relies upon suppositions that bodies plausibly behave according to these borrowed causal principles from geometry, acknowledging that bodies in the world may not actually behave this way. First, I consider Hobbes's relation to Aristotelian mixed mathematics and to Isaac Barrow's broadening of mixed mathematics in Mathematical Lectures (1683). I show that for Hobbes maker's knowledge from geometry provides the 'why' in mixed-mathematical explanations. Next, I examine two explanations from De corpore Part IV: (1) the explanation of sense in De corpore 25.1-2; and (2) the explanation of the swelling of parts of the body when they become warm in De corpore 27.3. In both explanations, I show Hobbes borrowing and citing geometrical principles and mixing these principles with appeals to experience. PMID:27083083

  9. Hobbes on natural philosophy as "True Physics" and mixed mathematics.

    PubMed

    Adams, Marcus P

    2016-04-01

    In this paper, I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for Hobbes is mixed because an explanation may combine observations from experience (the 'that') with causal principles from geometry (the 'why'). My argument shows that Hobbesian natural philosophy relies upon suppositions that bodies plausibly behave according to these borrowed causal principles from geometry, acknowledging that bodies in the world may not actually behave this way. First, I consider Hobbes's relation to Aristotelian mixed mathematics and to Isaac Barrow's broadening of mixed mathematics in Mathematical Lectures (1683). I show that for Hobbes maker's knowledge from geometry provides the 'why' in mixed-mathematical explanations. Next, I examine two explanations from De corpore Part IV: (1) the explanation of sense in De corpore 25.1-2; and (2) the explanation of the swelling of parts of the body when they become warm in De corpore 27.3. In both explanations, I show Hobbes borrowing and citing geometrical principles and mixing these principles with appeals to experience.

  10. Mathematical Modelling: A New Approach to Teaching Applied Mathematics.

    ERIC Educational Resources Information Center

    Burghes, D. N.; Borrie, M. S.

    1979-01-01

    Describes the advantages of mathematical modeling approach in teaching applied mathematics and gives many suggestions for suitable material which illustrates the links between real problems and mathematics. (GA)

  11. Mathematical and information maintenance of biometric systems

    NASA Astrophysics Data System (ADS)

    Boriev, Z.; Sokolov, S.; Nyrkov, A.; Nekrasova, A.

    2016-04-01

    This article describes the different mathematical methods for processing biometric data. A brief overview of methods for personality recognition by means of a signature is conducted. Mathematical solutions of a dynamic authentication method are considered. Recommendations on use of certain mathematical methods, depending on specific tasks, are provided. Based on the conducted analysis of software and the choice made in favor of the wavelet analysis, a brief basis for its use in the course of software development for biometric personal identification is given for the purpose of its practical application.

  12. 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…

  13. 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…

  14. 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…

  15. Negotiation of Mathematical Meaning and Learning Mathematics.

    ERIC Educational Resources Information Center

    Voigt, Jorg

    1994-01-01

    Presents a case study of a first-grade class and their teacher who were observed as they ascribed mathematical meanings of numbers and of numerical operations to empirical phenomena. Differences in ascriptions led to negotiation of meanings. Discusses some indirect relations between social interaction and mathematics learning. (Contains 60…

  16. Mathematical models of behavior of individual animals.

    PubMed

    Tsibulsky, Vladimir L; Norman, Andrew B

    2007-01-01

    This review is focused on mathematical modeling of behaviors of a whole organism with special emphasis on models with a clearly scientific approach to the problem that helps to understand the mechanisms underlying behavior. The aim is to provide an overview of old and contemporary mathematical models without complex mathematical details. Only deterministic and stochastic, but not statistical models are reviewed. All mathematical models of behavior can be divided into two main classes. First, models that are based on the principle of teleological determinism assume that subjects choose the behavior that will lead them to a better payoff in the future. Examples are game theories and operant behavior models both of which are based on the matching law. The second class of models are based on the principle of causal determinism, which assume that subjects do not choose from a set of possibilities but rather are compelled to perform a predetermined behavior in response to specific stimuli. Examples are perception and discrimination models, drug effects models and individual-based population models. A brief overview of the utility of each mathematical model is provided for each section.

  17. Design and mathematical modelling of a synthetic symbiotic ecosystem.

    PubMed

    Kambam, P K R; Henson, M A; Sun, L

    2008-01-01

    Artificial microbial ecosystems have been increasingly used to understand principles of ecology. These systems offer unique capabilities to mimic a variety of ecological interactions that otherwise would be difficult to study experimentally in a reasonable period of time. However, the elucidation of the genetic bases for these interactions remains a daunting challenge. To address this issue, we have designed and analysed a synthetic symbiotic ecosystem in which the genetic nature of the microbial interactions is defined explicitly. A mathematical model of the gene regulatory network in each species and their interaction through quorum sensing mediated intercellular signalling was derived to investigate the effect of system components on cooperative behaviour. Dynamic simulation and bifurcation analysis showed that the designed system admits a stable coexistence steady state for sufficiently large initial cell concentrations of the two species. The steady-state fraction of each species could be altered by varying model parameters associated with gene transcription and signalling molecule synthesis rates. The design also admitted a stable steady state corresponding to extinction of the two species for low initial cell concentrations and stable periodic solutions over certain domains of parameter space. The mathematical analysis was shown to provide insights into natural microbial ecosystems and to allow identification of molecular targets for engineering system behaviour.

  18. Perspectives from Mathematics Education.

    ERIC Educational Resources Information Center

    Sowder, Judith Threadgill

    1998-01-01

    Explores possible reasons for the gender differences in mathematics problem-solving strategies found in primary-grade students in the study by E. Fennema and others and considers implications of the findings for mathematics instruction. (SLD)

  19. 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.

  20. 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.

  1. Mental Mathematics Moves Ahead.

    ERIC Educational Resources Information Center

    Jones, Pamela

    1988-01-01

    The author suggests that the efficient use of mathematics in everyday life means translating situations into mathematical contexts, using a calculator and mental methods of calculation. Suggestions for teaching these concepts are included. (PK)

  2. Energy principles in architectural design

    SciTech Connect

    Dean, E.

    1981-01-01

    A foundation of basic information pertaining to design and energy use in buildings is presented with emphasis on principles and concepts rather than applications of particular solution. Energy impacts of landforms and topography, vegetation, wind and ventilation, and sun on planning and designing the site are discused. General design considerations involving passive heating, cooling, and lighting systems are detailed. For the design of active building systems, heating, cooling, lighting, and HVAC systems are described. (MCW)

  3. Exploring individual differences in children's mathematical skills: a correlational and dimensional approach.

    PubMed

    Sigmundsson, H; Polman, R C J; Lorås, H

    2013-08-01

    Individual differences in mathematical skills are typically explained by an innate capability to solve mathematical tasks. At the behavioural level this implies a consistent level of mathematical achievement that can be captured by strong relationships between tasks, as well as by a single statistical dimension that underlies performance on all mathematical tasks. To investigate this general assumption, the present study explored interrelations and dimensions of mathematical skills. For this purpose, 68 ten-year-old children from two schools were tested using nine mathematics tasks from the Basic Knowledge in Mathematics Test. Relatively low-to-moderate correlations between the mathematics tasks indicated most tasks shared less than 25% of their variance. There were four principal components, accounting for 70% of the variance in mathematical skill across tasks and participants. The high specificity in mathematical skills was discussed in relation to the principle of task specificity of learning. PMID:24340798

  4. Mathematics for Electronics.

    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…

  5. Making Mathematics Phenomenal

    ERIC Educational Resources Information Center

    Pratt, Dave

    2012-01-01

    Mathematics is often portrayed as an "abstract" cerebral subject, beyond the reach of many. In response, research with digital technology has led to innovative design in which mathematics can be experienced much like everyday phenomena. This lecture examines how careful design can "phenomenalise" mathematics and support not only engagement but…

  6. Mathematics and Comprehensive Ideals

    ERIC Educational Resources Information Center

    Watson, Anne

    2011-01-01

    This article revisits methods and debates about teaching mathematics that were common in the 1980s and early 1990s, and then moves up to date with the findings from three mathematics departments that set out to make a difference for their lowest attaining students. The methods they used were distinctly focused on core mathematical ideas, and how…

  7. Winning Women into Mathematics.

    ERIC Educational Resources Information Center

    Kenschaft, Patricia Clark, Ed.; Keith, Sandra Zaroodny, Ed.

    Mathematics is an auspicious discipline for young people of both sexes and all ethnic groups. This booklet aims to help members of the Mathematical Association of America (MAA) and others to increase future participation of women in mathematics, to better understand their present roles, and to develop a vision of a world with greater equal…

  8. Mathematics Teaching Today

    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,…

  9. Revisiting Mathematics Manipulative Materials

    ERIC Educational Resources Information Center

    Swan, Paul; Marshall, Linda

    2010-01-01

    It is over 12 years since "APMC" published Bob Perry and Peter Howard's research on the use of mathematics manipulative materials in primary mathematics classrooms. Since then the availability of virtual manipulatives and associated access to computers and interactive whiteboards have caused educators to rethink the use of mathematics manipulative…

  10. Rural Mathematics Educator, 2002.

    ERIC Educational Resources Information Center

    Rural Mathematics Educator, 2002

    2002-01-01

    This document contains the two issues of "Rural Mathematics Educator" published in 2002. This newsletter of the Appalachian Collaborative Center for Learning, Assessment, and Instruction in Mathematics (ACCLAIM) includes articles on rural mathematics education, as well as information and descriptions of professional development opportunities for…

  11. 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…

  12. Who Can Know Mathematics?

    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…

  13. Making Mathematics Culturally Relevant.

    ERIC Educational Resources Information Center

    Moyer, Patricia

    2001-01-01

    Examines three strands of elementary mathematics--numerals and counting, recording and calculating, and mathematics exploration and play--and provides ways to integrate culture and mathematics experiences in each area. Specific topics include Egyptian methods for multiplication, the abacus, and the words for the numbers 1-10 in seven different…

  14. Mathematical Epistemologies at Work.

    ERIC Educational Resources Information Center

    Noss, Richard

    In this paper, I draw together a corpus of findings derived from two sources: studies of students using computers to learn mathematics, and research into the use of mathematics in professional practice. Using this as a basis, I map some elements of a theoretical framework for understanding the nature of mathematical knowledge in use, and how it is…

  15. Contrasts in Mathematical Challenges in A-Level Mathematics and Further Mathematics, and Undergraduate Mathematics Examinations

    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…

  16. Mathematics and Sports

    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…

  17. 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…

  18. Topics in Mathematics.

    ERIC Educational Resources Information Center

    Posey, Johnsie Jo, Ed.; And Others

    This manual is a collection of materials and teaching strategies to motivate the development of mathematical ideas in secondary school mathematics programs or in beginning college mathematics programs. The unit is written for the instructor with step-by-step procedures including lists of needed materials. The exercises in this unit also appear in…

  19. 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…

  20. Latinos and Mathematics.

    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.…

  1. 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)

  2. 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" (Kathy R. Autrey and Leigh…

  3. Applying Mathematical Processes (AMP)

    ERIC Educational Resources Information Center

    Kathotia, Vinay

    2011-01-01

    This article provides insights into the "Applying Mathematical Processes" resources, developed by the Nuffield Foundation. It features Nuffield AMP activities--and related ones from Bowland Maths--that were designed to support the teaching and assessment of key processes in mathematics--representing a situation mathematically, analysing,…

  4. Mathematics and mysticism.

    PubMed

    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.

  5. Creating Words in Mathematics

    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…

  6. The Principles of Designing an Expert System in Teaching Mathematics

    ERIC Educational Resources Information Center

    Salekhova, Lailya; Nurgaliev, Albert; Zaripova, Rinata; Khakimullina, Nailya

    2013-01-01

    This study reveals general didactic concepts of the Expert Systems (ES) development process in the educational area. The proof of concept is based on the example of teaching the 8th grade Algebra subject. The main contribution in this work is the implementation of innovative approaches in analysis and processing of data by expert system as well as…

  7. Adequate mathematical modelling of environmental processes

    NASA Astrophysics Data System (ADS)

    Chashechkin, Yu. D.

    2012-04-01

    In environmental observations and laboratory visualization both large scale flow components like currents, jets, vortices, waves and a fine structure are registered (different examples are given). The conventional mathematical modeling both analytical and numerical is directed mostly on description of energetically important flow components. The role of a fine structures is still remains obscured. A variety of existing models makes it difficult to choose the most adequate and to estimate mutual assessment of their degree of correspondence. The goal of the talk is to give scrutiny analysis of kinematics and dynamics of flows. A difference between the concept of "motion" as transformation of vector space into itself with a distance conservation and the concept of "flow" as displacement and rotation of deformable "fluid particles" is underlined. Basic physical quantities of the flow that are density, momentum, energy (entropy) and admixture concentration are selected as physical parameters defined by the fundamental set which includes differential D'Alembert, Navier-Stokes, Fourier's and/or Fick's equations and closing equation of state. All of them are observable and independent. Calculations of continuous Lie groups shown that only the fundamental set is characterized by the ten-parametric Galilelian groups reflecting based principles of mechanics. Presented analysis demonstrates that conventionally used approximations dramatically change the symmetries of the governing equations sets which leads to their incompatibility or even degeneration. The fundamental set is analyzed taking into account condition of compatibility. A high order of the set indicated on complex structure of complete solutions corresponding to physical structure of real flows. Analytical solutions of a number problems including flows induced by diffusion on topography, generation of the periodic internal waves a compact sources in week-dissipative media as well as numerical solutions of the same

  8. Mathematical models of thermoregulation and heat transfer in mammals. A compendium of research

    NASA Technical Reports Server (NTRS)

    Shitzer, A.

    1972-01-01

    An annotated compendium on mathematical modeling of mammal thermoregulation systems is presented. Author abstracts, tables containing the more used mathematical models, solutions to these models, and each thermoregulation mechanism considered are included.

  9. Ten Problems in Experimental Mathematics

    SciTech Connect

    Bailey, David H.; Borwein, Jonathan M.; Kapoor, Vishaal; Weisstein, Eric

    2004-09-30

    This article was stimulated by the recent SIAM ''100 DigitChallenge'' of Nick Trefethen, beautifully described in a recent book. Indeed, these ten numeric challenge problems are also listed in a recent book by two of present authors, where they are followed by the ten symbolic/numeric challenge problems that are discussed in this article. Our intent was to present ten problems that are characteristic of the sorts of problems that commonly arise in ''experimental mathematics''. The challenge in each case is to obtain a high precision numeric evaluation of the quantity, and then, if possible, to obtain a symbolic answer, ideally one with proof. Our goal in this article is to provide solutions to these ten problems, and in the process present a concise account of how one combines symbolic and numeric computation, which may be termed ''hybrid computation'', in the process of mathematical discovery.

  10. 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)

  11. Inferring Mathematical Equations Using Crowdsourcing.

    PubMed

    Wasik, Szymon; Fratczak, Filip; Krzyskow, Jakub; Wulnikowski, Jaroslaw

    2015-01-01

    Crowdsourcing, understood as outsourcing work to a large network of people in the form of an open call, has been utilized successfully many times, including a very interesting concept involving the implementation of computer games with the objective of solving a scientific problem by employing users to play a game-so-called crowdsourced serious games. Our main objective was to verify whether such an approach could be successfully applied to the discovery of mathematical equations that explain experimental data gathered during the observation of a given dynamic system. Moreover, we wanted to compare it with an approach based on artificial intelligence that uses symbolic regression to find such formulae automatically. To achieve this, we designed and implemented an Internet game in which players attempt to design a spaceship representing an equation that models the observed system. The game was designed while considering that it should be easy to use for people without strong mathematical backgrounds. Moreover, we tried to make use of the collective intelligence observed in crowdsourced systems by enabling many players to collaborate on a single solution. The idea was tested on several hundred players playing almost 10,000 games and conducting a user opinion survey. The results prove that the proposed solution has very high potential. The function generated during weeklong tests was almost as precise as the analytical solution of the model of the system and, up to a certain complexity level of the formulae, it explained data better than the solution generated automatically by Eureqa, the leading software application for the implementation of symbolic regression. Moreover, we observed benefits of using crowdsourcing; the chain of consecutive solutions that led to the best solution was obtained by the continuous collaboration of several players. PMID:26713846

  12. Inferring Mathematical Equations Using Crowdsourcing

    PubMed Central

    Wasik, Szymon

    2015-01-01

    Crowdsourcing, understood as outsourcing work to a large network of people in the form of an open call, has been utilized successfully many times, including a very interesting concept involving the implementation of computer games with the objective of solving a scientific problem by employing users to play a game—so-called crowdsourced serious games. Our main objective was to verify whether such an approach could be successfully applied to the discovery of mathematical equations that explain experimental data gathered during the observation of a given dynamic system. Moreover, we wanted to compare it with an approach based on artificial intelligence that uses symbolic regression to find such formulae automatically. To achieve this, we designed and implemented an Internet game in which players attempt to design a spaceship representing an equation that models the observed system. The game was designed while considering that it should be easy to use for people without strong mathematical backgrounds. Moreover, we tried to make use of the collective intelligence observed in crowdsourced systems by enabling many players to collaborate on a single solution. The idea was tested on several hundred players playing almost 10,000 games and conducting a user opinion survey. The results prove that the proposed solution has very high potential. The function generated during weeklong tests was almost as precise as the analytical solution of the model of the system and, up to a certain complexity level of the formulae, it explained data better than the solution generated automatically by Eureqa, the leading software application for the implementation of symbolic regression. Moreover, we observed benefits of using crowdsourcing; the chain of consecutive solutions that led to the best solution was obtained by the continuous collaboration of several players. PMID:26713846

  13. Principles of project management

    NASA Technical Reports Server (NTRS)

    1982-01-01

    The basic principles of project management as practiced by NASA management personnel are presented. These principles are given as ground rules and guidelines to be used in the performance of research, development, construction or operational assignments.

  14. Intuitions, principles and consequences.

    PubMed

    Shaw, A B

    2001-02-01

    Some approaches to the assessment of moral intuitions are discussed. The controlled ethical trial isolates a moral issue from confounding factors and thereby clarifies what a person's intuition actually is. Casuistic reasoning from situations, where intuitions are clear, suggests or modifies principles, which can then help to make decisions in situations where intuitions are unclear. When intuitions are defended by a supporting principle, that principle can be tested by finding extreme cases, in which it is counterintuitive to follow the principle. An approach to the resolution of conflict between valid moral principles, specifically the utilitarian and justice principles, is considered. It is argued that even those who justify intuitions by a priori principles are often obliged to modify or support their principles by resort to the consideration of consequences.

  15. Chemical Principls Exemplified

    ERIC Educational Resources Information Center

    Plumb, Robert C.

    1973-01-01

    Two topics are discussed: (1) Stomach Upset Caused by Aspirin, illustrating principles of acid-base equilibrium and solubility; (2) Physical Chemistry of the Drinking Duck, illustrating principles of phase equilibria and thermodynamics. (DF)

  16. Biomagnetic fluid flow in an aneurysm using ferrohydrodynamics principles

    NASA Astrophysics Data System (ADS)

    Tzirtzilakis, E. E.

    2015-06-01

    In this study, the fundamental problem of biomagnetic fluid flow in an aneurysmal geometry under the influence of a steady localized magnetic field is numerically investigated. The mathematical model used to formulate the problem is consistent with the principles of ferrohydrodynamics. Blood is considered to be an electrically non-conducting, homogeneous, non-isothermal Newtonian magnetic fluid. For the numerical solution of the problem, which is described by a coupled, non-linear system of Partial Differential Equations (PDEs), with appropriate boundary conditions, the stream function-vorticity formulation is adopted. The solution is obtained by applying an efficient pseudotransient numerical methodology using finite differences. This methodology is based on the application of a semi-implicit numerical technique, transformations, stretching of the grid, and construction of the boundary conditions for the vorticity. The results regarding the velocity and temperature field, skin friction, and rate of heat transfer indicate that the presence of a magnetic field considerably influences the flow field, particularly in the region of the aneurysm.

  17. Las normas de desempeno matematico desde el preescolar hasta el segundo grado (Mathematics Standards for Pre-Kindergarten through Grade 2). ERIC Digest.

    ERIC Educational Resources Information Center

    Richardson, Kathy

    The National Council of Teachers of Mathematics recently published "Principles and Standards for School Mathematics." For the first time, these new standards include pre-kindergarten standards, while outlining the mathematics that children should learn as they progress through school. The standards present a broad view of what mathematics is and…

  18. MATHEMATICAL METHODS IN MEDICAL IMAGE PROCESSING

    PubMed Central

    ANGENENT, SIGURD; PICHON, ERIC; TANNENBAUM, ALLEN

    2013-01-01

    In this paper, we describe some central mathematical problems in medical imaging. The subject has been undergoing rapid changes driven by better hardware and software. Much of the software is based on novel methods utilizing geometric partial differential equations in conjunction with standard signal/image processing techniques as well as computer graphics facilitating man/machine interactions. As part of this enterprise, researchers have been trying to base biomedical engineering principles on rigorous mathematical foundations for the development of software methods to be integrated into complete therapy delivery systems. These systems support the more effective delivery of many image-guided procedures such as radiation therapy, biopsy, and minimally invasive surgery. We will show how mathematics may impact some of the main problems in this area, including image enhancement, registration, and segmentation. PMID:23645963

  19. Principles of Modern Soccer.

    ERIC Educational Resources Information Center

    Beim, George

    This book is written to give a better understanding of the principles of modern soccer to coaches and players. In nine chapters the following elements of the game are covered: (1) the development of systems; (2) the principles of attack; (3) the principles of defense; (4) training games; (5) strategies employed in restarts; (6) physical fitness…

  20. Chemical Principles Exemplified

    ERIC Educational Resources Information Center

    Plumb, Robert C.

    1970-01-01

    This is the first of a new series of brief ancedotes about materials and phenomena which exemplify chemical principles. Examples include (1) the sea-lab experiment illustrating principles of the kinetic theory of gases, (2) snow-making machines illustrating principles of thermodynamics in gas expansions and phase changes, and (3) sunglasses that…

  1. An exclusion principle and the importance of mobility for a class of biofilm models.

    PubMed

    Klapper, Isaac; Szomolay, Barbara

    2011-09-01

    Much of the earth's microbial biomass resides in sessile, spatially structured communities such as biofilms and microbial mats, systems consisting of large numbers of single-celled organisms living within self-secreted matrices made of polymers and other molecules. As a result of their spatial structure, these communities differ in important ways from well-mixed (and well-studied) microbial systems such as those present in chemostats. Here we consider a widely used class of 1D biofilm models in the context of a description of their basic ecology. It will be shown via an exclusion principle resulting from competition for space that these models lead to restrictions on ecological structure. Mathematically, this result follows from a classification of steady-state solutions based on a 0-stability condition: 0-stable solutions are in some sense determined by competitive balance at the biofilm base, whereas solutions that are not 0-stable, while less dependent on conditions at the biofilm base, are unstable at the base. As a result of the exclusion principle, it is argued that some form of downward mobility, against the favorable substrate gradient direction, is needed at least in models and possibly in actuality.

  2. Turbulence and the Stabilization Principle

    NASA Technical Reports Server (NTRS)

    Zak, Michail

    2010-01-01

    Further results of research, reported in several previous NASA Tech Briefs articles, were obtained on a mathematical formalism for postinstability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence). To recapitulate: Fictitious control forces are introduced to couple the dynamical equations with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in ordinary perceived three-dimensional space is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. Con sequently, the postinstability motion is represented by a set of functions describing the evolution of such statistical quantities as expectations and higher moments, and this representation is stable. The previously reported findings are analyzed from the perspective of the authors Stabilization Principle, according to which (1) stability is recognized as an attribute of mathematical formalism rather than of underlying physics and (2) a dynamical system that appears unstable when modeled by differentiable functions only can be rendered stable by modifying the dynamical equations to incorporate intrinsic stochasticity.

  3. Using Problem Solving to Assess Young Children's Mathematics Knowledge

    ERIC Educational Resources Information Center

    Charlesworth, Rosalind; Leali, Shirley A.

    2012-01-01

    Mathematics problem solving provides a means for obtaining a view of young children's understanding of mathematics as they move through the early childhood concept development sequence. Assessment information can be obtained through observations and interviews as children develop problem solutions. Examples of preschool, kindergarten, and primary…

  4. Teachers of Mathematics as Problem-Solving Applied Mathematicians

    ERIC Educational Resources Information Center

    Chick, Helen; Stacey, Kaye

    2013-01-01

    Some of mathematics teaching is routine, like an exercise from a textbook for which you have received instruction and already know what to do. On other occasions, however, teaching mathematics is challenging, involving problems of teaching for which the solutions may not be readily apparent. These situations require the application of mathematical…

  5. Early childhood mathematics intervention.

    PubMed

    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.

  6. Mathematical model for predicting human vertebral fracture

    NASA Technical Reports Server (NTRS)

    Benedict, J. V.

    1973-01-01

    Mathematical model has been constructed to predict dynamic response of tapered, curved beam columns in as much as human spine closely resembles this form. Model takes into consideration effects of impact force, mass distribution, and material properties. Solutions were verified by dynamic tests on curved, tapered, elastic polyethylene beam.

  7. Tutorial: Mathematical Modeling of Library Systems.

    ERIC Educational Resources Information Center

    Rouse, William B.

    1979-01-01

    Discusses the purpose of mathematical models and reviews the phases of the modeling process--defining performance, representing the problem, predicting performance, estimating parameters, defining optimization criterion, determining solution, and implementing results. Reviews of book-use, resource allocation, and library network models are…

  8. The International Mathematical Olympiad Training Session.

    ERIC Educational Resources Information Center

    Rousseau, Cecil; Patruno, Gregg

    1985-01-01

    The Mathematical Olympiad Training Session is designed to give United States students a problem-oriented exposure to subject areas (algebra, geometry, number theory, combinatorics, and inequalities) through an intensive three-week course. Techniques used during the session, with three sample problems and their solutions, are presented. (JN)

  9. Some Remarks on Creating Mathematical Concepts.

    ERIC Educational Resources Information Center

    Trzcieniecka-Schneider, Irena

    1993-01-01

    The author shows some causes of failure in the creation of mathematical concepts. One is the stiffening of concept cores, which prevents identification of atypical exemplars and solution of atypical problems and causes a bifurcation between the natural system of everyday concepts and the formal system of school concepts. (Author/MDH)

  10. Mathematical Ties That Bind.

    ERIC Educational Resources Information Center

    House, Peggy A.

    1994-01-01

    Describes some mathematical investigations of the necktie which includes applications of geometry, statistics, data analysis, sampling, probability, symmetry, proportion, problem solving, and business. (MKR)

  11. La Meme Chose: How Mathematics Can Explain the Thinking of Children and the Thinking of Children Can Illuminate Mathematical Philosophy

    NASA Astrophysics Data System (ADS)

    Cable, John

    2013-07-01

    This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which has been formally enunciated in mathematical philosophy but has universal application. It becomes necessary to identity fluid objects (both configured and unconfigured) and configured and unconfigured sets-of-objects. Issues emerge regarding the conflict between philosophic realism and anti-realism, including constructivism. Questions are asked concerning mathematics and mathematical philosophy, particularly over the nature of sets, the wisdom of the axiomatic method and aspects of the abstraction principle itself.

  12. Progress in recognizing typeset mathematics

    NASA Astrophysics Data System (ADS)

    Fateman, Richard J.; Tokuyasu, Taku A.

    1996-03-01

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

  13. Control principles of complex systems

    NASA Astrophysics Data System (ADS)

    Liu, Yang-Yu; Barabási, Albert-László

    2016-07-01

    A reflection of our ultimate understanding of a complex system is our ability to control its behavior. Typically, control has multiple prerequisites: it requires an accurate map of the network that governs the interactions between the system's components, a quantitative description of the dynamical laws that govern the temporal behavior of each component, and an ability to influence the state and temporal behavior of a selected subset of the components. With deep roots in dynamical systems and control theory, notions of control and controllability have taken a new life recently in the study of complex networks, inspiring several fundamental questions: What are the control principles of complex systems? How do networks organize themselves to balance control with functionality? To address these questions here recent advances on the controllability and the control of complex networks are reviewed, exploring the intricate interplay between the network topology and dynamical laws. The pertinent mathematical results are matched with empirical findings and applications. Uncovering the control principles of complex systems can help us explore and ultimately understand the fundamental laws that govern their behavior.

  14. 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…

  15. 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…

  16. 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…

  17. 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…

  18. Hands-On Mathematics: Two Cases from Ancient Chinese Mathematics

    ERIC Educational Resources Information Center

    Wang, Youjun

    2009-01-01

    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…

  19. 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…

  20. Physical vs. Mathematical Models in Rock Mechanics

    NASA Astrophysics Data System (ADS)

    Morozov, I. B.; Deng, W.

    2013-12-01

    One of the less noted challenges in understanding the mechanical behavior of rocks at both in situ and lab conditions is the character of theoretical approaches being used. Currently, the emphasis is made on spatial averaging theories (homogenization and numerical models of microstructure), empirical models for temporal behavior (material memory, compliance functions and complex moduli), and mathematical transforms (Laplace and Fourier) used to infer the Q-factors and 'relaxation mechanisms'. In geophysical applications, we have to rely on such approaches for very broad spatial and temporal scales which are not available in experiments. However, the above models often make insufficient use of physics and utilize, for example, the simplified 'correspondence principle' instead of the laws of viscosity and friction. As a result, the commonly-used time- and frequency dependent (visco)elastic moduli represent apparent properties related to the measurement procedures and not necessarily to material properties. Predictions made from such models may therefore be inaccurate or incorrect when extrapolated beyond the lab scales. To overcome the above challenge, we need to utilize the methods of micro- and macroscopic mechanics and thermodynamics known in theoretical physics. This description is rigorous and accurate, uses only partial differential equations, and allows straightforward numerical implementations. One important observation from the physical approach is that the analysis should always be done for the specific geometry and parameters of the experiment. Here, we illustrate these methods on axial deformations of a cylindrical rock sample in the lab. A uniform, isotropic elastic rock with a thermoelastic effect is considered in four types of experiments: 1) axial extension with free transverse boundary, 2) pure axial extension with constrained transverse boundary, 3) pure bulk expansion, and 4) axial loading harmonically varying with time. In each of these cases, an

  1. 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…

  2. Mathematical Metaphors: Problem Reformulation and Analysis Strategies

    NASA Technical Reports Server (NTRS)

    Thompson, David E.

    2005-01-01

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

  3. Issues in Teaching Mathematics

    ERIC Educational Resources Information Center

    Ediger, Marlow

    2013-01-01

    In this article, the author states that there are selected issues in mathematics instruction that educators should be well aware of when planning lessons and units of study. These issues provide a basis for thought and discussion when assisting pupils to attain more optimally. Purposeful studying of issues guides mathematics teachers in…

  4. Mathematics: The Universal Language?

    ERIC Educational Resources Information Center

    Hoffert, Sharon B.

    2009-01-01

    Mathematics is considered the universal language, but students who speak languages other than English have difficulty doing mathematics in English. For instance, because of a lack of familiarity with the problem's context, many have trouble understanding exactly what operations to perform. In the United States, approximately one in seven students…

  5. 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.

  6. Modularizing Remedial Mathematics

    ERIC Educational Resources Information Center

    Wong, Aaron

    2013-01-01

    As remedial mathematics education has become an increasingly important topic of conversation in higher education. Mathematics departments have been put under increased pressure to change their programs to increase the student success rate. A number of models have been introduced over the last decade that represent a wide range of new ideas and…

  7. Dyslexia, Dyspraxia and Mathematics.

    ERIC Educational Resources Information Center

    Yeo, Dorian

    This book explores how primary school children with dyslexia or dyspraxia and difficulty in math can learn math and provides practical support and detailed teaching suggestions. It considers cognitive features that underlie difficulty with mathematics generally or with specific aspects of mathematics. It outlines the ways in which children usually…

  8. 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…

  9. 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…

  10. 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…

  11. What Is Discrete Mathematics?

    ERIC Educational Resources Information Center

    Sharp, Karen Tobey

    This paper cites information received from a number of sources, e.g., mathematics teachers in two-year colleges, publishers, and convention speakers, about the nature of discrete mathematics and about what topics a course in this subject should contain. Note is taken of the book edited by Ralston and Young which discusses the future of college…

  12. Consumer Mathematics Curriculum Guide.

    ERIC Educational Resources Information Center

    Louisiana State Dept. of Education, Baton Rouge.

    This guide for high school consumer mathematics (one in a set of curriculum guides developed by Louisiana statewide mathematics curriculum committees) contains a course outline, performance objectives, and coordinated activities designed to teach skills that students will need as citizens and consumers. Background on the development,…

  13. 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…

  14. 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.

  15. 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…

  16. Learning Mathematics while Black

    ERIC Educational Resources Information Center

    Martin, Danny Bernard

    2012-01-01

    While research by scholars has contributed greatly to an emerging knowledge base on Black children and mathematics, there continues to be a dire need for insightful research that de-centers longstanding accounts that have contributed to the construction of Black children as mathematically illiterate and as less than ideal learners relative to…

  17. Intermediate Mathematics Study Guide.

    ERIC Educational Resources Information Center

    Stanford Univ., CA. School Mathematics Study Group.

    This SMSG study guide is intended to provide teachers who use "Intermediate Mathematics," as a textbook with references to materials which will help them to gain a better understanding of the mathematics contained in the text. For each chapter of the text a brief resume of its content is followed by a list of annotated references which are…

  18. Mathematics in History.

    ERIC Educational Resources Information Center

    Hallenberg, Harvey

    1995-01-01

    Presents ideas for creating mathematical classroom activities associated with the history of mathematics: calculating sums and products the way ancient Greeks did it, using an abacus or moving stones on a sanded floor, and engaging elementary students through role playing specific mathematicians. Suggests that through such techniques, mathematics…

  19. 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…

  20. Mathematical Graphic Organizers

    ERIC Educational Resources Information Center

    Zollman, Alan

    2009-01-01

    As part of a math-science partnership, a university mathematics educator and ten elementary school teachers developed a novel approach to mathematical problem solving derived from research on reading and writing pedagogy. Specifically, research indicates that students who use graphic organizers to arrange their ideas improve their comprehension…

  1. 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)…

  2. See a Different Mathematics

    ERIC Educational Resources Information Center

    Stallings, L. Lynn

    2007-01-01

    This article proposes four strategies for posing mathematics problems that raise the cognitive demands of the tasks given to students. Each strategy is illustrated with three common middle school mathematics examples: finding the greatest common factor, finding area or perimeter, and finding the equation of a line. Posing these types of problems…

  3. 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…

  4. Strengthen Your Mathematical Muscles

    ERIC Educational Resources Information Center

    Wohlhuter, Kay A.; Breyfogle, M. Lynn; McDuffie, Amy Roth

    2010-01-01

    Developing deep knowledge and understanding of mathematics is a lifelong process, and building the foundation for teachers' development must begin in preservice preparation and continue throughout one's professional life. While teaching mathematics content courses and methods courses, the authors have found that preservice elementary school…

  5. Mathematics: Content and Pedagogy

    ERIC Educational Resources Information Center

    Ediger, Marlow

    2009-01-01

    The debate has gone on for some time in terms of which is more salient for the teacher to be well versed in, mathematical content versus methods and approaches in teaching. Both are salient. They cannot be separated from each other. The mathematics teacher must indeed have broad, in-depth knowledge of subject matter as well as in teaching and…

  6. 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…

  7. [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 Learning and…

  8. Discrete Mathematics Re "Tooled."

    ERIC Educational Resources Information Center

    Grassl, Richard M.; Mingus, Tabitha T. Y.

    1999-01-01

    Indicates the importance of teaching discrete mathematics. Describes how the use of technology can enhance the teaching and learning of discrete mathematics. Explorations using Excel, Derive, and the TI-92 proved how preservice and inservice teachers experienced a new dimension in problem solving and discovery. (ASK)

  9. Mathematics and Gender.

    ERIC Educational Resources Information Center

    Fennema, Elizabeth, Ed.; Leder, Gilah C., Ed.

    This book reports on various studies that have increased our understanding of why females and males learn different kinds and amounts of mathematics. In particular, this book explicates the Autonomous Learning Behavior model, proposed by Fennema and Peterson, which is a possible explanation of the development of gender differences in mathematics.…

  10. Mathematics Knowledge for Teaching

    ERIC Educational Resources Information Center

    Mohr, Margaret

    2006-01-01

    Research indicates that U. S. teachers' mathematical knowledge continues to be weak, and there is an inherent difference between the mathematical knowledge needed to be an effective teacher and that needed by a mathematician. In this article, the author discusses pedagogical content knowledge. According to Schulman (1987), pedagogical content…

  11. Attitudes and Mathematics.

    ERIC Educational Resources Information Center

    Iben, Miriam F.

    1991-01-01

    Examines seventh and eighth grade students in Australia, Japan, and the United States for attitudes related to mathematics, and the relationship these attitudes have to students' development of abstract mathematical thought and spatial relations. Study uses the Iowa Algebra Aptitude Test, Differential Aptitude Test-Spatial Relations, and the…

  12. Developing Mathematical Vocabulary.

    ERIC Educational Resources Information Center

    Monroe, Eula Ewing; Orme, Michelle P.

    2002-01-01

    This article discusses the importance of mathematical vocabulary, difficulties students encounter in learning this vocabulary, and some instructional strategies. Two general methods for teaching vocabulary are discussed: context and explicit vocabulary instruction. The methods are summarized as they apply to mathematical vocabulary instruction and…

  13. Mathematics and Art

    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…

  14. Why physics needs mathematics

    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.

  15. Mathematical models of diabetes progression.

    PubMed

    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.

  16. Principles and the Development of Physical Theory: Case Studies

    NASA Astrophysics Data System (ADS)

    Hovis, Robert Corby

    Three separate articles make up the chapters of this dissertation. They were written with different aims and audiences in mind, but each deals in some way with one or more "principles" that have been invoked in argumentation and explanation in the physical sciences. The principles of concern are propositions which have an "aesthetic" or "foundational" or "philosophical" character and which are (or have been) generally believed to be widely applicable or particularly powerful--for example, the Principle of Plenitude, the Principle of Mathematical Beauty, Occam's Razor, the Cosmological Principle, and the Copernican Principle. Chapter 1 provides an overview of the nature and uses of principles in scientific reasoning and examines in some detail the use of the Principle of Plenitude in the introduction of "tachyons" (faster-than-light particles) into theoretical physics during the 1960s. Chapter 2 is a short biography of P. A. M. Dirac (1902-1984), one of the founders of quantum mechanics, who believed that the Principle of Mathematical Beauty should serve as physicists' guide to truth. Chapter 3 traces the history of the idea of faster-than-light particles in physics since the late 1800s; this idea matured with the rise of the subfield of tachyon physics in the 1960s, and (as mentioned above) physicists appealed to the Principle of Plenitude to argue for the existence of the particles, which are still only hypothetical. According to the thesis developed in these chapters, the epistemological status of principles has evolved over the history of science. While they were once hallowed as a priori truths, in modern science they have increasingly been employed critically, in light of the results of scientific inquiry. That is, science has moved toward making principles testable, subject to rejection or revision, on a par with other scientific propositions.

  17. 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…

  18. On nonholonomic systems and variational principles

    NASA Astrophysics Data System (ADS)

    Cronström, Christofer; Raita, Tommi

    2009-04-01

    We consider the compatibility of the equations of motion which follow from d'Alembert's principle in the case of a general autonomous nonholonomic mechanical system in N dimensions with those equations which follow for the same system by assuming the validity of a specific variational action principle, in which the nonholonomic conditions are implemented by means of the multiplication rule in the calculus of variations. The equations of motion which follow from the principle of d'Alembert are not identical to the equations which follow from the variational action principle. We give a proof that the solutions to the equations of motion which follow from d'Alembert's principle do not in general satisfy the equations which follow from the action principle with nonholonomic constraints. Thus the principle of d'Alembert and the minimal action principle involving the multiplication rule are not compatible in the case of systems with nonholonomic constraints. For simplicity the proof is given for autonomous systems only, with one general nonholonomic constraint, which is linear in the generalized velocities of the system.

  19. Physical principles of hearing

    NASA Astrophysics Data System (ADS)

    Martin, Pascal

    2015-10-01

    The following sections are included: * Psychophysical properties of hearing * The cochlear amplifier * Mechanosensory hair cells * The "critical" oscillator as a general principle of auditory detection * Bibliography

  20. Examining Fourth-Grade Mathematics Writing: Features of Organization, Mathematics Vocabulary, and Mathematical Representations

    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…

  1. Computer-Based Mathematics Instructions for Engineering Students

    NASA Technical Reports Server (NTRS)

    Khan, Mustaq A.; Wall, Curtiss E.

    1996-01-01

    Almost every engineering course involves mathematics in one form or another. The analytical process of developing mathematical models is very important for engineering students. However, the computational process involved in the solution of some mathematical problems may be very tedious and time consuming. There is a significant amount of mathematical software such as Mathematica, Mathcad, and Maple designed to aid in the solution of these instructional problems. The use of these packages in classroom teaching can greatly enhance understanding, and save time. Integration of computer technology in mathematics classes, without de-emphasizing the traditional analytical aspects of teaching, has proven very successful and is becoming almost essential. Sample computer laboratory modules are developed for presentation in the classroom setting. This is accomplished through the use of overhead projectors linked to graphing calculators and computers. Model problems are carefully selected from different areas.

  2. Assessing Students Beliefs about Mathematics.

    ERIC Educational Resources Information Center

    Spangler, Denise A.

    1992-01-01

    Presents 11 open-ended questions that can be presented to students and teachers at all educational levels in various formats to assess mathematical beliefs. Questions investigate beliefs toward mathematics, the problem-solving process, mathematicians, and mathematical applications. (MDH)

  3. Student Teachers' Mathematics Attitudes, Authentic Investigations and Use of Metacognitive Tools

    ERIC Educational Resources Information Center

    Afamasaga-Fuata'i, Karoline; Sooaemalelagi, Lumaava

    2014-01-01

    Based on findings from a semester-long study, this article examines the development of Samoan prospective teachers' mathematical understandings and mathematics attitudes when investigating authentic contexts and applying working mathematically processes, mental computations and problem-solving strategies to find solutions of problems. The…

  4. Secondary School Advanced Mathematics, Chapter 8, Systems of Equations. Student's Text.

    ERIC Educational Resources Information Center

    Stanford Univ., CA. School Mathematics Study Group.

    This text is the last of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. In this volume the solution of systems of linear and quadratic equations and inequalities in…

  5. A MATLAB-Aided Method for Teaching Calculus-Based Business Mathematics

    ERIC Educational Resources Information Center

    Liang, Jiajuan; Pan, William S. Y.

    2009-01-01

    MATLAB is a powerful package for numerical computation. MATLAB contains a rich pool of mathematical functions and provides flexible plotting functions for illustrating mathematical solutions. The course of calculus-based business mathematics consists of two major topics: 1) derivative and its applications in business; and 2) integration and its…

  6. Adolescent Mathematical Problem Solving: The Role of Metacognition, Strategies and Beliefs.

    ERIC Educational Resources Information Center

    Fitzpatrick, Corine

    Mathematical problem solving has been the focus of much concern. This study investigated the relationship of various cognitive factors, attributions, and gender to the solution of mathematics problems by 100 high school seniors. The independent variables examined in this study included: (1) mathematics knowledge as measured by a score on the…

  7. Improving Primary School Prospective Teachers' Understanding of the Mathematics Modeling Process

    ERIC Educational Resources Information Center

    Bal, Aytgen Pinar; Doganay, Ahmet

    2014-01-01

    The development of mathematical thinking plays an important role on the solution of problems faced in daily life. Determining the relevant variables and necessary procedural steps in order to solve problems constitutes the essence of mathematical thinking. Mathematical modeling provides an opportunity for explaining thoughts in real life by making…

  8. Promoting Students' Self-Directed Learning Ability through Teaching Mathematics for Social Justice

    ERIC Educational Resources Information Center

    Voss, Richard; Rickards, Tony

    2016-01-01

    Mathematics is a subject which is often taught using abstract methods and processes. These methods by their very nature may for students alienate the relationship between Mathematics and real life situations. Further, these abstract methods and processes may disenfranchise students from becoming self-directed learners of Mathematics. A solution to…

  9. 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.

  10. The mPowerNet Approach to NOF ICT Training in Primary Mathematics.

    ERIC Educational Resources Information Center

    Bunker, Dan

    2000-01-01

    Introduces a course using mPowerNet to develop course material by using computers to teach numeracy. Presents the guiding principles of the course, mathematics material, course material, and course guidance. (ASK)

  11. Mathematics as verbal behavior.

    PubMed

    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. PMID:25595115

  12. Mathematics as verbal behavior.

    PubMed

    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.

  13. Principles of learning.

    PubMed

    Voith, V L

    1986-12-01

    This article discusses some general principles of learning as well as possible constraints and how such principles can apply to horses. A brief review is presented of experiments that were designed to assess learning in horses. The use of behavior modification techniques to treat behavior problems in horses is discussed and several examples of the use of these techniques are provided. PMID:3492241

  14. Hamilton's Principle for Beginners

    ERIC Educational Resources Information Center

    Brun, J. L.

    2007-01-01

    I find that students have difficulty with Hamilton's principle, at least the first time they come into contact with it, and therefore it is worth designing some examples to help students grasp its complex meaning. This paper supplies the simplest example to consolidate the learning of the quoted principle: that of a free particle moving along a…

  15. Five Easy Principles to Make Math Moments Count

    ERIC Educational Resources Information Center

    Cutler, Carrie S.

    2011-01-01

    Preschool children are learning so many skills--how to cut with scissors, zip zippers, recognize the alphabet and their names, and share toys with others. A strong academic curriculum also requires that children learn more about math (National Council of Teachers of Mathematics [NCTM], 2000). By following the five easy principles outlined here,…

  16. The maximum principle for the Navier-Stokes equations

    NASA Astrophysics Data System (ADS)

    Akysh, Abdigali Sh.

    2016-08-01

    New connections were established between extreme values of the velocity, the density of kinetic energy (in particular local maximum) and the pressure of the Navier-Stokes equations. Validity of the maximum principle was shown for nonlinear Navier-Stokes equations using these connections, that is fundamentally-key from the mathematical point of view.

  17. Introducing Dynamic Analysis Using Malthus's Principle of Population.

    ERIC Educational Resources Information Center

    Pingle, Mark

    2003-01-01

    Declares the use of dynamic models is increasing in macroeconomics. Explains how to introduce dynamic models to students whose technical skills are modest or varied. Chooses Malthus's Principle of Population as a natural context for introducing dynamic analysis because it provides a method for reviewing the mathematical tools and theoretical…

  18. Lagrange Multipliers, Adjoint Equations, the Pontryagin Maximum Principle and Heuristic Proofs

    ERIC Educational Resources Information Center

    Ollerton, Richard L.

    2013-01-01

    Deeper understanding of important mathematical concepts by students may be promoted through the (initial) use of heuristic proofs, especially when the concepts are also related back to previously encountered mathematical ideas or tools. The approach is illustrated by use of the Pontryagin maximum principle which is then illuminated by reference to…

  19. The Physical Principles of Magnetism

    NASA Astrophysics Data System (ADS)

    Morrish, Allan H.

    2001-01-01

    " The Physical Principles of Magnetism . . . is such a classic a comprehensive introduction to all aspects of magnetism . . . The corrected reissue is a welcome addition to this much-needed archival series. Dr. Morrish presents an excellent introduction to the physics and mathematics of magnetism without oversimplification . . . This respected and timeless book clearly elucidates these principles."" Edward Della Torre, The George Washington University, President of the IEEE Magnetics Society The IEEE Press is pleased to reissue this essential book for understanding the basis of modern magnetic materials. Diamagnetism, paramagnetism, ferromagnetism, ferrimagnetism, and antiferromagnetism are covered in an integrated manner unifying subject matter from physics, chemistry, metallurgy, and engineering. Magnetic phenomena are discussed both from an experimental and theoretical point of view. The underlying physical principles are presented first, followed by macroscopic or microscopic theories. Although quantum mechanical theories are given, a phenomenological approach is emphasized. More than half the book is devoted to a discussion of strongly coupled dipole systems, where the molecular field theory is emphasized. THE PHYSICAL PRINCIPLES OF MAGNETISM is a classic must read for anyone working in the magnetics, electromagnetics, computing, and communications fields. About the Author Allan Henry Morrish is a distinguished professor of physics at the University of Manitoba, Canada. He received a B.Sc. degree from the University of Manitoba in 1943, an M.A. from the University of Toronto in 1946, and a Ph.D. from the University of Chicago in 1949, specializing in nuclear physics. From 1953 to 1964, Dr. Morrish was with the Department of Electrical Engineering at the University of Minnesota at Minneapolis, where he held the rank of professor from 1959. During 1974-1975, Dr. Morrish was president of the Canadian Association of Physicists and in 1977 he was awarded their gold

  20. A critique of principlism.

    PubMed

    Clouser, K D; Gert, B

    1990-04-01

    The authors use the term "principlism" to refer to the practice of using "principles" to replace both moral theory and particular moral rules and ideals in dealing with the moral problems that arise in medical practice. The authors argue that these "principles" do not function as claimed, and that their use is misleading both practically and theoretically. The "principles" are in fact not guides to action, but rather they are merely names for a collection of sometimes superficially related matters for consideration when dealing with a moral problem. The "principles" lack any systematic relationship to each other, and they often conflict with each other. These conflicts are unresolvable, since there is no unified moral theory from which they are all derived. For comparison the authors sketch the advantages of using a unified moral theory. PMID:2351895

  1. The Greatest Mathematical Discovery?

    SciTech Connect

    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.

  2. 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

  3. The solution of pharmacological problems with computers. Part 9: Kinetics of the inhibition of the enzyme morphine-N-demethylase by N-allylnormorphine. Mathematical analysis by a FORTRAN-program.

    PubMed

    Krüger-Thiemer, E; Feinberg, M

    1975-03-01

    In this paper, we present a method for statistical analysis of enzyme-kinetic data. This analysis allows determination of the character of the inhibition of an enzyme reaction, and computes the 95% confidence limits of the dissociation constants and of Vmax. This method involves the solution of the Michaelis-Menten equation, (see article for formula), using the Guass-Newton iteration.

  4. Mathematical and Statistical Opportunities in Cyber Security

    SciTech Connect

    Meza, Juan; Campbell, Scott; Bailey, David

    2009-03-23

    The role of mathematics in a complex system such as the Internet has yet to be deeply explored. In this paper, we summarize some of the important and pressing problems in cyber security from the viewpoint of open science environments. We start by posing the question 'What fundamental problems exist within cyber security research that can be helped by advanced mathematics and statistics'? Our first and most important assumption is that access to real-world data is necessary to understand large and complex systems like the Internet. Our second assumption is that many proposed cyber security solutions could critically damage both the openness and the productivity of scientific research. After examining a range of cyber security problems, we come to the conclusion that the field of cyber security poses a rich set of new and exciting research opportunities for the mathematical and statistical sciences.

  5. 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)

  6. 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)

  7. Standards in Mathematics Teaching.

    ERIC Educational Resources Information Center

    Brookes, Bill

    1978-01-01

    This article is based on a lecture given at the 1978 Easter Course at Padgate College of Higher Education. The lecture is an analysis of the complexity of mathematics teaching and the setting of teaching standards. (MN)

  8. Reciprocal Relationships between Attitude toward Mathematics and Achievement in Mathematics.

    ERIC Educational Resources Information Center

    Ma, Xin

    1997-01-01

    This study examined reciprocal relationships between attitude toward mathematics and mathematics achievement. High school seniors from the Dominican Republic completed mathematics achievement tests and a questionnaire on mathematics attitudes. Results indicated that reciprocal relationships existed, suggesting that the reciprocal nature between…

  9. 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…

  10. Applications of Secondary School Mathematics: Readings from the "Mathematics Teacher."

    ERIC Educational Resources Information Center

    Austin, Joe Dan, Ed.

    This book provides applications for use in the secondary school mathematics curriculum by selecting related articles appearing in the "Mathematics Teacher" during the last 15 years. The articles are grouped into chapters that reflect the main secondary school mathematics courses and categorized by the highest level of mathematics needed for…

  11. 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…

  12. Prospective Mathematics Teachers' Attitudes Towards Learning Mathematics with Technology

    ERIC Educational Resources Information Center

    Ipek, A. Sabri; Berigel, Muhammed; Albayrak, Mustafa

    2007-01-01

    Role of technology which is an important tool for new approaches in learning mathematics is rapidly increasing at focus point of learning mathematics with new designs. One of the biggest factors at learning and instructing technology based mathematic education is attitudes of mathematics teachers towards technology. At this study, attitudes of…

  13. 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…

  14. 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…

  15. Magic star puzzle for educational mathematics

    NASA Astrophysics Data System (ADS)

    Gan, Yee Siang; Fong, Wan Heng; Sarmin, Nor Haniza

    2013-04-01

    One of the interesting fields in recreational mathematics is the magic number arrangement. There are different kinds of arrays in the arrangement for a group of numbers. In particular, one of the arrays in magic number arrangement is called magic star. In fact, magic star involves combinatorics that contributes to geometrical analysis and number theory. Hence, magic star is suitable to be introduced as educational mathematics to cultivate interest in different area of mathematics. To obtain the solutions of normal magic stars of order six, the possible sets of numbers for every line in a magic star have been considered. Previously, the calculation for obtaining the solutions has been done manually which is time-consuming. Therefore, a programming code to generate all the fundamental solutions for normal magic star of order six without including the properties of rotation and reflection has been done. In this puzzle, a magic star puzzle is created by using Matlab software, which enables a user to verify the entries for the cells of magic star of order six. Moreover, it is also user-friendly as it provides interactive commands on the inputs given by the user, which enables the user to detect the incorrect inputs. In addition, user can also choose to view all the fundamental solutions as generated by the programming code.

  16. Supporting African American Students' Learning of Mathematics: A Problem of Practice

    ERIC Educational Resources Information Center

    Jackson, Kara; Wilson, Jonee

    2012-01-01

    This article reports on a review of the mathematics education research literature 1989-May 2011 specific to K-12 African American students' opportunities to learn mathematics. Although we identify important developments in the literature, we conclude that the existing research base generally remains at the level of broad principles or orientations…

  17. Examining Sources of Gender DIF in Mathematics Assessments Using a Confirmatory Multidimensional Model Approach

    ERIC Educational Resources Information Center

    Mendes-Barnett, Sharon; Ercikan, Kadriye

    2006-01-01

    This study contributes to understanding sources of gender differential item functioning (DIF) on mathematics tests. This study focused on identifying sources of DIF and differential bundle functioning for boys and girls on the British Columbia Principles of Mathematics Exam (Grade 12) using a confirmatory SIBTEST approach based on a…

  18. Quantum algorithm for solving some discrete mathematical problems by probing their energy spectra

    NASA Astrophysics Data System (ADS)

    Wang, Hefeng; Fan, Heng; Li, Fuli

    2014-01-01

    When a probe qubit is coupled to a quantum register that represents a physical system, the probe qubit will exhibit a dynamical response only when it is resonant with a transition in the system. Using this principle, we propose a quantum algorithm for solving discrete mathematical problems based on the circuit model. Our algorithm has favorable scaling properties in solving some discrete mathematical problems.

  19. The Mathematics of Three N-Localizers Used Together for Stereotactic Neurosurgery

    PubMed Central

    2015-01-01

    The N-localizer enjoys widespread use in image-guided stereotactic neurosurgery and radiosurgery. This article derives the mathematical equations that are used with three N-localizers and provides analogies, explanations, and appendices in order to promote a deeper understanding of the mathematical principles that govern the N-localizer. PMID:26594605

  20. Space Mathematics, A Resource for Teachers Outlining Supplementary Space-Related Problems in Mathematics.

    ERIC Educational Resources Information Center

    Reynolds, Thomas D.; And Others

    This compilation of 138 problems illustrating applications of high school mathematics to various aspects of space science is intended as a resource from which the teacher may select questions to supplement his regular course. None of the problems require a knowledge of calculus or physics, and solutions are presented along with the problem…

  1. A Protocol for Evaluating Contextual Design Principles

    PubMed Central

    Stamps, Arthur

    2014-01-01

    This paper explains how scientific data can be incorporated into urban design decisions, such as evaluating contextual design principles. The recommended protocols are based on the Cochrane Reviews that have been widely used in medical research. The major concepts of a Cochrane Review are explained, as well as the underlying mathematics. The underlying math is meta-analysis. Data are reported for three applications and seven contextual design policies. It is suggested that use of the Cochrane protocols will be of great assistance to planners by providing scientific data that can be used to evaluate the efficacies of contextual design policies prior to implementing those policies. PMID:25431448

  2. Adapting mudharabah principle in Islamic option

    NASA Astrophysics Data System (ADS)

    Suhaimi, Siti Noor Aini binti; Salleh, Hassilah binti

    2013-04-01

    Most of the options today use the Black-Scholes model as the basis in valuing their price. This conventional model involves the elements that are strictly prohibited in Islam namely riba, gharar and maisir. Hence, this paper introduces a new mathematical model that has been adapted with mudharabah principle to replace the Black-Scholes model. This new model which is more compatible with Islamic values produces a new Islamic option which avoids any form of oppression and injustice to all parties involved.

  3. Lagrange's principle in extremum problems with constraints

    NASA Astrophysics Data System (ADS)

    Avakov, E. R.; Magaril-Il'yaev, G. G.; Tikhomirov, V. M.

    2013-06-01

    In this paper a general result concerning Lagrange's principle for so-called smoothly approximately convex problems is proved which encompasses necessary extremum conditions for mathematical and convex programming, the calculus of variations, Lyapunov problems, and optimal control problems with phase constraints. The problem of local controllability for a dynamical system with phase constraints is also considered. In an appendix, results are presented that relate to the development of a 'Lagrangian approach' to problems where regularity is absent and classical approaches are meaningless. Bibliography: 33 titles.

  4. In the Beginning: The Study of Mathematically Precocious Youth (SMPY).

    ERIC Educational Resources Information Center

    Stanley, Julian C.

    This paper contains a brief description of the founding and early years of the Study of Mathematically Precocious Youth (SMPY) from 1968 to the present. Several of the guiding principles behind SMPY are discussed. SMPY led to the formation of strong regional, state, and local centers that now blanket the United States with annual talent searches…

  5. Rethinking Mathematics: Teaching Social Justice by the Numbers

    ERIC Educational Resources Information Center

    Gutstein, Eric, Ed.; Peterson, Bob, Ed.

    2005-01-01

    This unique collection of more than 30 articles shows teachers how to weave social-justice principles throughout the math curriculum, and how to integrate social-justice math into other curricular areas as well. "Rethinking Mathematics" presents teaching ideas, lesson plans and reflections by practicing classroom teachers and distinguished…

  6. Mathematics Enrichment: Grade 5. Curriculum Bulletin Number 237.

    ERIC Educational Resources Information Center

    Johnston, Patsy

    Enrichment activities for fifth-grade mathematics are presented. They are intended to be a continuation of the program started in the fourth grade. Some of the activities reinforce principles taught in the regular program; others introduce new concepts to challenge students. The activities are divided into the following categories: number…

  7. Mathematics Enrichment: Grade 4. Curriculum Bulletin Number 236.

    ERIC Educational Resources Information Center

    Johnston, Patsy

    Enrichment activities for fourth-grade mathematics are presented. Some of the activities reinforce principles taught in the regular program; others introduce new concepts to challenge students. The activities are divided into the following categories: number pictures; multiplying or dividing by 10, 100, or 1000; tic-tac-toe word problems; map…

  8. Using a Card Trick to Teach Discrete Mathematics

    ERIC Educational Resources Information Center

    Simonson, Shai; Holm, Tara S.

    2003-01-01

    We present a card trick that can be used to review or teach a variety of topics in discrete mathematics. We address many subjects, including permutations, combinations, functions, graphs, depth first search, the pigeonhole principle, greedy algorithms, and concepts from number theory. Moreover, the trick motivates the use of computers in…

  9. Quantum Theory from Observer's Mathematics Point of View

    SciTech Connect

    Khots, Dmitriy; Khots, Boris

    2010-05-04

    This work considers the linear (time-dependent) Schrodinger equation, quantum theory of two-slit interference, wave-particle duality for single photons, and the uncertainty principle in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics, see [1]. Certain theoretical results and communications pertaining to these theorems are also provided.

  10. Designing Professional Learning Tasks for Mathematics Learning Trajectories

    ERIC Educational Resources Information Center

    Wilson, P. Holt; Sztajn, Paola; Edgington, Cyndi

    2013-01-01

    In this paper, we present an emerging set of learning conjectures and design principles to be used in the development of professional learning tasks that support elementary teachers' learning of mathematics learning trajectories. We outline our theoretical perspective on teacher knowledge of learning trajectories, review the literature concerning…

  11. Statistical mechanical theory for steady state systems. VI. Variational principles.

    PubMed

    Attard, Phil

    2006-12-01

    Several variational principles that have been proposed for nonequilibrium systems are analyzed. These include the principle of minimum rate of entropy production due to Prigogine [Introduction to Thermodynamics of Irreversible Processes (Interscience, New York, 1967)], the principle of maximum rate of entropy production, which is common on the internet and in the natural sciences, two principles of minimum dissipation due to Onsager [Phys. Rev. 37, 405 (1931)] and to Onsager and Machlup [Phys. Rev. 91, 1505 (1953)], and the principle of maximum second entropy due to Attard [J. Chem.. Phys. 122, 154101 (2005); Phys. Chem. Chem. Phys. 8, 3585 (2006)]. The approaches of Onsager and Attard are argued to be the only viable theories. These two are related, although their physical interpretation and mathematical approximations differ. A numerical comparison with computer simulation results indicates that Attard's expression is the only accurate theory. The implications for the Langevin and other stochastic differential equations are discussed.

  12. Principles of Equilibrium Statistical Mechanics

    NASA Astrophysics Data System (ADS)

    Chowdhury, Debashish; Stauffer, Dietrich

    2000-09-01

    This modern textbook provides a complete survey of the broad field of statistical mechanics. Based on a series of lectures, it adopts a special pedagogical approach. The authors, both excellent lecturers, clearly distinguish between general principles and their applications in solving problems. Analogies between phase transitions in fluids and magnets using continuum and spin models are emphasized, leading to a better understanding. Such special features as historical notes, summaries, problems, mathematical appendix, computer programs and order of magnitude estimations distinguish this volume from competing works. Due to its ambitious level and an extensive list of references for technical details on advanced topics, this is equally a must for researchers in condensed matter physics, materials science, polymer science, solid state physics, and astrophysics. From the contents Thermostatics: phase stability, phase equilibria, phase transitions; Statistical Mechanics: calculation, correlation functions, ideal classical gases, ideal quantum gases; Interacting Systems: models, computer simulation, mean-field approximation; Interacting Systems beyond Mean-field Theory: scaling and renormalization group, foundations of statistical mechanics "The present book, however, is unique that it both is written in a very pedagogic, easily comprehensible style, and, nevertheless, goes from the basic principles all the way to these modern topics, containing several chapters on the various approaches of mean field theory, and a chapter on computer simulation. A characteristic feature of this book is that often first some qualitative arguments are given, or a "pedestrians's approach", and then a more general and/or more rigorous derivation is presented as well. Particularly useful are also "supplementary notes", pointing out interesting applications and further developments of the subject, a detailed bibliography, problems and historical notes, and many pedagogic figures."

  13. Physical and mathematical cochlear models

    NASA Astrophysics Data System (ADS)

    Lim, Kian-Meng

    2000-10-01

    The cochlea is an intricate organ in the inner ear responsible for our hearing. Besides acting as a transducer to convert mechanical sound vibrations to electrical neural signals, the cochlea also amplifies and separates the sound signal into its spectral components for further processing in the brain. It operates over a broad-band of frequency and a huge dynamic range of input while maintaining a low power consumption. The present research takes the approach of building cochlear models to study and understand the underlying mechanics involved in the functioning of the cochlea. Both physical and mathematical models of the cochlea are constructed. The physical model is a first attempt to build a life- sized replica of the human cochlea using advanced micro- machining techniques. The model takes a modular design, with a removable silicon-wafer based partition membrane encapsulated in a plastic fluid chamber. Preliminary measurements in the model are obtained and they compare roughly with simulation results. Parametric studies on the design parameters of the model leads to an improved design of the model. The studies also revealed that the width and orthotropy of the basilar membrane in the cochlea have significant effects on the sharply tuned responses observed in the biological cochlea. The mathematical model is a physiologically based model that includes three-dimensional viscous fluid flow and a tapered partition with variable properties along its length. A hybrid asymptotic and numerical method provides a uniformly valid and efficient solution to the short and long wave regions in the model. Both linear and non- linear activity are included in the model to simulate the active cochlea. The mathematical model has successfully reproduced many features of the response in the biological cochlea, as observed in experiment measurements performed on animals. These features include sharply tuned frequency responses, significant amplification with inclusion of activity

  14. 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 book was put together…

  15. What Counts as Mathematical Discourse?

    ERIC Educational Resources Information Center

    Moschkovich, Judit

    2003-01-01

    In this paper I use situated and socio-cultural perspective (Gee, 1996 & 1999) to examine descriptions of mathematical discourse and an example of student talk in a mathematics classroom. Using this example, I discuss how the distinction between everyday and mathematical discourse can help or hinder us in hearing the mathematical content in…

  16. 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)

  17. Perceptions of Mathematics and Gender

    ERIC Educational Resources Information Center

    Kloosterman, Peter; Tassel, Janet; Ponniah, Ann G.; Esses, N. Kathryn

    2008-01-01

    This study examined students' perceptions about gender and the subject of mathematics, as well as gender and mathematics learning. Secondary school students and pre-service elementary teachers were surveyed using the Mathematics as a Gendered Domain and Who and Mathematics instruments developed by Leder and Forgasz (Leder, 2001). The data indicate…

  18. 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…

  19. 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.…

  20. 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…

  1. Improving Pupils' Mathematical Communication Abilities through Computer-Supported Reciprocal Peer Tutoring

    ERIC Educational Resources Information Center

    Yang, Euphony F. Y.; Chang, Ben; Cheng, Hercy N. H.; Chan, Tak-Wai

    2016-01-01

    This study examined how to foster pupils' mathematical communication abilities by using tablet PCs. Students were encouraged to generate math creations (including mathematical representation, solution, and solution explanation of word problems) as their teaching materials and reciprocally tutor classmates to increase opportunities for mathematical…

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

    ERIC Educational Resources Information Center

    Cosler, Norma, Ed.

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

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

    ERIC Educational Resources Information Center

    Johnston, Peter R.

    2013-01-01

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

  4. Discovering the structure of mathematical problem solving.

    PubMed

    Anderson, John R; Lee, Hee Seung; Fincham, Jon M

    2014-08-15

    The goal of this research is to discover the stages of mathematical problem solving, the factors that influence the duration of these stages, and how these stages are related to the learning of a new mathematical competence. Using a combination of multivariate pattern analysis (MVPA) and hidden Markov models (HMM), we found that participants went through 5 major phases in solving a class of problems: A Define Phase where they identified the problem to be solved, an Encode Phase where they encoded the needed information, a Compute Phase where they performed the necessary arithmetic calculations, a Transform Phase where they performed any mathematical transformations, and a Respond Phase where they entered an answer. The Define Phase is characterized by activity in visual attention and default network regions, the Encode Phase by activity in visual regions, the Compute Phase by activity in regions active in mathematical tasks, the Transform Phase by activity in mathematical and response regions, and the Respond phase by activity in motor regions. The duration of the Compute and Transform Phases were the only ones that varied with condition. Two features distinguished the mastery trials on which participants came to understand a new problem type. First, the duration of late phases of the problem solution increased. Second, there was increased activation in the rostrolateral prefrontal cortex (RLPFC) and angular gyrus (AG), regions associated with metacognition. This indicates the importance of reflection to successful learning. PMID:24746954

  5. Discovering the structure of mathematical problem solving.

    PubMed

    Anderson, John R; Lee, Hee Seung; Fincham, Jon M

    2014-08-15

    The goal of this research is to discover the stages of mathematical problem solving, the factors that influence the duration of these stages, and how these stages are related to the learning of a new mathematical competence. Using a combination of multivariate pattern analysis (MVPA) and hidden Markov models (HMM), we found that participants went through 5 major phases in solving a class of problems: A Define Phase where they identified the problem to be solved, an Encode Phase where they encoded the needed information, a Compute Phase where they performed the necessary arithmetic calculations, a Transform Phase where they performed any mathematical transformations, and a Respond Phase where they entered an answer. The Define Phase is characterized by activity in visual attention and default network regions, the Encode Phase by activity in visual regions, the Compute Phase by activity in regions active in mathematical tasks, the Transform Phase by activity in mathematical and response regions, and the Respond phase by activity in motor regions. The duration of the Compute and Transform Phases were the only ones that varied with condition. Two features distinguished the mastery trials on which participants came to understand a new problem type. First, the duration of late phases of the problem solution increased. Second, there was increased activation in the rostrolateral prefrontal cortex (RLPFC) and angular gyrus (AG), regions associated with metacognition. This indicates the importance of reflection to successful learning.

  6. La Meme Chose: How Mathematics Can Explain the Thinking of Children and the Thinking of Children Can Illuminate Mathematical Philosophy

    ERIC Educational Resources Information Center

    Cable, John

    2014-01-01

    This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which…

  7. Mathematical formula recognition using graph grammar

    NASA Astrophysics Data System (ADS)

    Lavirotte, Stephane; Pottier, Loic

    1998-04-01

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

  8. Archimedes' Principle in Action

    ERIC Educational Resources Information Center

    Kires, Marian

    2007-01-01

    The conceptual understanding of Archimedes' principle can be verified in experimental procedures which determine mass and density using a floating object. This is demonstrated by simple experiments using graduated beakers. (Contains 5 figures.)

  9. Chemical Principles Exemplified

    ERIC Educational Resources Information Center

    Plumb, Robert C.

    1972-01-01

    Collection of two short descriptions of chemical principles seen in life situations: the autocatalytic reaction seen in the bombardier beetle, and molecular potential energy used for quick roasting of beef. Brief reference is also made to methanol lighters. (PS)

  10. Archimedes' principle in action

    NASA Astrophysics Data System (ADS)

    Kireš, Marián

    2007-09-01

    The conceptual understanding of Archimedes' principle can be verified in experimental procedures which determine mass and density using a floating object. This is demonstrated by simple experiments using graduated beakers.

  11. Problems Relating Mathematics and Science in the High School.

    ERIC Educational Resources Information Center

    Morrow, Richard; Beard, Earl

    This document contains various science problems which require a mathematical solution. The problems are arranged under two general areas. The first (algebra I) contains biology, chemistry, and physics problems which require solutions related to linear equations, exponentials, and nonlinear equations. The second (algebra II) contains physics…

  12. The Music of Mathematics: Toward a New Problem Typology

    NASA Astrophysics Data System (ADS)

    Quarfoot, David

    Halmos (1980) once described problems and their solutions as "the heart of mathematics". Following this line of thinking, one might naturally ask: "What, then, is the heart of problems?". In this work, I attempt to answer this question using techniques from statistics, information visualization, and machine learning. I begin the journey by cataloging the features of problems delineated by the mathematics and mathematics education communities. These dimensions are explored in a large data set of students working thousands of problems at the Art of Problem Solving, an online company that provides adaptive mathematical training for students around the world. This analysis is able to concretely show how the fabric of mathematical problems changes across different subjects, difficulty levels, and students. Furthermore, it locates problems that stand out in the crowd -- those that synergize cognitive engagement, learning, and difficulty. This quantitatively-heavy side of the dissertation is partnered with a qualitatively-inspired portion that involves human scoring of 105 problems and their solutions. In this setting, I am able to capture elusive features of mathematical problems and derive a fuller picture of the space of mathematical problems. Using correlation matrices, principal components analysis, and clustering techniques, I explore the relationships among those features frequently discussed in mathematics problems (e.g., difficulty, creativity, novelty, affective engagement, authenticity). Along the way, I define a new set of uncorrelated features in problems and use these as the basis for a New Mathematical Problem Typology (NMPT). Grounded in the terminology of classical music, the NMPT works to quickly convey the essence and value of a problem, just as terms like "etude" and "mazurka" do for musicians. Taken together, these quantitative and qualitative analyses seek to terraform the landscape of mathematical problems and, concomitantly, the current thinking

  13. First principle-based AKMC modelling of the formation and medium-term evolution of point defect and solute-rich clusters in a neutron irradiated complex Fe-CuMnNiSiP alloy representative of reactor pressure vessel steels

    NASA Astrophysics Data System (ADS)

    Ngayam-Happy, R.; Becquart, C. S.; Domain, C.

    2013-09-01

    The formation and medium-term evolution of point defect and solute-rich clusters under neutron irradiation have been modelled in a complex Fe-CuMnNiSiP alloy representative of RPV steels, by means of first principle-based atomistic kinetic Monte Carlo simulations. The results obtained reproduce most features observed in available experimental studies, highlighting the very good agreement between both series. According to simulation, solute-rich clusters form and develop via an induced segregation mechanism on either the vacancy or interstitial clusters, and these point defect clusters are efficiently generated only in cascade debris and not Frenkel pair flux. The results have revealed the existence of two distinct populations of clusters with different characteristic features. Solute-rich clusters in the first group are bound essentially to interstitial clusters and they are enriched in Mn mostly, but also Ni to a lesser extent. Over the low dose regime, their density increases in the alloy as a result of the accumulation of highly stable interstitial clusters. In the second group, the solute-rich clusters are merged with vacancy clusters, and they contain mostly Cu and Si, but also substantial amount of Mn and Ni. The formation of a sub-population of pure solute clusters has been observed, which results from annihilation of the low stable vacancy clusters on sinks. The results indicate finally that the Mn content in clusters is up to 50%, Cu, Si, and Ni sharing the other half in more or less equivalent amounts. This composition has not demonstrated any noticeable modification with increasing dose over irradiation.

  14. Principles of Tendon Transfer.

    PubMed

    Wilbur, Danielle; Hammert, Warren C

    2016-08-01

    Tendon transfers provide a substitute, either temporary or permanent, when function is lost due to neurologic injury in stroke, cerebral palsy or central nervous system lesions, peripheral nerve injuries, or injuries to the musculotendinous unit itself. This article reviews the basic principles of tendon transfer, which are important when planning surgery and essential for an optimal outcome. In addition, concepts for coapting the tendons during surgery and general principles to be followed during the rehabilitation process are discussed. PMID:27387072

  15. Equilibrium I: Principles. Independent Learning Project for Advanced Chemistry (ILPAC). Unit P2.

    ERIC Educational Resources Information Center

    Inner London Education Authority (England).

    This unit on the principles of equilibrium is one of 10 first year units produced by the Independent Learning Project for Advanced Chemistry (ILPAC). The unit consists of two levels. After a treatment of non-mathematical aspects in level one (the idea of a reversible reaction, characteristics of an equilibrium state, the Le Chatelier's principle),…

  16. Design of Learning Objects for Concept Learning: Effects of Multimedia Learning Principles and an Instructional Approach

    ERIC Educational Resources Information Center

    Chiu, Thomas K. F.; Churchill, Daniel

    2016-01-01

    Literature suggests using multimedia learning principles in the design of instructional material. However, these principles may not be sufficient for the design of learning objects for concept learning in mathematics. This paper reports on an experimental study that investigated the effects of an instructional approach, which includes two teaching…

  17. Mathematical modeling of wax deposition in oil pipeline systems

    SciTech Connect

    Svendsen, J.A. . Dept. of Chemical Engineering)

    1993-08-01

    Deposition of wax on the wall of oil pipelines is often regarded as a problem since the tube diameter is reduced. Consequently, more power is needed to force the same amount of oil through the system. A mathematical model for quantitative prediction of wax deposition for each hydrocarbon component has been developed. Each component is characterized by weight fraction, heat of fusion, and melting point temperature. A model explains how a phase transition in the flow from liquid oil to waxy crystals may create a local density gradient and mass flux, which depends on the local temperature gradient. The model predicts that wax deposition can be considerably reduced even when the wall temperature is below the wax appearance point, provided the liquid/solid phase transition, expressed by the change in moles of liquid with temperature, is small at the wall temperature. Deposition as function of time has been obtained as a solution of differential equations derived from the principles of mass and energy conservation and the laws of diffusion.

  18. A finite element formulation of Euler equations for the solution of steady transonic flows

    NASA Technical Reports Server (NTRS)

    Ecer, A.; Akay, H. U.

    1982-01-01

    The main objective of the considered investigation is related to the development of a relaxation scheme for the analysis of inviscid, rotational, transonic flow problems. To formulate the equations of motion for inviscid flows in a fixed coordinate system, an Eulerian type variational principle is required. The derivation of an Eulerian variational principle which is employed in the finite element formulation is discussed. The presented numerical method describes the mathematical formulation and the application of a numerical process for the direct solution of steady Euler equations. The development of the procedure as an extension of existing potential flow formulations provides the applicability of previous procedures, e.g., proper application of the artificial viscosity for supersonic elements, and the accurate modeling of the shock.

  19. Design principles for riboswitch function.

    PubMed

    Beisel, Chase L; Smolke, Christina D

    2009-04-01

    Scientific and technological advances that enable the tuning of integrated regulatory components to match network and system requirements are critical to reliably control the function of biological systems. RNA provides a promising building block for the construction of tunable regulatory components based on its rich regulatory capacity and our current understanding of the sequence-function relationship. One prominent example of RNA-based regulatory components is riboswitches, genetic elements that mediate ligand control of gene expression through diverse regulatory mechanisms. While characterization of natural and synthetic riboswitches has revealed that riboswitch function can be modulated through sequence alteration, no quantitative frameworks exist to investigate or guide riboswitch tuning. Here, we combined mathematical modeling and experimental approaches to investigate the relationship between riboswitch function and performance. Model results demonstrated that the competition between reversible and irreversible rate constants dictates performance for different regulatory mechanisms. We also found that practical system restrictions, such as an upper limit on ligand concentration, can significantly alter the requirements for riboswitch performance, necessitating alternative tuning strategies. Previous experimental data for natural and synthetic riboswitches as well as experiments conducted in this work support model predictions. From our results, we developed a set of general design principles for synthetic riboswitches. Our results also provide a foundation from which to investigate how natural riboswitches are tuned to meet systems-level regulatory demands. PMID:19381267

  20. Analysis of a bio-dynamic model via Lyapunov principle and small-world network for tuberculosis.

    PubMed

    Chung, H-Y; Chung, C-Y; Ou, S-C

    2012-10-01

    The study will apply Lyapunov principle to construct a dynamic model for tuberculosis (TB). The Lyapunov principle is commonly used to examine and determine the stability of a dynamic system. To simulate the transmissions of vector-borne diseases and discuss the related health policies effects on vector-borne diseases, the authors combine the multi-agent-based system, social network and compartmental model to develop an epidemic simulation model. In the identity level, the authors use the multi-agent-based system and the mirror identity concept to describe identities with social network features such as daily visits, long-distance movement, high degree of clustering, low degree of separation and local clustering. The research will analyse the complex dynamic mathematic model of TB epidemic and determine its stability property by using the popular Matlab/Simulink software and relative software packages. Facing the current TB epidemic situation, the development of TB and its developing trend through constructing a dynamic bio-mathematical system model of TB is investigated. After simulating the development of epidemic situation with the solution of the SMIR epidemic model, the authors will come up with a good scheme to control epidemic situation to analyse the parameter values of a model that influence epidemic situation evolved. The authors will try to find the quarantining parameters that are the most important factors to control epidemic situation. The SMIR epidemic model and the results via numerical analysis may offer effective prevention with reference to controlling epidemic situation of TB.

  1. Analysis of a bio-dynamic model via Lyapunov principle and small-world network for tuberculosis.

    PubMed

    Chung, H-Y; Chung, C-Y; Ou, S-C

    2012-10-01

    The study will apply Lyapunov principle to construct a dynamic model for tuberculosis (TB). The Lyapunov principle is commonly used to examine and determine the stability of a dynamic system. To simulate the transmissions of vector-borne diseases and discuss the related health policies effects on vector-borne diseases, the authors combine the multi-agent-based system, social network and compartmental model to develop an epidemic simulation model. In the identity level, the authors use the multi-agent-based system and the mirror identity concept to describe identities with social network features such as daily visits, long-distance movement, high degree of clustering, low degree of separation and local clustering. The research will analyse the complex dynamic mathematic model of TB epidemic and determine its stability property by using the popular Matlab/Simulink software and relative software packages. Facing the current TB epidemic situation, the development of TB and its developing trend through constructing a dynamic bio-mathematical system model of TB is investigated. After simulating the development of epidemic situation with the solution of the SMIR epidemic model, the authors will come up with a good scheme to control epidemic situation to analyse the parameter values of a model that influence epidemic situation evolved. The authors will try to find the quarantining parameters that are the most important factors to control epidemic situation. The SMIR epidemic model and the results via numerical analysis may offer effective prevention with reference to controlling epidemic situation of TB. PMID:23101874

  2. 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…

  3. High School Mathematics Teachers' Perspectives on the Purposes of Mathematical Proof in School Mathematics

    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…

  4. Attitudes toward Mathematics: Relationships to Mathematics Achievement, Gender, Mathematics Course-taking Plans, and Career Interests.

    ERIC Educational Resources Information Center

    Thorndike-Christ, Tracy

    The relationship of attitudes toward mathematics to mathematics performance, gender, mathematics course-taking plans, and career interests were investigated. Students enrolled in public middle and high school mathematics courses (722 male, 794 female) served as subjects. The Fennema-Sherman Math Attitude scales were used to measure attitudes…

  5. Computational mathematics and physics of fusion reactors

    PubMed Central

    Garabedian, Paul R.

    2003-01-01

    Theory has contributed significantly to recent advances in magnetic fusion research. New configurations have been found for a stellarator experiment by computational methods. Solutions of a free-boundary problem are applied to study the performance of the plasma and look for islands in the magnetic surfaces. Mathematical analysis and numerical calculations have been used to study equilibrium, stability, and transport of optimized fusion reactors. PMID:14614129

  6. Mathematical and computational models of plasma flows

    NASA Astrophysics Data System (ADS)

    Brushlinsky, K. V.

    Investigations of plasma flows are of interest, firstly, due to numerous applications, and secondly, because of their general principles, which form a special branch of physics: the plasma dynamics. Numerical simulation and computation, together with theoretic and experimental methods, play an important part in these investigations. Speaking on flows, a relatively dense plasma is mentioned, so its mathematical models appertain to the fluid mechanics, i.e., they are based on the magnetohydrodynamic description of plasma. Time dependent two dimensional models of plasma flows of two wide-spread types are considered: the flows across the magnetic field and those in the magnetic field plane.

  7. Basic mathematical cognition.

    PubMed

    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. PMID:26263425

  8. Rockets: An Educator's Guide with Activities in Science, Mathematics, and Technology.

    ERIC Educational Resources Information Center

    National Aeronautics and Space Administration, Washington, DC.

    This educational guide discusses rockets and includes activities in science, mathematics, and technology. It begins with background information on the history of rocketry, scientific principles, and practical rocketry. The sections on scientific principles and practical rocketry focus on Sir Isaac Newton's Three Laws of Motion. These laws explain…

  9. Wurtzite structure Sc{sub 1-x}Al{sub x}N solid solution films grown by reactive magnetron sputter epitaxy: Structural characterization and first-principles calculations

    SciTech Connect

    Hoeglund, Carina; Birch, Jens; Bareno, Javier; Persson, Per O. A.; Wingqvist, Gunilla; Zukauskaite, Agne; Hultman, Lars; Alling, Bjoern; Czigany, Zsolt

    2010-06-15

    AlN(0001) was alloyed with ScN with molar fractions up to {approx}22%, while retaining a single-crystal wurtzite (w-) structure and with lattice parameters matching calculated values. Material synthesis was realized by magnetron sputter epitaxy of thin films starting from optimal conditions for the formation of w-AlN onto lattice-matched w-AlN seed layers on Al{sub 2}O{sub 3}(0001) and MgO(111) substrates. Films with ScN contents between 23% and {approx}50% exhibit phase separation into nanocrystalline ScN and AlN, while ScN-rich growth conditions yield a transformation to rocksalt structure Sc{sub 1-x}Al{sub x}N(111) films. The experimental results are analyzed with ion beam analysis, x-ray diffraction, and transmission electron microscopy, together with ab initio calculations of mixing enthalpies and lattice parameters of solid solutions in wurtzite, rocksalt, and layered hexagonal phases.

  10. The Principle of Energetic Consistency: Application to the Shallow-Water Equations

    NASA Technical Reports Server (NTRS)

    Cohn, Stephen E.

    2009-01-01

    If the complete state of the earth's atmosphere (e.g., pressure, temperature, winds and humidity, everywhere throughout the atmosphere) were known at any particular initial time, then solving the equations that govern the dynamical behavior of the atmosphere would give the complete state at all subsequent times. Part of the difficulty of weather prediction is that the governing equations can only be solved approximately, which is what weather prediction models do. But weather forecasts would still be far from perfect even if the equations could be solved exactly, because the atmospheric state is not and cannot be known completely at any initial forecast time. Rather, the initial state for a weather forecast can only be estimated from incomplete observations taken near the initial time, through a process known as data assimilation. Weather prediction models carry out their computations on a grid of points covering the earth's atmosphere. The formulation of these models is guided by a mathematical convergence theory which guarantees that, given the exact initial state, the model solution approaches the exact solution of the governing equations as the computational grid is made more fine. For the data assimilation process, however, there does not yet exist a convergence theory. This book chapter represents an effort to begin establishing a convergence theory for data assimilation methods. The main result, which is called the principle of energetic consistency, provides a necessary condition that a convergent method must satisfy. Current methods violate this principle, as shown in earlier work of the author, and therefore are not convergent. The principle is illustrated by showing how to apply it as a simple test of convergence for proposed methods.

  11. The traveltime holographic principle

    NASA Astrophysics Data System (ADS)

    Huang, Yunsong; Schuster, Gerard T.

    2015-01-01

    Fermat's interferometric principle is used to compute interior transmission traveltimes τpq from exterior transmission traveltimes τsp and τsq. Here, the exterior traveltimes are computed for sources s on a boundary B that encloses a volume V of interior points p and q. Once the exterior traveltimes are computed, no further ray tracing is needed to calculate the interior times τpq. Therefore this interferometric approach can be more efficient than explicitly computing interior traveltimes τpq by ray tracing. Moreover, the memory requirement of the traveltimes is reduced by one dimension, because the boundary B is of one fewer dimension than the volume V. An application of this approach is demonstrated with interbed multiple (IM) elimination. Here, the IMs in the observed data are predicted from the migration image and are subsequently removed by adaptive subtraction. This prediction is enabled by the knowledge of interior transmission traveltimes τpq computed according to Fermat's interferometric principle. We denote this principle as the `traveltime holographic principle', by analogy with the holographic principle in cosmology where information in a volume is encoded on the region's boundary.

  12. Perception determinants in learning mathematics

    NASA Astrophysics Data System (ADS)

    Mokhtar, Siti Fairus; Ali, Noor Rasidah; Rashid, Nurazlina Abdul

    2015-05-01

    This article described a statistical study of students' perception in mathematics. The objective of this study is to identify factors related to perception about learning mathematics among non mathematics' student. This study also determined the relationship between of these factors among non mathematics' student. 43 items questionnaires were distributed to one hundred students in UiTM Kedah who enrolled in the Business Mathematics course. These items were measured by using a semantic scale with the following anchors: 1 = strongly disagree to 7 = strongly agree. A factor analysis of respondents were identified into five factors that influencing the students' perception in mathematics. In my study, factors identified were attitude, interest, role of the teacher, role of peers and usefulness of mathematics that may relate to the perception about learning mathematics among non mathematics' student.

  13. "Real Teaching" in the Mathematics Classroom: A Comparison of the Instructional Practices of Elementary Teachers in Urban High-Poverty Schools

    ERIC Educational Resources Information Center

    McKinney, Sueanne E.; Robinson, Jack; Berube, Clair T.

    2013-01-01

    The National Council of Teachers of Mathematics' "Principles and Standards for School Mathematics" outlines fundamental elements that are crucial for creating a problem-solving and inquiry-driven classroom learning environment that highlights conceptual understandings of mathematics ideas. Even though this document outlines…

  14. 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.

  15. Mathematics in modern immunology

    PubMed Central

    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

  16. Mathematics in modern immunology.

    PubMed

    Castro, Mario; Lythe, Grant; Molina-París, Carmen; Ribeiro, Ruy M

    2016-04-01

    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.

  17. Fundamental base closure environmental principles

    SciTech Connect

    Yim, R.A.

    1994-12-31

    Military base closures present a paradox. The rate, scale and timing of military base closures is historically unique. However, each base itself typically does not present unique problems. Thus, the challenge is to design innovative solutions to base redevelopment and remediation issues, while simultaneously adopting common, streamlined or pre-approved strategies to shared problems. The author presents six environmental principles that are fundamental to base closure. They are: remediation not clean up; remediation will impact reuse; reuse will impact remediation; remediation and reuse must be coordinated; environmental contamination must be evaluated as any other initial physical constraint on development, not as an overlay after plans are created; and remediation will impact development, financing and marketability.

  18. Mathematical programming formulations for satellite synthesis

    NASA Technical Reports Server (NTRS)

    Bhasin, Puneet; Reilly, Charles H.

    1987-01-01

    The problem of satellite synthesis can be described as optimally allotting locations and sometimes frequencies and polarizations, to communication satellites so that interference from unwanted satellite signals does not exceed a specified threshold. In this report, mathematical programming models and optimization methods are used to solve satellite synthesis problems. A nonlinear programming formulation which is solved using Zoutendijk's method and a gradient search method is described. Nine mixed integer programming models are considered. Results of computer runs with these nine models and five geographically compatible scenarios are presented and evaluated. A heuristic solution procedure is also used to solve two of the models studied. Heuristic solutions to three large synthesis problems are presented. The results of our analysis show that the heuristic performs very well, both in terms of solution quality and solution time, on the two models to which it was applied. It is concluded that the heuristic procedure is the best of the methods considered for solving satellite synthesis problems.

  19. Spaceborne receivers: Basic principles

    NASA Technical Reports Server (NTRS)

    Stacey, J. M.

    1984-01-01

    The underlying principles of operation of microwave receivers for space observations of planetary surfaces were examined. The design philosophy of the receiver as it is applied to operate functionally as an efficient receiving system, the principle of operation of the key components of the receiver, and the important differences among receiver types are explained. The operating performance and the sensitivity expectations for both the modulated and total power receiver configurations are outlined. The expressions are derived from first principles and are developed through the important intermediate stages to form practicle and easily applied equations. The transfer of thermodynamic energy from point to point within the receiver is illustrated. The language of microwave receivers is applied statistics.

  20. A Mathematical Model of Cancer Treatment by Radiotherapy

    PubMed Central

    Yang, Chenxue

    2014-01-01

    A periodic mathematical model of cancer treatment by radiotherapy is presented and studied in this paper. Conditions on the coexistence of the healthy and cancer cells are obtained. Furthermore, sufficient conditions on the existence and globally asymptotic stability of the positive periodic solution, the cancer eradication periodic solution, and the cancer win periodic solution are established. Some numerical examples are shown to verify the validity of the results. A discussion is presented for further study. PMID:25478002