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Sample records for principle mathematical solutions

  1. Physical principles versus mathematical rigor

    NASA Astrophysics Data System (ADS)

    Patterson, Jim

    2000-04-01

    A kinematics problem in which a ball is thrown into the air and a second ball is dropped sometime later is presented. The solution is simplified by close attention to the mathematical details, and the physical significance of the resulting function is discussed.

  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. Mathematical models for principles of gyroscope theory

    NASA Astrophysics Data System (ADS)

    Usubamatov, Ryspek

    2017-01-01

    Gyroscope devices are primary units for navigation and control systems that have wide application in engineering. The main property of the gyroscope device is maintaining the axis of a spinning rotor. This gyroscope peculiarity is represented in terms of gyroscope effects in which known mathematical models have been formulated on the law of kinetic energy conservation and the change in the angular momentum. The gyroscope theory is represented by numerous publications, which mathematical models do not match the actual torques and motions in these devices.. The nature of gyroscope effects is more complex than represented in known publications. Recent investigations in this area have demonstrated that on a gyroscope can act until eleven internal torques simultaneously and interdependently around two axes. These gyroscope torques are generated by spinning rotor's mass-elements and by the gyroscope center-mass based on action of several inertial forces. The change in the angular momentum does not play first role for gyroscope motions. The external load generates several internal torques which directions may be distinguished. This situation leads changing of the angular velocities of gyroscope motions around two axes. Formulated mathematical models of gyroscope internal torques are representing the fundamental principle of gyroscope theory. In detail, the gyroscope is experienced the resistance torque generated by the centrifugal and Coriolis forces of the spinning rotor and the precession torque generated by the common inertial forces and the change in the angular momentum. The new mathematical models for the torques and motions of the gyroscope confirmed for most unsolvable problems. The mathematical models practically tested and the results are validated the theoretical approach.

  5. Four Reactions to "Principles and Standards for School Mathematics."

    ERIC Educational Resources Information Center

    Addington, Susan; Clemens, Herbert; Howe, Roger; Saul, Mark

    2000-01-01

    This essay presents four reactions to the National Council of Teachers of Mathematics (NCTM) "Principles and Standards for School Mathematics" (PSSM). The four respondents include three university mathematics professors and one teacher. The first author describes the publication as refreshingly free of mathematics education jargon,…

  6. Teaching Mathematics: Issues and Solutions

    ERIC Educational Resources Information Center

    Little, Mary E.

    2009-01-01

    The ability to compute, problem solve, and apply concepts and skills in mathematics influences multiple decisions in our lives. The National Research Council (1989) reported that mathematics is especially evident in our technology-rich society, where number sense and problem solving skills have increased the importance and demands of advanced…

  7. 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…

  8. A Mathematical Solution to the Motorway Problem

    ERIC Educational Resources Information Center

    Michaelson, Matthew T.

    2009-01-01

    This article presents a mathematical solution to a motorway problem. The motorway problem is an excellent application in optimisation. As it integrates the concepts of trigonometric functions and differentiation, the motorway problem can be used quite effectively as the basis for an assessment tool in senior secondary mathematics subjects.…

  9. 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…

  10. Principles for Designing Intervention in Mathematics

    ERIC Educational Resources Information Center

    National Center on Intensive Intervention, 2016

    2016-01-01

    The purpose of this guide is to provide brief explanations of practices that can be implemented when working with students in need of intensive intervention in mathematics. Special education instructors, math interventionists, and others working with students who struggle with mathematics may find this guide helpful. Specific topics covered…

  11. 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.

  12. Mathematics-like Principles Inferred from the Petroglyphs.

    ERIC Educational Resources Information Center

    Moore, Charles G.

    1988-01-01

    Identifies certain principles of mathematics-like thought participated in by the carvers of the petroglyphs: (1) iteration; (2) recursion; (3) similitude; (4) tiling; and (5) symmetry. Provides illustrations and verbal descriptions of each process and concludes with four suggested classroom activities to help students appreciate the talents of the…

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

    NASA Astrophysics Data System (ADS)

    Priatna, Nanang

    2017-08-01

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

  14. System principles, mathematical models and methods to ensure high reliability of safety systems

    NASA Astrophysics Data System (ADS)

    Zaslavskyi, V.

    2017-04-01

    Modern safety and security systems are composed of a large number of various components designed for detection, localization, tracking, collecting, and processing of information from the systems of monitoring, telemetry, control, etc. They are required to be highly reliable in a view to correctly perform data aggregation, processing and analysis for subsequent decision making support. On design and construction phases of the manufacturing of such systems a various types of components (elements, devices, and subsystems) are considered and used to ensure high reliability of signals detection, noise isolation, and erroneous commands reduction. When generating design solutions for highly reliable systems a number of restrictions and conditions such as types of components and various constrains on resources should be considered. Various types of components perform identical functions; however, they are implemented using diverse principles, approaches and have distinct technical and economic indicators such as cost or power consumption. The systematic use of different component types increases the probability of tasks performing and eliminates the common cause failure. We consider type-variety principle as an engineering principle of system analysis, mathematical models based on this principle, and algorithms for solving optimization problems of highly reliable safety and security systems design. Mathematical models are formalized in a class of two-level discrete optimization problems of large dimension. The proposed approach, mathematical models, algorithms can be used for problem solving of optimal redundancy on the basis of a variety of methods and control devices for fault and defects detection in technical systems, telecommunication networks, and energy systems.

  15. Mathematics for Computer Scientists: Problems and Solutions

    ERIC Educational Resources Information Center

    Alexander, Sylvia; Bishop, Pam; Crawford, Ewan; McCartney, Mark

    2006-01-01

    The results of a survey of the mathematics provision within UK university computer science departments are presented. In particular it is found that many academics are dissatisfied with the level of "mathematical preparedness" of their students. A number of recommendations and resources are suggested to address this. (Contains 6 figures.)

  16. Multidrug Resistance: Physiological Principles and Nanomedical Solutions

    PubMed Central

    Storm, Gert; Kiessling, Fabian; Lammers, Twan

    2014-01-01

    Multidrug (MDR) resistance 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. PMID:24120954

  17. 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.

  18. 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…

  19. From geometry to algebra and vice versa: Realistic mathematics education principles for analyzing geometry tasks

    NASA Astrophysics Data System (ADS)

    Jupri, Al

    2017-04-01

    In this article we address how Realistic Mathematics Education (RME) principles, including the intertwinement and the reality principles, are used to analyze geometry tasks. To do so, we carried out three phases of a small-scale study. First we analyzed four geometry problems - considered as tasks inviting the use of problem solving and reasoning skills - theoretically in the light of the RME principles. Second, we tested two problems to 31 undergraduate students of mathematics education program and other two problems to 16 master students of primary mathematics education program. Finally, we analyzed student written work and compared these empirical to the theoretical results. We found that there are discrepancies between what we expected theoretically and what occurred empirically in terms of mathematization and of intertwinement of mathematical concepts from geometry to algebra and vice versa. We conclude that the RME principles provide a fruitful framework for analyzing geometry tasks that, for instance, are intended for assessing student problem solving and reasoning skills.

  20. 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)

  1. 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,…

  2. Connection of Scattering Principles: A Visual and Mathematical Tour

    ERIC Educational Resources Information Center

    Broggini, Filippo; Snieder, Roel

    2012-01-01

    Inverse scattering, Green's function reconstruction, focusing, imaging and the optical theorem are subjects usually studied as separate problems in different research areas. We show a physical connection between the principles because the equations that rule these "scattering principles" have a similar functional form. We first lead the reader…

  3. Connection of Scattering Principles: A Visual and Mathematical Tour

    ERIC Educational Resources Information Center

    Broggini, Filippo; Snieder, Roel

    2012-01-01

    Inverse scattering, Green's function reconstruction, focusing, imaging and the optical theorem are subjects usually studied as separate problems in different research areas. We show a physical connection between the principles because the equations that rule these "scattering principles" have a similar functional form. We first lead the reader…

  4. Probability: Actual Trials, Computer Simulations, and Mathematical Solutions.

    ERIC Educational Resources Information Center

    Walton, Karen Doyle; Walton, J. Doyle

    The purpose of this teaching unit is to approach elementary probability problems in three ways. First, actual trials are performed and results are recorded. Second, a simple computer simulation of the problem provided on diskette and written for Apple IIe and IIc computers, is run several times. Finally, the mathematical solution of the problem is…

  5. Rational Number and Proportional Reasoning in Early Secondary School: Towards Principled Improvement in Mathematics

    ERIC Educational Resources Information Center

    Howe, Christine; Luthman, Stefanie; Ruthven, Kenneth; Mercer, Neil; Hofmann, Riikka; Ilie, Sonia; Guardia, Paula

    2015-01-01

    Reflecting concerns about student attainment and participation in mathematics and science, the Effecting Principled Improvement in STEM Education ("epiSTEMe") project attempted to support pedagogical advancement in these two disciplines. Using principles identified as effective in the research literature (and combining these in a novel…

  6. Design principles for radiation-resistant solid solutions

    NASA Astrophysics Data System (ADS)

    Schuler, Thomas; Trinkle, Dallas R.; Bellon, Pascal; Averback, Robert

    2017-05-01

    We develop a multiscale approach to quantify the increase in the recombined fraction of point defects under irradiation resulting from dilute solute additions to a solid solution. This methodology provides design principles for radiation-resistant materials. Using an existing database of solute diffusivities, we identify Sb as one of the most efficient solutes for this purpose in a Cu matrix. We perform density-functional-theory calculations to obtain binding and migration energies of Sb atoms, vacancies, and self-interstitial atoms in various configurations. The computed data informs the self-consistent mean-field formalism to calculate transport coefficients, allowing us to make quantitative predictions of the recombined fraction of point defects as a function of temperature and irradiation rate using homogeneous rate equations. We identify two different mechanisms according to which solutes lead to an increase in the recombined fraction of point defects; at low temperature, solutes slow down vacancies (kinetic effect), while at high temperature, solutes stabilize vacancies in the solid solution (thermodynamic effect). Extension to other metallic matrices and solutes are discussed.

  7. Multi-criteria optimisation problems for chemical engineering systems and algorithms for their solution based on fuzzy mathematical methods.

    PubMed

    Orazbayev, B B; Orazbayeva, K N; Kurmangaziyeva, L T; Makhatova, V E

    2015-01-01

    Mathematical equations for the multi-criteria task of the optimisation of chemical engineering systems, for example for the optimisation of working regimes for industrial installations for benzene production, have been formulated and developed, and based on fuzzy mathematical methods, algorithms for their solution have been developed. Since the chemical engineering system, which is being researched, is characterised by multiple criteria and often functions in conditions of uncertainty, the presenting problem is formulated in the form of multi-criteria equations for fuzzy mathematical programming. New mathematical formulations for the problems being solved in a fuzzy environment and heuristic algorithms for their solution have been developed by the modification of various optimisation principles based on fuzzy mathematical methods.

  8. Multi-criteria optimisation problems for chemical engineering systems and algorithms for their solution based on fuzzy mathematical methods

    PubMed Central

    Orazbayev, B. B.; Orazbayeva, K. N.; Kurmangaziyeva, L. T.; Makhatova, V.E.

    2015-01-01

    Mathematical equations for the multi-criteria task of the optimisation of chemical engineering systems, for example for the optimisation of working regimes for industrial installations for benzene production, have been formulated and developed, and based on fuzzy mathematical methods, algorithms for their solution have been developed. Since the chemical engineering system, which is being researched, is characterised by multiple criteria and often functions in conditions of uncertainty, the presenting problem is formulated in the form of multi-criteria equations for fuzzy mathematical programming. New mathematical formulations for the problems being solved in a fuzzy environment and heuristic algorithms for their solution have been developed by the modification of various optimisation principles based on fuzzy mathematical methods. PMID:28275318

  9. 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…

  10. 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…

  11. Connections through the Development of Mathematical Ideas: The Case of Solution to High Degree Polynomial Equations in Medieval Chinese Mathematics.

    ERIC Educational Resources Information Center

    Fung, Chun-Ip; Wong, Ngai-Ying

    1998-01-01

    Discusses the importance of making connections among mathematical topics and connections between mathematics and other disciplines. Emphasizes that such connections naturally arise from historical development of mathematical concepts. Illustrates the idea by portraying the development from extracting roots to the solution of high-degree polynomial…

  12. 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…

  13. Photoelectron Spectra of Aqueous Solutions from First Principles

    SciTech Connect

    Gaiduk, Alex P.; Govoni, Marco; Seidel, Robert; Skone, Jonathan H.; Winter, Bernd; Galli, Giulia

    2016-06-08

    We present a combined computational and experimental study of the photoelectron spectrum of a simple aqueous solution of NaCl. Measurements were conducted on microjets, and first-principles calculations were performed using hybrid functionals and many-body perturbation theory at the G0W0 level, starting with wave functions computed in ab initio molecular dynamics simulations. We show excellent agreement between theory and experiments for the positions of both the solute and solvent excitation energies on an absolute energy scale and for peak intensities. The best comparison was obtained using wave functions obtained with dielectric-dependent self-consistent and range-separated hybrid functionals. Our computational protocol opens the way to accurate, predictive calculations of the electronic properties of electrolytes, of interest to a variety of energy problems.

  14. 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.

  15. 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…

  16. A Historical Analysis of Primary Mathematics Curricula in Terms of Teaching Principles

    ERIC Educational Resources Information Center

    Ozmantar, Mehmet Fatih

    2017-01-01

    This study carries out a comparative analysis of primary mathematics curricula put into practice during Turkish Republican period. The data for this study are composed of official curricula documents which are examined in terms of teaching principles. The study adopts a qualitative approach and employs document analysis method. The official…

  17. 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.

  18. Applying Cognitive Psychology Based Instructional Design Principles in Mathematics Teaching and Learning: Introduction

    ERIC Educational Resources Information Center

    Verschaffel, Lieven; Van Dooren, W.; Star, J.

    2017-01-01

    This special issue comprises contributions that address the breadth of current lines of recent research from cognitive psychology that appear promising for positively impacting students' learning of mathematics. More specifically, we included contributions (a) that refer to cognitive psychology based principles and techniques, such as explanatory…

  19. 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…

  20. [3D echocardiography. Mathematical principles and technical realization].

    PubMed

    Wollschläger, H

    1995-08-01

    The ultimate goal of any imaging technique for the investigation of the anatomy of the beating heart is a 3D-display of the cardiac morphology throughout a complete heart cycle. The reason for this interest is quite clear: 3D-imaging has the potential for a better understanding of the individual morphology under normal and pathological conditions and especially, if complex therapeutic decisions have to been made. In the clinical practice, the echocardiographer attempts to obtain a spatial information by a mental reassembling of the 2D echocardiographic images, that are obtained from different imaging planes. This procedure, however, is very subjective and, thus, highly susceptible for errors. Therefore, the 3D-echocardiography has been developed to replace this mental process by an "objective" and reproducible computerized reconstruction. Prerequisite for such a 3D-surface reconstruction is a cubic, isotropic digital data set with cubic data volumes, so called "Voxels" (Figure 1). The term "isotropic" means, that the resolution is identical in all directions, and that the data density within the cube is homogeneous. Those cubes are the mathematical basis for any 3D-reconstruction. At the first step on the way to 3D-images, the data cubes have to be filled with 2D echo information. So far, three principal modalities of image acquisition are available for the clinical routine: parallel scanning from the esophagus (Figure 2), rotational scanning (transesophageal--Figure 3a--or transthoracic--Figure 3b). In all cases, the imaging planes are incremented by an external stepper motor using a dedicated computer logic for gated image acquisition. At the present time, despite geometrical shortcomings, the TEE omniplane probe with rotational scanning is the most widely used system. It can be applied for standard investigations as well as for "3D"-data acquisition after only minor modifications. The process of 3D-reconstruction is a sequence of repeated steps of image

  1. [Fuzzy mathematic quantitative law of composing principle in the study of traditional Chinese medicine].

    PubMed

    Liu, Ming; Gao, Yue; Xiao, Rui; Zhang, Bo-li

    2009-01-01

    This study is to analyze microcosmic significance of Chinese medicine composing principle "principal, assistant, complement and mediating guide" and it's fuzzy mathematic quantitative law. According to molecular biology and maximal membership principle, fuzzy subset and membership functions were proposed. Using in vivo experiment on the effects of SiWu Decoction and its ingredients on mice with radiation-induced blood deficiency, it is concluded that DiHuang and DangGui belonged to the principal and assistant subset, BaiShao belonged to the contrary complement subset, ChuanXiong belonged to the mediating guide subset by maximal membership principle. It is discussed that traditional Chinese medicine will be consummate medical science when its theory can be described by mathematic language.

  2. 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…

  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. First-principles investigation of solute-hydrogen interaction in a α-Ti solid solution

    NASA Astrophysics Data System (ADS)

    Hu, Q. M.; Xu, D. S.; Yang, R.; Li, D.; Wu, W. T.

    2002-08-01

    In this paper, a first-principles method is used to calculate the interaction energy between substitutional solute atoms and hydrogen in α-Ti. The results show that simple metal (SM) solute atoms are repulsive to H and therefore are detraps for H, whereas transition metal (TM) solute atoms, with smaller sizes than that of the host atoms, attract H and provide traps for H. The relationship between the interaction energy and lattice distortion as well as the electronic structure is investigated. The SM-H and TM-H interactions are dominated by different factors. The repulsive interaction between SM atoms and H is mainly due to the hybridization between the electrons of SM atoms and H when they are close to each other. The interaction between the TM solutes and H is attributable to the atomic size effect, and can be described satisfactorily by Matsumoto's strain field relaxation model. From the solute-H interaction energy and available measured terminal solubility of hydrogen (TSH), the relationship between the solute trapping of hydrogen and TSH in α-Ti is discussed. No coherent relationship is found between the theoretical hydrogen trapping effect and the experimental TSH in α-Ti alloys.

  5. 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…

  6. 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…

  7. Solute-vehicle-skin interactions in percutaneous absorption: the principles and the people.

    PubMed

    Roberts, M S

    2013-01-01

    An appreciation of solute-vehicle-skin interactions underpins our current understanding of the processes of percutaneous absorption as well as in the prediction of the extent of absorption. This understanding has been reached through principles developed and validated over the last century through the work of a number of authors, including Dale Wurster, Takeru Higuchi, Irvin Blank, Robert Scheuplein, Gordon Flynn, Boyd Poulsen and Tom Franz, as well as by many scientists from my and younger generations. Their work has led to an appreciation of the rate-limiting steps in percutaneous penetration, the role played by the physicochemical properties of the solute, vehicle and skin and the variability that may arise from using various experimental/mathematical/pharmacokinetic models to quantify absorption as well as enabling the prediction of local and systemic efficacy and toxicity. In addition, unexpected behaviour may result from non-ideality in solute-vehicle-skin effects, including dehydration, chemical enhancement, supersaturation, metabolism, sequestration and vascular effects, including those of nanosystems on the local vasculature. In general, in vitro skin penetration profiles are predictive of in vivo profiles but a number of exceptions also exist.

  8. Predicting Mg Strength from First-Principles: Solid-Solution Strengthening, Softening, and Cross-Slip

    NASA Astrophysics Data System (ADS)

    Trinkle, Dallas R.; Yasi, Joseph A.; Hector, Louis G.

    Predictive modeling of strength from first-principles electronic structure methods offers great promise to inform Mg alloy design. Simulating the mechanical behavior for new alloys requires an understanding of mechanisms for deformation at atomic-length scales, with accurate chemistry, extended to larger length- and time-scales. To design ductile Mg alloys, we identify solutes that strengthen basal slip and increase cross-slip. First-principles modeling of dislocations predict dislocation motion under stress through a field of solutes at a finite temperature. First-principles flexible boundary conditions compute accurate core structures of basal and prismatic dislocations, and dislocation/solute interactions. We develop new models to predict the solute-strengthening for basal dislocations; cross-slip from basal- to prismatic-slip for α-type screw dislocations; and cross-slip stress with solutes. First-principles data provides insight into the response of dislocations to solutes and quantitative data to build new predictive models.

  9. Applications of homogenous balanced principle on investigating exact solutions to a series of time fractional nonlinear PDEs

    NASA Astrophysics Data System (ADS)

    Rui, Weiguo

    2017-06-01

    By using a counterexample, we proved the fractional chain rule appeared in many references does not hold under Riemann-Liouville definition and Caputo definition of fractional derivative. It shows that this chain rule is invalid in investigating exact solutions of nonlinear fractional partial differential equations (PDEs). In this paper, based on the homogenous balanced principle, the function-expansion method of separation variable type are introduced. By using this method, a series of nonlinear time fractional PDEs such as time fractional KdV equation and Burgers equation, time fractional diffusion-convection equations are studied from mathematical viewpoint. The dynamical properties of these exact solutions are discussed and the profiles of several representative exact solutions are illustrated.

  10. The Algebra Solution to Mathematics Reform: Completing the Equation

    ERIC Educational Resources Information Center

    Spielhagen, Frances R.

    2011-01-01

    How can we increase mathematics achievement among all students? This book provides a straightforward explanation of how changing mathematics tracking policies to provide algebra instruction to all students by at least eighth grade can bring about changes in both student achievement and teacher performance. Spielhagen chronicles the success of a…

  11. The Algebra Solution to Mathematics Reform: Completing the Equation

    ERIC Educational Resources Information Center

    Spielhagen, Frances R.

    2011-01-01

    How can we increase mathematics achievement among all students? This book provides a straightforward explanation of how changing mathematics tracking policies to provide algebra instruction to all students by at least eighth grade can bring about changes in both student achievement and teacher performance. Spielhagen chronicles the success of a…

  12. Investigation of the blood behaviour and vascular diseases by using mathematical physic principles

    NASA Astrophysics Data System (ADS)

    Yardimci, Ahmet; Simsek, Buket

    2017-07-01

    In this paper we prepare a short survey for using of mathematical physic principles in blood flow and vascular diseases researches. The study of the behavior of blood flow in the blood vessels provides understanding on connection between flow and the development of dieseases such as atherosclerosis, thrombosis, aneurysms etc. and how the flow dynamics is changed under these conditions. Blood flow phenomena are often too complex that it would be possible to describe them entirely analytically, although simple models, such as Poiseuille model, can still provide some insight into blood flow. Blood is not an "ideal fluid" and energy is lost as flowing blood overcomes resistance. Resistance to blood flow is a function of viscosity, vessel radius, and vessel length. So, mathematical Physic principles are useful tools for blood flow research studies. Blood flow is a function of pressure gradient and resistance and resistance to flow can be estimates using Poiseuille's law. Reynold's number can be used to determine whether flow is laminar or turbulent.

  13. 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)

  14. 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)

  15. Student Preferences in the Design of Worked Solutions in Undergraduate Mathematics

    ERIC Educational Resources Information Center

    Mendiolea, David

    2013-01-01

    The ubiquitous practice of providing worked solutions to exercises in mathematics education has been under-researched. Little is known about what elements of a worked solution are valued by students. This exploratory study sought in-depth feedback from six undergraduate students who experienced a range of worked solutions designed to encourage…

  16. The Relationship between Students' Metacognitive Awareness and Their Solutions to Similar Types of Mathematical Problems

    ERIC Educational Resources Information Center

    Yildirim, Sevda; Ersozlu, Zehra Nur

    2013-01-01

    This study was designed to investigate the relationship between the metacognitive awareness of university students and their solutions to the similar mathematical problem types. Participants were 97 freshmen from department of mathematics at a state university in Turkey. Two different scales were used for data collection: "Metacognitive…

  17. Using Predictor-Corrector Methods in Numerical Solutions to Mathematical Problems of Motion

    ERIC Educational Resources Information Center

    Lewis, Jerome

    2005-01-01

    In this paper, the author looks at some classic problems in mathematics that involve motion in the plane. Many case problems like these are difficult and beyond the mathematical skills of most undergraduates, but computational approaches often require less insight into the subtleties of the problems and can be used to obtain reliable solutions.…

  18. The Relationship between Students' Metacognitive Awareness and Their Solutions to Similar Types of Mathematical Problems

    ERIC Educational Resources Information Center

    Yildirim, Sevda; Ersozlu, Zehra Nur

    2013-01-01

    This study was designed to investigate the relationship between the metacognitive awareness of university students and their solutions to the similar mathematical problem types. Participants were 97 freshmen from department of mathematics at a state university in Turkey. Two different scales were used for data collection: "Metacognitive…

  19. Mathematical modeling of methoxyanabasine C11H16N2O polymer solution ultrafiltration

    NASA Astrophysics Data System (ADS)

    Satayev, Marat; Shakirov, Birzhan; Mutaliyeva, Botagoz; Satayeva, Lazzat; Altynbekov, Rustem; Baiysbay, Omirbek; Alibekov, Ravshanbek

    2012-06-01

    This work covers the mathematical modeling of ultrafiltration with immobile membranes for physiologically-active of methoxyanabasine C11H16N2O polymer solution. Methoxyanabasine is used as low toxic antineoplastic drug. On the basis of theoretical and experimental analysis of mass transfer and hydrodynamics, it is offered the mathematical model of permeability of membranes at an ultrafiltration of polymer solutions. Further the formulas for determination of factor of concentration polarization and ultrafiltration selectivity are calculated.

  20. 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

  1. Remembering Zoltan Dienes, a Maverick of Mathematics Teaching and Learning: Applying the Variability Principles to Teach Algebra

    ERIC Educational Resources Information Center

    Gningue, Serigne Mbaye

    2016-01-01

    This paper is written in honor of Zoltan Paul Dienes, an internationally renowned mathematician and educator, who passed away in January 2014. It is an attempt to describe, analyze and apply Dienes' theory on how mathematical structures can be taught by applying his four principles of learning upon which he believed a teacher can base concept…

  2. Remembering Zoltan Dienes, a Maverick of Mathematics Teaching and Learning: Applying the Variability Principles to Teach Algebra

    ERIC Educational Resources Information Center

    Gningue, Serigne Mbaye

    2016-01-01

    This paper is written in honor of Zoltan Paul Dienes, an internationally renowned mathematician and educator, who passed away in January 2014. It is an attempt to describe, analyze and apply Dienes' theory on how mathematical structures can be taught by applying his four principles of learning upon which he believed a teacher can base concept…

  3. 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…

  4. Teaching and assessment of mathematical principles for software correctness using a reasoning concept inventory

    NASA Astrophysics Data System (ADS)

    Drachova-Strang, Svetlana V.

    As computing becomes ubiquitous, software correctness has a fundamental role in ensuring the safety and security of the systems we build. To design and develop software correctly according to their formal contracts, CS students, the future software practitioners, need to learn a critical set of skills that are necessary and sufficient for reasoning about software correctness. This dissertation presents a systematic approach to both introducing these reasoning skills into the curriculum, and assessing how well the students have learned them. Specifically, it introduces a comprehensive Reasoning Concept Inventory (RCI) that captures the fine details of basic reasoning skills that are ideally learned across the undergraduate curriculum to reason about software correctness, to develop high quality software, and to understand why software works as specified. The RCI forms the basis for developing learning outcomes that help educators to assess the adequacy of current techniques and pinpoint necessary improvements. This dissertation contains results from experimentation and assessment over the past few years in multiple CS courses. The results show that the finer principles of mathematical reasoning of software correctness can be taught effectively and continuously improved with the help of the RCI using suitable teaching practices, and supporting methods and tools.

  5. 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…

  6. 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.

  7. 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…

  8. 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…

  9. Minimalism as a Guiding Principle: Linking Mathematical Learning to Everyday Knowledge

    ERIC Educational Resources Information Center

    Inoue, Noriyuki

    2008-01-01

    Studies report that students often fail to consider familiar aspects of reality in solving mathematical word problems. This study explored how different features of mathematical problems influence the way that undergraduate students employ realistic considerations in mathematical problem solving. Incorporating familiar contents in the word…

  10. 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.

  11. First-principles calculations of transition metal solute interactions with hydrogen in tungsten

    NASA Astrophysics Data System (ADS)

    Kong, Xiang-Shan; Wu, Xuebang; Liu, C. S.; Fang, Q. F.; Hu, Q. M.; Chen, Jun-Ling; Luo, G.-N.

    2016-02-01

    We have performed systematic first-principles calculations to predict the interaction between transition metal (TM) solutes and hydrogen in the interstitial site as well as the vacancy in tungsten. We showed that the site preference of the hydrogen atom is significantly influenced by the solute atoms, which can be traced to the charge density perturbation in the vicinity of the solute atom. The solute-H interactions are mostly attractive except for Re, which can be well understood in terms of the competition between the chemical and elastic interactions. The chemical interaction dominates the solute-H interaction for the TM solutes with a large atomic volume and small electronegativity compared to tungsten, while the elastic interaction is primarily responsible for the solute-H interaction for the TM solutes with a small atomic volume and large electronegativity relative to tungsten. The presence of a hydrogen atom near the solute atom has a negative effect on the binding of other hydrogen atoms. The large positive binding energies among the solute, vacancy and hydrogen suggest that they would easily form a defect cluster in tungsten, where the solute-vacancy and vacancy-H interaction contribute greatly while the solute-H interaction contributes a little. Our result provides a sound theoretical explanation for recent experimental phenomena of hydrogen retention in the tungsten alloy and further recommends a suitable W-Re-Ta ternary alloy for possible plasma-facing materials (PFMs) including the consideration of the hydrogen retention.

  12. 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.

  13. Ab initio identified design principles of solid-solution strengthening in Al.

    PubMed

    Ma, Duancheng; Friák, Martin; von Pezold, Johann; Raabe, Dierk; Neugebauer, Jörg

    2013-04-01

    Solid-solution strengthening in six Al-X binary systems is investigated using first-principle methods. The volumetric mismatch parameter and the solubility enthalpy per solute were calculated. We derive three rules for designing solid-solution strengthened alloys: (i) the solubility enthalpy per solute is related to the volumetric mismatch by a power law; (ii) for each annealing temperature, there exists an optimal solute-volume mismatch to achieve maximum strength; and (iii) the strengthening potential of high volumetric mismatch solutes is severely limited by their low solubility. Our results thus show that the thermodynamic properties of the system (here Al-X alloys) set clear upper bounds to the achievable strengthening effects owing to the reduced solubility with increasing volume mismatch.

  14. Teaching students to think spatially through embodied actions: Design principles for learning environments in science, technology, engineering, and mathematics.

    PubMed

    DeSutter, D; Stieff, M

    2017-01-01

    Spatial thinking is a vital component of the science, technology, engineering, and mathematics curriculum. However, to date, broad development of learning environments that target domain-specific spatial thinking is incomplete. The present article visits the problem of improving spatial thinking by first reviewing the evidence that the human mind is embodied: that cognition, memory, and knowledge representation maintain traces of sensorimotor impressions from acting and perceiving in a physical environment. In particular, we review the evidence that spatial cognition and the ways that humans perceive and conceive of space are embodied. We then propose a set of design principles to aid researchers, designers, and practitioners in creating and evaluating learning environments that align principled embodied actions to targets of spatial thinking in science, technology, engineering, and mathematics.

  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…

  16. Partial regularity of viscosity solutions for a class of Kolmogorov equations arising from mathematical finance

    NASA Astrophysics Data System (ADS)

    Rosestolato, M.; Święch, A.

    2017-02-01

    We study value functions which are viscosity solutions of certain Kolmogorov equations. Using PDE techniques we prove that they are C 1 + α regular on special finite dimensional subspaces. The problem has origins in hedging derivatives of risky assets in mathematical finance.

  17. Mathematical and physical aspects of controlling the exact solutions of the 3D Gross-Pitaevskii equation

    NASA Astrophysics Data System (ADS)

    Fedele, Renato; Jovanović, Dušan; De Nicola, Sergio; Eliasson, Bengt; Shukla, Padma K.

    2010-01-01

    The possibility of the decomposition of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) into a pair of coupled Schrödinger-type equations, is investigated. It is shown that, under suitable mathematical conditions, it is possible to construct the exact controlled solutions of the 3D GPE from the solutions of a linear 2D Schrödinger equation coupled with a 1D nonlinear Schrödinger equation (the transverse and longitudinal components of the GPE, respectively). The coupling between these two equations is the functional of the transverse and the longitudinal profiles. The applied method of nonlinear decomposition, called the controlling potential method (CPM), yields the full 3D solution in the form of the product of the solutions of the transverse and longitudinal components of the GPE. It is shown that the CPM constitutes a variational principle and sets up a condition on the controlling potential well. Its physical interpretation is given in terms of the minimization of the (energy) effects introduced by the control. The method is applied to the case of a parabolic external potential to construct analytically an exact BEC state in the form of a bright soliton, for which the quantitative comparison between the external and controlling potentials is presented.

  18. Mathematical modeling of solute segregation and redistribution during freezing in peat and overlying water

    SciTech Connect

    Li, S.M.

    1985-01-01

    Freezing of the water in a peatland causes the redistribution of existing solutes in both the shallow water and the peat zone. Such solute redistribution phenomena are of interest for establishing the geochronology of deposits and determining the nature of pollutant burial. Understanding these phenomena is important for the consideration of peatlands as multi-use resources. This work presents the theoretical analyses and mathematical models to describe the solute redistribution processes during freezing in overlying water and interstitial water in the porous peat. The analyses include the segregation of the solute at the ice-water interface in both the overlying water and the peat zone, solute transport in overlying water, as well as adsorbable solute and non-adsorbable solute transport in the interstitial water of the peat zone. An algorithm has been developed to solve these nonlinear moving interface problems. A parameter estimation technique has been used to determine parameters in the model that are difficult to obtain directly from the experimental data. Computer simulation using this model provides good predictions for solute concentration profiles in the frozen water and the peat zones, as compared to independent experimental data. The basic theoretical analysis and the mathematical model have been utilized to describe the salt ice formation process and macrosegregation during freezing of binary alloys.

  19. A mathematical structure of the separated variational principles of steady states for multi-forces and multi-currents

    NASA Astrophysics Data System (ADS)

    Okada, Kanzo

    2017-03-01

    Separated variational principles of steady states for multi-forces and multi-currents in transport phenomena were recently proposed by Suzuki (Suzuki, 2013) by extending the principle of minimum integrated entropy production for a single force found by the same author (Suzuki, 2013). On the other hand, in non-equilibrium thermodynamics, Edelen (Edelen, 1974) generalized the linear Onsager theory to those irreversible processes with significant thermodynamic forces by means of Onsager fluxes. Onsager fluxes by definition satisfy a nonlinear system of reciprocity relations, vanish in thermodynamic equilibrium, and satisfy the second law of thermodynamics. Each system of Onsager fluxes is derivable from a dissipation potential sometimes called the flux potential. This paper aims to elucidate a mathematical structure of the separated variational principles based on the above work of Edelen.

  20. Similarity solutions of nonlinear diffusion problems related to mathematical hydraulics and the Fokker-Planck equation.

    PubMed

    Daly, Edoardo; Porporato, Amilcare

    2004-11-01

    Similarity solutions of the shallow-water equation with a generalized resistance term are studied for open channel flows when both inertial and gravity forces are negligible. The resulting model encompasses various particular cases that appear, in addition to mathematical hydraulics, in diverse physical phenomena, such as gravity currents, creeping flows of Newtonian and non-Newtonian fluids, thin films, and nonlinear Fokker-Planck equations. Solutions of both source-type and dam-break problems are analyzed. Closed-form solutions are discussed, when possible, along with a qualitative study of two phase-plane formulations based on two different variable transformations.

  1. Computational experiment on the numerical solution of some inverse problems of mathematical physics

    NASA Astrophysics Data System (ADS)

    Vasil'ev, V. I.; Kardashevsky, A. M.; Sivtsev, PV

    2016-11-01

    In this article the computational experiment on the numerical solution of the most popular linear inverse problems for equations of mathematical physics are presented. The discretization of retrospective inverse problem for parabolic equation is performed using difference scheme with non-positive weight multiplier. Similar difference scheme is also used for the numerical solution of Cauchy problem for two-dimensional Laplace equation. The results of computational experiment, performed on model problems with exact solution, including ones with randomly perturbed input data are presented and discussed.

  2. A Mathematical Model of Solute Coupled Water Transport in Toad Intestine Incorporating Recirculation of the Actively Transported Solute

    PubMed Central

    Larsen, Erik Hviid; Sørensen, Jakob Balslev; Sørensen, Jens Nørkær

    2000-01-01

    A mathematical model of an absorbing leaky epithelium is developed for analysis of solute coupled water transport. The non-charged driving solute diffuses into cells and is pumped from cells into the lateral intercellular space (lis). All membranes contain water channels with the solute passing those of tight junction and interspace basement membrane by convection-diffusion. With solute permeability of paracellular pathway large relative to paracellular water flow, the paracellular flux ratio of the solute (influx/outflux) is small (2–4) in agreement with experiments. The virtual solute concentration of fluid emerging from lis is then significantly larger than the concentration in lis. Thus, in absence of external driving forces the model generates isotonic transport provided a component of the solute flux emerging downstream lis is taken up by cells through the serosal membrane and pumped back into lis, i.e., the solute would have to be recirculated. With input variables from toad intestine (Nedergaard, S., E.H. Larsen, and H.H. Ussing, J. Membr. Biol. 168:241–251), computations predict that 60–80% of the pumped flux stems from serosal bath in agreement with the experimental estimate of the recirculation flux. Robust solutions are obtained with realistic concentrations and pressures of lis, and with the following features. Rate of fluid absorption is governed by the solute permeability of mucosal membrane. Maximum fluid flow is governed by density of pumps on lis-membranes. Energetic efficiency increases with hydraulic conductance of the pathway carrying water from mucosal solution into lis. Uphill water transport is accomplished, but with high hydraulic conductance of cell membranes strength of transport is obscured by water flow through cells. Anomalous solvent drag occurs when back flux of water through cells exceeds inward water flux between cells. Molecules moving along the paracellular pathway are driven by a translateral flow of water, i.e., the model

  3. Transferable ionic parameters for first-principles Poisson-Boltzmann solvation calculations: Neutral solutes in aqueous monovalent salt solutions

    NASA Astrophysics Data System (ADS)

    Ringe, Stefan; Oberhofer, Harald; Reuter, Karsten

    2017-04-01

    Implicit solvation calculations based on a Stern-layer corrected size-modified Poisson-Boltzmann (SMPB) model are an effective approach to capture electrolytic effects in first-principles electronic structure calculations. For a given salt solution, they require a range of ion-specific parameters, which describe the size of the dissolved ions as well as thickness and shape of the Stern layer. Out of this defined parameter space, we show that the Stern layer thickness expressed in terms of the solute's electron density and the resulting ionic cavity volume completely determine ion effects on the stability of neutral solutes. Using the efficient SMPB functionality of the full-potential density-functional theory package FHI-aims, we derive optimized such Stern layer parameters for neutral solutes in various aqueous monovalent electrolytes. The parametrization protocol relies on fitting to reference Setschenow coefficients that describe solvation free energy changes with ionic strength at low to medium concentrations. The availability of such data for NaCl solutions yields a highly predictive SMPB model that allows to recover the measured Setschenow coefficients with an accuracy that is comparable to prevalent quantitative regression models. Correspondingly derived SMPB parameters for other salts suffer from a much scarcer experimental data base but lead to Stern layer properties that follow a physically reasonable trend with ionic hydration numbers.

  4. 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.

  5. Transferring Ions from Solution to the Gas Phase: The Two Basic Principles

    NASA Astrophysics Data System (ADS)

    Teunissen, Sebastiaan F.; Eberlin, Marcos N.

    2017-08-01

    The efficient formation of gaseous ions is the crucial step in all successful mass spectrometric experiments. The invention of electrospray ionization (ESI) has strongly facilitated this step by transferring preformed ions directly from solution to the gas phase - thereby circumventing the need to first convert analytes to the gas phase and then ionize them - and therefore ESI has become an extremely useful and widely applied MS technique. The invention of sonic spray ionization (SSI) has also allowed for the transfer of ions from solution into the gas phase, but without the assistance of a voltage or heating. Numerous ionization techniques, using similar principles to those applied in either ESI or SSI, have subsequently been developed. Although experimental conditions used in such techniques vary markedly, herein we argue that they are all based on either one of two basic principles by which ions can be transferred from solution to the gas phase, that is: via (1) neutralizing the counter ion, or (2) separating the ions. We have selected 35 such techniques and categorized them accordingly. This article thereby aims to establish the basic principles by which gaseous ions can be obtained from solvated ions. We further propose that any new ionization technique used to transfer solvated ions to the gas phase will similarly fall into one of these two mechanistic categories. [Figure not available: see fulltext.

  6. 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.

  7. Mathematical model of building daylighting based on first principles of astrometry, solid geometry, and optical radiation transfer

    SciTech Connect

    Chou, C.P.

    1987-01-01

    Many methods exist for quantifying diffuse daylight distribution for use in the design of buildings, but the methods vary widely both in technique and capability. Moreover, no present method deals with direct daylight (sunshine) distribution. Additionally, none have taken advantage of improvements in computer technology that make feasible more-complex mathematical computational models for dealing with direct and diffuse daylight together. This dissertation describes the theoretical development and computer implementation of a new mathematical approach to analyzing the distribution of direct and diffuse daylight. This approach examines light transfer from extraterrestrial space to the inside of a room based on the principles of astrometry, solid geometry, and radiation transfer. This study discusses and analyzes certain aspects critical to develop a mathematical model for evaluating daylight performance and compares the results of the proposed model with 48 scale-model studies to determine the validity of using this mathematical model to predict the daylight distribution of a room. Subsequent analysis revealed no significant variation between scale-model studies and this computer simulation.

  8. Promoting Self-Explanation to Improve Mathematics Learning: A Meta-Analysis and Instructional Design Principles

    ERIC Educational Resources Information Center

    Rittle-Johnson, Bethany; Loehr, Abbey M.; Durkin, Kelley

    2017-01-01

    Promoting self-explanation (i.e., generating explanations for oneself in an attempt to make sense of new information) is a recommended study strategy and instructional practice. A meta-analysis of the literature on prompting self-explanation to improve mathematics learning confirmed that prompted self-explanation leads to a small to moderate…

  9. Prediction of color changes in acetaminophen solution using the time-temperature superposition principle.

    PubMed

    Mochizuki, Koji; Takayama, Kozo

    2016-01-01

    A prediction method for color changes based on the time-temperature superposition principle (TTSP) was developed for acetaminophen solution. Color changes of acetaminophen solution are caused by the degradation of acetaminophen, such as hydrolysis and oxidation. In principle, the TTSP can be applied to only thermal aging. Therefore, the impact of oxidation on the color changes of acetaminophen solution was verified. The results of our experiment suggested that the oxidation products enhanced the color changes in acetaminophen solution. Next, the color changes of acetaminophen solution samples of the same head space volume after accelerated aging at various temperatures were investigated using the Commission Internationale de l'Eclairage (CIE) LAB color space (a*, b*, L* and ΔE*ab), following which the TTSP was adopted to kinetic analysis of the color changes. The apparent activation energies using the time-temperature shift factor of a*, b*, L* and ΔE*ab were calculated as 72.4, 69.2, 72.3 and 70.9 (kJ/mol), respectively, which are similar to the values for acetaminophen hydrolysis reported in the literature. The predicted values of a*, b*, L* and ΔE*ab at 40 °C were obtained by calculation using Arrhenius plots. A comparison between the experimental and predicted values for each color parameter revealed sufficiently high R(2) values (>0.98), suggesting the high reliability of the prediction. The kinetic analysis using TTSP was successfully applied to predicting the color changes under the controlled oxygen amount at any temperature and for any length of time.

  10. 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…

  11. 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.

  12. Violation of ethical principles in clinical research. Influences and possible solutions for Latin America.

    PubMed

    Cornejo Moreno, Borys Alberto; Gómez Arteaga, Gress Marissell

    2012-12-16

    Even though we are now well into the 21st century and notwithstanding all the abuse to individuals involved in clinical studies that has been documented throughout History, fundamental ethical principles continue to be violated in one way or another. Here are some of the main factors that contribute to the abuse of subjects participating in clinical trials: paternalism, improper use of informed consent, lack of strict ethical supervision, pressure exerted by health institutions to increase the production of scientific material, and the absence of legislation regarding ethics in terms of health care and research. Are researchers ready to respect fundamental ethical principles in light of the ample window of information provided by individual genomes, while defending the rights of the subjects participating in clinical studies as a major priority? As one of the possible solutions to this problem, education regarding fundamental ethical principles is suggested for participants in research studies as an initial method of cognitive training in ethics, together with the promotion of ethical behavior in order to encourage the adoption of reasonable policies in the field of values, attitudes and behavior.

  13. Researching Principles of Lesson Design to Realize the Pedagogical Opportunities of Mathematics Analysis Software

    ERIC Educational Resources Information Center

    Pierce, Robyn; Stacey, Kaye

    2009-01-01

    Taking advantage of pedagogical opportunities afforded by new technology requires appropriately designed lessons. This article reports on the use of "lesson study" to research principles for the design of a lesson aiming to take advantage of multiple representations. The lesson, for year 10 students who had personal access to TI-Nspire, focused on…

  14. 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…

  15. 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…

  16. 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.

  17. 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.

  18. Structure Shapes Dynamics and Directionality in Diverse Brain Networks: Mathematical Principles and Empirical Confirmation in Three Species

    NASA Astrophysics Data System (ADS)

    Moon, Joon-Young; Kim, Junhyeok; Ko, Tae-Wook; Kim, Minkyung; Iturria-Medina, Yasser; Choi, Jee-Hyun; Lee, Joseph; Mashour, George A.; Lee, Uncheol

    2017-04-01

    Identifying how spatially distributed information becomes integrated in the brain is essential to understanding higher cognitive functions. Previous computational and empirical studies suggest a significant influence of brain network structure on brain network function. However, there have been few analytical approaches to explain the role of network structure in shaping regional activities and directionality patterns. In this study, analytical methods are applied to a coupled oscillator model implemented in inhomogeneous networks. We first derive a mathematical principle that explains the emergence of directionality from the underlying brain network structure. We then apply the analytical methods to the anatomical brain networks of human, macaque, and mouse, successfully predicting simulation and empirical electroencephalographic data. The results demonstrate that the global directionality patterns in resting state brain networks can be predicted solely by their unique network structures. This study forms a foundation for a more comprehensive understanding of how neural information is directed and integrated in complex brain networks.

  19. 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…

  20. A Review of the Fundamental Principles and Applications of Solution Blow Spinning.

    PubMed

    Daristotle, John L; Behrens, Adam M; Sandler, Anthony D; Kofinas, Peter

    2016-12-28

    Solution blow spinning (SBS) is a technique that can be used to deposit fibers in situ at low cost for a variety of applications, which include biomedical materials and flexible electronics. This review is intended to provide an overview of the basic principles and applications of SBS. We first describe a method for creating a spinnable polymer solution and stable polymer solution jet by manipulating parameters such as polymer concentration and gas pressure. This method is based on fundamental insights, theoretical models, and empirical studies. We then discuss the unique bundled morphology and mechanical properties of fiber mats produced by SBS, and how they compare with electrospun fiber mats. Applications of SBS in biomedical engineering are highlighted, showing enhanced cell infiltration and proliferation versus electrospun fiber scaffolds and in situ deposition of biodegradable polymers. We also discuss the impact of SBS in applications involving textiles and electronics, including ceramic fibers and conductive composite materials. Strategies for future research are presented that take advantage of direct and rapid polymer deposition via cost-effective methods.

  1. Mathematics.

    ERIC Educational Resources Information Center

    Mac Lane, Saunders

    1980-01-01

    This is a review of the current research in mathematics involving breadth of ideas. Research includes topics in number theory, classification of all finite simple groups, the representation of group aids in their application to the study of symmetry. (Author/SA)

  2. Mathematics.

    ERIC Educational Resources Information Center

    Costellano, Janet; Scaffa, Matthew

    The product of a Special Studies Institute, this teacher developed resource guide for the emotionally handicapped (K-6) presents 37 activities designed to develop mathematics concepts and skills utilizing the urban out-of-doors. Focus is on experiencing math models, patterns, problems, and relationships found in an urban environment. Activities…

  3. 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.

  4. Autocrine ligand binding to cell receptors. Mathematical analysis of competition by solution "decoys".

    PubMed Central

    Forsten, K E; Lauffenburger, D A

    1992-01-01

    Autocrine ligands have been demonstrated to regulate cell proliferation, cell adhesion, and cell migration in a number of different systems and are believed to be one of the underlying causes of malignant cell transformation. Binding of these ligands to their cellular receptors can be compromised by diffusive transport of ligand away from the secreting cell. Exogenous addition of antibodies or solution receptors capable of competing with cellular receptors for these autocrine ligands has been proposed as a means of inhibiting autocrine-stimulated cell behavioral responses. Such "decoys" complicate cellular binding by offering alternative binding targets, which may also be capable of aiding or abating transport of the ligand away from the cell surface. We present a mathematical model incorporating autocrine ligand production and the presence of competing cellular and solution receptors. We elucidate effects of key system parameters including ligand diffusion rate, binding rate constants, cell density, and secretion rate on the ability of solution receptors to inhibit cellular receptor binding. Both plated and suspension cell systems are considered. An approximate analytical expression relating the key parameters to the critical concentration of solution "decoys" required for inhibition is derived and compared to the numerical calculations. We find that in order to achieve essentially complete inhibition of surface receptor binding, the concentration of decoys may need to be as much as four to eight orders of magnitude greater than the equilibrium disociation constant for ligand binding to surface receptors. PMID:1312367

  5. 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.

  6. 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. Copyright © 2010 Elsevier B.V. All rights reserved.

  7. 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.

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

    SciTech Connect

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

    2016-10-17

    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. In such simulations we often perform them 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. In order 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. These 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.

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

    DOE PAGES

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

    2016-10-17

    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. In such simulations we often perform them at elevated temperaturesmore » 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. In order 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. These 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.« less

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

    PubMed

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

    2016-10-21

    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.

  11. 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.

  12. Report on a Study to Determine the Effect of Knowledge of Recursive Definitions upon Subsequent Application of the Principle of Mathematical Induction.

    ERIC Educational Resources Information Center

    Waters, William Meade, Jr.

    The objective of the study was to determine the effect which a unit dealing with recursive definitions would have on students' achievement in applying the principle of mathematical induction (PMI). Twenty-four secondary school students were randomly assigned to control and experimental groups. Students in the control group studied programmed units…

  13. There Is More Variation "within" than "across" Domains: An Interview with Paul A. Kirschner about Applying Cognitive Psychology-Based Instructional Design Principles in Mathematics Teaching and Learning

    ERIC Educational Resources Information Center

    Kirschner, Paul A.; Verschaffel, Lieven; Star, Jon; Van Dooren, Wim

    2017-01-01

    In this interview we asked Paul A. Kirschner about his comments and reflections regarding the idea to apply cognitive psychology-based instructional design principles to mathematics education and some related issues. With a main focus on cognitive psychology, educational psychology, educational technology and instructional design, this…

  14. Principles of rapid polymerase chain reactions: mathematical modeling and experimental verification.

    PubMed

    Whitney, Scott E; Sudhir, Alugupally; Nelson, R Michael; Viljoen, Hendrik J

    2004-07-01

    Polymerase chain reaction (PCR) is an important diagnostic tool for the amplification of DNA. The PCR process can be treated as a problem in biochemical engineering. This study focuses on the development of a mathematical model of the polymerase chain reaction. The PCR process consists of three steps: denaturation of target DNA, annealing of sequence-specific oligonucleotide primers and the enzyme-catalyzed elongation of the annealed complex (primer:DNA:polymerase). The denaturation step separates the double strands of DNA; this model assumes denaturation is complete. The annealing step describes the formation of a primer-fragment complex followed by the attachment of the polymerase to form a ternary complex. This step is complicated by competitive annealing between primers and incomplete fragments including primer-primer reactions. The elongation step is modeled by a stochastic method. Species that compete during the elongation step are deoxynucleotide triphosphates dCTP, dATP, dTTP, dGTP, dUTP, and pyrophosphate. Thermal deamination of dCTP to form dUTP is included in the model. The probability for a species to arrive at the active site is based on its molar fraction. The number of random insertion events depends on the average processing speed of the polymerase and the elongation time of the simulation. The numerical stochastic experiment is repeated a sufficient number of times to construct a probability density distribution (PDF). The moment of the PDF and the annealing step products provide the product distribution at the end of the elongation step. The overall yield is compared to six experimental values of the yield. In all cases the comparisons are very good.

  15. Mathematical Model Formulation And Validation Of Water And Solute Transport In Whole Hamster Pancreatic Islets

    PubMed Central

    Benson, Charles T.; Critser, John K.

    2014-01-01

    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 ± S.D.). 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

  16. 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. Copyright © 2014 Elsevier Inc. All rights reserved.

  17. 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…

  18. 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.

  19. 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

  20. 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

  1. First-principles study of the solid solution of hydrogen in lanthanum

    NASA Astrophysics Data System (ADS)

    Schöllhammer, Gunther; Herzig, Peter; Wolf, Walter; Vajda, Peter; Yvon, Klaus

    2011-09-01

    Results from first-principles investigations of the energetical, structural, electronic, and vibrational properties of model structures probing the metal-rich region of the lanthanum-hydrogen system, i.e., the region of the solid solution of hydrogen in lanthanum, are presented. We have studied the site preference and the ordering tendency of hydrogen atoms interstitially bonded in close-packed lanthanum. Spatially separated hydrogen atoms have turned out to exhibit an energetical preference for the occupation of octahedral interstitial sites at low temperature. Indications for a reversal of the site preference in favor of the occupation of tetrahedral interstitial sites at elevated temperature have been found. Linear arrangements consisting of pairs of octahedrally and/or tetrahedrally coordinated hydrogen atoms collinearly bonded to a central lanthanum atom have turned out to be energetically favorable structure elements. Further stabilization is achieved if such hydrogen pairs are in turn linked together so that extended chains of La-H bonds are formed. Pair formation and chain linking counteract the energetical preference for octahedral coordination observed for separated hydrogen atoms.

  2. Maximum-principle-satisfying space-time conservation element and solution element scheme applied to compressible multifluids

    NASA Astrophysics Data System (ADS)

    Shen, Hua; Wen, Chih-Yung; Parsani, Matteo; Shu, Chi-Wang

    2017-02-01

    A maximum-principle-satisfying space-time conservation element and solution element (CE/SE) scheme is constructed to solve a reduced five-equation model coupled with the stiffened equation of state for compressible multifluids. We first derive a sufficient condition for CE/SE schemes to satisfy maximum-principle when solving a general conservation law. And then we introduce a slope limiter to ensure the sufficient condition which is applicative for both central and upwind CE/SE schemes. Finally, we implement the upwind maximum-principle-satisfying CE/SE scheme to solve the volume-fraction-based five-equation model for compressible multifluids. Several numerical examples are carried out to carefully examine the accuracy, efficiency, conservativeness and maximum-principle-satisfying property of the proposed approach.

  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. Khayyam with Cabri: Experiences of Pre-Service Mathematics Teachers with Khayyam's Solution of Cubic Equations in Dynamic Geometry Environment

    ERIC Educational Resources Information Center

    Baki, Adnan; Guven, Bulent

    2009-01-01

    The study reported in this article deals with the observed actions of Turkish pre-service mathematics teachers in dynamic geometry environment (DGE) as they were learning Khayyam's method for solving cubic equations formed as x[superscript 3] + ax = b. Having learned the method, modelled it in DGE and verified the correctness of the solution,…

  5. First-Principles Studies of Conformation and Solution Effects on DNA Transport

    NASA Astrophysics Data System (ADS)

    Tan, Bikan

    DNA charge transport (CT) has attracted considerable attention by the scientific community over the past 20 years. This interest reflects the potential of DNA CT to provide a sensitive route for signaling, whether in the construction of a nano-scale biosensor or as an enzymatic tool to detect damage in the genome. Research in DNA CT began as a quest to determine whether the DNA double helix with pi-stacked base pairs might share the conductive characteristics of pi-stacked solids. Physicists carried out sophisticated experiments to measure the conductivity of DNA. But the means to connect DNA to the electrodes, as well as the conditions under which the conductivity was measured are different among many experiments, as the results of the current measurements. DNA CT was seen to depend upon the connection between electrodes and DNA, and coupling between the DNA base pair stacks. Importantly, for those studies that utilized well-characterized connections to the DNA and preserved the duplex native conformation in buffered solution, significant electron conductivities were achieved. Certainly, the debate among researches has shifted from "Is DNA CT possible?" to "How does it work?". To investigate the remarkable characteristics of the double-helix molecule, we use a first-principle technique combined with molecular dynamics simulations to calculate the transport properties of B-DNA sandwiched between carbon nanotubes via alkane linkers. The quantum results using the NEGF method are calculated from snapshots recorded in MD trajectories. In chapter 1, we will go through the basic quantum and classic theories on which our calculations are based. The subject of DNA structure, electronic properties and its potential application in many fields will be introduced in chapter 2. In chapter 3, we discuss our results towards the understanding of the mechanism of DNA charge transport.

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

    NASA Astrophysics Data System (ADS)

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

    2015-05-01

    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 rd 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 P is less or greater than that of Al under RS. This paper verifies a linear relation of substitution energy change versus rd and ϕ P under RS, which might be instructive for composition design of long life alloys serving in high stress condition.

  7. 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.

  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.

    2016-11-01

    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.

  9. Mathematical simulation of lithium bromide solution laminar falling film evaporation in vertical tube

    NASA Astrophysics Data System (ADS)

    Shi, Chengming; Wang, Yang; Hu, Huili; Yang, Ying

    2010-06-01

    For utilization of the residual heat of flue gas to drive the absorption chillers, a lithium-bromide falling film in vertical tube type generator is presented. A mathematical model was developed to simulate the heat and mass coupled problem of laminar falling film evaporation in vertical tube. In the model, the factor of mass transfer was taken into account in heat transfer performance calculation. The temperature and concentration fields were calculated. Some tests were conducted for the factors such as Re number, heating flux, the inlet concentration and operating pressure which can affect the heat and mass transfer performance in laminar falling film evaporation. The heat transfer performance is enhanced with the increasing of heat flux. An increasing inlet concentration can weaken the heat transfer performance. The operating pressure hardly affects on heat and mass transfer. The bigger inlet Re number means weaker heat transfer effects and stronger mass transfer. The mass transfer obviously restrains the heat transfer in the falling film solution. The relation between dimensionless heat transfer coefficient and the inlet Re number is obtained.

  10. 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.

  11. 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 respond…

  12. 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…

  13. First-Principles Calculation of Solution Energy of Alkaline-Earth Metal Elements to BaTiO3

    NASA Astrophysics Data System (ADS)

    Moriwake, Hiroki; Hirayama, Tsukasa; Ikuhara, Yuichi; Tanaka, Isao

    2007-10-01

    Quantitative analysis of the solution energy of alkaline-earth metal elements to perovskite-type BaTiO3 was carried out by a first-principles calculation combined with thermodynamics theory. The solution energies of neutral solute and a compensated solute with an oxygen vacancy were systematically calculated. They were obtained for two cation sites and four thermodynamical conditions with different chemical potentials of constituent atoms. Both Ca and Sr preferably occupy the Ba site of BaTiO3. On the other hand, Mg occupies the Ti site. This corresponds well to the widely accepted experimental findings regarding site preference. Moreover, under the condition of coexising BaO, CaO and BaTiO3, energy difference between the Ba-site solution and O-vacancy compensated Ti-site solution of Ca ions has been found to be smaller than that of Sr. Under this condition, the O-vacancy compensated Ti-site solution of Ca should be favorable compared with that of Sr. The same number of oxygen vacancies as Ca ions occupying Ti sites can be introduced. This also explains well experimental feature of the Ca-doped BaTiO3-based nonreducible multilayer ceramics capacitor (MLCC) materials regarding solution site of the Ca ion and abundance of O-vacancy.

  14. Transport of reacting solutes in porous media: Relation between mathematical nature of problem formulation and chemical nature of reactions

    USGS Publications Warehouse

    Rubin, Jacob

    1983-01-01

    Examples involving six broad reaction classes show that the nature of transport-affecting chemistry may have a profound effect on the mathematical character of solute transport problem formulation. Substantive mathematical diversity among such formulations is brought about principally by reaction properties that determine whether (1) the reaction can be regarded as being controlled by local chemical equilibria or whether it must be considered as being controlled by kinetics, (2) the reaction is homogeneous or heterogeneous, (3) the reaction is a surface reaction (adsorption, ion exchange) or one of the reactions of classical chemistry (e.g., precipitation, dissolution, oxidation, reduction, complex formation). These properties, as well as the choice of means to describe them, stipulate, for instance, (1) the type of chemical entities for which a formulation's basic, mass-balance equations should be written; (2) the nature of mathematical transformations needed to change the problem's basic equations into operational ones. These and other influences determine such mathematical features of problem formulations as the nature of the operational transport-equation system (e.g., whether it involves algebraic, partial-differential, or integro-partial-differential simultaneous equations), the type of nonlinearities of such a system, and the character of the boundaries (e.g., whether they are stationary or moving). Exploration of the reasons for the dependence of transport mathematics on transport chemistry suggests that many results of this dependence stem from the basic properties of the reactions' chemical-relation (i.e., equilibrium or rate) equations.

  15. Are There Any Places that Students Use Their Heads? Principles of High-Quality Japanese Mathematics Instruction

    ERIC Educational Resources Information Center

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

    2010-01-01

    Previous research gives evidence that Japanese mathematics teachers "may have a more detailed and widely shared theory about how to teach effectively" when compared to their U.S. counterparts (Jacobs & Morita, 2002). This study explores the conceptions and cultural scripts of a group of Japanese mathematics teachers by analyzing the…

  16. Are There Any Places that Students Use Their Heads? Principles of High-Quality Japanese Mathematics Instruction

    ERIC Educational Resources Information Center

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

    2010-01-01

    Previous research gives evidence that Japanese mathematics teachers "may have a more detailed and widely shared theory about how to teach effectively" when compared to their U.S. counterparts (Jacobs & Morita, 2002). This study explores the conceptions and cultural scripts of a group of Japanese mathematics teachers by analyzing the…

  17. Quantum algorithms and mathematical formulations of biomolecular solutions of the vertex cover problem in the finite-dimensional hilbert space.

    PubMed

    Chang, Weng-Long; Ren, Ting-Ting; Feng, Mang

    2015-01-01

    In this paper, it is shown that the proposed quantum algorithm for implementing Boolean circuits generated from the DNA-based algorithm solving the vertex-cover problem of any graph G with m edges and n vertices is the optimal quantum algorithm. Next, it is also demonstrated that mathematical solutions of the same biomolecular solutions are represented in terms of a unit vector in the finite-dimensional Hilbert space. Furthermore, for testing our theory, a nuclear magnetic resonance (NMR) experiment of three quantum bits to solve the simplest vertex-cover problem is completed.

  18. Alloying Solid Solution Strengthening of Fe-Ga Alloys: A First-Principle Study

    DTIC Science & Technology

    2006-01-01

    effect from alloying additions of Nb, Mo, V, Cr and Co in cubic solid solution of Fe-Ga alloys. Mayer bond order "BO" values were used to evaluate the...that transition metal Nb achieves the best strengthening effect in Fe-Ga alloys. The solid solution strengthening follows a trend from larger to

  19. Some emerging principles underlying the physical properties, biological actions, and utility of vitrification solutions.

    PubMed

    Fahy, G M; Levy, D I; Ali, S E

    1987-06-01

    Vitrification solutions are aqueous cryoprotectant solutions which do not freeze when cooled at moderate rates to very low temperatures. Vitrification solutions have been used with great success for the cryopreservation of some biological systems but have been less successful or unsuccessful with other systems, and more fundamental knowledge about vitrification solutions is required. The purpose of the present survey is to show that a general understanding of the physical behavior and biological effects of vitrification solutions, as well as an understanding of the conditions under which vitrification solutions are required, is gradually emerging. Detailed nonequilibrium phase diagram information in combination with specific information on the tolerance of biological systems to ice and to cryoprotectant at subzero temperatures provides a quantitative theoretical basis for choosing between vitrification and freezing. The vitrification behavior of mixtures of cryoprotective agents during cooling is predictable from the behavior of the individual agents, and the behavior of individual agents is gradually becoming predictable from the details of their molecular structures. Progress is continuing concerning the elucidation of mechanisms and cellular sites of toxicity and mechanisms for the reduction of toxicity. Finally, important new information is rapidly emerging concerning the crystallization of previously vitrified cryoprotectant solutions during warming. It appears that vitrification tendency, toxicity, and devitrification all depend on subtle variations in the organization of water around dissolved substances.

  20. 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.

  1. First-principles appraisal of solute ultra-fast diffusion in hcp Zr and Ti

    NASA Astrophysics Data System (ADS)

    Pasianot, R. C.; Pérez, R. A.

    2013-03-01

    We revisit the ultra-fast diffusion characteristics of Fe, Co, Ni, and Cu solutes, in the hcp hosts Ti and Zr, by using Density Functional Theory. The energetics of several point defect configurations, deemed relevant for solute diffusion, is evaluated. The results support the long standing beliefs that the diffusing species is interstitial in nature, and that some kind of complexing is involved at low temperatures. Though quantitative agreement with experiment is difficult to assess, we show that a rather simple dissociative model is able to rationalize the observed trends, in particular, why the Arrhenius graphs are straight for Ti whereas, generally, they are curved downwards for Zr.

  2. A first-principles based force-field for Li+ and OH- in ethanolic solution.

    PubMed

    Milek, Theodor; Meyer, Bernd; Zahn, Dirk

    2013-10-14

    We report on the development of force-field parameters for accurately modeling lithium and hydroxide ions in ethanol in solution. Based on quantum calculations of small molecular clusters mimicking the solvent structure of individual ions as well as the solvated LiOH dimer, significant improvements of off-the-shelf force-fields are obtained. The quality of our model is demonstrated by comparison to ab initio molecular dynamics of the bulk solution and to experimental data available for ethanol/water mixtures.

  3. Team-Assisted Individualization: A Cooperative Learning Solution for Adaptive Instruction in Mathematics.

    ERIC Educational Resources Information Center

    Slavin, Robert E.

    The Team-Assisted Individualization (TAI) mathematics program has been developed in an attempt to make individualized instruction workable in the classroom by adding components of cooperative learning. This paper presents the rationale for the development of TAI and describes results of three field experiments conducted to assess the effect of TAI…

  4. Problem-Solving Strategies for Efficient and Elegant Solutions: A Resource for the Mathematics Teacher.

    ERIC Educational Resources Information Center

    Posamentier, Alfred S.; Krulik, Stephen

    In this book, 10 strategies that are widely used in problem-solving both in mathematics and real-life situations are examined. Approximately 200 problems are selected to illustrate these strategies. Chapters include: (1) Introduction To Problem-Solving Strategies; (2) Working Backwards; (3) Finding a Pattern; (4) Adopting a Different Point of…

  5. 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…

  6. 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…

  7. 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…

  8. 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…

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

    PubMed

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

    2004-12-01

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

  10. 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

  11. 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.

  12. 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.

  13. 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.

  14. Solutions in chronostratigraphy: the Paleocene/Eocene boundary debate, and Aubry vs. Hedberg on chronostratigraphic principles

    NASA Astrophysics Data System (ADS)

    Walsh, Stephen L.

    2004-01-01

    In several recent papers, M.-P. Aubry et al. have argued that "Hedbergian" principles of chronostratigraphy are being violated by the International Commission on Stratigraphy (ICS) when selecting Global Stratotype Sections and Points (GSSPs) for the formal divisions of the geological time scale. The current debate over the definition of the Paleocene/Eocene (P/E) boundary has been a major focus of their arguments. Unfortunately, Aubry et al. have obscured matters by misusing the term "unit stratotype," and by equivocally using the term "stage" for the very different concepts of "synthem" and "global chronostratigraphic stage." The P/E boundary option most repugnant to Aubry et al. (Carbon Isotope Excursion (CIE)=P/E=Thanetian/Ypresian boundary) is perfectly compatible with H.D. Hedberg's views. In contrast, another option preferred by Aubry et al. (recognition of new ˜1 m.y. duration age/stage between Thanetian and Ypresian) is inconsistent with Hedberg's views. Additional problems with the P/E boundary arguments of Aubry et al. include the fact that a "Ypresian unit stratotype" does not exist, the fact that the base of the Ypresian synthem is not immutable, and the fact that the nannofossil Tribrachiatus digitalis is of dubious relevance to the boundary debate. As for chronostratigraphy in general, Aubry et al. have misrepresented Hedberg's views by: (1) falsely claiming that the content of a stage is what determines its boundaries; (2) misunderstanding the general concept of the boundary stratotype; (3) distorting the "base defines boundary" principle; (4) falsely claiming that traditional (pre-GSSP) chronostratigraphic boundaries cannot be changed; (5) falsely implying that traditional stage unit stratotype boundaries can be adjusted by no more than 300,000 years when defining formal age/stage boundaries with GSSPs; (6) falsely claiming that the definition of a geochronologic/chronostratigraphic boundary should precede its correlation; (7) claiming that

  15. 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.

  16. Thermodynamically accurate modeling of the catalytic cycle of photosynthetic oxygen evolution: a mathematical solution to asymmetric Markov chains.

    PubMed

    Vinyard, David J; Zachary, Chase E; Ananyev, Gennady; Dismukes, G Charles

    2013-07-01

    Forty-three years ago, Kok and coworkers introduced a phenomenological model describing period-four oscillations in O2 flash yields during photosynthetic water oxidation (WOC), which had been first reported by Joliot and coworkers. The original two-parameter Kok model was subsequently extended in its level of complexity to better simulate diverse data sets, including intact cells and isolated PSII-WOCs, but at the expense of introducing physically unrealistic assumptions necessary to enable numerical solutions. To date, analytical solutions have been found only for symmetric Kok models (inefficiencies are equally probable for all intermediates, called "S-states"). However, it is widely accepted that S-state reaction steps are not identical and some are not reversible (by thermodynamic restraints) thereby causing asymmetric cycles. We have developed a mathematically more rigorous foundation that eliminates unphysical assumptions known to be in conflict with experiments and adopts a new experimental constraint on solutions. This new algorithm termed STEAMM for S-state Transition Eigenvalues of Asymmetric Markov Models enables solutions to models having fewer adjustable parameters and uses automated fitting to experimental data sets, yielding higher accuracy and precision than the classic Kok or extended Kok models. This new tool provides a general mathematical framework for analyzing damped oscillations arising from any cycle period using any appropriate Markov model, regardless of symmetry. We illustrate applications of STEAMM that better describe the intrinsic inefficiencies for photon-to-charge conversion within PSII-WOCs that are responsible for damped period-four and period-two oscillations of flash O2 yields across diverse species, while using simpler Markov models free from unrealistic assumptions. Copyright © 2013 Elsevier B.V. All rights reserved.

  17. Student Solution Manual for Essential Mathematical Methods for the Physical Sciences

    NASA Astrophysics Data System (ADS)

    Riley, K. F.; Hobson, M. P.

    2011-02-01

    1. Matrices and vector spaces; 2. Vector calculus; 3. Line, surface and volume integrals; 4. Fourier series; 5. Integral transforms; 6. Higher-order ODEs; 7. Series solutions of ODEs; 8. Eigenfunction methods; 9. Special functions; 10. Partial differential equations; 11. Solution methods for PDEs; 12. Calculus of variations; 13. Integral equations; 14. Complex variables; 15. Applications of complex variables; 16. Probability; 17. Statistics.

  18. First principles pulse pile-up balance equation and fast deterministic solution

    NASA Astrophysics Data System (ADS)

    Sabbatucci, Lorenzo; Fernández, Jorge E.

    2017-08-01

    Pulse pile-up (PPU) is an always present effect which introduces a distortion into the spectrum measured with radiation detectors and that worsen with the increasing emission rate of the radiation source. It is fully ascribable to the pulse handling circuitry of the detector and it is not comprised in the detector response function which is well explained by a physical model. The PPU changes both the number and the height of the recorded pulses, which are related, respectively, with the number of detected particles and their energy. In the present work, it is derived a first principles balance equation for second order PPU to obtain a post-processing correction to apply to X-ray measurements. The balance equation is solved for the particular case of rectangular pulse shape using a deterministic iterative procedure for which it will be shown the convergence. The proposed method, deterministic rectangular PPU (DRPPU), requires minimum amount of information and, as example, it is applied to a solid state Si detector with active or off-line PPU suppression circuitry. A comparison shows that the results obtained with this fast and simple approach are comparable to those from the more sophisticated procedure using precise detector pulse shapes.

  19. Require safer substitutes and solutions: making the substitution principle the cornerstone of sustainable chemical policies.

    PubMed

    Thorpe, Beverley; Rossi, Mark

    2007-01-01

    Currently, chemical regulations in the United States do not prioritize the production and use of inherently safe chemicals. At present, when regulations get passed to target a chemical for control, safer substitutes are not the goal nor are there specific guidelines or tools used to achieve Green Chemistry, Clean Production, or sustainable product design. In most cases, the replacement is often just as hazardous or simply a reduction of the quantity or concentration of the toxic substance that has been targeted. In contrast, by placing the Substitution Principle at the heart of new chemical policies and regulations, hazardous chemicals would be replaced with less hazardous alternatives or preferably alternatives for which no hazards can be identified. This would hasten the uptake of Green Chemistry, or environmentally benign chemical synthesis. Substituting hazardous chemicals goes beyond finding a drop-in chemical alternative and can include systems, materials or process changes. Regulatory drivers include a clear timeline for phase out of priority chemicals based on their inherent hazard, mandatory substitution planning for hazardous chemicals, financial and technical support for companies to find safer materials, and increased funding for green chemistry development and uptake by companies.

  20. First-principles studies of conformation and solution effects on DNA transport

    NASA Astrophysics Data System (ADS)

    Tan, Bikan; Hodak, Miroslav; Lu, Wenchang; Bernholc, Jerry

    2014-03-01

    The electrical conductivity of DNA molecules is of fundamental interest in the life sciences. We use first-principles techniques combined with molecular dynamical (MD) simulations to calculate transport properties of B-DNA connected to carbon nanotubes via alkane linkers. The quantum transport properties are calculated for over a hundred of snapshots recorded in MD trajectories. We discover that the DNA conformation and especially the overlaps between sequential guanine bases play a critical role in electron transport. DNA charge transport is indeed governed by charge delocalization with wavefunctions extent controlled by geometrical overlaps. Solvent atoms also affect the conductivity, with counterions decreasing the conductance by a factor of 2-3. In addition, we find that water molecules around the double helix screen the negatively-charged phosphate groups suppressing the conductance of DNA. Comparing transport properties of 4-base-pair (BP) with 10-BP DNA, we find weak distance dependence of the conductivity. Finally, we discuss the effect of sequence on DNA conductivity.

  1. Using "First Principles of Instruction" to Design Secondary School Mathematics Flipped Classroom: The Findings of Two Exploratory Studies

    ERIC Educational Resources Information Center

    Lo, Chung Kwan; Hew, Khe Foon

    2017-01-01

    Flipping the classroom is a current pedagogical innovation in many schools and universities. Although interest in flipped classroom (or Inverted Classroom) continues to grow, its implementation so far has been driven more by teachers' intuitive beliefs, rather than empirically-based principles. Many studies merely replace in-class instructions…

  2. Theoretical Application of Irreversible (Nonequilibrium) Thermodynamic Principles to Enhance Solute Fluxes across Nanofabricated Hemodialysis Membranes

    PubMed Central

    Hedayat, Assem; Elmoselhi, Hamdi; Shoker, Ahmed

    2012-01-01

    Objective. Nanotechnology has the potential to improve hemodialysis membrane technology. Thus, a major objective is to understand how to enhance toxic solute fluxes across these membranes. The aim of this concept building study is to review the application of irreversible thermodynamic (IT) to solute fluxes. Methods. We expanded the application of the Nernst-Planck equation to include the Kedem-Katchalsky equation, pH, membrane thickness, pore size, and electric potential as variables. Results. (1) Reducing the membrane's thickness from 25 μm to 25 nm increased the flux of creatinine, β2-microglobulin, and tumor necrosis factor-α (TNF-α) by a thousand times but prevented completely albumin flux, (2) applying an electric potential of 50–400 mV across the membrane enhanced the flux of the respective molecules by 71.167 × 10−3, 38.7905 × 10−8, and 0.595 × 10−13 mol/s, and (3) changing the pH from 7.35 to 7.42 altered the fluxes minimally. Conclusions. The results supported an argument to investigate the application of IT to study forces of fluxes across membranes. Reducing the membrane's thickness—together with the application of an electrical potential—qualities achievable by nanotechnology, can enhance the removal of uremic toxins by many folds. However, changing the pH at a specific membrane thickness does not affect the flux significantly. PMID:23209903

  3. The integration of solution-focused brief therapy principles in nursing: a literature review.

    PubMed

    Ferraz, H; Wellman, N

    2008-01-01

    The ongoing movement from institutional care to community-orientated care has gradually spread around the developed world. This shift in the philosophy of care has resulted in a reduction in the length of inpatient admissions and contributed to a decline in the number of inpatient beds. This literature review seeks to establish the suitability and relevance of solution-focused brief therapy (SFBT) to mental health nursing practice, with particular emphasis being given to acute inpatient settings. Databases searched for published material in English between 1980 and 2006 were: Cumulative Index of Nursing and Allied Health Literature; MEDLINE; Applied Social Sciences Index and Abstracts; Sociological abstracts; and social service abstracts. Search terms included: SFBT and solution-focused approaches. Only nine papers from the original 203 citations met the inclusion criteria and were thus reviewed. These papers indicated that SFBT constitutes an appropriate set of techniques for use in mental health nursing particularly where staff have relatively brief contact with patients. Preliminary data suggest that SFBT is congruent with the philosophical underpinning of contemporary mental health nursing. However, its clinical utility and effectiveness is not well established and methodologically rigorous studies are urgently needed to determine the appropriateness and effectiveness of such approach to nursing practice.

  4. 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.

  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. 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; ...

    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

  7. 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.

  8. Ion Association in AlCl3 Aqueous Solutions from Constrained First-Principles Molecular Dynamics

    SciTech Connect

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

    2012-10-15

    Ab initio molecular dynamics was used to investigate the ion pairing behavior between Cl- and the Al3+ ion in an aqueous AlCl3 solution containing 63 water molecules. A series of constrained simulations was carried out at 300 K for up to 16 ps each, by fixing the inter-nuclear separation (rAl-Cl) between the Al3+ ion and one of the Cl- ions. The calculated potential of mean force of the Al3+-Cl- ion pair shows a pronounced minimum at rAl-Cl = 2.3 Å corresponding to a contact ion pair (CIP). Two local minima assigned to solvent separated ion pairs (SSIP) are identified at rAl-Cl= 4.4 and 6.0 Å. The positions of the free energy minima coincide with the hydration shell intervals of the Al3+ cation suggesting that the Cl- ion is inclined to reside in regions of low concentration of waters, i.e. between the 1st and 2nd shells of Al3+ and between the 2nd shell and bulk. A detailed analysis of solvent structure around the Al3+ and Cl- ions as a function of rAl-Cl is presented. The results are compared to structure data from X-ray measurements and unconstrained AIMD simulations of single ions Al3+ and Cl- and AlCl3 solutions. The dipole moment of the water molecules inside the 1st and 2nd hydration shells of Al3+ and in the bulk region and those of the Clion were calculated as a function of rAl-Cl. Major changes in the electronic structure of the system result from the removal of Cl- from the 1st hydration shell of the Al3+ cation. Finally, two unconstrained AIMD simulations of aqueous AlCl3 solutions corresponding to CIP and SSIP configurations were performed (17 ps, 300 K). Only minor structural changes are observed in these systems, confirming their stability.

  9. First-principles investigation of vanadium isotope fractionation in solution and during adsorption

    NASA Astrophysics Data System (ADS)

    Wu, Fei; Qin, Tian; Li, Xuefang; Liu, Yun; Huang, Jen-How; Wu, Zhongqing; Huang, Fang

    2015-09-01

    Equilibrium fractionation factors of vanadium (V) isotopes among tri- (V(III)), tetra- (V(IV)) and penta-valent (V(V)) inorganic V species in aqueous system and during adsorption of V(V) to goethite are estimated using first-principles calculation. Our results highlight the dependence of V isotope fractionation on valence states and the chemical binding environment. The heavy V isotope (51V) is enriched in the main V species following a sequence of V(III) < V(IV) < V(V). According to our calculations, at 25 °C, the equilibrium isotope fractionation factor between [V5+O2(OH)2]- and [V4+O(H2O)5]2+ (ln ⁡α V (V)- V (IV)) is 3.9‰, and the equilibrium isotope fractionation factor between [V5+O2(OH)2]- and [V3+(OH)3(H2O)3] (ln ⁡α V (V)- V (III)) is 6.4‰. In addition, isotope fractionation between +5 valence species [V5+O2(OH)2]- and [V5+O2(H2O)4]+ is 1.5‰ at 25 °C, which is caused by their different bond lengths and coordination numbers (CN). Theoretical calculations also show that light V isotope (50V) is preferentially adsorbed on the surface of goethite. Our work reveals that V isotopes can be significantly fractionated in the Earth's surface environments due to redox reaction and mineral adsorption, indicating that V isotope data can be used to monitor toxic V(V) attenuation processes through reduction or adsorption in natural water systems. In addition, a simple mass balance model suggests that V isotope composition of seawater might vary with change of ambient oxygen levels. Thus our theoretical investigations imply a promising future for V isotopes as a potential new paleo-redox tracer.

  10. The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations

    NASA Astrophysics Data System (ADS)

    Jensen, Robert

    1988-03-01

    We prove that viscosity solutions in W 1,∞ of the second order, fully nonlinear, equation F( D 2 u, Du, u) = 0 are unique when (i) F is degenerate elliptic and decreasing in u or (ii) F is uniformly elliptic and nonincreasing in u. We do not assume that F is convex. The method of proof involves constructing nonlinear approximation operators which map viscosity subsolutions and supersolutions onto viscosity subsolutions and supersolutions, respectively. This method is completely different from that used in Lions [8, 9] for second order problems with F convex in D 2 u and from that used by Crandall & Lions [3] and Crandall, Evans & Lions [2] for fully nonlinear first order problems.

  11. Tissue-Engineered Solutions in Plastic and Reconstructive Surgery: Principles and Practice.

    PubMed

    Al-Himdani, Sarah; Jessop, Zita M; Al-Sabah, Ayesha; Combellack, Emman; Ibrahim, Amel; Doak, Shareen H; Hart, Andrew M; Archer, Charles W; Thornton, Catherine A; Whitaker, Iain S

    2017-01-01

    Recent advances in microsurgery, imaging, and transplantation have led to significant refinements in autologous reconstructive options; however, the morbidity of donor sites remains. This would be eliminated by successful clinical translation of tissue-engineered solutions into surgical practice. Plastic surgeons are uniquely placed to be intrinsically involved in the research and development of laboratory engineered tissues and their subsequent use. In this article, we present an overview of the field of tissue engineering, with the practicing plastic surgeon in mind. The Medical Research Council states that regenerative medicine and tissue engineering "holds the promise of revolutionizing patient care in the twenty-first century." The UK government highlighted regenerative medicine as one of the key eight great technologies in their industrial strategy worthy of significant investment. The long-term aim of successful biomanufacture to repair composite defects depends on interdisciplinary collaboration between cell biologists, material scientists, engineers, and associated medical specialties; however currently, there is a current lack of coordination in the field as a whole. Barriers to translation are deep rooted at the basic science level, manifested by a lack of consensus on the ideal cell source, scaffold, molecular cues, and environment and manufacturing strategy. There is also insufficient understanding of the long-term safety and durability of tissue-engineered constructs. This review aims to highlight that individualized approaches to the field are not adequate, and research collaboratives will be essential to bring together differing areas of expertise to expedite future clinical translation. The use of tissue engineering in reconstructive surgery would result in a paradigm shift but it is important to maintain realistic expectations. It is generally accepted that it takes 20-30 years from the start of basic science research to clinical utility

  12. 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.

  13. 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.

  14. On the existence and stability conditions for mixed-hybrid finite element solutions based on Reissner's variational principle

    NASA Technical Reports Server (NTRS)

    Karlovitz, L. A.; Atluri, S. N.; Xue, W.-M.

    1985-01-01

    The extensions of Reissner's two-field (stress and displacement) principle to the cases wherein the displacement field is discontinuous and/or the stress field results in unreciprocated tractions, at a finite number of surfaces ('interelement boundaries') in a domain (as, for instance, when the domain is discretized into finite elements), is considered. The conditions for the existence, uniqueness, and stability of mixed-hybrid finite element solutions based on such discontinuous fields, are summarized. The reduction of these global conditions to local ('element') level, and the attendant conditions on the ranks of element matrices, are discussed. Two examples of stable, invariant, least-order elements - a four-node square planar element and an eight-node cubic element - are discussed in detail.

  15. Tissue-Engineered Solutions in Plastic and Reconstructive Surgery: Principles and Practice

    PubMed Central

    Al-Himdani, Sarah; Jessop, Zita M.; Al-Sabah, Ayesha; Combellack, Emman; Ibrahim, Amel; Doak, Shareen H.; Hart, Andrew M.; Archer, Charles W.; Thornton, Catherine A.; Whitaker, Iain S.

    2017-01-01

    Recent advances in microsurgery, imaging, and transplantation have led to significant refinements in autologous reconstructive options; however, the morbidity of donor sites remains. This would be eliminated by successful clinical translation of tissue-engineered solutions into surgical practice. Plastic surgeons are uniquely placed to be intrinsically involved in the research and development of laboratory engineered tissues and their subsequent use. In this article, we present an overview of the field of tissue engineering, with the practicing plastic surgeon in mind. The Medical Research Council states that regenerative medicine and tissue engineering “holds the promise of revolutionizing patient care in the twenty-first century.” The UK government highlighted regenerative medicine as one of the key eight great technologies in their industrial strategy worthy of significant investment. The long-term aim of successful biomanufacture to repair composite defects depends on interdisciplinary collaboration between cell biologists, material scientists, engineers, and associated medical specialties; however currently, there is a current lack of coordination in the field as a whole. Barriers to translation are deep rooted at the basic science level, manifested by a lack of consensus on the ideal cell source, scaffold, molecular cues, and environment and manufacturing strategy. There is also insufficient understanding of the long-term safety and durability of tissue-engineered constructs. This review aims to highlight that individualized approaches to the field are not adequate, and research collaboratives will be essential to bring together differing areas of expertise to expedite future clinical translation. The use of tissue engineering in reconstructive surgery would result in a paradigm shift but it is important to maintain realistic expectations. It is generally accepted that it takes 20–30 years from the start of basic science research to clinical utility

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

    PubMed

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

    2007-09-06

    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.

  17. 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.

  18. First-Principles Simulation Study of Vibrational Spectral Diffusion and Hydrogen Bond Fluctuations in Aqueous Solution of N-Methylacetamide.

    PubMed

    Yadav, Vivek Kumar; Chandra, Amalendu

    2015-07-30

    We have presented a first-principles simulation study of the vibrational spectral diffusion and hydrogen bond dynamics in an aqueous solution of N-methylacetamide (NMA). We have studied the spectral diffusion of local OD stretch modes of deuterated water in the first hydration shells of the carbonyl (CO) and deuterated amide (ND) modes and their relations to the dynamics of hydrogen bonds formed by water with these groups. The frequency fluctuations of the amide I and amide A modes of the solute are also investigated. It is found that the vibrational spectral diffusion of water molecules in the first hydration shell of the carbonyl oxygen of NMA proceeds with three time scales: A short-time relaxation (∼100 fs) originating from the dynamics of NMA-water hydrogen bonds without breaking, a slower relaxation (∼3.3 ps) arising from the breaking dynamics of NMA(CO)-water hydrogen bonds, and another longer time constant (∼14 ps) coming from the escape dynamics of water from the first hydration shell of carbonyl oxygen. The current results show that the NMA(CO)-water hydrogen bonds have a longer lifetime than those between water molecules, although frequency calculations reveal a slightly higher stretch frequency of the water molecules in the first hydration shell of the carbonyl oxygen of NMA. An analysis of the vibrational spectral diffusion of solute modes is also presented in terms of the dynamics of solute-water hydrogen bonds. Effects of dispersion interactions on various calculated properties of the NMA-water system are also investigated in the present work.

  19. 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.

  20. 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

  1. 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.

  2. Optimal solutions for a bio mathematical model for the evolution of smoking habit

    NASA Astrophysics Data System (ADS)

    Sikander, Waseem; Khan, Umar; Ahmed, Naveed; Mohyud-Din, Syed Tauseef

    In this study, we apply Variation of Parameter Method (VPM) coupled with an auxiliary parameter to obtain the approximate solutions for the epidemic model for the evolution of smoking habit in a constant population. Convergence of the developed algorithm, namely VPM with an auxiliary parameter is studied. Furthermore, a simple way is considered for obtaining an optimal value of auxiliary parameter via minimizing the total residual error over the domain of problem. Comparison of the obtained results with standard VPM shows that an auxiliary parameter is very feasible and reliable in controlling the convergence of approximate solutions.

  3. 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.

  4. 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 mathematical…

  5. 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.

  6. Crick's gossip test and Watson's boredom principle: A pseudo-mathematical analysis of effort in scientific research.

    PubMed

    Charlton, Bruce G

    2008-01-01

    Crick and Watson gave complementary advice to the aspiring scientist based on the insight that to do your best work you need to make your greatest possible effort. Crick made the positive suggestion to work on the subject which most deeply interests you, the thing about which you spontaneously gossip - Crick termed this 'the gossip test'. Watson made the negative suggestion of avoiding topics and activities that bore you - which I have termed 'the boredom principle'. This is good advice because science is tough and the easy things have already been done. Solving the harder problems that remain requires a lot of effort. But in modern biomedical science individual effort does not necessarily correlate with career success as measured by salary, status, job security, etc. This is because Crick and Watson are talking about revolutionary science - using Thomas Kuhn's distinction between paradigm-shifting 'revolutionary' science and incremental 'normal' science. There are two main problems with pursuing a career in revolutionary science. The first is that revolutionary science is intrinsically riskier than normal science, the second that even revolutionary success in a scientific backwater may be less career-enhancing than mundane work in a trendy field. So, if you pick your scientific problem using the gossip test and the boredom principle, you might also be committing career suicide. This may explain why so few people follow Crick and Watson's advice. The best hope for future biomedical science is that it will evolve towards a greater convergence between individual effort and career success.

  7. Mathematical model of sediment and solute transport along slope land in different rainfall pattern conditions

    NASA Astrophysics Data System (ADS)

    Tao, Wanghai; Wu, Junhu; Wang, Quanjiu

    2017-03-01

    Rainfall erosion is a major cause of inducing soil degradation, and rainfall patterns have a significant influence on the process of sediment yield and nutrient loss. The mathematical models developed in this study were used to simulate the sediment and nutrient loss in surface runoff. Four rainfall patterns, each with a different rainfall intensity variation, were applied during the simulated rainfall experiments. These patterns were designated as: uniform-type, increasing-type, increasing- decreasing -type and decreasing-type. The results revealed that changes in the rainfall intensity can have an appreciable impact on the process of runoff generation, but only a slight effect on the total amount of runoff generated. Variations in the rainfall intensity in a rainfall event not only had a significant effect on the process of sediment yield and nutrient loss, but also the total amount of sediment and nutrient produced, and early high rainfall intensity may lead to the most severe erosion and nutrient loss. In this study, the calculated data concur with the measured values. The model can be used to predict the process of surface runoff, sediment transport and nutrient loss associated with different rainfall patterns.

  8. Mathematical model of sediment and solute transport along slope land in different rainfall pattern conditions

    PubMed Central

    Tao, Wanghai; Wu, Junhu; Wang, Quanjiu

    2017-01-01

    Rainfall erosion is a major cause of inducing soil degradation, and rainfall patterns have a significant influence on the process of sediment yield and nutrient loss. The mathematical models developed in this study were used to simulate the sediment and nutrient loss in surface runoff. Four rainfall patterns, each with a different rainfall intensity variation, were applied during the simulated rainfall experiments. These patterns were designated as: uniform-type, increasing-type, increasing- decreasing -type and decreasing-type. The results revealed that changes in the rainfall intensity can have an appreciable impact on the process of runoff generation, but only a slight effect on the total amount of runoff generated. Variations in the rainfall intensity in a rainfall event not only had a significant effect on the process of sediment yield and nutrient loss, but also the total amount of sediment and nutrient produced, and early high rainfall intensity may lead to the most severe erosion and nutrient loss. In this study, the calculated data concur with the measured values. The model can be used to predict the process of surface runoff, sediment transport and nutrient loss associated with different rainfall patterns. PMID:28272431

  9. Mathematical analysis of vortex dynamics

    NASA Astrophysics Data System (ADS)

    Caflisch, Russel E.

    This review paper discusses the mathematical theory of vortex dynamics for incompressible, inviscid flow in two and three dimensions. The surveyed results include existence and uniqueness of time-dependent solutions, instability and singularity formation, convergence of numerical methods, and existence and stability of steady states. A simple integral formulation for the evolution of a three dimensional vortex sheet and a variational principle for the Batchelor flow problem are presented.

  10. 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.

  11. 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.

  12. Empirical and mathematical model of rapid expansion of supercritical solution (RESS) process of acetaminophen

    NASA Astrophysics Data System (ADS)

    Kien, Le Anh

    2017-09-01

    Rapid Expansion of Supercritical Solutions (RESS) is a solvent-free technology to produce small solid particles with very narrow size distribution. RESS process is simple and easy to control in comparison with other methods based on supercritical techniques. In this study, the engineering of nano (or submicron) acetaminophen particles using rapid expansion CO2 supercritical solution (RESS) was investigated. Empirical model with response surface methodology was used to evaluate the effects of processing parameters, i.e. extraction temperature T (313-333 K), extraction pressure P (90-150 bar) and pre-expansion temperature Texp (353-373 K), on the size of precipitated acetaminophen particles. The results show that the smallest particle size, i.e. 52.08 nm can be achieved at 90 bar, 313 K and 353 K (P, T, Texp, respectively). To better understand and develop a mechanistic predictive tool for RESS process, a one dimensional steady flow model was used in this work to describe the subsonic expansion process inside the capillary nozzle and the supersonic expansion process outside expansion nozzle. It was shown that particle characteristics are governed by both operation parameters such as pre-expansion temperature, pre-expansion pressure, and expansion temperature. These parameters affects particle size in the same trend as that was found from experiment data and empirical model.

  13. 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.

  14. Student Solution Manual for Mathematical Methods for Physics and Engineering Third Edition

    NASA Astrophysics Data System (ADS)

    Riley, K. F.; Hobson, M. P.

    2006-03-01

    Preface; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics.

  15. 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

  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. 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.

  18. 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.

  19. 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…

  20. 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…

  1. 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…

  2. 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…

  3. Some Meaningful Mathematics in Two Chapters: Chapter T1, The Binomial Expansion and Related Topics; Chapter T2, The Principle of Math Induction and Related Conjectures.

    ERIC Educational Resources Information Center

    Titterton, J. Patrick

    The author presents material suitable for use by teachers of gifted students in the junior or senior year of high school. The mathematics presented includes mathematical induction, the binomial expansion, number theory and Pascal's triangle. The author weaves much of the history of mathematics into the materials. Included are student tests and…

  4. Mathematics 9th Year.

    ERIC Educational Resources Information Center

    New York City Board of Education, Brooklyn, NY. Bureau of Curriculum Development.

    The Materials in this bulletin indicate suggested teaching procedures needed to implement the teaching of "mathematics, 9th Year" as outlined in Curriculum Bulletin No. 3, 1958-59 series, Course of Study Mathematics 7-8-9. Whereas the course of study suggests the application of mathematical principles such as commutativity,…

  5. Mathematics Instruction in Inner-City Intermediate Schools: An Inductive Approach to Identifying Problems and Crafting Solutions. Research Report #8.

    ERIC Educational Resources Information Center

    Manning, Philip; Matthews, Sarah H.

    An exploration of sources of gang activity in an urban area used ethnographic research with researchers posing as mathematics tutors for 1 year in a school comprising seventh and eighth grades. The "tutors" attended six eighth grade mathematics classes and acted as assistants to the teacher. The classes of 25 to 30 students lasted 40 minutes and…

  6. 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.

  7. Investigation and Mathematical Description of the Real Driving Force of Passive Transport of Drug Molecules from Supersaturated Solutions.

    PubMed

    Borbás, Enikő; Sinkó, Bálint; Tsinman, Oksana; Tsinman, Konstantin; Kiserdei, Éva; Démuth, Balázs; Balogh, Attila; Bodák, Brigitta; Domokos, András; Dargó, Gergő; Balogh, György T; Nagy, Zsombor K

    2016-11-07

    The aim of this study was to investigate the impact of formulation excipients and solubilizing additives on dissolution, supersaturation, and membrane transport of an active pharmaceutical ingredient (API). When a poorly water-soluble API is formulated to enhance its dissolution, additives, such as surfactants, polymers, and cyclodextrins, have an effect not only on dissolution profile but also on the measured physicochemical properties (solubility, pKa, permeability) of the drug while the excipient is present, therefore also affecting the driving force of membrane transport. Meloxicam, a nonsteroidal anti-inflammatory drug, was chosen as a poorly water-soluble model drug and formulated in order to enhance its dissolution using solvent-based electrospinning. Three polyvinylpyrrolidone (PVP) derivatives (K30, K90, and VA 64), Soluplus, and (2-hydroxypropyl)-β-cyclodextrin were used to create five different amorphous solid dispersions of meloxicam. Through experimental design, the various formulation additives that could influence the characteristics of dissolution and permeation through artificial membrane were observed by carrying out a simultaneous dissolution-permeation study with a side-by-side diffusion cell, μFLUX. Although the dissolution profiles of the formulations were found to be very similar, in the case of Soluplus containing formulation the flux was superior, showing that the driving force of membrane transport cannot be simplified to the concentration gradient. Supersaturation gradient, the difference in degree of supersaturation (defined as the ratio of dissolved amount of the drug to its thermodynamic solubility) between the donor and acceptor side, was found to be the driving force of membrane transport. It was mathematically derived from Fick's first law, and experimentally proved to be universal on several meloxicam containing ASDs and DMSO stock solution.

  8. The principle of minimum of partial local variations for determining convective flows in the numerical solution of one-dimensional nonlinear scalar hyperbolic equations

    NASA Astrophysics Data System (ADS)

    Goloviznin, V. M.; Kanaev, A. A.

    2011-05-01

    For the CABARET finite difference scheme, a new approach to the construction of convective flows for the one-dimensional nonlinear transport equation is proposed based on the minimum principle of partial local variations. The new approach ensures the monotonicity of solutions for a wide class of problems of a fairly general form including those involving discontinuous and nonconvex functions. Numerical results illustrating the properties of the proposed method are discussed.

  9. A mathematical model of a steady flow through the Kaplan turbine - The existence of a weak solution in the case of an arbitrarily large inflow

    NASA Astrophysics Data System (ADS)

    Neustupa, Tomáš

    2017-07-01

    The paper presents the mathematical model of a steady 2-dimensional viscous incompressible flow through a radial blade machine. The corresponding boundary value problem is studied in the rotating frame. We provide the classical and weak formulation of the problem. Using a special form of the so called "artificial" or "natural" boundary condition on the outflow, we prove the existence of a weak solution for an arbitrarily large inflow.

  10. 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.

  11. 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.

  12. 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.

  13. First-Principles Calculation of the Structural, Magnetic, and Electronic Properties of the CoxCu1-x Solid Solutions Using Special Quasirandom Structures

    NASA Astrophysics Data System (ADS)

    Kong, Yi; Liu, Baixin

    2007-02-01

    We investigate, in the present study, the structural properties, magnetic moments and charge distribution of the solid solution in an immiscible Co-Cu system at equilibrium by first-principles calculation using special quasirandom structures (SQS). In order to mimic the pair and multisite correlation functions of the randomly substitutional fcc solid solutions, the original SQS is developed to include five 16-atom SQS unit cells, i.e., 1/16, 2/16, 3/16, 4/16, and 8/16, enabling to mimic at nine specific alloys compositions. Correspondingly, a new error analysis method is proposed for comparing the situations of various alloy compositions within the SQS unit cells having a same number of atoms. The developed SQS are then applied in the first-principles calculation to study the CoxCu1-x solid solutions (x refers to the Co concentration). It turns out that the calculated results of the lattice constants and magnetic moments versus the Co concentration are in good agreement with the experimental data, and especially, the sharp drop in the magnetic moment near the composition x=0.1 is well reproduced. The heats of formation are also calculated and in good agreement with those obtained from Mediema’s thermodynamic theory and available experimental data. At the alloy compositions x=0.25 and 0.75, some hypothetical crystalline structures of the Co-Cu compounds are respectively calculated and their heats of formation are found to be higher than the solid solution counterparts. Finally, the electron distribution among the atoms in the CoxCu1-x solid solutions is studied and the obtained charge densities show that in the CoxCu1-x solid solutions, the charge distributes mostly between the Co-Co atoms, thus forming attractive covalent bonding.

  14. 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

  15. 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.

  16. 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)

  17. Capturing CO2 in Monoethanolamine (MEA) Aqueous Solutions: Fingerprints of Carbamate Formation Assessed with First-Principles Simulations.

    PubMed

    Ma, Changru; Pietrucci, Fabio; Andreoni, Wanda

    2014-05-15

    Chemical absorption in amine aqueous solutions is a widespread technology for postcombustion carbon capture, and a large effort is ongoing to improve their performance. Characterization of the "reactant" and "product" solutions at the microscopic level is highly desirable for process optimization. Recently X-ray scattering experiments and "in situ" infrared spectroscopy have been applied to this aim, but a complete and convincing interpretation is missing. We present large-scale ab initio molecular dynamics simulations of monoethanolamine solutions at experimental concentration and temperature and analyze how structural and vibrational properties change after carbamate formation. An exhaustive account of the experimental data is obtained. Fingerprints of the reaction products and specific interactions are unravelled. Hydration effects are specific to each component of the solution and are essential for a correct assignment of the experimental data.

  18. 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…

  19. 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…

  20. 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.

  1. 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.

  2. 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…

  3. 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…

  4. The strong maximum principle revisited

    NASA Astrophysics Data System (ADS)

    Pucci, Patrizia; Serrin, James

    In this paper we first present the classical maximum principle due to E. Hopf, together with an extended commentary and discussion of Hopf's paper. We emphasize the comparison technique invented by Hopf to prove this principle, which has since become a main mathematical tool for the study of second order elliptic partial differential equations and has generated an enormous number of important applications. While Hopf's principle is generally understood to apply to linear equations, it is in fact also crucial in nonlinear theories, such as those under consideration here. In particular, we shall treat and discuss recent generalizations of the strong maximum principle, and also the compact support principle, for the case of singular quasilinear elliptic differential inequalities, under generally weak assumptions on the quasilinear operators and the nonlinearities involved. Our principal interest is in necessary and sufficient conditions for the validity of both principles; in exposing and simplifying earlier proofs of corresponding results; and in extending the conclusions to wider classes of singular operators than previously considered. The results have unexpected ramifications for other problems, as will develop from the exposition, e.g. two point boundary value problems for singular quasilinear ordinary differential equations (Sections 3 and 4); the exterior Dirichlet boundary value problem (Section 5); the existence of dead cores and compact support solutions, i.e. dead cores at infinity (Section 7); Euler-Lagrange inequalities on a Riemannian manifold (Section 9); comparison and uniqueness theorems for solutions of singular quasilinear differential inequalities (Section 10). The case of p-regular elliptic inequalities is briefly considered in Section 11.

  5. New: Variational principle-exact solutions and conservation laws for modified ion-acoustic shock waves and double layers with electron degenerate in plasma

    NASA Astrophysics Data System (ADS)

    EL-Kalaawy, O. H.

    2017-03-01

    The nonlinear propagation of modified ion acoustic shock waves and double layers in a relativistic degenerate plasma is considered. This plasma system is proposed for containing inertial viscous positive and negative ion fluids, relativistic electron fluids, and negatively charged immobile heavy ions. The basic set of fluid equations is reduced to modified Burgers (MB) and further modified Burgers (FMB) or (Gardner) or Mamun and Zobaer (M-Z) equations by using the reductive perturbation method. The basic features of these shocks obtained from this analysis are observed to be significantly different from those obtained from the standard Burgers equation. By introducing two special functions and He's semi-inverse method, a variational principle and conservation laws for the Gardner (FmB) equation are obtained. A set of new exact solutions for the Gardner (FmB) equation are obtained by the auto-Bäcklund transformations. Finally, we will study the physical meanings of solutions.

  6. 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.

  7. A DESCRIPTION OF VARIABLES AND THEIR IMPLEMENTATION IN STUDIES OF PRINCIPLES FOR THE PROGRAMING OF HIGH SCHOOL ALGEBRA. COMPARATIVE STUDIES OF PRINCIPLES FOR PROGRAMING MATHEMATICS IN AUTOMATED INSTRUCTION, TECHNICAL REPORT NO. 8.

    ERIC Educational Resources Information Center

    ROSEN, ELLEN F.; STOLUROW, LAWRENCE M.

    MANIPULATION OF FRAMES WITHIN PROGRAMED MATHEMATICS TEXTS IN ORDER TO STUDY FOUR VARIABLES YIELDED, IN A PREVIOUSLY REPORTED PAPER, CORRELATIONAL DATA (FOR RELATIVELY SMALL TREATMENT GROUPS) THAT ARE PRESENTED HERE. FIRST, THE ORDER OF PRESENTATION OF PROGRAMED MATERIAL (BEFORE, AFTER, AND WITHOUT CONVENTIONAL INSTRUCTION) HAD NO EFFECT ON…

  8. 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.

  9. Mathematics Projects Handbook.

    ERIC Educational Resources Information Center

    Hess, Adrien L.

    This handbook is designed as a guide for teachers and students in choosing and developing mathematics projects, from simple demonstrations of mathematical problems or principles that the teacher has assigned as classroom learning experiences to complex, sophisticated exhibits, intended for entrance in fairs and competitions. The use of projects to…

  10. Mathematics Projects Handbook.

    ERIC Educational Resources Information Center

    Hess, Adrien L.

    This handbook is designed as a guide for teachers and students in choosing and developing mathematics projects, from simple demonstrations of mathematical problems or principles that the teacher has assigned as classroom learning experiences to complex, sophisticated exhibits, intended for entrance in fairs and competitions. The use of projects to…

  11. A first-principle study of CO2 binding by monoethanolamine and mono-n-propanolamine solutions

    NASA Astrophysics Data System (ADS)

    Li, Hsueh-Chien; Tsai, Ming-Kang

    2015-05-01

    Monoethanolamine (MEA) and mono-n-propanolamine (MPA) molecules were investigated for CO2 binding using Density Functional Theory. MPA was predicted to bind CO2 better than MEA along the bimolecular and trimolecular pathways. The additional CH2 in MPA provided additional polarization to reduce the electrostatic repulsion for the charge-separated zwitterionic intermediates (ZW) as shown in the Polarizable Continuum Model calculations; also became more polar solvent to stabilize ZW. 25% and 50% CO2 loading at 400 K were studied by first-principle molecular dynamic simulations. With including the explicit solvation effect, CO2 in alcoholamines favored a reduced-hydrogen-bonding (HB) environment. The probability of identifying the HB precursors-(MEA)2 and (MPA)2 for the subsequent trimolecular pathway decreased. Moreover, higher CO2 uptake accompanied with more OH⋯N HB, and the lone pairs of N were blocked to CO2. Water also preferred to form intermolecular OH⋯N HB so that the accesses of CO2 were hindered.

  12. The Solvation Structure of Lithium Ions in an Ether Based Electrolyte Solution from First-Principles Molecular Dynamics.

    PubMed

    Callsen, Martin; Sodeyama, Keitaro; Futera, Zdeněk; Tateyama, Yoshitaka; Hamada, Ikutaro

    2017-01-12

    The solvation and desolvation of the Li ion play a crucial role in the electrolytes of Li based secondary batteries, and their understanding at the microscopic level is of great importance. Oligoether (glyme) based electrolytes have attracted much attention as electrolytes used in Li based secondary batteries, such as Li-ion, Li-S, and Li-O2 batteries. However, the solvation structure of the Li ion in glyme based electrolytes has not been fully clarified yet. We present a computational study on the solvation structure of lithium ions in the mixture of triglyme and lithium bis(trifluoromethylsulfonyl)-amide (LiTFSA) by means of molecular orbital and molecular dynamics calculations based on density functional theory. We found that, in the electrolyte solution composed of the equimolar mixture of triglyme and LiTFSA, lithium ions are solvated mainly by crown-ether-like curled triglyme molecules and in direct contact with an TFSA anion. We also found the aggregate formed with Li ion and TFSA anions and/or triglyme molecule(s) is equally stable, which has not been reported in the previous classical molecular dynamics simulations, suggesting that in reality a small fraction of Li ions form aggregates and they might have a significant impact on the Li ion transport. Our results demonstrate the importance of performing electronic structure based molecular dynamics of electrolyte solution to clarify the detailed solvation structure of the Li ion.

  13. Capture and Release of CO₂ in Monoethanolamine Aqueous Solutions: New Insights from First-Principles Reaction Dynamics.

    PubMed

    Ma, Changru; Pietrucci, Fabio; Andreoni, Wanda

    2015-07-14

    Aqueous monoethanolamine (MEA) solution is commonly used for post-combustion carbon capture via chemical absorption. Extensive research has been carried out to characterize both uptake and release of carbon dioxide (CO2), with the aim of improving process performance. However, an intensive research is still needed on fundamental aspects of the key chemical reactions, to achieve a comprehensive understanding of the cyclic process at the microscopic level and a quantitative assessment. We present several ab initio simulations of MEA solutions at a concentration of 30 wt %-the current standard in the industry-and study the dynamics of key multistep chemical reactions, using the metadynamics technique. Pathways for the entire cycle are investigated and characterized in terms of related free-energy and enthalpy barriers, and of the accompanying variations in both structural and electronic properties. The results of this study lead us to propose, among competing processes, an unforeseen scenario in which the zwitterion acts as sn intermediate not only of CO2 uptake, in the form of carbamate, but also of its release. Rate-limiting steps are the formation of the zwitterion for the former and MEAH(+) deprotonation for the latter. Water is shown to play a multifaceted role, which is crucial in determining the development and the energetics of each step of the reactions. The level of comprehension here achieved for MEA should help defining a strategy for solvent optimization.

  14. Analogs of the double-Reissner-Nordstroem solution in magnetostatics and dilaton gravity: Mathematical description and basic physical properties

    SciTech Connect

    Manko, V. S.; Sanchez-Mondragon, J.; Ruiz, E.

    2009-04-15

    In this paper we consider a magnetic analog of the double-Reissner-Nordstroem solution and construct the corresponding magnetic potential A{sub {phi}} in the explicit form. The behavior of the resulting solution under the Harrison transformation then naturally singles out the asymmetric black diholes--configurations composed of two nonextreme black holes possessing unequal masses, and charges equal in magnitude but opposite in sign - as its most general subclass for which equilibrium of the black-hole constituents can be achieved with the aid of the external magnetic (or electric) field. We also generalize the double-Reissner-Nordstroem solution to dilaton gravity with arbitrary dilaton coupling, yielding the four-dimensional double-Gibbons-Maeda spacetime. The study of some physical properties of the solutions obtained leads, in particular, to very simple formulas for the areas of the horizons and surface gravities.

  15. 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…

  16. 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…

  17. Mathematical modeling in neuroendocrinology.

    PubMed

    Bertram, Richard

    2015-04-01

    Mathematical models are commonly used in neuroscience, both as tools for integrating data and as devices for designing new experiments that test model predictions. The wide range of relevant spatial and temporal scales in the neuroendocrine system makes neuroendocrinology a branch of neuroscience with great potential for modeling. This article provides an overview of concepts that are useful for understanding mathematical models of the neuroendocrine system, as well as design principles that have been illuminated through the use of mathematical models. These principles are found over and over again in cellular dynamics, and serve as building blocks for understanding some of the complex temporal dynamics that are exhibited throughout the neuroendocrine system.

  18. Mathematical and physical model of gravity-fed infusion outflow: application to soft-bag-packed solutions.

    PubMed

    Simon, N; Décaudin, B; Lannoy, D; Barthélémy, C; Lemdani, M; Odou, P

    2011-12-01

    Gravity-fed infusion (GFI) systems are acknowledged as being unable to keep their flow-rate constant. This may affect drug plasma levels such as aminoglycosides. Numerous factors have previously been cited, but their relative importance has never been quantified so far. The objective of this work is to identify the main factors that influence GFI in vitro outflow and to propose a mathematical model of flow-rate evolution as a function of time. In this model, pressure loss and infusion device creep have been considered as the main variation factors. Concomitantly, two experiments were undertaken. Firstly, the flow-rate evolution of an in vitro infusion of 250 mL of dextrose 5% was assessed. Secondly, the creep occurring on an infusion device was measured through a stress relaxation experiment. The experimental infusion flow-rate decreased by as much as 28.5% over 1 h. Simulated and experimental data are well correlated (r = 0.987; P < 0.0001). The maximum creep effect happens during the first 15 min of infusion. In this work, height of the liquid in the bag and tube creep were found to be the main variation factors in GFI flow-rate. This new mathematical model should help to explain the differences observed in drug plasma levels with gravity-fed devices.

  19. 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…

  20. 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…

  1. 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…

  2. Inpatient Falls: Defining the Problem and Identifying Possible Solutions. Part II: Application of Quality Improvement Principles to Hospital Falls.

    PubMed

    Cumbler, Ethan U; Simpson, Jennifer R; Rosenthal, Laura D; Likosky, David J

    2013-10-01

    In this 2 part series, analysis of the risk stratification tools that are available and definition of the scope of the problem and potential solutions through a review of the literature is presented. A systematic review was used to identify articles for risk stratification and interventions. Three risk stratification systems are discussed, STRATIFY, Morse Fall Scale, and the Hendrich Fall Risk Model (HFRM). Of these scoring systems, the HFRM is the easiest to use and score. Predominantly, multifactorial interventions are used to prevent patient falls. Education and rehabilitation are common themes in studies with statistically significant results. The second article presents a guide to implementing a quality improvement project around hospital falls. A 10-step approach to Plan-Do-Study-Act (PDSA) cycles is described. Specific examples of problems and analysis are easily applicable to any institution. Furthermore, the sustainability of interventions and targeting new areas for improvement are discussed. Although specific to falls in the hospitalized patient, the goal is to present a stepwise approach that is broadly applicable to other areas requiring quality improvement.

  3. Electronic structures of anatase (TiO2)1-x(TaON)x solid solutions: a first-principles study.

    PubMed

    Dang, Wenqiang; Chen, Hungru; Umezawa, Naoto; Zhang, Junying

    2015-07-21

    Sensitizing wide band gap photo-functional materials under visible-light irradiation is an important task for efficient solar energy conversion. Although nitrogen doping into anatase TiO2 has been extensively studied for this purpose, it is hard to increase the nitrogen content in anatase TiO2 because of the aliovalent nitrogen substituted for oxygen, leading to the formation of secondary phases or defects that hamper the migration of photoexcited charge carriers. In this paper, electronic structures of (TiO2)1-x(TaON)x (0 ≤ x ≤ 1) solid solutions, in which the stoichiometry is satisfied with the co-substitution of Ti for Ta along with O for N, are investigated within the anatase crystal structure using first-principles calculations. Our computational results show that the solid solutions have substantially narrower band gaps than TiO2, without introducing any localized energy states in the forbidden gap. In addition, in comparison with the pristine TiO2, the solid solution has a direct band gap when the content of TaON exceeds 0.25, which is advantageous to light absorption. The valence band maximum (VBM) of the solid solutions, which is mainly composed of N 2p states hybridized with O 2p, Ti 3d or Ta 5d orbitals, is higher in energy than that of pristine anatase TiO2 consisting of non-bonding O 2p states. On the other hand, incorporating TaON into TiO2 causes the formation of d-d bonding states through π interactions and substantially lowers the conduction band minimum (CBM) because of the shortened distance between some metal atoms. As a result, the anatase (TiO2)1-x(TaON)x is expected to become a promising visible-light absorber. In addition, some atomic configurations are found to possess exceptionally narrow band gaps.

  4. A class of traveling wave solutions for space-time fractional biological population model in mathematical physics

    NASA Astrophysics Data System (ADS)

    Akram, Ghazala; Batool, Fiza

    2017-10-01

    The (G'/G)-expansion method is utilized for a reliable treatment of space-time fractional biological population model. The method has been applied in the sense of the Jumarie's modified Riemann-Liouville derivative. Three classes of exact traveling wave solutions, hyperbolic, trigonometric and rational solutions of the associated equation are characterized with some free parameters. A generalized fractional complex transform is applied to convert the fractional equations to ordinary differential equations which subsequently resulted in number of exact solutions. It should be mentioned that the (G'/G)-expansion method is very effective and convenient for solving nonlinear partial differential equations of fractional order whose balancing number is a negative integer.

  5. A class of traveling wave solutions for space-time fractional biological population model in mathematical physics

    NASA Astrophysics Data System (ADS)

    Akram, Ghazala; Batool, Fiza

    2017-05-01

    The (G'/G) -expansion method is utilized for a reliable treatment of space-time fractional biological population model. The method has been applied in the sense of the Jumarie's modified Riemann-Liouville derivative. Three classes of exact traveling wave solutions, hyperbolic, trigonometric and rational solutions of the associated equation are characterized with some free parameters. A generalized fractional complex transform is applied to convert the fractional equations to ordinary differential equations which subsequently resulted in number of exact solutions. It should be mentioned that the (G'/G) -expansion method is very effective and convenient for solving nonlinear partial differential equations of fractional order whose balancing number is a negative integer.

  6. ATHOS: a computer program for thermal-hydraulic analysis of steam generators. Volume 1. Mathematical and physical models and method of solution. [PWR

    SciTech Connect

    Singhal, A.K.; Keeton, L.W.; Spalding, D.B.; Srikantiah, G.S.

    1982-10-01

    ATHOS (Analysis of the Thermal Hydraulics of Steam Generators) is a computer code developed by CHAM of North America Incorporated, under the contract RP 1066-1 from the Electric Power Research Institute, Palo Alto, California. ATHOS supersedes the earlier code URSULA2. ATHOS is designed for three-dimensional, steady state and transient analyses of PWR steam generators. The current version of the code has been checked out for: three different configurations of the recirculating-type U-tube steam generators; the homogeneous and algebraic-slip flow models; and full and part load operating conditions. The description of ATHOS is divided into four volumes. Volume 1 includes the mathematical and physical models and method of solution.

  7. 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

  8. 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.

  9. 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.

  10. Applied Mathematics Should Be Taught Mixed.

    ERIC Educational Resources Information Center

    Brown, Gary I.

    1994-01-01

    Discusses the differences between applied and pure mathematics and provides extensive history of mixed mathematics. Argues that applied mathematics should be taught allowing for speculative mathematics, which involves breaking down a given problem into simpler parts until one arrives at first principles. (ASK)

  11. Facilitating Mathematical Practices through Visual Representations

    ERIC Educational Resources Information Center

    Murata, Aki; Stewart, Chana

    2017-01-01

    Effective use of mathematical representation is key to supporting student learning. In "Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014), "use and connect mathematical representations" is one of the effective Mathematics Teaching Practices. By using different representations, students examine concepts…

  12. Some Pluses and Minuses of Radical Constructivism in Mathematics Education.

    ERIC Educational Resources Information Center

    Ellerton, Nerida; Clements, M. A.

    1992-01-01

    Reviews the radical constructivism movement in mathematics education. Benefits identified include learner ownership of mathematical learning; importance of social interaction; and identification of principles for improving mathematics teaching and learning. Weaknesses identified include overzealousness of some radical constructivists; downplaying…

  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. 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.

  15. Problems for Computer Mathematics.

    ERIC Educational Resources Information Center

    Allison, Ronald; And Others

    This booklet contains some 80 problems in mathematics suitable for computer solution. The problems range from very simple to complex. Problems have been included from most mathematic disciplines, including number theory, analytical geometry, probability and statistics, trigonometry, equations, and sequence and limits. For the most part these…

  16. A First-Principles Molecular Dynamics Study of the Solvation Shell Structure, Vibrational Spectra, Polarity, and Dynamics around a Nitrate Ion in Aqueous Solution.

    PubMed

    Yadav, Sushma; Choudhary, Ashu; Chandra, Amalendu

    2017-09-15

    A first-principles molecular dynamics study is presented for the structural, dynamical, vibrational, and dipolar properties of the solvation shell of a nitrate ion in deuterated water. A detailed description of the anisotropic structure of the solvation shell is presented through calculations of various structural distributions in different conical shells around the perpendicular axis of the ion. The nitrate ion-water dimer potential energies are also calculated for many different orientations of water. The average vibrational stretch frequency of OD modes in the solvation shell is found to be higher than that of other OD modes in the bulk, which signifies a weakening of hydrogen bonds in the hydration shell. A splitting of the NO stretch frequencies and an associated fast spectral diffusion of the solute are also observed in the current study. The dynamics of rotation and hydrogen bond relaxation are found to be faster in the hydration shell than that in the bulk water. The residence time of water in the hydration shell is, however, found to be rather long. The nitrate ion is found to have a dipole moment of 0.9 D in water which can be attributed to its fluctuating interactions with the surrounding water.

  17. 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).

  18. 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…

  19. 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.)

  20. Post-instability in continuous systems. I - Failure of differentiability of solutions in continuum mechanics

    NASA Technical Reports Server (NTRS)

    Zak, M.

    1982-01-01

    It is pointed out that mathematical models of continua are based on certain assumptions regarding functions which must be at least piece-wise differentiable. The assumption about smoothness of the functions makes it possible to use the mathematical technique of differentiable equations. However, this artificial mathematical limitation follows neither from the principles of mechanics nor from the definition of a continuum. The price paid for such a mathematical convenience is instability (in the class of smooth functions) of the solutions to the corresponding governing equations in some regions of the parameters. A new mathematical technique should, therefore, be developed to describe the solutions which are not necessarily differentiable. The present investigation is concerned with the criteria of applicability of the classical models of continua from the view point of stability of the corresponding solutions, postinstability models derived by reformulation of the original models, and postinstability models in enlarged classes of functions.

  1. Post-instability in continuous systems. I - Failure of differentiability of solutions in continuum mechanics

    NASA Technical Reports Server (NTRS)

    Zak, M.

    1982-01-01

    It is pointed out that mathematical models of continua are based on certain assumptions regarding functions which must be at least piece-wise differentiable. The assumption about smoothness of the functions makes it possible to use the mathematical technique of differentiable equations. However, this artificial mathematical limitation follows neither from the principles of mechanics nor from the definition of a continuum. The price paid for such a mathematical convenience is instability (in the class of smooth functions) of the solutions to the corresponding governing equations in some regions of the parameters. A new mathematical technique should, therefore, be developed to describe the solutions which are not necessarily differentiable. The present investigation is concerned with the criteria of applicability of the classical models of continua from the view point of stability of the corresponding solutions, postinstability models derived by reformulation of the original models, and postinstability models in enlarged classes of functions.

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

    NASA Technical Reports Server (NTRS)

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

    2017-01-01

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

  3. 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…

  4. ATHOS3: a computer program for thermal-hydraulic analysis of steam generators. Volume 1. Mathematical and physical models and method of solution

    SciTech Connect

    Keeton, L.W.; Singhal, A.K.; Srikantiah, G.S.

    1986-07-01

    The mathematical and physical models as well as the method of solution are presented for ATHOS3. ATHOS3 is a computer code for three-dimensional, steady-state and transient analyses of PWR steam generators. It has been developed by upgrading an earlier code, ATHOS (Analysis of the Thermal Hydraulics of Steam Generators). Both ATHOS and ATHOS3 have been developed by CHAM of North America, Inc., under the contract RP1066-1 from the Electric Power Research Institute. ATHOS3 supercedes ATHOS and all other intermediate versions of the code. ATHOS3 has several additional capabilities, including a much improved and generalized geometry pre-processor module, and has been developed in a fully upwards-compatible manner from the predecessor ATHOS code. For the convenience of new users, the ATHOS3 code is documented in four self-contained volumes, i.e. no reference to the earlier ATHOS volumes is necessary. Furthermore, for the benefit of old (i.e. ATHOS code) users, it may be stated that the new (ATHOS3) documentation has been produced by updating and modifying the earlier documentation.

  5. Dissolution enhancement and mathematical modeling of removal of residual trichloroethene in sands by ozonation during flushing with micro-nano-bubble solution

    NASA Astrophysics Data System (ADS)

    Sung, Menghau; Teng, Chun-Hao; Yang, Tsung-Hsien

    2017-07-01

    Soil flushing using micro-nano-sized bubbles (MNB) in water as the flushing solution was tested in laboratory sand columns for the cleanup of residual trichloroethene (TCE) non-aqueous-phase-liquid (NAPL). Experiments considering flushing with MNB as well as ozone MNB (OZMNB) in water to treat soils contaminated with residual TCE liquid were conducted to examine effects of ozone on dissolution enhancement. The degrees of residual TCE saturation in soils, ranging from 0.44% to 7.6%, were tested. During flushings, aqueous TCE concentrations at the column exit were monitored and TCE masses remained in the columns after flushing were determined. Experimental results between runs with MNB and OZMNB in water revealed that dissolution enhancement was dependent on residual saturation conditions, and the maximum enhancement was around 9%. Governing equations consisting of three coupled partial differential equations (PDEs) were developed to model the system, and high-order finite difference (HOFD) method was employed to solve these PDEs. From mathematical modeling of reactive mass transfer under low residual saturation conditions (0.44% and 1.9%), experimental data were simulated and important controlling mechanisms were identified. It was concluded that a specific parameter pertinent to NAPL-water interfacial area in the Sherwood number had to be modified to satisfactorily describe the dissolution of TCE in the presence of MNB in water.

  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. 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…

  8. 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…

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

    ERIC Educational Resources Information Center

    Perrin, John Robert

    2012-01-01

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

  10. Scaffolding Math Learning with Spreadsheets. Learning Connections--Mathematics

    ERIC Educational Resources Information Center

    Niess, Margaret L.

    2005-01-01

    NCTM's "Technology Principle" challenges mathematics teachers to rethink the mathematics they teach, investigate technological tools for learning mathematics, and consider how they can support students in learning mathematics with technology as a tool. In concert with the NCTM's emphasis on using technology as a tool in mathematics, ISTE's NETS…

  11. Effects of SKF-83566 and haloperidol on performance on progressive ratio schedules maintained by sucrose and corn oil reinforcement: quantitative analysis using a new model derived from the Mathematical Principles of Reinforcement (MPR).

    PubMed

    Olarte-Sánchez, C M; Valencia-Torres, L; Cassaday, H J; Bradshaw, C M; Szabadi, E

    2013-12-01

    Mathematical models can assist the interpretation of the effects of interventions on schedule-controlled behaviour and help to differentiate between processes that may be confounded in traditional performance measures such as response rate and the breakpoint in progressive ratio (PR) schedules. The effects of a D1-like dopamine receptor antagonist, 8-bromo-2,3,4,5-tetrahydro-3-methyl-5-phenyl-1H-3-benzazepin-7-ol hydrobromide (SKF-83566), and a D2-like receptor antagonist, haloperidol, on rats' performance on PR schedules maintained by sucrose and corn oil reinforcers were assessed using a new model derived from Killeen's (Behav Brain Sci 17:105-172, 1994) Mathematical Principles of Reinforcement. Separate groups of rats were trained under a PR schedule using sucrose or corn oil reinforcers. SKF-83566 (0.015 and 0.03 mg kg(-1)) and haloperidol (0.05 and 0.1 mg kg(-1)) were administered intraperitoneally (five administrations of each treatment). Running and overall response rates in successive ratios were analysed using the new model, and estimates of the model's parameters were compared between treatments. Haloperidol reduced a (the parameter expressing incentive value) in the case of both reinforcers, but did not affect the parameters related to response time and post-reinforcement pausing. SKF-83566 reduced a and k (the parameter expressing sensitivity of post-reinforcement pausing to the prior inter-reinforcement interval) in the case of sucrose, but did not affect any of the parameters in the case of corn oil. The results are consistent with the hypothesis that blockade of both D1-like and D2-like receptors reduces the incentive value of sucrose, whereas the incentive value of corn oil is more sensitive to blockade of D2-like than D1-like receptors.

  12. 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…

  13. 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…

  14. 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…

  15. Mathematics Projects Handbook. Third Edition.

    ERIC Educational Resources Information Center

    Hess, Adrien L.; And Others

    This handbook is designed as a guide for teachers and students in choosing and developing mathematics projects. Included are materials ranging from simple demonstrations of mathematical problems or principles that the teachers had assigned as classroom learning experiences to complex, sophisticated exhibits intended for fairs and competitions. The…

  16. Mathematics Projects Handbook. Second Edition.

    ERIC Educational Resources Information Center

    Hess, Adrien L.

    This updated handbook is designed as a guide for teachers and students in choosing and developing mathematics projects, from simple demonstrations of mathematical problems or principles that the teacher has assigned as classroom learning experiences to complex, sophisticated exhibits, intended for entries in fairs and competitions. The use of…

  17. Mathematics Projects Handbook. Second Edition.

    ERIC Educational Resources Information Center

    Hess, Adrien L.

    This updated handbook is designed as a guide for teachers and students in choosing and developing mathematics projects, from simple demonstrations of mathematical problems or principles that the teacher has assigned as classroom learning experiences to complex, sophisticated exhibits, intended for entries in fairs and competitions. The use of…

  18. Mathematics Projects Handbook. Third Edition.

    ERIC Educational Resources Information Center

    Hess, Adrien L.; And Others

    This handbook is designed as a guide for teachers and students in choosing and developing mathematics projects. Included are materials ranging from simple demonstrations of mathematical problems or principles that the teachers had assigned as classroom learning experiences to complex, sophisticated exhibits intended for fairs and competitions. The…

  19. 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…

  20. 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

  1. 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.

  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. New Challenges in the Teaching of Mathematics.

    ERIC Educational Resources Information Center

    Bourguignon, Jean Pierre

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

  4. 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…

  5. 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…

  6. 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)…

  7. 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…

  8. 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…

  9. 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…

  10. 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.

  11. 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…

  12. 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…

  13. Mathematical marriages: intercourse between mathematics and Semiotic choice.

    PubMed

    Wagner, Roy

    2009-04-01

    This paper examines the interaction between Semiotic choices and the presentation and solution of a family of contemporary mathematical problems centred around the so-called 'stable marriage problem'. I investigate how a socially restrictive choice of signs impacts mathematical production both in terms of problem formation and of solutions. I further note how the choice of gendered language ends up constructing a reality, which duplicates the very structural framework that it imported into mathematical analysis in the first place. I go on to point out some semiotic lines of flight from this interlocking grip of mathematics and gendered language.

  14. 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

  15. 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.

  16. Characterizing Students' Understandings of Mathematical Proof.

    ERIC Educational Resources Information Center

    Knuth, Eric J.; Elliott, Rebekah L.

    1998-01-01

    Discusses the characteristics of students' responses in terms of mathematical sophistication demonstrated that might be expected as they engage in a rich mathematical task that requires them to justify their solutions. (ASK)

  17. Mathematic Terminology.

    ERIC Educational Resources Information Center

    Hanh, Vu Duc, Ed.

    This document gives a listing of mathematical terminology in both the English and Vietnamese languages. Vocabulary used in algebra and geometry is included along with a translation of mathematical symbols. (DT)

  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 Misteaks

    ERIC Educational Resources Information Center

    Carman, Robert A.

    1971-01-01

    A mathematical misteak" is an incorrect operation that leads to a correct result. An introduction to the use of the misteak" to emphasize the mathematical operations being taught. Examples and brief explanations of several types of misteaks" are given. (FL)

  20. Mathematics disorder

    MedlinePlus

    ... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...

  1. Communication and Representation as Elements in Mathematical Literacy

    ERIC Educational Resources Information Center

    Thompson, Denisse R.; Chappell, Michaele F.

    2007-01-01

    The process standards of communication and representation in the "Principles and Standards for School Mathematics" are critical tools to help students develop mathematical literacy. In the mathematics classroom, students need to be encouraged to use speaking, listening, reading, and writing to communicate their understanding of mathematics words,…

  2. 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…

  3. 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…

  4. 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.

  5. 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,…

  6. 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…

  7. 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…

  8. 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…

  9. Hypermedia: Making the Mathematics Connection.

    ERIC Educational Resources Information Center

    Babbitt, Beatrice C.

    1993-01-01

    This article uses a cognitive problem-solving model to explore the application of hypermedia authoring software to mathematics in general and to mathematical problem solving in particular. Hypermedia is presented as a method of exploring alternative solution processes to remediate or prevent learning problems. (JDD)

  10. 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.

  11. A Mathematical Private Eye

    ERIC Educational Resources Information Center

    Lee, Ji-Eun; Kim, Kyoung-Tae

    2007-01-01

    This article proposes an instructional idea where students can figure out an individual's secret personal information using the power of mathematics, particularly the power of algebraic thinking. The proposed examples in this article start with a personalized context that other people do not know and end up with generalized patterns of solutions.…

  12. Theoretical Mathematics

    NASA Astrophysics Data System (ADS)

    Stöltzner, Michael

    Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.

  13. Mathematical modelling for the new millenium: medicine by numbers.

    PubMed

    Smye, Stephen W; Clayton, Richard H

    2002-11-01

    Physicists, engineers and mathematicians are accustomed to the combination of elegance, rigour and utility that characterise mathematical models. They are familiar with the need to dip into their mathematical toolbox to select the technique of choice. However, medicine and biology have not been characterised, in general, by a mathematical formalism. The relative paucity of mathematical models in biology and medicine reflects in part the difficulty in making accurate and appropriate experimental measurements in the field. Signal noise, the lack of appropriate sensors, and uncertainty as to what constitutes the significant measurements are largely to blame for this. The purpose of this paper is to characterise a 'good' model, encourage the development and application of such models to new areas, and outline future developments in the field. It is proposed that a good model will be accurate, predictive, economical, unique and elegant. These principles will be illustrated with reference to four models: radiosensitisation of tumours, modelling solute clearance in haemodialysis, the myogenic response in reactive hyperaemia and cardiac electrical activity. It is suggested that, in the immediate future, the mathematical model will become a useful adjunct to laboratory experiment (and possibly clinical trial), and the provision of 'in silico' models will become routine.

  14. Mathematical modelling of the transport of low molecular weight solutes across biological membranes. The transport of Leu, His and Glu into human blood platelets.

    PubMed

    Walkowiak, B; Cierniewski, C S

    1988-10-01

    A model describing the transport of low molecular weight solutes across cell membranes is presented. The model accounts for many different systems which may mediate the fluxes of various solutes, for the effect of Na+ ions, and for time dependence of the processes. It generalizes the classical three-parameter equation for transport. Solutions to the model were employed to interprete experimental data obtained for the uptake of DL-leu, L-his and L-glu by human blood platelets.

  15. Water in Hydration Shell of an Iodide Ion: Structure and Dynamics of Solute-Water Hydrogen Bonds and Vibrational Spectral Diffusion from First-Principles Simulations.

    PubMed

    Karmakar, Anwesa; Chandra, Amalendu

    2015-07-09

    The dynamics of hydrogen bonds and vibrational spectral diffusion of water in the hydration shell of an iodide ion and in bulk have been investigated for aqueous iodide solutions of two different concentrations by using ab initio molecular dynamics simulations. The effects of dispersion interactions on the dynamics have also been investigated by using a dispersion corrected density functional. For the dilute solution containing a single iodide ion, three time scales are found for the spectral diffusion of solvation shell water: A short time scale of ∼150 fs, a slower time scale of ∼2-3 ps and a yet longer time scale of ∼14-16 ps. The long time scale of ∼14-16 ps is not noticed when calculations are done for all OD modes for both the dilute and concentrated solutions. It is found that a clear separation between the solvation shell and bulk water does not exist in terms of OD stretching frequencies for the concentrated solution. The dynamics of vibrational spectral diffusion is explained in terms of hydrogen bond dynamics, other dynamical modes such as orientational relaxation and molecular diffusion, and also structural aspects of water molecules in the solvation shells. The current results are compared with those of available experimental and other theoretical studies.

  16. 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.…

  17. 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.

  18. Experimental and first-principles calculation study of the pressure-induced transitions to a metastable phase in GaP O4 and in the solid solution AlP O4-GaP O4

    NASA Astrophysics Data System (ADS)

    Angot, E.; Huang, B.; Levelut, C.; Le Parc, R.; Hermet, P.; Pereira, A. S.; Aquilanti, G.; Frapper, G.; Cambon, O.; Haines, J.

    2017-08-01

    α -Quartz-type gallium phosphate and representative compositions in the AlP O4-GaP O4 solid solution were studied by x-ray powder diffraction and absorption spectroscopy, Raman scattering, and by first-principles calculations up to pressures of close to 30 GPa. A phase transition to a metastable orthorhombic high-pressure phase along with some of the stable orthorhombic C m c m CrV O4 -type material is found to occur beginning at 9 GPa at 320 ∘C in GaP O4 . In the case of the AlP O4-GaP O4 solid solution at room temperature, only the metastable orthorhombic phase was obtained above 10 GPa. The possible crystal structures of the high-pressure forms of GaP O4 were predicted from first-principles calculations and the evolutionary algorithm USPEX. A predicted orthorhombic structure with a P m n 21 space group with the gallium in sixfold and phosphorus in fourfold coordination was found to be in the best agreement with the combined experimental data from x-ray diffraction and absorption and Raman spectroscopy. This method is found to very powerful to better understand competition between different phase transition pathways at high pressure.

  19. Conditions of the Maximum Principle in the Problem of Optimal Control over an Aggregate of Dynamic Systems and Their Application to Solution of the Problems of Optimal Control of Spacecraft Motion

    NASA Astrophysics Data System (ADS)

    Grigoriev, I. S.; Grigoriev, K. G.

    2003-05-01

    The necessary first-order conditions of strong local optimality (conditions of maximum principle) are considered for the problems of optimal control over a set of dynamic systems. To derive them a method is suggested based on the Lagrange principle of removing constraints in the problems on a conditional extremum in a functional space. An algorithm of conversion from the problem of optimal control of an aggregate of dynamic systems to a multipoint boundary value problem is suggested for a set of systems of ordinary differential equations with the complete set of conditions necessary for its solution. An example of application of the methods and algorithm proposed is considered: the solution of the problem of constructing the trajectories of a spacecraft flight at a constant altitude above a preset area (or above a preset point) of a planet's surface in a vacuum (for a planet with atmosphere beyond the atmosphere). The spacecraft is launched from a certain circular orbit of a planet's satellite. This orbit is to be determined (optimized). Then the satellite is injected to the desired trajectory segment (or desired point) of a flyby above the planet's surface at a specified altitude. After the flyby the satellite is returned to the initial circular orbit. A method is proposed of correct accounting for constraints imposed on overload (mixed restrictions of inequality type) and on the distance from the planet center: extended (nonpointlike) intermediate (phase) restrictions of the equality type.

  20. 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.

  1. SolEq: Solution Equilibria, Principles and Applications, Release 1 by SolEq Project Team: L. D. Pettit, K. J. Powell, and R. W. Ramette

    NASA Astrophysics Data System (ADS)

    Koether, Marina C.

    2000-11-01

    SolEq teaches solution equilibria in an interactive tutorial fashion suitable for undergraduate lecture and laboratory use with applications in environmental, industrial, biological, speciation, and coordination chemistry. In addition, it can be used as an introduction to research in these areas. I highly recommend SolEq to be used as an educational tool and will probably use it in both the quantitative analytical chemistry and the environmental chemistry laboratory courses.

  2. A standardized nursing mathematics competency program.

    PubMed

    Middleton, Debra A

    2008-01-01

    Mathematics competency in nursing is an ongoing problem. The author discusses a standardized mathematics competency program based on current practices reported in nursing literature. Dimensional analysis is the method that students learn to find solutions to nursing problems that require mathematics and is important to the success of the program.

  3. Exploring Metacognition in Preservice Teachers: Problem Solving Processes in Elementary Mathematics

    ERIC Educational Resources Information Center

    Sparkman, Dana; Harris, Kymberly

    2009-01-01

    In Principles and Standards for School Mathematics (2000), the (U.S.) National Council of Teachers of Mathematics recommended that students communicate their mathematical thinking in a logical manner, and use the language of mathematics to express their thinking accurately and logically. Students should not only learn mathematics content, but…

  4. Experimental Mathematics and Mathematical Physics

    SciTech Connect

    Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Zudilin, Wadim

    2009-06-26

    One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.

  5. A MATHEMATICAL MODEL FOR AN HOURGLASS MAGNETIC FIELD

    SciTech Connect

    Ewertowski, Bartek; Basu, Shantanu

    2013-04-10

    Starting with a mathematical boundary value problem for the magnetic vector potential in an axisymmetric cylindrical coordinate system, we derive a general solution for any arbitrary current distribution using the method of Green's functions. We use this to derive an analytic form for an hourglass magnetic field pattern created by electrical currents that are concentrated near (but not confined within) the equatorial plane of a cylindrical coordinate system. Our solution is not characterized by a cusp at the equatorial plane, as in previous solutions based on a current sheet. The pattern we derive provides a very good fit to hourglass magnetic field patterns emerging from three-dimensional numerical simulations of core formation, and can in principle be used for source-fitting of observed magnetic hourglass patterns.

  6. Why Mathematics?

    ERIC Educational Resources Information Center

    McClellan, Kathryn T.

    Why mathematics should be learned is discussed. Its role as an important active force in the development of our civilization, and as the most useful subject taught in our schools, next to English, is noted. The primary objective of all mathematics work is to help man study nature, and some practical achievements of this connection are noted.…

  7. Mathematics Chapter.

    ERIC Educational Resources Information Center

    Davis, Robert B.

    Suggestions are offered for more effective implementation and creativity in developing new mathematics programs. The new mathematics materials and projects have not significantly altered the educational experiences of students because of (1) difficulty in identifying distinctive features of the various projects, (2) widespread assumptions that the…

  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. 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…

  11. 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…

  12. Mathematical Literacy

    ERIC Educational Resources Information Center

    Martin, Hope

    2007-01-01

    "Mathematical literacy" implies that a person is able to reason, analyze, formulate, and solve problems in a real-world setting. Mathematically literate individuals are informed citizens and intelligent consumers. They have the ability to interpret and analyze the vast amount of information they are inundated with daily in newspapers, on…

  13. Laser principles.

    PubMed

    Bogdan Allemann, Inja; Kaufman, Joely

    2011-01-01

    Since the construction of the first laser in the 1960s, the role that lasers play in various medical specialities, including dermatology, has steadily increased. However, within the last 2 decades, the technological advances and the use of lasers in the field of dermatology have virtually exploded. Many treatments have only become possible with the use of lasers. Especially in aesthetic medicine, lasers are an essential tool in the treatment armamentarium. Due to better research and understanding of the physics of light and skin, there is now a wide and increasing array of different lasers and devices to choose from. The proper laser selection for each indication and treatment requires a profound understanding of laser physics and the basic laser principles. Understanding these principles will allow the laser operator to obtain better results and help avoid complications. This chapter will give an in-depth overview of the physical principles relevant in cutaneous laser surgery. Copyright © 2011 S. Karger AG, Basel.

  14. A (Not Really) Complex Method for Finding Solutions to Linear Differential Equations. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 497.

    ERIC Educational Resources Information Center

    Uebelacker, James W.

    This module considers ordinary linear differential equations with constant coefficients. The "complex method" used to find solutions is discussed, with numerous examples. The unit includes both problem sets and an exam, with answers provided for both. (MP)

  15. 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.

  16. 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.

  17. Using Storytelling to Teach Mathematics Concepts

    ERIC Educational Resources Information Center

    Goral, Mary Barr; Gnadinger, Cindy Meyers

    2006-01-01

    Young students often struggle with abstract concepts in mathematics, causing primary teachers to continue to search for ways to help teach such concepts. "Principles and Standards for School Mathematics" (NCTM, 2000) recommends using concrete models and physical materials before moving on to more abstract ideas. However, some children…

  18. 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…

  19. 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…

  20. Mathematical modelling in developmental biology.

    PubMed

    Vasieva, Olga; Rasolonjanahary, Manan'Iarivo; Vasiev, Bakhtier

    2013-06-01

    In recent decades, molecular and cellular biology has benefited from numerous fascinating developments in experimental technique, generating an overwhelming amount of data on various biological objects and processes. This, in turn, has led biologists to look for appropriate tools to facilitate systematic analysis of data. Thus, the need for mathematical techniques, which can be used to aid the classification and understanding of this ever-growing body of experimental data, is more profound now than ever before. Mathematical modelling is becoming increasingly integrated into biological studies in general and into developmental biology particularly. This review outlines some achievements of mathematics as applied to developmental biology and demonstrates the mathematical formulation of basic principles driving morphogenesis. We begin by describing a mathematical formalism used to analyse the formation and scaling of morphogen gradients. Then we address a problem of interplay between the dynamics of morphogen gradients and movement of cells, referring to mathematical models of gastrulation in the chick embryo. In the last section, we give an overview of various mathematical models used in the study of the developmental cycle of Dictyostelium discoideum, which is probably the best example of successful mathematical modelling in developmental biology.

  1. Analytical Solution and Symbolic Computation for the Temperature Distribution of the Annular Fin under Fully Wet-Surface Condition

    NASA Astrophysics Data System (ADS)

    Koonprasert, Sanoe; Sangsawang, Rilrada

    2008-09-01

    This paper presents the analytical solutions and symbolic computations for the temperature distribution of the annular fin under fully-wet surface condition. During the process of dehumidification, the annular fin is separated into two regions. The mathematical models for each region are based on the conservation of energy principle. An assumption used in this paper is the humidity ratio of the saturated air on the wet surface varies linearly with the local fin temperature. The mathematical models are solved by the Cauchy-Euler Equation and modified Bessel Equation to form analytical solutions. Besides, the symbolic computations are shown by the Maple software to visualize the temperature distribution along the fin.

  2. Applying the four principles.

    PubMed

    Macklin, R

    2003-10-01

    Gillon is correct that the four principles provide a sound and useful way of analysing moral dilemmas. As he observes, the approach using these principles does not provide a unique solution to dilemmas. This can be illustrated by alternatives to Gillon's own analysis of the four case scenarios. In the first scenario, a different set of factual assumptions could yield a different conclusion about what is required by the principle of beneficence. In the second scenario, although Gillon's conclusion is correct, what is open to question is his claim that what society regards as the child's best interest determines what really is in the child's best interest. The third scenario shows how it may be reasonable for the principle of beneficence to take precedence over autonomy in certain circumstances, yet like the first scenario, the ethical conclusion relies on a set of empirical assumptions and predictions of what is likely to occur. The fourth scenario illustrates how one can draw different conclusions based on the importance given to the precautionary principle.

  3. Probing Mach's principle

    NASA Astrophysics Data System (ADS)

    Annila, Arto

    2012-06-01

    The principle of least action in its original form á la Maupertuis is used to explain geodetic and frame-dragging precessions which are customarily accounted for a curved space-time in general relativity. The least-time equations of motion agree with observations and are also in concert with general relativity. Yet according to the least-time principle, gravitation does not relate to the mathematical metric of space-time, but to a tangible energy density embodied by photons. The density of free space is in balance with the total mass of the Universein accord with the Planck law. Likewise, a local photon density and its phase distribution are in balance with the mass and charge distribution of a local body. Here gravitational force is understood as an energy density difference that will diminish when the oppositely polarized pairs of photons co-propagate from the energy-dense system of bodies to the energy-sparse system of the surrounding free space. Thus when the body changes its state of motion, the surrounding energy density must accommodate the change. The concurrent resistance in restructuring the surroundings, ultimately involving the entire Universe, is known as inertia. The all-around propagating energy density couples everything with everything else in accord with Mach’s principle.

  4. Developing analytical solutions for transverse, matrix strain magnification and fibre strain reduction in uniaxially aligned continuous fibre reinforced composites, based on the principle of conservation of strain energy and the Reuss rule

    NASA Astrophysics Data System (ADS)

    Maringa, M.; Masu, L. M.

    2017-06-01

    Analytical solutions for transverse matrix strain magnification and transverse fibre strain reduction in uniaxially aligned continuous fibre reinforced composites developed here for a Representative Volume Element (RVE), based on the Reuss rule and the principle of constant strain energy. The results obtained show respective matrix and fibre transverse strain magnification and reduction that increase with increasing volume fraction of the reinforcing fibre for both square and hexagonal fibre packing geometries. The square arrays register higher values of matrix and fibre transverse strain magnification and reduction, respectively, than hexagonal arrays. The values of transverse stress ratio between the fibre and matrix in the RVE central sub-region, and between the two and the RVE central sub-region composite are seen to vary with the volume fraction of reinforcing fibre. The results obtained here denote a dependency of respective matrix and fibre transverse strain magnification and reduction as well a stress ratio on the reinforcing fibre packing geometry and volume fraction.

  5. 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…

  6. 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…

  7. 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)

  8. Mathematics Detective.

    ERIC Educational Resources Information Center

    Johnson, Jerry

    1997-01-01

    Presents 12 questions related to a given real-life situation about a man shaving and the number of hairs in his beard in order to help students see the connection between mathematics and the world around them. (ASK)

  9. Children's Understanding of the Addition/Subtraction Complement Principle

    ERIC Educational Resources Information Center

    Torbeyns, Joke; Peters, Greet; De Smedt, Bert; Ghesquière, Pol; Verschaffel, Lieven

    2016-01-01

    Background: In the last decades, children's understanding of mathematical principles has become an important research topic. Different from the commutativity and inversion principles, only few studies have focused on children's understanding of the addition/subtraction complement principle (if a - b = c, then c + b = a), mainly relying on verbal…

  10. Children's Understanding of the Addition/Subtraction Complement Principle

    ERIC Educational Resources Information Center

    Torbeyns, Joke; Peters, Greet; De Smedt, Bert; Ghesquière, Pol; Verschaffel, Lieven

    2016-01-01

    Background: In the last decades, children's understanding of mathematical principles has become an important research topic. Different from the commutativity and inversion principles, only few studies have focused on children's understanding of the addition/subtraction complement principle (if a - b = c, then c + b = a), mainly relying on verbal…

  11. 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.

  12. Focus in High School Mathematics: Reasoning and Sense Making

    ERIC Educational Resources Information Center

    National Council of Teachers of Mathematics, 2009

    2009-01-01

    Addressing the direction of high school mathematics in the 21st century, this resource builds on the ideas of NCTM's Principles and Standards for School Mathematics and focuses on how high school mathematics can better prepare students for future success. Reasoning and sense making are at the heart of the high school curriculum. Discover the…

  13. 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…

  14. 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…

  15. 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…

  16. 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…

  17. 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.

  18. 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.

  19. 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

  20. 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.

  1. Multi-response optimization using Taguchi design and principle component analysis for removing binary mixture of alizarin red and alizarin yellow from aqueous solution by nano γ-alumina.

    PubMed

    Zolgharnein, Javad; Asanjrani, Neda; Bagtash, Maryam; Azimi, Gholamhasan

    2014-05-21

    The nanostructure of γ-alumina was used as an effective adsorbent for simultaneous removing of a mixture of alizarin red and alizarin yellow from aqueous solutions. The Taguchi design and principle component analysis were applied to explore effective parameters for achieving a higher adsorption capacity and removal percentage of the binary mixture containing alizarin red and alizarin yellow. Seven factors including temperature, contact time, initial pH value, the shaker rate, the sorbent dose, and initial concentrations of alizarin red and alizarin yellow in three levels were considered through the Taguchi technique. A L27 orthogonal array was used to determine the signal-to-noise ratio. Then, the removal percentage (R%) and adsorption capacity (q) of the above-mentioned dyes were transformed into an accurate S/N ratio. The Taguchi method indicates that the solution pH has the most contribution in controlling the removal percentage of alizarin red and alizarin yellow. Under optimal condition, the maximum removal percentages of 99% and 78.5%, and the capacity uptake of 54.4 and 39.0mg g(-1) were obtained for both alizarin red and alizarin yellow, respectively. Isotherm modeling and kinetic investigations showed that Langmuir, modified Langmuir, and pseudo-second-order models describe both the adsorption equilibrium and kinetic behavior well. The Fourier transform infrared analysis also firmly confirmed the involving active sites of nano γ-alumina in the adsorption process.

  2. Mathematical vistas

    SciTech Connect

    Malkevitch, J. ); McCarthy, D. )

    1990-01-01

    The papers in this volume represent talks given at the monthly meetings of the Mathematics Section of the New York Academy of Sciences. They reflect the operating philosophy of the Section in its efforts to make a meaningful contribution to the mathematical life of a community that is exceedingly rich in cultural resources and intellectual opportunities. Each week during the academic year a dazzling abundance of mathematical seminars and colloquia is available in the New York metropolitan area. Most of these offer highly technical treatments intended for specialists. At the New York Academy we try to provide a forum of a different sort, where interesting ideas are presented in a congenial atmosphere to a broad mathematical audience. Many of the Section talks contain substantial specialized material, but we ask our speakers to include a strong expository component aimed at working mathematicians presumed to have no expert knowledge of the topic at hand. We urge speakers to try to provide the motivating interest they themselves would like to find in an introduction to a field other than their own. The same advice has been given to the authors of the present papers, with the goal of producing a collection that will be both accessible and stimulating to mathematical minds at large. We have tried to provide variety in the mathematical vistas offered; both pure and applied mathematics are well represented. Since the papers are presented alphabetically by author, some guidance seems appropriate as to what sorts of topics are treated, and where. There are three papers in analysis: those by Engber, Narici and Beckenstein, and Todd. Engber's deals with complex analysis on compact Riemann surfaces; Narici and Beckenstein provide an introduction to analysis on non-Archimendean fields; Todd surveys an area of contemporary functional analysis.

  3. 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

  4. Mathematical methods in systems biology.

    PubMed

    Kashdan, Eugene; Duncan, Dominique; Parnell, Andrew; Schattler, Heinz

    2016-12-01

    The editors of this Special Issue of Mathematical Biosciences and Engineering were the organizers for the Third International Workshop "Mathematical Methods in System Biology" that took place on June 15-18, 2015 at the University College Dublin in Ireland. As stated in the workshop goals, we managed to attract a good mix of mathematicians and statisticians working on biological and medical applications with biologists and clinicians interested in presenting their challenging problems and looking to find mathematical and statistical tools for their solutions.

  5. Mathematics Education Values Questionnaire for Turkish Preservice Mathematics Teachers: Design, Validation, and Results

    ERIC Educational Resources Information Center

    Dede, Yuksel

    2011-01-01

    The purpose of this study was to develop a questionnaire that could measure preservice mathematics teachers' mathematics educational values. Development and validation of the questionnaire involved a sequential inquiry in which design principles were established from the existing literature and a pool of items was constructed then submitted to…

  6. Preservice and Inservice Mathematics Teachers' Perspectives of High-Quality Mathematics Instruction

    ERIC Educational Resources Information Center

    Clooney, Sarah; Cunningham, Robert F.

    2017-01-01

    This study examined the perspectives of what high-quality mathematics instruction looks like. Written responses from preservice (n = 20) and inservice (n = 16) mathematics teachers were collected and categorized according to the Ten Principles developed by Anthony & Walshaw (2009). The responses of preservice teachers more often than inservice…

  7. 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

  8. Quotable Quotes in Mathematics

    ERIC Educational Resources Information Center

    Lo, Bruce W. N.

    1983-01-01

    As a way to dispel negative feelings toward mathematics, a variety of quotations are given. They are categorized by: what mathematics is, mathematicians, mathematics and other disciplines, different areas of mathematics, mathematics and humor, applications of mathematics, and pure versus applied mathematics. (MNS)

  9. 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.

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

    PubMed

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

    2015-03-06

    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. 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. 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. 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 methods approaches to investigating newly-introduced interventions. Published by the BMJ Publishing

  11. Outdoor Mathematics

    ERIC Educational Resources Information Center

    Kennard, Jackie

    2007-01-01

    One of the most interesting developments in teaching has been the growing importance of the outdoor environment. Whether it be playground, garden or field, the outdoors offers a range of challenging experiences, especially in the delivery of early mathematics. Oral feedback to parents, together with photographic displays, can show them that…

  12. Outdoor Mathematics

    ERIC Educational Resources Information Center

    Kennard, Jackie

    2007-01-01

    One of the most interesting developments in teaching has been the growing importance of the outdoor environment. Whether it be playground, garden or field, the outdoors offers a range of challenging experiences, especially in the delivery of early mathematics. Oral feedback to parents, together with photographic displays, can show them that…

  13. 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…

  14. Handicap principle implies emergence of dimorphic ornaments.

    PubMed

    Clifton, Sara M; Braun, Rosemary I; Abrams, Daniel M

    2016-11-30

    Species spanning the animal kingdom have evolved extravagant and costly ornaments to attract mating partners. Zahavi's handicap principle offers an elegant explanation for this: ornaments signal individual quality, and must be costly to ensure honest signalling, making mate selection more efficient. Here, we incorporate the assumptions of the handicap principle into a mathematical model and show that they are sufficient to explain the heretofore puzzling observation of bimodally distributed ornament sizes in a variety of species. © 2016 The Author(s).

  15. 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.

  16. Mathematical solutions of the TG-43 geometry function for curved line, ring, disk, sphere, dome and annulus sources, and applications for quality assurance.

    PubMed

    Deufel, Christopher; Furutani, Keith M; Thomson, Rowan M; Antolak, John A

    2011-08-21

    Analytic solutions for the TG-43 geometry function for curved line, ring, disk, sphere, dome and annulus shapes containing uniform distributions of air-kerma are derived. These geometry functions describe how dose distributions vary strictly due to source geometry and not including attenuation or scatter effects. This work extends the use of geometry functions for individual sources to applicators containing multiple sources. Such geometry functions may be used to verify dose distributions computed using advanced techniques, including QA of model-based dose calculation algorithms. The impact of source curvature on linear and planar implants is considered along with the specific clinical case of brachytherapy eye plaques. For eye plaques, the geometry function for a domed distribution is used with published Monte Carlo dose distributions to determine a radial dose function and anisotropy function which includes all the scatter and attenuation effects due to the phantom, eye plaque and sources. This TG-43 model of brachytherapy eye plaques exactly reproduces azimuthally averaged Monte Carlo calculations, both inside and outside the eye.

  17. Mathematical solutions of the TG-43 geometry function for curved line, ring, disk, sphere, dome and annulus sources, and applications for quality assurance

    NASA Astrophysics Data System (ADS)

    Deufel, Christopher; Furutani, Keith M.; Thomson, Rowan M.; Antolak, John A.

    2011-08-01

    Analytic solutions for the TG-43 geometry function for curved line, ring, disk, sphere, dome and annulus shapes containing uniform distributions of air-kerma are derived. These geometry functions describe how dose distributions vary strictly due to source geometry and not including attenuation or scatter effects. This work extends the use of geometry functions for individual sources to applicators containing multiple sources. Such geometry functions may be used to verify dose distributions computed using advanced techniques, including QA of model-based dose calculation algorithms. The impact of source curvature on linear and planar implants is considered along with the specific clinical case of brachytherapy eye plaques. For eye plaques, the geometry function for a domed distribution is used with published Monte Carlo dose distributions to determine a radial dose function and anisotropy function which includes all the scatter and attenuation effects due to the phantom, eye plaque and sources. This TG-43 model of brachytherapy eye plaques exactly reproduces azimuthally averaged Monte Carlo calculations, both inside and outside the eye.

  18. Modelling non-equilibrium thermodynamic systems from the speed-gradient principle

    NASA Astrophysics Data System (ADS)

    Khantuleva, Tatiana A.; Shalymov, Dmitry S.

    2017-03-01

    The application of the speed-gradient (SG) principle to the non-equilibrium distribution systems far away from thermodynamic equilibrium is investigated. The options for applying the SG principle to describe the non-equilibrium transport processes in real-world environments are discussed. Investigation of a non-equilibrium system's evolution at different scale levels via the SG principle allows for a fresh look at the thermodynamics problems associated with the behaviour of the system entropy. Generalized dynamic equations for finite and infinite number of constraints are proposed. It is shown that the stationary solution to the equations, resulting from the SG principle, entirely coincides with the locally equilibrium distribution function obtained by Zubarev. A new approach to describe time evolution of systems far from equilibrium is proposed based on application of the SG principle at the intermediate scale level of the system's internal structure. The problem of the high-rate shear flow of viscous fluid near the rigid plane plate is discussed. It is shown that the SG principle allows closed mathematical models of non-equilibrium processes to be constructed. This article is part of the themed issue 'Horizons of cybernetical physics'.

  19. Modelling non-equilibrium thermodynamic systems from the speed-gradient principle.

    PubMed

    Khantuleva, Tatiana A; Shalymov, Dmitry S

    2017-03-06

    The application of the speed-gradient (SG) principle to the non-equilibrium distribution systems far away from thermodynamic equilibrium is investigated. The options for applying the SG principle to describe the non-equilibrium transport processes in real-world environments are discussed. Investigation of a non-equilibrium system's evolution at different scale levels via the SG principle allows for a fresh look at the thermodynamics problems associated with the behaviour of the system entropy. Generalized dynamic equations for finite and infinite number of constraints are proposed. It is shown that the stationary solution to the equations, resulting from the SG principle, entirely coincides with the locally equilibrium distribution function obtained by Zubarev. A new approach to describe time evolution of systems far from equilibrium is proposed based on application of the SG principle at the intermediate scale level of the system's internal structure. The problem of the high-rate shear flow of viscous fluid near the rigid plane plate is discussed. It is shown that the SG principle allows closed mathematical models of non-equilibrium processes to be constructed.This article is part of the themed issue 'Horizons of cybernetical physics'.

  20. First-principles study of the effect of iron on the crystal structure, stability and chemical bonding in the β-based AlCu ordered η2-phase and the pretransition state of a solid solution

    NASA Astrophysics Data System (ADS)

    Shalaeva, E. V.; Medvedeva, N. I.

    2012-05-01

    First-principles calculations showed that the thermodynamic stability of β-based ordered η2-AlCu phase doped with Fe is due to iron substitution in the copper sublattice (FeCu), which corresponds to the maximum number of Fe-Al bonds in the first cubic coordination polyhedron. This iron localisation leads to stable ω-like atomic displacements and pentagonal Al-nets in the (010) plane of η2-AlCu(Fe). This phase with iron substituting copper (e/a = 1.925) is an energetically preferred η-based non-canonical approximant of the icosahedral phase (e/a = 1.86). The energy gain for the FeCu position is determined by strong covalent Fe3d-Al3p bonding, while there is a weak Fe3d-Cu4s3d hybridisation for the FeAl substitution. Using a composite cluster model, we demonstrate that short-range order in the pretransition state of the β-Al-Cu-Fe solid solution observed prior to the precipitation of η-phase is stabilised due to formation of Fe-Al bonds in the first cubic coordination polyhedron of the composite cluster.

  1. 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…

  2. Current problems of mathematical physics and computational mathematics

    NASA Astrophysics Data System (ADS)

    Tikhonov, A. N.

    This collection, designed to honor the work of Academician A. A. Samarskii on his 60th birthday, treats such subjects as theoretical and mathematical physics, the general theory of numerical methods and algorithms, and the numerical study of applied problems of mechanics and plasma physics. Particular attention is given to the acceleration of charged particles by laser radiation, numerical methods for solving problems of MHD equilibrium, the use of the small-parameter method to solve differential equations, mathematical models of the initial stage of tokamak discharges, and radiative energy losses during the ultrahigh compression of laser fusion targets. Also considered are mixed strategies in differential games, methods for the numerical modeling of turbulent flows of viscous incompressible fluids, mathematical modeling of systems for the formation and focusing of charged-particle beams, and the use of variational principles in numerical modeling.

  3. 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…

  4. 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.

  5. 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

  6. 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.

  7. 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…

  8. Conceptual Structures in Mathematical Problem Solving.

    ERIC Educational Resources Information Center

    Cifarelli, Victor

    The processes by which conceptual knowledge is constructed during mathematical problem solving were studied, focusing on the cognitive activity of learners (i.e., the ways they elaborate, reorganize, and reconceptualize their solution activity). Underlying this research is the view that learners' mathematical conceptions evolve from their activity…

  9. Discrete Mathematics Course Supported by CAS MATHEMATICA

    ERIC Educational Resources Information Center

    Ivanov, O. A.; Ivanova, V. V.; Saltan, A. A.

    2017-01-01

    In this paper, we discuss examples of assignments for a course in discrete mathematics for undergraduate students majoring in business informatics. We consider several problems with computer-based solutions and discuss general strategies for using computers in teaching mathematics and its applications. In order to evaluate the effectiveness of our…

  10. 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…

  11. 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…

  12. Devising Principles of Design for Numeracy Tasks

    ERIC Educational Resources Information Center

    Geiger, Vince; Forgasz, Helen; Goos, Merrilyn; Bennison, Anne

    2014-01-01

    Numeracy is a fundamental component of the Australian National Curriculum as a General Capability identified in each F-10 subject. In this paper, we consider the principles of design necessary for the development of numeracy tasks specific to subjects other than mathematics--in this case, the subject of English. We explore the nature of potential…

  13. Principles And Applications Of Dual Adaptive Control

    NASA Technical Reports Server (NTRS)

    Mookerjee, Purusottam

    1990-01-01

    Simulations indicate superiority of dual controller over "cautious" controller. Report discusses principles of design of actively adaptive dual controllers. Focus is upon derivation of control laws for dual controller enhancing identification of parameters of mathematical model of multiple-input/multiple-output system, while controlling it at same time. Tasks of identification and control impose competing requirements.

  14. Mathematics Worth Teaching, Mathematics Worth Understanding.

    ERIC Educational Resources Information Center

    Romberg, Thomas A.; Kaput, James J.

    This chapter examines the scope of the mathematical content educators expect students to understand after they have participated in mathematics courses. It is organized under four headings: (1) Traditional School Mathematics, to clarify what the shift is away from; (2) Mathematics as Human Activity, to portray the direction the shift is toward;…

  15. Mathematical Literacy and Standardized Mathematical Assessments

    ERIC Educational Resources Information Center

    Matteson, Shirley M.

    2006-01-01

    Mathematical literacy is an important skill that is gaining the attention of mathematics educators. Students are increasingly challenged on standardized assessments to read, create, use, and comprehend numerous mathematical representations as a way of demonstrating mathematical literacy. Test items assessing algebra concepts from the Texas…

  16. Teachers' Mathematics as Mathematics-at-Work

    ERIC Educational Resources Information Center

    Bednarz, Nadine; Proulx, Jérôme

    2017-01-01

    Through recognising mathematics teachers as professionals who use mathematics in their workplace, this article traces a parallel between the mathematics enacted by teachers in their practice and the mathematics used in workplaces found in studies of professionals (e.g. nurses, engineers, bankers). This parallel is developed through the five…

  17. 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…

  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. 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…

  1. Applications of Massive Mathematical Computations

    DTIC Science & Technology

    1990-04-01

    computational fluid dynamics, computational astrophysics, number theory, complex analysis , Teichmuller spaces, mathematical physics and quantum field theory. In...used computational tool in industry for the solution of complex technological problems. For the highest efficiency to be realized on a parallel computer ...optimization of the code for machine execution, particularly: issues of communication, mini- mization of the computational complexity of the code

  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. Symbolic Computation in a Constructive Approach to Methods of Mathematical Physics

    NASA Astrophysics Data System (ADS)

    Lopez, Robert

    2001-10-01

    Mastery of the discipline of physics requires not only expertise and intuition in science, but also a measure of competence in mathematical understanding and technique. In fact, courses in methods of mathematical physics are important stepping-stones to progress in physics education. In this talk, we shall illustrate the role that a computer algebra system can play in a more efficient and effective mastery of mathematical techniques needed in the physics curriculum. To do this, we will present a series of examples taken from the undergraduate math curriculum at RHIT where the author has just published Advanced Engineering Mathematics, a new applied math book based on the availability of a computer algebra system. We will discuss the solution of boundary value problems, including the wave equation on the finite string, the heat equation in a finite rod and cylinder, and the potential equation in rectangles, disks, and spheres. We will also discuss coupled oscillators and normal modes. Finally, we will discuss the calculus of variations and Hamilton's principle, setting up and solving the single and double plane pendulum problems, and the spherical pendulum problem. Throughout, we will show how the use of modern computer tools makes so much more mathematics available to the student, and makes it so much easier to obtain physical insights.

  4. 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…

  5. Derivation and computation of discrete-delay and continuous-delay SDEs in mathematical biology.

    PubMed

    Allen, Edward J

    2014-06-01

    Stochastic versions of several discrete-delay and continuous-delay differential equations, useful in mathematical biology, are derived from basic principles carefully taking into account the demographic, environmental, or physiological randomness in the dynamic processes. In particular, stochastic delay differential equation (SDDE) models are derived and studied for Nicholson's blowflies equation, Hutchinson's equation, an SIS epidemic model with delay, bacteria/phage dynamics, and glucose/insulin levels. Computational methods for approximating the SDDE models are described. Comparisons between computational solutions of the SDDEs and independently formulated Monte Carlo calculations support the accuracy of the derivations and of the computational methods.

  6. Uses and abuses of mathematics in biology.

    PubMed

    May, Robert M

    2004-02-06

    In the physical sciences, mathematical theory and experimental investigation have always marched together. Mathematics has been less intrusive in the life sciences, possibly because they have until recently been largely descriptive, lacking the invariance principles and fundamental natural constants of physics. Increasingly in recent decades, however, mathematics has become pervasive in biology, taking many different forms: statistics in experimental design; pattern seeking in bioinformatics; models in evolution, ecology, and epidemiology; and much else. I offer an opinionated overview of such uses--and abuses.

  7. 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.

  8. 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)

  9. 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)

  10. Contemplating Symbolic Literacy of First Year Mathematics Students

    ERIC Educational Resources Information Center

    Bardini, Caroline; Pierce, Robyn; Vincent, Jill

    2015-01-01

    Analysis of mathematical notations must consider both syntactical aspects of symbols and the underpinning mathematical concept(s) conveyed. We argue that the construct of "syntax template" provides a theoretical framework to analyse undergraduate mathematics students' written solutions, where we have identified several types of…

  11. 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.

  12. New Optical Evaluation Approach for Parabolic Trough Collectors: First-Principle OPTical Intercept Calculation

    SciTech Connect

    Zhu, G.; Lewandowski, A.

    2012-11-01

    A new analytical method -- First-principle OPTical Intercept Calculation (FirstOPTIC) -- is presented here for optical evaluation of trough collectors. It employs first-principle optical treatment of collector optical error sources and derives analytical mathematical formulae to calculate the intercept factor of a trough collector. A suite of MATLAB code is developed for FirstOPTIC and validated against theoretical/numerical solutions and ray-tracing results. It is shown that FirstOPTIC can provide fast and accurate calculation of intercept factors of trough collectors. The method makes it possible to carry out fast evaluation of trough collectors for design purposes. The FirstOPTIC techniques and analysis may be naturally extended to other types of CSP technologies such as linear-Fresnel collectors and central-receiver towers.

  13. 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)

  14. Teaching Mathematical Proofs That Rely on Ideas from Physics.

    ERIC Educational Resources Information Center

    Hanna, Gila; Jahnke, H. Niels; DeBruyn, Ysbrand; Lomas, Dennis

    2001-01-01

    Describes empirical research into the effectiveness of using concepts and principles of physics in the teaching of geometrical proofs. Demonstrates, tentatively, that proofs from physics could be a viable addition to the mathematics curriculum. (Author/MM)

  15. Machine perception and intelligent control architecture for multirobot coordination based on biological principles

    NASA Astrophysics Data System (ADS)

    Thomopoulos, Stelios C.; Braught, Grant

    1996-10-01

    Intelligent control, inspired by biological and AI (artificial intelligence) principles, has increased the understanding of controlling complex processes without precise mathematical model of the controlled process. Through customized applications, intelligent control has demonstrated that it is a step in the right direction. However, intelligent control has yet to provide a complete solution to the problem of integrated manufacturing systems via intelligent reconfiguration of the robotics systems. The aim of this paper is to present an intelligent control architecture and design methodology based on biological principles that govern self-organization of autonomous agents. Two key structural elements of the proposed control architecture have been tested individually on key pilot applications and shown promising results. The proposed intelligent control design is inspired by observed individual and collective biological behavior in colonies of living organisms that are capable of self-organization into groups of specialized individuals capable of collectively achieving a set of prescribed or emerging objectives. The nervous and brain system in the proposed control architecture is based on reinforcement learning principles and conditioning and modeled using adaptive neurocontrollers. Mathematical control theory (e.g. optimal control, adaptive control, and neurocontrol) is used to coordinate the interactions of multiple robotics agents.

  16. Promoting Mathematical Argumentation

    ERIC Educational Resources Information Center

    Rumsey, Chepina; Langrall, Cynthia W.

    2016-01-01

    The Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) highlight the mathematical habits that educators should be fostering in mathematics classrooms throughout K-grade 12 education. That argumentation and discourse are important components of developing mathematically proficient…

  17. 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…

  18. Promoting Mathematical Argumentation

    ERIC Educational Resources Information Center

    Rumsey, Chepina; Langrall, Cynthia W.

    2016-01-01

    The Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) highlight the mathematical habits that educators should be fostering in mathematics classrooms throughout K-grade 12 education. That argumentation and discourse are important components of developing mathematically proficient…

  19. Inverse problems in mathematical physics

    NASA Astrophysics Data System (ADS)

    Glasko, V. B.

    Procedures for the correct formulation and solution of inverse problems, which usually belong to the class of ill-posed problems, are discussed. Attention is given to the concept of the conditionally correct statement of a problem, the concept of quasi-solution, and the fundamentals of regularization theory. The discussion also covers the uniqueness of solutions to inverse problems in mathematical physics, with consideration given to problems involving layered media, impedance problems, gravimetric problems, and inverse problems of heat conduction. The problem of stability and regularizing operators are also discussed.

  20. Pre-Service Teachers' Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

    ERIC Educational Resources Information Center

    Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc

    2016-01-01

    Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…

  1. Pre-Service Teachers' Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

    ERIC Educational Resources Information Center

    Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc

    2016-01-01

    Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…

  2. The fractal heart — embracing mathematics in the cardiology clinic

    PubMed Central

    Captur, Gabriella; Karperien, Audrey L.; Hughes, Alun D.; Francis, Darrel P.; Moon, James C.

    2017-01-01

    For clinicians grappling with quantifying the complex spatial and temporal patterns of cardiac structure and function (such as myocardial trabeculae, coronary microvascular anatomy, tissue perfusion, myocyte histology, electrical conduction, heart rate, and blood-pressure variability), fractal analysis is a powerful, but still underused, mathematical tool. In this Perspectives article, we explain some fundamental principles of fractal geometry and place it in a familiar medical setting. We summarize studies in the cardiovascular sciences in which fractal methods have successfully been used to investigate disease mechanisms, and suggest potential future clinical roles in cardiac imaging and time series measurements. We believe that clinical researchers can deploy innovative fractal solutions to common cardiac problems that might ultimately translate into advancements for patient care. PMID:27708281

  3. Mathematics and Cognition

    NASA Astrophysics Data System (ADS)

    Kasturirangan, Rajesh

    2014-07-01

    Mathematics is a human pursuit. Whether the truths of mathematics lie outside the human mind or emerge out of it, the actual practice of mathematics is conducted by human beings. In other words, human mathematics is the only kind of mathematics that we can pursue and human mathematics has to be built on top of cognitive capacities that are possessed by all human beings. Another way of stating the same claim is that mathematics is experienced by human beings using their cognitive capacities. This paper argues that exploring the experience of mathematics is a useful way to make headway on the foundations of mathematics. Focusing on the experience of mathematics is an empirical approach to the study of mathematics that sidesteps some of the thorniest debates from an earlier era about Platonism and Formalism in the foundations of mathematics.

  4. From the Concrete to the Abstract: Mathematics for Deaf Children.

    ERIC Educational Resources Information Center

    Fridriksson, Thor; Stewart, David A.

    1988-01-01

    An examination of the status of teaching mathematics to deaf students showed that teachers ignore the hands-on exploration of objects that promotes conceptualization of basic mathematic principles. An arithmetic teaching strategy is proposed which is activity-based and is derived from Piaget's theory of intellectual development in children.…

  5. 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…

  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. Mathematics in the K-8 Classroom and Library

    ERIC Educational Resources Information Center

    McKinney, Sueanne; Hinton, KaaVonia

    2010-01-01

    Two experts on education offer a rich and diverse selection of children's literature and teaching strategies for the K-8 mathematics classroom. To date, a vast majority of classrooms continue to fall short in the implementation and direction of NCTM Principles and Standards for School Mathematics (PSSM), in part because most of these classrooms…

  8. 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…

  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. Investigations in Mathematics Education. Volume 18, Number 3.

    ERIC Educational Resources Information Center

    Suydam, Marilyn N., Ed.; Kasten, Margaret L., Ed.

    1985-01-01

    Abstracts of 12 mathematics education research reports and critical comments (by the abstractors) about the reports are provided in this issue of Investigations in Mathematics Education. The reports are: "More Precisely Defining and Measuring the Order-Irrelevance Principle" (Arthur Baroody); "Children's Relative Number Judgments:…

  11. Modern Mathematics for Elementary Teachers: A Laboratory Approach

    ERIC Educational Resources Information Center

    Callahan, John; And Others

    Reports on the development of a sample course in modern mathematics for elementary teachers. The approach to the course was based on three methodological principles--(1) that emphasis should be placed on mathematics as an organization of (experimental and other) information and not primarily as a deductive system, (2) that it is important to use…

  12. The Technological Revolution and the Reform of School Mathematics.

    ERIC Educational Resources Information Center

    Heid, M. Kathleen

    1997-01-01

    Evaluates the ways in which empirical research supports the use of technology and technology-intensive mathematics curricula as catalysts for the mathematics education reform movement. It describes the theories, principles, and issues that influence the role of this technological revolution and discusses the ways in which technology influences the…

  13. 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…

  14. 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.

  15. 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…

  16. Mathematics Instruction across the Grades: What Consultants Should Know

    ERIC Educational Resources Information Center

    Graeber, Anna O.

    2006-01-01

    This article describes current goals for K-8 school mathematics and outlines 7 critical areas in which students frequently experience difficulty. Effective mathematics teaching is related to teaching that takes into account the 3 learning principles articulated in the National Research Council (2006) publication, "How Students Learn". Research…

  17. 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…

  18. Examining of Model Eliciting Activities Developed by Mathematics Student Teachers

    ERIC Educational Resources Information Center

    Dede, Ayse Tekin; Hidiroglu, Çaglar Naci; Güzel, Esra Bukova

    2017-01-01

    The purpose of this study is to examine the model eliciting activities developed by the mathematics student teachers in the context of the principles of the model eliciting activities. The participants of the study conducted as a case study design were twenty one mathematics student teachers working on seven groups. The data collection tools were…

  19. Elementary School Teachers' Interpretation and Promotion of Creativity in the Learning of Mathematics: A Grounded Theory Study

    ERIC Educational Resources Information Center

    Shen, Yinjing

    2014-01-01

    Creativity is important for young children learning mathematics. Comparing the investment theory of creativity and national standards and principles for early mathematics shows that doing mathematics is more than applying rules and procedures; rather, learning mathematics takes a lot of creativity. However, much literature claimed that creativity…

  20. 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…

  1. 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…

  2. 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…

  3. 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…

  4. 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…

  5. Mathematics Education Computer Software and Mathematics Teachers.

    ERIC Educational Resources Information Center

    Ozgun-Koca, S. Asli

    2000-01-01

    Presents results from a study that uses questionnaires to ask mathematics teachers' (N=64) opinions about mathematics education computer software. Indicates that respondents overwhelmingly favored discovery and remediation as the purpose of using software in mathematics classrooms. Teachers believed that real world situations and multiple…

  6. 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…

  7. 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…

  8. Discrete Mathematics and the Secondary Mathematics Curriculum.

    ERIC Educational Resources Information Center

    Dossey, John

    Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…

  9. Mathematical Investigation of Bode's Law and Quantilization of Gravity

    NASA Astrophysics Data System (ADS)

    Lu, K. U.

    1995-03-01

    A non-static General Relativistic mathematical solution for the gravitational field around a star is obtained. From this mathematical solution, the orbits of the planets around the Sun are calculated and compared with Bode's law and the mean distances of the orbits, the origin of the Moon is deduced, and a theory for quantilization of gravity is concluded.

  10. The application of mathematical modeling for the development of devices as an example of viscous fluid purification from magnetic impurity

    NASA Astrophysics Data System (ADS)

    Zhukov, V. A.; Masyutkin, E. P.; Avdeyev, B. A.

    2017-02-01

    The mathematical model of a coagulation phenomenon and a coagulation process of ferromagnetic particles under the influence of a constant magnetic field are given in the article. The principles that need to be followed during mathematical modeling are stated.

  11. 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.

  12. Modelling Mathematical Reasoning in Physics Education

    NASA Astrophysics Data System (ADS)

    Uhden, Olaf; Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche

    2012-04-01

    Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

  13. 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

  14. 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)

  15. [Mathematical models of hysteresis

    SciTech Connect

    Mayergoyz, I.D.

    1991-01-01

    The research described in this proposal is currently being supported by the US Department of Energy under the contract Mathematical Models of Hysteresis''. Thus, before discussing the proposed research in detail, it is worthwhile to describe and summarize the main results achieved in the course of our work under the above contract. Our ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories''. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. Our research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. Our study has by and large been centered around the following topics: various generalizations and extensions of the classical Preisach model, finding of necessary and sufficient conditions for the representation of actual hysteretic nonlinearities by various Preisach type models, solution of identification problems for these models, numerical implementation and experimental testing of Preisach type models. Although the study of Preisach type models has constituted the main direction of the research, some effort has also been made to establish some interesting connections between these models and such topics as: the critical state model for superconducting hysteresis, the classical Stoner-Wohlfarth model of vector magnetic hysteresis, thermal activation type models for viscosity, magnetostrictive hysteresis and neural networks.

  16. Learning Mathematics from Examples and by Doing

    DTIC Science & Technology

    1987-09-29

    experiences in John Dewey’s prescriptions for progressive education. A number of followers of Dewey and Piaget have been strong advocates of learning by...selective principles that modify the sequence in which possible solutions will be examined in the problem space; (2) the selective principles are obtained...accordance with the usual principles for shaping behavior, learners could attend to one or a few 5 Learning from Examples 16 July 1987 aspects of the

  17. Physical Principles of Evolution

    NASA Astrophysics Data System (ADS)

    Schuster, Peter

    Theoretical biology is incomplete without a comprehensive theory of evolution, since evolution is at the core of biological thought. Evolution is visualized as a migration process in genotype or sequence space that is either an adaptive walk driven by some fitness gradient or a random walk in the absence of (sufficiently large) fitness differences. The Darwinian concept of natural selection consisting in the interplay of variation and selection is based on a dichotomy: All variations occur on genotypes whereas selection operates on phenotypes, and relations between genotypes and phenotypes, as encapsulated in a mapping from genotype space into phenotype space, are central to an understanding of evolution. Fitness is conceived as a function of the phenotype, represented by a second mapping from phenotype space into nonnegative real numbers. In the biology of organisms, genotype-phenotype maps are enormously complex and relevant information on them is exceedingly scarce. The situation is better in the case of viruses but so far only one example of a genotype-phenotype map, the mapping of RNA sequences into RNA secondary structures, has been investigated in sufficient detail. It provides direct information on RNA selection in vitro and test-tube evolution, and it is a basis for testing in silico evolution on a realistic fitness landscape. Most of the modeling efforts in theoretical and mathematical biology today are done by means of differential equations but stochastic effects are of undeniably great importance for evolution. Population sizes are much smaller than the numbers of genotypes constituting sequence space. Every mutant, after all, has to begin with a single copy. Evolution can be modeled by a chemical master equation, which (in principle) can be approximated by a stochastic differential equation. In addition, simulation tools are available that compute trajectories for master equations. The accessible population sizes in the range of 10^7le Nle 10

  18. 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…

  19. An Examination of Preservice Teachers' Capacity to Create Mathematical Modeling Problems for Children

    ERIC Educational Resources Information Center

    Paolucci, Catherine; Wessels, Helena

    2017-01-01

    This study examined preservice teachers' (PSTs) capacity to create mathematical modeling problems (MMPs) for grades 1 to 3. PSTs created MMPs for their choice of grade level and aligned the mathematical content of their MMPs with the relevant mathematics curriculum. PSTs were given criteria adapted from Galbraith's MMP design principles to guide…

  20. Vygotskian Theory and Mathematics Education: Resolving the Conceptual-Procedural Dichotomy

    ERIC Educational Resources Information Center

    Schmittau, Jean

    2004-01-01

    The aim of this paper is to demonstrate that in spite of some superficial similarities the current mathematics reform in the US based on constructivist principles differs substantially from mathematical education based on Vygotskian cultural-historical theory (V.V. Davydov's mathematics program), and to illustrate the manner in which Davydov's…

  1. 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…

  2. 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…

  3. 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…

  4. 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…

  5. 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…

  6. 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…

  7. 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…

  8. It's all just mathematics

    NASA Astrophysics Data System (ADS)

    Tegmark, Max

    2014-02-01

    The world can be described using mathematical equations and numbers, but why does maths do it so well? In his new book Our Mathematical Universe, a section of which is abridged and edited here, Max Tegmark makes the radical proposal that our reality isn't just described by mathematics - it is mathematics.

  9. Learning To Talk Mathematics.

    ERIC Educational Resources Information Center

    Lo, Jane-Jane; And Others

    Calls for increased student involvement in mathematics classroom learning situations are due primarily to the recognition that a traditional lecture/demonstration format within school mathematics instruction is not effective in fostering and promoting students' problem-solving abilities, mathematical reasoning power, and mathematical communication…

  10. 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…

  11. 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…

  12. 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…

  13. Mathematics "Is" Motivating

    ERIC Educational Resources Information Center

    Ricks, Thomas E.

    2010-01-01

    Mathematics is motivating; at least, it should be. I argue that mathematical activity is an inherently attractive enterprise for human beings because as intellectual organisms, we are naturally enticed by the intellectual stimulation of mathematizing, and, as social beings, we are drawn to the socializing aspects of mathematical activity. These…

  14. Computer Mathematics: An Introduction.

    ERIC Educational Resources Information Center

    New York City Board of Education, Brooklyn, NY. Div. of Curriculum and Instruction.

    This document describes a mathematics course that uses the computer to solve mathematics problems. It was developed to be used with students who have completed at least one year of general mathematics or are not achieving success in the traditional mathematics program. The course is intended to review, reinforce, and extend concepts included in…

  15. Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

    ERIC Educational Resources Information Center

    Mumcu, Hayal Yavuz

    2016-01-01

    The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

  16. 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…

  17. 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…

  18. 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…

  19. 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…

  20. 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…

  1. Mathematical Physics in Italy in the XIX Century: The Theory of Elasticity

    NASA Astrophysics Data System (ADS)

    Capecchi, Danilo

    In the second half of the nineteenth century there was in Italy an important group of mathematicians who focused their attention on mathematical physics. The most prominent of them were Enrico Betti, Eugenio Beltrami, Gregorio Ricci-Curbastro and some others (Vito Volterra, Carlo Somigliana and Tullio Levi Civita) whose activity persevered for many years in the twentieth century. In this article, I will write about the contribution of this group to the theory of elasticity. The best representative writing on continuum mechanics and elasticity as theories of mathematical physics is presented in the book Teoria della elasticità by Enrico Betti. The book is interesting not only for the particular results found but also for its structure which became paradigmatic for the development of subsequent texts on elasticity, not only those in Italian. Betti's interest was concentrated on the mathematical aspects of a physical theory. Physical principles are not discussed; they are only exposed in the most formal way possible. The objective is to arrive, without discussing epistemological or empirical problems, at the formulation and solution of differential equations that rule elasticity, as had become classic in the emerging mathematical physics. Beltrami wrote no complete books on elasticity; however, his contribution to this field was perhaps more original than that of Betti. A similar consideration holds true for Volterra and Somigliana.

  2. Scattered Radiation Emission Imaging: Principles and Applications

    PubMed Central

    Nguyen, M. K.; Truong, T. T.; Morvidone, M.; Zaidi, H.

    2011-01-01

    Imaging processes built on the Compton scattering effect have been under continuing investigation since it was first suggested in the 50s. However, despite many innovative contributions, there are still formidable theoretical and technical challenges to overcome. In this paper, we review the state-of-the-art principles of the so-called scattered radiation emission imaging. Basically, it consists of using the cleverly collected scattered radiation from a radiating object to reconstruct its inner structure. Image formation is based on the mathematical concept of compounded conical projection. It entails a Radon transform defined on circular cone surfaces in order to express the scattered radiation flux density on a detecting pixel. We discuss in particular invertible cases of such conical Radon transforms which form a mathematical basis for image reconstruction methods. Numerical simulations performed in two and three space dimensions speak in favor of the viability of this imaging principle and its potential applications in various fields. PMID:21747823

  3. Intuitions, principles and consequences

    PubMed Central

    Shaw, A

    2001-01-01

    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. Key Words: Intuitions • principles • consequences • utilitarianism PMID:11233371

  4. 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. Copyright © 2015 Elsevier Ltd. All rights reserved.

  5. Mathematical origin of time arrow

    NASA Astrophysics Data System (ADS)

    Shimansky, Yury

    2005-03-01

    Laws describing the main types of physical interactions are symmetrical with respect to the direction of time flow. At the same time, many virtually irreversible processes are observed. This ``time arrow'' paradox usually is associated with the law of entropy increase. The fact that physical systems obey this law regardless of their physical nature suggests that it may be based on a certain, yet unknown, mathematical principle. Here it is demonstrated that, if, on a time micro scale, the intensity of fluctuations of a certain parameter depends on the parameter's value, it would appear to an external observer on a time macro scale that the parameter tends to be modified in the direction of fluctuation intensity decrease. It is shown that the law of entropy increase is a consequence of this principle, if it is applied to entropy as a state variable of a thermodynamic system. The fundamental nature of this principle suggests that it must operate on virtually every level of physical reality. The principle is of great potential value for understanding mechanisms of self-organization, learning, adaptation, and evolution.

  6. 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.

  7. 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)

  8. 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)

  9. 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.

  10. 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.

  11. The Principles of Asymmetry

    DTIC Science & Technology

    2005-05-26

    THE PRINCIPLES OF ASYMMETRY A monograph presented to the Faculty of the US Army School of Advanced Military Studies in...DATES COVERED Monograph 4. TITLE AND SUBTITLE The Principles pf Asymmetry 5. FUNDING NUMBERS 6. AUTHOR(S) Stephen D. Pomper Major, USA 7... principles of asymmetry. The ultimate goal of producing principles should allow soldiers to better appreciate a difficult, but important concept in

  12. Sound Blending of Techniques in Mathematics and Physics (abstract)

    NASA Astrophysics Data System (ADS)

    Malmini, Ranasinghe

    2009-04-01

    This paper discusses methods that can be used to inspire physics students to learn advanced differential equations. Numerous problems in physics are described by this type of equation. There has been rapid advancement in computer technology and development of computational mathematics-a branch of mathematics using computers to generate solutions to advanced differential equations. Arguably, this branch of mathematics is becoming more important to physicists than traditional analytical mathematics. Computer Algebra Software (CAS) packages have also emerged as a means to perform elaborate and complicated analytical mathematics much faster than possible by humans.

  13. 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…

  14. 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…

  15. 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.

  16. 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.

  17. Einstein's equivalence principle in quantum mechanics revisited

    NASA Astrophysics Data System (ADS)

    Nauenberg, Michael

    2016-11-01

    The gravitational equivalence principle in quantum mechanics is of considerable importance, but it is generally not included in physics textbooks. In this note, we present a precise quantum formulation of this principle and comment on its verification in a neutron diffraction experiment. The solution of the time dependent Schrödinger equation for this problem also gives the wave function for the motion of a charged particle in a homogeneous electric field, which is also usually ignored in textbooks on quantum mechanics.

  18. 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…

  19. 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.

  20. Principlism and communitarianism.

    PubMed

    Callahan, D

    2003-10-01

    The decline in the interest in ethical theory is first outlined, as a background to the author's discussion of principlism. The author's own stance, that of a communitarian philosopher, is then described, before the subject of principlism itself is addressed. Two problems stand in the way of the author's embracing principlism: its individualistic bias and its capacity to block substantive ethical inquiry. The more serious problem the author finds to be its blocking function. Discussing the four scenarios the author finds that the utility of principlism is shown in the two scenarios about Jehovah's Witnesses but that when it comes to selling kidneys for transplantation and germline enhancement, principlism is of little help.